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Capturing Teachers’ Generative Change: A Follow-Up Study of Professional Development in Mathematics
Abstract
This study documents how teachers who participated in a professional development program on understanding the development of students’ mathematical thinking continued to implement the principles of the program 4 years after it ended. Twenty-two teachers participated in follow-up interviews and classroom observations. All 22 teachers maintained some use of children’s thinking and 10 teachers continued learning in noticeable ways. The 10 teachers engaged in generative growth (a) viewed children’s thinking as central, (b)possessed detailed knowledge about children’s thinking, (c) discussed frameworks for characterizing the development of children’s mathematical thinking, (d) perceived themselves as creating and elaborating their own knowledge about children’s thinking, and (e) sought colleagues who also possessed knowledge about children’s thinking for support. The follow-up revealed insights about generative growth, sustainability of changed practice and professional development.
... The study involved monitoring the development of four online ELTeachers CoPs and their respective Coordinators' patterns of involvement and response using a mixed-methods approach which combined quantitative data and qualitative research of collective case studies (Dornyei, 2007) of the four groups of teachers. A comparison of the Coordinators' implementation of meaningful professional development (Franke et al., 2001) activities "before" and "after" their involvement in the online CoPs was carried out. Findings delineate the extent of the Coordinators' "reformed" training practice in terms of professional development activities provided to the teachers "before" and "after" their CoP involvement as well as their report on their teachers' and their own perceived benefit. ...
... 1) To what extent do the Coordinators display "reformed" training practice in terms of professional development activities (Franke et al., 2001) provided to the teachers "during" their participation in the CoPs compared with the ones "before" their participation? ...
... To what extent do the Coordinators display "reformed" training practice in terms of professional development activities (Franke et al., 2001) provided to the teachers "during" their participation in the CoPs compared with the ones "before" their participation? ...
This paper examines Greek EFL Coordinators’ involvement in online ELTeachers Communities of Practice (CoPs) and its impact on their own and their trainees’/teachers’ professional development. The study focuses on four (4) Greek EFL School Advisors who acted as Coordinators of four online CoPs training fourty-nine (49) EFL teachers using an online platform named 2gather developed by the University of Athens in the context of a national in-service professional development project in Greece. Founded on the theory of situated learning, CoPs have been defined as “groups of people who share a concern, a set of problems, or a passion about a topic, and who deepen their knowledge and expertise in this area by interacting on an ongoing basis” (Wenger et al., 2002). The study involved monitoring the development of four online ELTeachers CoPs and their respective Coordinators’ patterns of involvement and response using a mixed-methods approach which combined quantitative data and qualitative research of collective case studies (Dornyei, 2007) of the four groups of teachers. A comparison of the Coordinators’ implementation of meaningful professional development (Franke et al., 2001) activities “before” and “after” their involvement in the online CoPs was carried out. Findings delineate the extent of the Coordinators’ “reformed” training practice in terms of professional development activities provided to the teachers “before” and “after” their CoP involvement as well as their report on their teachers’ and their own perceived benefit. Results also highlight the role of the Coordinators’ attitude towards the innovative model of teacher education for its feasibility and viability in Greece and contribute to furthering our understanding of effective implementation of online CoPs in the context of continuing professional development.
... classroom climate), offer diverse learning resources. Prior research found teachers' noticing of those content-specific classroom events is positively related to their PCK (Copur-Gencturk and Tolar 2022; Franke et al. 2001). Continued attention to students' thinking and effective use of these observations in teaching help teachers develop an understanding of students' mathematical thinking, a key aspect of PCK, even long after completing professional development (Franke et al. 2001). ...
... Prior research found teachers' noticing of those content-specific classroom events is positively related to their PCK (Copur-Gencturk and Tolar 2022; Franke et al. 2001). Continued attention to students' thinking and effective use of these observations in teaching help teachers develop an understanding of students' mathematical thinking, a key aspect of PCK, even long after completing professional development (Franke et al. 2001). These findings indicate that content-specific noticing may influence the development of PCK. ...
... However, our findings also indicated that noticing was not associated with the development of teachers' PCK. Prior work by Franke et al. (2001) showed that noticing played a role in the development of teachers' PCK, but only when teachers consciously viewed the noticing of students' mathematical thinking and their own instruction as learning resources and leveraged what they noticed in the classroom. Thus, noticing alone may not lead to gains in teachers' PCK unless they also consciously reflect on what they notice in class and transform those fleeting moments into action in their practice. ...
Pedagogical content knowledge (PCK) has been widely recognised as an important aspect of the expertise for teaching. However, the extent to which teachers' own teaching practice can be a learning resource for them to develop PCK has not been systematically explored. This empirical study aimed to explore the unique contribution of the work of teaching in teachers' PCK growth by concurrently considering other external professional learning opportunities teachers may have on the job and the changes in their PCK. Using longitudinal data from 207 elementary and middle school teachers in the United States, we found that teachers increased their PCK through teaching on their own, albeit at different rates. Our findings were robust when other external learning opportunities teachers had were taken into account. Our findings underscored the importance of teachers' robust knowledge of school mathematics in the development of their PCK through teaching.
... classroom climate), offer diverse learning resources. Prior research found teachers' noticing of those content-specific classroom events is positively related to their PCK (Copur-Gencturk and Tolar 2022; Franke et al. 2001). Continued attention to students' thinking and effective use of these observations in teaching help teachers develop an understanding of students' mathematical thinking, a key aspect of PCK, even long after completing professional development (Franke et al. 2001). ...
... Prior research found teachers' noticing of those content-specific classroom events is positively related to their PCK (Copur-Gencturk and Tolar 2022; Franke et al. 2001). Continued attention to students' thinking and effective use of these observations in teaching help teachers develop an understanding of students' mathematical thinking, a key aspect of PCK, even long after completing professional development (Franke et al. 2001). These findings indicate that content-specific noticing may influence the development of PCK. ...
... However, our findings also indicated that noticing was not associated with the development of teachers' PCK. Prior work by Franke et al. (2001) showed that noticing played a role in the development of teachers' PCK, but only when teachers consciously viewed the noticing of students' mathematical thinking and their own instruction as learning resources and leveraged what they noticed in the classroom. Thus, noticing alone may not lead to gains in teachers' PCK unless they also consciously reflect on what they notice in class and transform those fleeting moments into action in their practice. ...
Pedagogical content knowledge (PCK) has been widely recognised as an important aspect of the expertise for teaching. However, the extent to which teachers' own teaching practice can be a learning resource for them to develop PCK has not been systematically explored. This empirical study aimed to explore the unique contribution of the work of teaching in teachers' PCK growth by concurrently considering other external professional learning opportunities teachers may have on the job and the changes in their PCK. Using longitudinal data from 207 elementary and middle school teachers in the United States, we found that teachers increased their PCK through teaching on their own, albeit at different rates. Our findings were robust when other external learning opportunities teachers had were taken into account. Our findings underscored the importance of teachers' robust knowledge of school mathematics in the development of their PCK through teaching.
... Brodie (2011) states that working with learners' thinking, is key to mathematical reform across the globe. This would entail engaging learners actively in collaborative tasks, encouraging an exchange of ideas through learners' talk, and challenging thinking through tasks with a high cognitive demand (Franke et al., 2001;Savery & Duffy, 1995;Webb, 2009). This research study was based on the following research questions: ...
... This, is in sharp contrast with research findings that teacher-centred instruction continues to dominate the classroom discourse, while learners are quiet (Cazden, 2001). In learner-centred teaching, learners articulate their own mathematical ideas rather than reproduce the teacher's ideas (Franke et al., 2001). Dawes (2004) lists the advantages of genuine classroom talk, noting among others, its power to allow the creation of meaning within the learner's mind, through shared ideas and understandings. ...
... A hurdle to overcome in the constructivist classroom is the reluctance of learners to expose themselves by asking questions, especially at the socially sensitive age between 10 and 12 years (Graesser & Olde, 2003). Franke et al. (2001) and Ball and Bass (2000) advised that learners should be encouraged to ask questions through the creation of a situation conducive to learner participation. Graesser and Olde (2003) state that few learners will ask high-quality thinking or cognitive questions, whereas most of them ask questions that are factual, procedural, or closed. ...
In this article, we report on two case studies in which we investigated two different pedagogical approaches in teaching the comparison of common fractions at Grade 6, one where fractions were represented in a concrete/experiential form, and the other in a numerical/symbolic form. The two modes could be linked to a constructivist and behaviourist instructional approach respectively. On one hand, the constructivist approach is associated with relational understanding which emphasises the development of a deep conceptual understanding of underlying principles and the focus is on making the connection between different ideas. On the other hand, the behaviourist approach is associated with instrumental understanding and the focus is on procedural knowledge and the application of algorithms. The anchor theory guiding the classroom observation during the data collection phase was Shulman's pedagogical content knowledge (PCK) supported by the theory of mathematical knowledge for teaching (MKT). The theoretical framework for the analysis and interpretation of the data was the new-Piagetian cognitive development theory (CDT). In the analysis of our observation, we came to the enlightening realisation that at the Grade 6 level, both representational forms of fractions, that is, concrete, and symbolic, need to be incorporated in instructional practices to meet the required representational capacity of the learner at that developmental level. However, there are conditions for integrating representational forms to render the merge cognitively accessible. Apart from subject content knowledge and pedagogical skills, the teacher, therefore, needs a third dimension of understanding, namely the insight into the cognitive demand of the task in relation to the cognitive abilities of the learner in the age range 10-12 years.
... Responsive teaching is complex and can be difficult for teachers to enact (Hammer et al., 2012;Lampert, 2001). However, professional development that focuses on eliciting and attending to students' mathematical thinking can have positive effects on both teacher and N. Placa student learning (Carpenter et al., 2000;Fennema et al., 1996;Franke et al., 2001). Clinical interviews, which are conducted one-on-one usually in settings outside the classroom, are a specific strategy focused on students' thinking that has the potential to help teachers develop their skills in eliciting and understanding student thinking (Ambrose, 2004;Buschman, 2001;Ginsburg et al., 1998;Hunting, 1997). ...
... Finally, deciding how to respond to student thinking includes making decisions such as whether or not to ask a student a follow-up question, what follow up questions to ask or highlighting a particular detail of a strategy. These skills are complex, and research has shown that years are required to develop the skills needed to teach in ways that effectively incorporate listening to children's mathematics (Franke et al., 2001;Jacobs et al., 2007;Steinberg et al., 2004). ...
... Becoming curious about student thinking can change the way in which teachers approach their interactions with students and their desire to elicit student thinking (Franke et al., 2001). ...
Eliciting and attending to students’ thinking is an important component of teaching mathematics for understanding. Clinical interview protocols have shown the potential to support teachers in developing these skills. However, less is known about how to support teacher leaders’ knowledge and development of these skills. Given that teacher leaders provide opportunities to foster teachers’ knowledge of these ideas, more needs to be known about teacher leaders’ abilities and knowledge in this area, and how clinical interviews might support teacher leaders’ pedagogical knowledge. This study explored the nuances in understanding the ways in which teacher leaders elicited and attended to student thinking when conducting clinical interviews. Findings show that while the majority of teacher leaders who engaged in conducting clinical interviews asked probing questions and engaged in observational thinking, they also faced challenges in moving toward responsive listening, particularly when students struggled with providing justification for a task.
... As teachers shift away from 'telling' the science and move towards students producing their own science knowledge, they learn that students are capable of complex thinking about science ideas. Such understanding of student learning can reinforce shifts in instructional practice driving teacher learning and change (Franke et al. 2001, Lee et al. 2009, McNeill 2011, Taylor 2023. Changes in teachers' beliefs and practices more often result when teachers notice what students say and do, interpret their ideas, and respond to advance student thinking (Preminger et al. under review). ...
... In order to understand how interactions across domains influenced differential teacher change, we first needed to categorise the degree of teacher change. Thus, as part of the larger study, we analysed teacher interviews, post-lesson memos, and video observational notes for evidence of the following (drawing on Grossman et al. 1999 appropriation schema): 1) Understanding: teachers' expressed understanding of SLP pedagogical principles and practices (conceptual tools; Longhurst et al. 2021); 2) Implementation: congruence between pedagogical outcomes and teacher instructional practice (practical tools); and 3) Perceived Change: how teachers described having changed their understanding and implementation over their involvement with SLP (Table 3) (Franke et al. 2001). If their described change differed from what was seen in the observation, we noted the discrepancy in the memo. ...
... In Theme I, teachers who had pedagogical beliefs closely aligned with SLP principles more easily adapted SLP strategies into their instructional practices (Franke et al. 2001, Rivera Maulucci et al. 2015). Yet, analysing the teachers' context more holistically revealed additional processes occurring in interaction with Theme I that influenced teacher learning. ...
... Ideally, when students learn mathematics, they learn ways of thinking that go beyond a collection of disconnected procedures for carrying out calculations. Within this context, children learn how to generate mathematical ideas, how to express these ideas (in any way that makes sense to them), and how to explain these ideas and those of others (Carpenter et al., 2015;Franke et al., 2001). More than three decades of research on children's mathematical thinking has shown that elementary school children are capable of engaging in this type of mathematical learning, but often they are not given the opportunity to do so (Campbell et al., 1998;Carpenter et al., 1996;Carpenter et al., 2015;Carpenter et al., 1989;Empson, 2014;Empson et al., 2020;Empson et al., 2006;Empson & Levi, 2011;Franke et al., 2001;Jacobs et al., 2019;Jacobs et al., 2007). ...
... Within this context, children learn how to generate mathematical ideas, how to express these ideas (in any way that makes sense to them), and how to explain these ideas and those of others (Carpenter et al., 2015;Franke et al., 2001). More than three decades of research on children's mathematical thinking has shown that elementary school children are capable of engaging in this type of mathematical learning, but often they are not given the opportunity to do so (Campbell et al., 1998;Carpenter et al., 1996;Carpenter et al., 2015;Carpenter et al., 1989;Empson, 2014;Empson et al., 2020;Empson et al., 2006;Empson & Levi, 2011;Franke et al., 2001;Jacobs et al., 2019;Jacobs et al., 2007). ...
... Additionally, in these early strategies children tend to distribute wholes without considering the number of people sharing (Hackenberg & Lee, 2015). Similar strategies for solving problems with whole numbers have been documented in the work of Franke et al. (2001), Jacobs and Ambrose (2008), and Jacobs et al. (2007), among others. Children can at times also use procedures and conventions for solving problems. ...
This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-onone interview and of the circulating portion of a mathematics class from a secondgrade classroom. We use these examples to foreground instructional practices, for
researchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal manipulation to a more academically ample discussion of perspectives that investigate critically both mathematical concepts and their modes of transmission, which involve language practices, that are crucial for educating bilingual children.
... Another approach to narrowing the research-practice gap is a form of teacher PD known as Cognitively Guided Instruction (CGI; Carpenter, Fennema, Franke, Levi, & Empson, 2014;Carpenter, Fennema, Peterson, Chiang, & Loef, 1989). At its core, CGI is an approach to working with teachers that involves sharing research on children's mathematical thinking and then using this knowledge as a basis for assessment and instruction (Carpenter et al., 1989;Franke, Carpenter, Levi, & Fennema, 2001). For example, as described in various iterations of this model, teachers are introduced to research-based frameworks for understanding children's arithmetic development and strategy use (e.g., identifying different problem types and the mental actions associated with each problem type). ...
... If teachers' numerical cognition knowledge is more related to student learning than self-perceived knowledge, then we should expect to see greater evidence of student gains in Year 1 than Year 2. Indeed, there was stronger evidence for improvements in numerical reasoning by students in Year 1 compared with Year 2. This finding is consistent with prior research, in which teachers' understanding of different facets of children's numerical thinking (e.g., arithmetic strategies) has been associated with gains in students' numerical thinking (e.g., see Carpenter et al., 1989;Fennema et al., 1996;Franke et al., 2001). However, upon closer reflection, it is clear that this trend in the current data needs to be interpreted with caution. ...
This study reports on the design, implementation, and effects of a 16-week (25-hour) mathematics Professional Development (PD) model for K-3 educators (N=45) and their students (N=180). A central goal of the PD was to better integrate numerical cognition research and mathematics education. The results of the first iteration (Year 1), indicated that compared to a control group, both teachers and students benefitted from the intervention. Teachers demonstrated gains in self-perceived and actual numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on a measure of self-perceived numerical cognition knowledge, but no gains in actual numerical cognition knowledge. At the student level, there was some evidence of gains in numeration. Given the mixed findings, questions remain as to why the model may be effective in one school context but not another.
... While originally conceived for the professional development of educators, I have recalibrated the Model of Generative Change to cater to students, with the aim of fostering generative learning. Generative knowledge, as characterised by Franke et al. (2001), emerges when learners discern the necessity to assimilate new information with their existing knowledge base, propelling continuous learning and enabling the application of this integrated knowledge to novel and unfamiliar problems. ...
... This synthesis leads to the creation of knowledge that is not only new but also practically applicable to their teaching challenges and responsive to their learners' educational requirements. Drawing from the ideas of Franke et al. (2001), knowledge transitions to a generative state when educators perceive the necessity of fusing newly gained understanding with their existing educational framework, prompting a continuous reevaluation and reinforcement of their knowledge base. This notion of generative change refers to an ongoing transformative process where an educator's teaching methods are constantly being shaped and enriched by pedagogical strategies and theoretical frameworks. ...
This Participatory Action Research (PAR) investigates the integration of informal music learning in Macau’s educational context, guided by the Model of Generative Change (Ball, 2009). Engaging the participating college students ( N = 41), this study explores how learners perceive the formal–informal learning continuum (Folkestad, 2006) through the four stages of informal learning experiences: awakening, agency, advocacy and efficacy (Ball, 2009). Through multiple data collection methods and qualitative analysis, students experienced (a) autonomous learning, (b) joyful peer learning, (c) creative exploration and skill development and (d) resilience through challenges. Moreover, the study highlights the stages of awakening, introspection and critique from the students’ perspectives. Notably, a subset of students, predominantly those with prior formal instrumental training, expressed critiques concerning informal learning, predominantly regarding its perceived lack of systematic structure and foundational skills. These insights suggest a need to further embed informal music learning in Macau to foster a dynamic change towards generativity and a ‘multileveled cultural world’ (Law & Ho, 2015). The implications point to a broader pedagogical shift that values diverse learning experiences, which may enhance the development of a more adaptable, innovative and well-rounded musical skill set within the student population in Macau.
... There are many studies that show the positive effects of in-service teacher training on teacher pedagogical knowledge and skills and student success (Academy for Educational Development, 2002;Borko et al., 2005;Grossman, Wineburg, & Woolworth, 2001;King, 2011;Mulholland & Wallace, 2005;Opfer & Pedder, 2011;Sachs, 2016;Smith, 2007). Franke et al. (2001) define in-service teacher training as a process that helps to develop individuals' learning skills and they emphasize the effectiveness of quality in-service teacher training. However, in-service teacher training studies conducted in Türkiye generally focus on teachers' views on the training provided and their expectations from in-service training (Bümen, Ateş, Çakar, Ural, & Acar, 2012;Demir, Böyük, & Erol, 2012;Kaçan, 2004;Karaaslan, 2003). ...
... Until the reinforcement step, both triadic and chain patterns were utilized. This lengthy step, which lasted from week 5 to week 18, proves that a long time is required to change teachers' approach (Borko, 2004;Franke et al., 2001). By weeks 19 and 20, each teacher was used to dialogicalinteractive structures. ...
Professional development programs enable teachers to familiarize themselves with new teaching methods. However, practicing what one learns in the process depends on one’s internalization. This study aims to present how teachers manage these processes of acceptance. A professional development model supporting teachers was created for this long-term case study, which observed the teachers’ development. A 3-day hands-on training program was organized for a group of volunteer teachers, three of whom were provided with on-the-job support for one academic year. During the on-the-job support process provided through scaffolding, internal barriers against new applications were identified. Changes in these barriers were classified into affective and communicative categories and presented holistically in this study.
... How are you going to solve this mathematical MERGA problem?). In this way, the tool goes beyond standardised norm-referenced testing and existing assessment tools (Allsopp et al., 2008;Franke et al., 2001;Wright et al., 2006). ...
... These questions are productoriented, designed to assess the correctness of the child's answer. Although correctness of answers is important, obtaining process information as opposed to product (i.e., outcome) information should prevail for the dynamic mathematics interview to have added value near standardised tests (Franke et al., 2001). ...
In this quasi-experimental study involving 23 fourth grade teachers, we investigated the effect of implementing teacher-child dynamic mathematics interviews to improve mathematics teaching behavior in the classroom. After a baseline period of 13 months, the teachers participated in a professional development program to support the use of dynamic mathematics interviews followed by a period of practice in mathematics interviewing to identify children's mathematics learning needs. To determine the effects of the teacher professional development program, pretest and posttest videos of mathematics interviews were compared. To analyse the effects of the intervention, mathematics teaching behavior, mathematics teaching self-efficacy and perceived mathematical knowledge for teaching were measured. Results showed not only the effect of the program on the quality of the dynamic mathematics interviews, but also the effects of the intervention on mathematics teaching behavior, mathematics teaching self-efficacy and mathematical knowledge for teaching.
... Second, more profound knowledge could be obtained Moreno & Valdez, 2007). Third, a better understanding of student (naïve) conceptions and comprehension of conveyed subject matter could be achieved (Franke et al., 2001;Santagata et al., 2007;. Fourthly, there is even evidence of improved emotion regulation in learners (Kumschick et al., 2018). ...
... Second, more profound knowledge could be obtained Moreno & Valdez, 2007). Third, a better understanding of student (naïve) conceptions and comprehension of conveyed subject matter could be achieved (Franke et al., 2001;Santagata et al., 2007;. Fourthly, there is even evidence of improved emotion regulation in learners (Kumschick et al., 2018). ...
In recent years, many test instruments have been developed to assess the professional vision of (preservice) teachers. These instruments entail significant differences. They vary in the terminology used for the construct itself as well as in the assumed underlying dimensionality of a given test. Regarding methodological aspects, most tests use short realistic video clips as item stimuli, but task formats range from standardised tasks or rating items to open responses and written texts. Meanwhile, some studies have revealed only a low-to-moderate correlation between different task formats, which indicates low convergent validity. Finally, although construct validity has been commonly examined, information on the predictive validity of such tests remains limited.
This chapter first provides an overview of characteristics and validation steps of existing video-based instruments. Then, it addresses the convergent and predictive validity of different task formats using its own data.
In a correlational study, 85 preservice teachers worked on three different task formats measuring the professional vision of classroom management. They then taught a lesson in an internship, which students evaluated in terms of classroom management. Multilevel analyses indicated correlations with classroom management quality only for one task format. The chapter concludes with a critical review of the results and their implications.
... The misconception noticing skills of the comparison group preservice teachers, unlike the lesson study group pre-service teachers, did not go above level 1 or level 2 in any lesson.From this point of view, it can be said that the lesson study professional development model positively affected preservice teachers' noticing skills. Similar to this result of the study, some studies in the literature also state that professional development models positively affect noticing (Franke, Carpenter, Levi, Fennema, 2001;Lee, 2019;Lewis, Friedkin, Baker, & Perry, 2011). ...
The aim of the study is to examine how lesson study activities affect pre-service classroom teachers' noticing of students' misconceptions. A qualitative research approach was adopted and action research method was used. The study was conducted with 9 pre-service teachers. The data were obtained from the observation form, video recordings, reflection reports and content notes in order to reveal how the lesson study model affected the noticing development of pre-service teachers. In addition to these, the "video exam" at the end of the Teaching Practicum-II course also constituted one of the data collection tools. Descriptive analysis was used in the study. The data obtained were analyzed by adapting the theoretical framework of "Levels of Noticing of Students' Mathematical Thinking" developed by van Es (2011) as "Levels of Noticing of Students' Misconceptions" in order to reveal pre-service teachers' noticing of students' mathematical thinking. As a result of the study, it was concluded that the noticing skills of the lesson study group pre-service teachers, were mainly level 3 or level 4, while the noticing skills of the comparison group pre-service teachers were mainly level 1 and level 2.
... Lärares kompetens definieras i forskningssammanhang som bestående av ämnesskicklighet (Borko, 2004;Anderson, 1989), pedagogisk skicklighet (Franke, Carpenter, Levi & Fennema, 2001), kunskap om lärande, samt reflexivt tänkande (Castle & Aichele, 1994). Litteraturen framhåller att kompetensutvecklingsprogram behöver ge lärare tillfälle att utveckla kompetens inom samtliga områden. ...
In 2007 the Swedish government decided to put resources in a project that offered active teachers to develop disciplinary and pedagogical competence through doctoral studies. Among ten others the Royal College of Music in Stockholm succeeded with their application and got the chance to educate 10 music teachers from the compulsory school towards a “half” PhD exam, that is called a Licentiate exam in Sweden. The teachers come from all of Sweden and are registered at one of five participating higher music education institutions. At the same time they work for 20 % in their ordinary schools. The common education is organized as courses and in virtual meeting rooms of different kinds. The motive for that is that the teachers are participating in several communities of practice at the same time, aiming to develop as researching practicing teachers in a broad way. In a developing research project the growing of the teachers – eg identity development and professional learning - is followed, guided by the following questions: What becomes the task for higher education when the teachers are taking part in a PhD education at the same time as they work, and are expected to go back to their ordinary work in schools? How can a research school be organized in as a developing learning system where individual experiences have possibility to be shared by others? What are the possibilities for good learning and identity development, and which are the challenges? How can learning trajectories between the research school, the research communities and the everyday practice seen as communities of practice, be encouraged? What authentic questions are engaging the teachers and how do they develop in the social interplay? The methods used are teachers’ continually encouraged written reflections and documented group discussions.
... Recent literature on teacher professional development highlights collaboration among teachers [3,9] and semiotic analysis of students' thinking as key factors for supporting teacher learning (e.g., [32,50,78]). Studies by Gonzalez and Maxwell [34] and Franke et al. [31] have shown that teachers who have knowledge of students' diverse learning approaches, problem-solving strategies, and can adapt their instruction accordingly, can provide inclusive, innovative and appropriate teaching activities in the classroom [57]. However, in many European countries (and beyond), teacher education is often disregarded or provided in a manner that does not fully address teachers' actual needs (see the 2018 OECD Survey). ...
This paper discusses the lack of compulsory practices for mathematics teachers’ professional development in Italy, as well as the challenges that arise when trying to implement changes in teaching and learning practices. The 2018 OECD Teaching and Learning International Survey shows that merely providing a body of knowledge may leave some teachers uncertain about the necessary steps to enact meaningful changes. Barriers such as scheduling conflicts and insufficient incentives further hinder participation in professional development programs, while transforming teaching practices remains challenging due to cultural, psychological, pedagogical, and disciplinary issues. Scholars provide the epistemological legitimacy of the taught knowledge, but there is a need for sustainable mathematics teacher education, as well as research into cultural and social aspects to enable mathematics teachers’ critical reflection. This study uses Lotman’s Semiosphere lens to analyse data collected during Lesson Study experiences in mathematics, which is a Chinese teacher professional development methodology that can trigger critical reflection. Examining two case studies involving grade 5 and grade 12 students in the domains of probability and combinatorics, the research illustrates the essential activation of teachers’ reflective practices concerning both the mathematical concept itself and instructional methodologies within this culturally sensitive practice for professional development. The presented case studies serve as examples illustrating the theoretical positioning. As a research finding, mathematics teacher education that also focuses on cultural aspects has a more sustainable and fruitful outcome.
... There is also a body of literature on factors related to the design of PD that might facilitate its impact on classroom practice. One such factor is the availability of coaching or mentoring during or after PD (Franke et al. 2001, Ingvarson et al. 2005, Snyder et al. 2018 or expert scaffolding (Kleickmann et al. 2015). Another such factor is the provision or availability of implementation scaffolds (curriculum resources, protocols/tools) (Banilower et al. 2005, Remillard 2005, Penuel et al. 2007. ...
It is well known that teacher professional development may not result in meaningful change to classroom instruction. A recent theoretical model by McChesney and Aldridge (2021) posited that this phenomenon may be explained on account of ‘implementation barriers’ to professional development delivery. The present study thus investigated the nature, structure, and distribution of such barriers to the impact of teacher professional development on classroom practice. Using survey data collected from three Illinois school districts (N = 274), we identified six distinct but non-orthogonal barriers (e.g. school culture, relevance, teacher resistance) and found that the most commonly perceived specific implementation barriers were time constraints and pressures, other curricular mandates or demands, and stress or burnout. Repeated-measures analysis of variance also showed some differences in the profiles of the six barriers across the school districts.
... However, LTT will fail to occur if teachers do not routinely embrace what multiple scholars define as teacher noticing (see Mason, 2002;Sherin et al., 2011;Zazkis & Mamolo, 2018). Within LTT, this involves actively looking for and recognizing student thinking as a valuable part of education, a contention that highlights the fact that teachers learn from students as well (Franke et al., 2001;Jacobs & Empson, 2016). Beyond planning and implementing, many researchers studying teacher education position reflecting on one's practice as the primary means for LTT to occur (see Mason, 2002;Salmon et al., 2020;Santagata et al., 2018;Zaslavsky & Leikin, 2004). ...
While research has shown that students benefit from student-centered pedagogies, few studies have considered the benefits of this pedagogical approach for educators as they learn through teaching. In response to this need, we analyzed interviews, lesson plans, and video observations from five teachers in elementary schools across the United States who varyingly engaged student-centered and teacher-centered pedagogies. Our analyses revealed that the participating teachers developed a wide breadth of teacher knowledge regardless of their pedagogical approach. However, the teachers who employed student-centered teaching reported more pedagogical content knowledge gains for themselves than the teachers who used direct teaching.
... Providing content-focused professional development (PD) for mathematics teachers has been a federal policy pathway intended to improve teacher effectiveness and ultimately boost student mathematics performance in the United States (e.g., Every Student Succeeds Act, 2015). Prior empirical evidence also suggests that high-quality PD contributes to mathematics teachers' content knowledge for teaching (e.g., Copur-Gencturk, Plowman, & Bai, 2019;Franke et al., 2001;Garet et al., 2016;Jacob et al., 2017), quality of instructional practice (e.g., Garet et al., 2016;Jacobs et al., 2007;Kraft & Blazar, 2017), and student learning outcomes (e.g., Campbell & Malkus, 2011;Carpenter et al., 1989;Jacobs et al., 2007). ...
https://theconversation.com/ai-can-teach-math-teachers-how-to-improve-student-skills-218210
... These findings illustrate how Piagetian constructs can explain a teacher's mathematical learning in the context of understanding student thinking at a fine-grained cognitive level. Researchers have repeatedly advocated teaching-becomes-learning (Franke et al., 2001;Leikin & Zazkis, 2010;Sherin, 2002;Steinberg et al., 2004) and student-teacher interaction as a site for teachers to develop their knowledge (Seymour & Lehrer, 2006). The identified mental processes demonstrate how such learning occurs as a teacher learns from her student, which is an active response to Thompson's (2016) call for research on teachers' process of knowing (as opposed to evaluating the knowledge they possess) to unpack the learning mechanisms of how the teacher comes to know. ...
Teachers’ knowledge of students’ mathematical thinking is a growing area of research in mathematics education. The literature has reported plentiful evidence of the interplays between teachers’ mathematical knowledge and their knowledge of students’ mathematical thinking. The present study builds on this body of work to explain how such interplays occur. Over a semester, I worked in partnership with a secondary school mathematics teacher on cycles of task design, interactions with a student, and in-depth reflection on the student’s thinking about linear programming. Adopting and extending Piagetian constructs of assimilation and accommodation, I describe several key mental processes that illuminate the teacher’s learning of mathematics and of the student’s mathematical thinking. I conclude with a discussion of the study’s empirical and theoretical contributions to understanding teachers’ mathematical learning in relation to student thinking.
... Some studies reported that teachers' mathematics content knowledge was associated with the mathematics courses they took during their undergraduate years (Rowan, Correnti, and Miller, 2002;Wayne and Youngs, 2003). On the other hand, it is also emphasized that these courses are not sufficient for teachers to teach mathematics and that the structure and characteristics of mathematics content knowledge should take into consideration the classroom context (Franke, Carpenter, Levi and Fennema, 2001;Hiebert, Gallimore and Stigler, 2002). Studies dealing with mathematics content knowledge in the context of the classroom stated that there are significant deficiencies in teachers' content knowledge on different subjects (such as numbers, fractions, algebra) (An, Kulm, and Wu, 2004;Işıksal, 2006;Simon and Blume, 1994;Tzmantar and BingTlbali, 2009). ...
... He follows-up them three and four years later and found that the majority were still using cognitively guided instruction, but participants differed in how they perceived this instruction and how they applied it. Franke et al. (2001), who conducted a post-service survey of teachers four years after completing a program on students' mathematical thinking reported that they cultivated some such thinking in their students. Raikou (2019) also investigates the effects of an educational intervention on the ability to develop critical thinking in pre-service kindergarten teachers six years after the initial intervention and noted that the educational intervention has an impact on them six years later. ...
This paper follows up on the impact of a distance learning teachers’ professional development program on their self-efficacy beliefs in the long term. Specifically, it measures the personal self-efficacy beliefs and outcome expectancy beliefs of a group of 122 in-service elementary teachers before the start of the program, immediately after its completion, and two years later. The quantitative was used as the data collection method of the research. The results advocate that both the personal self-efficacy beliefs and the outcome expectancy beliefs of the research participants improved immediately after the program was completed and the former remained relatively improved two years after completion of the program, while the latter returned to the levels they had had before attending the program. Recommendations are made for future research.
... Moreover, school-based PD often focuses on concrete skills and tools that are immediately useful for practice (Postholm, 2018) at the cost of conceptualizing (Cravens & Wang, 2017;Molle, 2013) and creating integrated knowledge structures (Cameron et al., 2013;Franke et al., 2001). While traditional modes of PD are criticized for their difficulty in connecting theories to practices, school-based PD is criticized for its difficulty in connecting practices to theories (Korthagen, 2017). ...
Based on qualitative and quantitative data collected from an investigation of the flagship National Teacher Training Project (NTTP) in China, this study compares the impacts of teacher professional development (PD) programs located at different distances from the participants’ workplaces. The study argues that local and nonlocal programs play different roles in teacher PD. While local programs are conducive to teachers’ mastery of context-specific knowledge and skills that are directly connected to subject teaching, nonlocal programs are crucial for teachers’ continuous professional development in the long term. The two types of programs are supplementary to each other, and teachers need access to both types of programs.
... There has been remarkably little research on the influence of teacher development programs on student achievement (Gersten et al., 2014;Hill, 2007;Bautista, 2015;Bautista and Ortega-Ruiz, 2015;Sztajn et al., 2017). Recent studies, however, have begun to show that teacher professional development may be associated with improved student learning (Darling-Hammond, Hyler, and Gardner, 2017;Akiba & Liang, 2016;Desimone et al., 2013;Franke et al., 2001;Lindvall, 2015;Sample McMeeking et al., 2012;Santagata et al., 2011;Pournara et al., 2015;and Saxe et al., 2001). Successful teacher development programs tend to focus on mathematics content as well as conditions favoring active learning, collaboration among teachers, effective teaching practices, expert support, and sustained opportunities for feedback and reflection. ...
We examine the possible contribution of teachers' participation in a teacher development program to the learning of mathematics by Black, Latinx, and White students in grades 3-8, in a multi-ethnic district in greater Boston, MA, US. The three courses in the program use functions and their representations to integrate topics in the K-12 curriculum and to engage teachers in understanding and promoting deeper student learning. Participating teachers were encouraged to promote classroom discussions about open-ended contextualized problems, search for generalizations, and use of multiple representations for relations between quantities, including students' own diagrams, number lines, variables, algebra notation, and functions in the Cartesian space. Answers to anonymous surveys and lessons teachers analyzed, designed, and implemented over the year suggest that they had adopted content and pedagogical approaches promoted by the program. Results of state assessment
... These participants aimed to elicit students' ideas, which they then used to learn about student thought processes or to incorporate students' ideas into class discussions. Instructors who regularly leverage student thinking can improve student learning, create more equitable participation, and support the development of specialized teaching knowledge, even in large classes (100 to 300 students) (19)(20)(21)(22)(23). ...
Instructor discourse, defined as verbal interactions with students in the classroom, can play an important role in student learning. Instructors who use dialogic discourse invite students to develop their own ideas, and both students and the instructor share ideas in back-and-forth exchanges. This type of discourse is well-suited to facilitate deep learning for students but is rare in undergraduate biology classrooms. Understanding the reasoning that underlies the use of dialogic discourse can inform teaching professional development for instructors who are learning to use discourse to support student learning. Through classroom video recordings to identify dialogic discourse and stimulated recall interviews to elicit instructor reasoning, we investigated why undergraduate biology instructors used dialogic discourse in active-learning lessons. Using inductive and deductive qualitative analysis of interview transcripts, we identified and characterized seven reasons that instructors used dialogic discourse, including three aligned with a theoretical framework of student cognitive engagement and four that emerged from our data set. In addition to aiming to prompt generative cognitive engagement in 34% of instances of dialogic discourse, instructors used dialogic discourse to prompt activity, supply information, provide feedback, decipher student thinking, leverage student thinking, and cue students to make connections. Reasoning varied across different types of dialogic discourse. These findings provide valuable insights that can inform research, teaching professional development, and individual instructors’ reflections.
... Despite receiving great scores in a number of areas, students often struggle to apply their acquired information, abilities, and attitudes in other contexts (Isabelli-García, 2006). Students do have some knowledge, but a lot of it is information that they learn from teachers because they are not used to looking for information or knowledge on their own (Pintrich, 2002) (Barton & Levstik, 2004) (Franke et al., 2001) (Prosser et al., 1994). As a result, the information has no practical application (Burnham & Anderson, 1998). ...
Researchers found that a mean score of 12.24 was achieved when measuring the level of student enthusiasm to learn while using an active learning strategy. Students whose education follows the traditional model report an average (mean) level of motivation to learn of 11.2. The "t" test's calculations led to the following results: t count = 3.49, and t table = 2.01 for the price. If the number of students taught using an active learning strategy is larger than the number of students taught using a traditional learning approach, then Ho might be rejected. Therefore, this study has successfully demonstrated that the active learning technique, as opposed to the conventional learning approach, increases student learning motivation.
... Across different conceptualizations and research strategies, teachers' diagnostic competences have repeatedly been identified as necessary for reacting to students' utterances in student-centered and adaptive ways (Ball and Cohen 1999;Empson and Jacobs 2008) and as having a significant impact on students' learning gains (Brunner et al. 2013;Franke et al. 2001;Wilson and Berne 1999). Prospective and practicing teachers' informal or formal formative assessments have been investigated from many perspectives, such as noticing practices and diagnostic thinking processes, examining diagnostic competence (i.e., the knowledge, skills, beliefs) and motivations needed to carry out diagnostic processes (e.g., preparing, organizing, executing, and reflecting diagnostic situations, activities and judgments), and assessing task complexity in order to direct didactical actions (Artelt and Gräsel 2009;Leuders et al. 2018;Stahnke et al. 2016;Weinert et al. 1990). ...
Teachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles ( N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves.
Mathematics teaching is complex, involving the skilled enactment of practices coupled with responsive decision-making in the moment. Preparing teachers for the skilled enactment of ambitious practices demands teacher learning designs embedded in practice. This study contributes to the effort to articulate such designs by describing side-by-side coaching and examining what three elementary mathematics teachers learned from working with a coach in their classrooms for 7–8 sessions during 1 month of teaching. Qualitative analysis of video records of case study teachers’ practice before and after coaching found three substantive and shared shifts: increased eliciting of student thinking, increased open-ended questions, and an expanded repertoire of moves to support meaning-making. This study adds further support for practice-based approaches and provides evidence of teacher learning outcomes for a one-on-one coaching design.
The chapter, “Building Smarter Educators: Merging Cognitive and Emotional Intelligence in Teacher Development,” emphasises the integration of cognitive and emotional intelligence into teacher training. It highlights how these competencies help teachers recognise and address students' needs, create effective lesson plans, mentor and inspire students, manage conflicts, and cope with professional challenges, leading to reduced burnout, job satisfaction, and student success. Strategies discussed include mentoring, collaborative enquiry, mindfulness, SEL programmes, peer coaching, reflective practices, and leveraging technology. Challenges like resource constraints, cultural differences, and balancing personal and professional growth are addressed with solutions such as continuous evaluation, stress management, and fostering supportive environments. The chapter underscores the need for emotionally and cognitively intelligent teachers to foster student-centred learning and enhance academic and professional outcomes.
Supporting teachers to transfer their learnings from innovative professional development settings to the classroom is challenging. In this paper, we investigate a novel approach to teacher learning, in which teachers from seven US districts taught in a mathematics summer camp using a research-based curriculum centered on student reasoning and mindset messages. We examined the practices teachers did and did not implement in their camp and school-year classrooms, as well as the possible reasons for the greater or lesser changes in practice. Through analysis of classroom video, teacher artifacts, and teacher interviews, we found that teachers implemented several important practices in both camp and school-year classrooms, namely posing open tasks, giving students ample time to collaborate, and asking questions that pushed students to reason. Interview analysis revealed that the act of centering students’ reasoning and witnessing their subsequent engagement seemed to motivate teacher uptake of these practices. At the same time, however, teachers less frequently integrated mindset messaging directly into their teaching and gave space for the exploration of students’ mistakes and struggles. These findings suggest implications for innovative professional development efforts outside of the school year, as well as incremental approaches.
Multiple meta-analyses have now documented small positive effects of teacher professional development (PD) on pupil test scores. However, the field lacks any validated explanatory account of what differentiates more from less effective in-service training. As a result, researchers have little in the way of advice for those tasked with designing or commissioning better PD. We set out to remedy this by developing a new theory of effective PD based on combinations of causally active components targeted at developing teachers’ insights, motivating change, developing teaching techniques, and then embedding these changes in teachers’ practice. We test two important implications of the theory using data identified through a systematic review and meta-analysis of 104 randomized controlled trials, finding qualified empirical support for the theory. The main contribution of the article is to provide a testable theory of what makes PD more effective, which can be used to guide future empirical research on this topic.
In this paper, we explore the critical practice of making sense of students’ mathematical ideas. We extend previous research by studying stances prospective teachers adopt, the extent or depth to which they do so, and the types of prospective teachers making sense of students’ mathematical ideas. Analyzing the responses of 123 prospective teachers to students’ different ideas on an ambiguous mathematical task, our study identifies various stances—descriptive, evaluative, comparative, interpretive, inquiry-based, connective, and projective—and explores the complexity of attributing value, meaning, and significance to student ideas. Our findings offer insights into various types of making sense of students’ ideas and suggest that different kinds of attributions are at play for the purposes of observation, assessment, understanding and projection/prediction.
Background or Context
Teachers knowing their students is consequential for students’ participation and learning. Evidence in mathematics education points to the ways that knowing the details of students’ mathematical thinking supports teacher and student learning. What it means to know students and what teachers learn about their students are situated in the everyday practices of schooling.
Purpose, Objective, Research Question, or Focus of Study
This study investigates how teachers characterized their students mathematically and how they considered meeting students’ needs in math class.
Research Design
This qualitative study focused on interviews conducted over four years with 61 teachers of kindergarten through second grade across two school districts.
Conclusions or Recommendations
This study found that rather than describing what they knew about the details of their students’ mathematical thinking or detailing specific tasks, tools, or teacher moves that supported their students, many teachers characterized students in ways that were in line with practices that organize districts, schools, and classrooms. Our data raise questions about the ways in which the structures and common practices of schools are shaping teachers’ descriptions of their students in mathematics, and the corresponding classroom practices then engaged.
It is known that teacher noticing skills improve through different interventions such as video clubs, lesson study, and short-term professional development programs. However, it is not known whether this improvement is permanent and whether teachers can transfer their noticing skills into the classroom. It is extremely important to provide an enduring change in teacher noticing skills. Rather than short-term programs, implementing long-running professional development programs, which last almost 2 years, enables teachers to maintain their noticing skills. At this point, the current study aims to develop in-service middle school mathematics teachers’ professional noticing of students’ mathematical thinking on pattern generalization during their involvement in a 2-year online professional development program enriched with collaborative discussion. Accordingly, the study was built on the professional noticing of children’s mathematical thinking framework, including three noticing skills: attending, interpreting, and deciding how to respond. Participants comprised 31 in-service middle school mathematics teachers with up to 15 years of professional experience working in public schools in seven different provinces of Türkiye. The teachers participated in the online PDP, including scenarios involving student strategies of particular mathematics content. The analysis of the data gathered from the pre-test and post-test let us conclude that the three noticing skills of the in-service middle school teachers exhibited incredible progress through their involvement in collaborative discussion in a long-running online PDP. Based on this result, the characteristics of the online PDP are put forth to develop teachers’ noticing skills.
In this contribution, we theorize generativity as a heuristic for impact-driven management scholars seeking to address grand challenges through research. We use generativity to suggest engaging diverse actors in pluralistic inquiry to create conditions for future flourishing. Our theorization applies a pragmatist worldview and builds on insights from the multidisciplinary literature on generativity to envisage researchers as agents of care, collective learning, and transformative change. We synthesize four tenets for researchers seeking both academic and real-world impact. These tenets can support researchers addressing grand challenges by guiding their efforts to diversify inputs, distribute agency, conduct experiments, and pursue prospective impacts. We illustrate generativity in action by drawing on our experience in a transdisciplinary research project on small- and medium-sized enterprises taking climate action in Canada. We show how the four tenets foster generativity to promote an inclusive understanding of grand challenges and a bias toward action, thereby providing an optimistic stance toward addressing issues of social concern.
Instructional shifts required by equitable, reform‐based science instruction are challenging, especially in the elementary context. Such shifts require professional development (PD) that supports teacher internalization of new pedagogical strategies as well as changes in beliefs about how students learn. Because of this complexity, many PD programs struggle to foster lasting pedagogical shifts, necessitating further investigation into why some teachers successfully embrace reform practices while others do not. This qualitative study uses a nonlinear, iterative model of teacher learning (Interconnected Model of Professional Growth; Clarke & Hollingsworth, 2002) alongside professional noticing to help understand why elementary teachers in science PD differentially make sense of and internalize new pedagogies. Findings indicate that teachers most likely to adopt reform‐based instructional practices from the PD were those who clearly connected student learning to their instructional moves. In addition, teachers who more actively attended to student sensemaking and productive struggle took up pedagogies from the PD more substantively than did colleagues who attended solely to student engagement and affect. Finally, teachers who attended to and valued novel ideas from students’ lived experiences were more likely to change their beliefs about students’ capacity to learn science, and thus more likely to see the value of instructional practices from the PD. In sum, structuring PD to build on these specific teacher noticing skills can encourage more teachers to move away from traditional, teacher‐directed instructional practice, and more fully support reform‐based instructional practices.
Chemistry graduate teaching assistants (GTAs) have substantial facetime with undergraduate students at large research institutions where they lead discussion and lab sessions. Emerging research describes GTAs’ content and teaching knowledge for introductory chemistry classes, but we need to know more about how GTAs manage their classes in the moment and how they assess student learning during class time. We conducted classroom observations and post-observation interviews with six chemistry GTAs with various years of teaching experience and who were teaching a variety of classes ( e.g. , general chemistry discussion, biochemistry discussion, organic chemistry lab, computational chemistry lab, and more). These GTAs were each observed and interviewed multiple times over the course of a semester. Through qualitative analysis guided by the teacher noticing framework, we describe what chemistry GTAs notice, or pay attention to, regarding student learning in their teaching sessions and how they interpret what they notice. We found that chemistry GTAs often paid attention to the types of questions that students asked but relied on their students to take initiative to ask questions in order to assess their learning. Also, GTAs often focused on superficial features of their class sessions to assess learning, like whether students finished their tasks and left their session early. However, some GTAs noticed more sophisticated evidence of student understanding, such as when students connected content covered across multiple class sessions. The results from this study contribute to our understanding of how chemistry GTAs lead their sessions and evaluate student learning during their sessions. Results serve to inform potential training designs that can support chemistry GTAs’ teacher learning through learning to notice—and to create opportunities to notice—significant features of their classrooms.
Background
As more education practitioners adopt techniques of improvement science to address problems of practice, there is an increasing demand for leaders with the knowledge and capacity to lead improvement efforts. However, little research explores how school leaders learn to lead improvement science in their school context or the challenges they may face in doing so. To ensure leaders are supported in learning increasingly common school improvement frameworks, there is a need to understand better the contextual conditions that may influence how practitioners come to learn and lead improvement science in their school contexts.
Purpose
The purpose of this research paper is twofold: first, to understand how contextual conditions throughout a learner’s journey into, during, and after an educational leadership program could influence aspiring and current leaders’ efforts to lead improvement science. Second, the study aimed to explore the broader question of how context influences a practitioner’s ability to mobilize new knowledge into action. The researchers introduced the concept of “improvement science fluency” as a methodological contribution to specify the capabilities required to learn and lead improvement science effectively. The research question guiding the inquiry was: “What are the conditions that influenced the development of educational leaders’ improvement science fluency?”
Research Design
The study focused on participants who completed a 10-week improvement science course as part of an educational leadership preparatory program at a large public university in Southern California. The research team conducted semistructured interviews with 17 participants who met the inclusion criteria of recalling and using the course concepts in their work since graduating from the program. Interviews were audio-recorded, transcribed, and coded using a weighted coding schema to assess participants’ improvement science fluency in guiding principles, tools, and dispositions. The research team analyzed the data to identify conditions that influenced participants’ application and adaptation of improvement science, categorized as professional experiences prior to the course, experiences within the course, and conditions in the organizational environment post-course. Contrasting cases were considered to enhance the robustness of the analysis and acknowledge potential variations within the dataset.
Conclusions/Recommendations
The findings provided insights into the contextual factors that challenge or support the application of improvement knowledge to action, offering implications for designing and enhancing school leadership preparation programs to cultivate effective educational leaders for sustainable school improvement. The study emphasizes that organizational role and slack play a crucial role in shaping practitioners’ authority, opportunities for practice and application, and access to continued training and coaching, ultimately impacting their fluency in improvement science. To effectively support moving improvement knowledge to action, the paper recommends: (1) activating prior knowledge to prepare for future learning; (2) attending to the importance of the learning problem and its relevance to practitioners’ roles, scaffolding for role by providing support for practicing new knowledge within professional contexts; (3) addressing the organizational context to create an environment conducive to innovation; and (4) offering follow-up learning opportunities through sustained communities of practice. The study concludes that changing practice is not solely a matter of will and skill but requires careful attention to the broader context before, during, and after the learning experience to support innovations in practice effectively.
This study provides a portrait of Ms. Grace, a veteran English teacher at a high school in Silicon Valley. I examine how Ms. Grace’s perspectives on her immigrant-origin Latine students informed her teaching, highlighting the perspectives and practices that guided her pedagogy. Analysis of the data demonstrates the cyclical nature of how this teacher’s perspectives on her students led her to embody a cultural competence that demonstrated a moral ethic of cariño. Through Ethnographic Case Study methodology, this study highlights the importance of cultivating cultural competencies in the teaching of immigrant-origin Latine youth, and the ways in which teachers enact and embody such competencies. I highlight how a moral ethic of cariño emerges in both the teaching practices and in the perspectives toward her immigrant-origin students, demonstrating the critical role that teachers play in providing a more inclusive learning space for the teaching of immigrant-origin Latine youth.
Al fine di indagare criticità e potenzialità del Digital Learning nei percorsi di formazione per docenti specializzati sulle attività di sostegno, il presente contributo focalizza l'attenzione sulla qualità e sull'efficacia delle metodologie di insegnamento-apprendimento veicolate proprio tramite l'utilizzo delle Tecnologie dell'Informazione e della Comunicazione (TIC). In particolar modo, oggetto della presente indagine sono le percezioni di un campione di 237 futuri docenti di sostegno circa l'uso di un repository online di video tutorial, di cui hanno beneficiato durante il loro percorso formativo, in qualità di mediatore e dispositivo didattico. Tramite la valutazione dei risultati di apprendimento e dei feedback formativi, la riflessione si direziona, in conclusione, sulle modalità di implementazione dei percorsi di formazione volti alla costruzione di profili professionali in grado di utilizzare le tecnologie a supporto del Digital Inclusion nei contesti formativi.
Bu araştırmada, okul öncesi ve sınıf öğretmeni adaylarının çocuklarda matematiksel düşüncenin gelişimini desteklemeye yönelik yeterliklerini arttırmak amacıyla gerçekleştirilen bir projenin, mesleki gelişim sürecindeki rolünün katılımcı görüşlerine göre incelenmesi amaçlanmıştır. Araştırma, nitel araştırma desenlerinden durum çalışması olarak desenlenmiştir. Amaçlı örnekleme yöntemlerinden ölçüt ve maksimum çeşitlilik örnekleme yöntemlerine göre katılımcı grubu belirlenmiştir. Katılımcılar, 20 farklı üniversiteden seçilen 24 okul öncesi ve sınıf öğretmeni adayından oluşmaktadır. Veriler öğretmen adaylarının yansıtıcı günlüklerinden toplanmış ve içerik analizi yöntemi ile analiz edilmiştir. Araştırma sonucunda, öğretmen adaylarının öğrenme yörüngelerine dayalı matematik eğitimi kapsamında çocuklarda matematiksel düşüncenin gelişimine dair bilgi edindikleri tespit edilmiştir. Ayrıca adaylar, çocukların öğrenme rotasında ilerleyebilmesi için uygun öğretim etkinlikleri dizisi geliştirebilme becerisi kazanmışlar ve matematik öğrenme ve öğretmeye yönelik olumlu tutum-inanç geliştirmişlerdir. Gerçekleştirilen projenin öğretmen adaylarına, çocukta matematiksel düşüncenin gelişimini desteklemeye yönelik bilgi ve beceri kazandırdığı, ayrıca adayların matematiğe ilişkin bakış açılarını olumlu yönde geliştirdiği sonucuna ulaşılmıştır. Bu sonuçlara göre okul öncesi ve sınıf eğitimi lisans ve lisansüstü programlarında verilen ders içeriklerinin öğrenme yörüngelerine dayalı matematik eğitiminin bileşenleri açısından güçlendirilmesi yönünde önerilerde bulunulmuştur.
Undergraduate peer drop-in mathematics tutoring is a common form of support at the university level, yet research regarding how to train this specific group of tutors is underspecified. This paper aims to describe a training program for this population that is grounded in mathematics education research. It serves as a first step in conducting a design experiment on how training impacts tutor behaviours. This paper addresses the research question: How can mathematics education research inform tutor training design? First, the specific context for the training program is characterized, followed by challenges to training programs. Then, ways in which research on mathematics classroom teaching and learning can apply to tutoring are discussed. Finally, the training program is described in detail, including the research which informed the design, as well as the learning outcomes, activities, and feedback mechanisms. Broadly, the goals of the training program are to promote productive beliefs regarding tutoring and learning mathematics, to increase the use of NCTM’s [(2014). Principles to action.] teacher/student actions in tutoring practices, and to develop reflective practitioners. To guide the development of these skills and dispositions in tutors, tutors engage with tutoring scenarios, excerpts, and case studies. Tutors are also provided with opportunities to reflect on their own tutoring practices.
Lehrkräftefortbildungen bieten in Deutschland im Rahmen der dritten Phase der Lehrkräftebildung eine zentrale Lerngelegenheit für die Kompetenzentwicklung der Lehr-kräfte (Avalos, 2011; Guskey & Yoon, 2009). In dieser Phase können Lehrkräfte aus einem Angebot an berufsbegleitenden Lerngelegenheiten wählen, die auf die Anpassung und Weiterentwicklung ihrer professionellen Kompetenzen abzielen. Im Rahmen dieser Professionalisierungsmaßnahmen haben Lehrkräfte Gelegenheit zur Reflexion und Weiterentwicklung ihrer Unterrichtspraxis. Deshalb sind Lehrkräftefortbildungen auch für die Entwicklung von Unterrichtsqualität und das Lernen der Schüler:innen bedeutsam (Lipowsky, 2014). Ergebnisse der Nutzungsforschung zeigen jedoch, dass das Fortbildungsangebot nicht von allen Lehrkräften im vollen Umfang genutzt wird und sich Lehrkräfte in dem Nutzungsumfang dieser beruflichen Lerngelegenheiten unterscheiden (Hoffmann & Richter, 2016). Das hat zur Folge, dass das Wirkpotenzial des Fortbildungsangebots nicht voll ausgeschöpft werden kann. Um die Nutzung von Lehrkräftefortbildungen zu fördern, werden auf unterschiedlichen Ebenen verschiedene Steuerungsinstrumente von Akteuren eingesetzt. Die Frage nach der Steuerungsmöglichkeit im Rahmen der dritten Phase der Lehrkräftebildung ist bislang jedoch weitestgehend unbearbeitet geblieben. Die vorliegende Arbeit knüpft an die bestehende Forschung zur Lehrkräftefortbildung an und nutzt die theoretische Perspektive der Educational Governance, um im Rahmen von vier Teilstudien der Frage nachzugehen, welche Instrumente und Potenziale der Steue-rung auf den unterschiedlichen Ebenen des Lehrkräftefortbildungssystems bestehen und wie diese durch die verschiedenen politischen und schulischen Akteure umgesetzt werden. Außerdem soll der Frage nachgegangen werden, wie wirksam die genutzten Steuerungsinstrumente im Hinblick auf die Nutzung von Lehrkräftefortbildungen sind. Die übergeordnete Fragestellung wird vor dem Hintergrund eines für das Lehrkräftefortbildungssystem abgelei-teten theoretischen Rahmenmodells in Form eines Mehrebenenmodells bearbeitet, welches als Grundlage für die theoretische Verortung der nachfolgenden empirischen Untersuchungen zur Fortbildungsnutzung und der Wirksamkeit verschiedener Steuerungsinstrumente dient. Studie I nimmt vor diesem Hintergrund die Ebene der politischen Akteure in den Blick und geht der Frage nach, wie bedeutsam die gesetzliche Fortbildungspflicht für die Fortbildungsbeteiligung von Lehrkräften ist. Hierzu wurde untersucht, inwiefern Zusammenhänge zwischen der Fortbildungsteilnahme von Lehrkräften und der Zugehörigkeit zu Bundesländern mit und ohne konkreter Fortbildungsverpflichtung sowie zu Bundesländern mit und ohne Nachweispflicht absolvierter Fortbildungen bestehen. Dazu wurden Daten aus dem IQB-Ländervergleich 2011 und 2012 sowie dem IQB-Bildungstrend 2015 mittels logistischer und linearer Regressionsmodelle analysiert. Studie II und Studie III widmen sich den Rahmenbedingungen für schulinterne Fortbildungen. Studie II befasst sich zunächst mit schulformspezifischen Unterschieden bei der Wahl der Fortbildungsthemen. Studie III untersucht das schulinterne Fortbildungsangebot hinsichtlich des Nutzungsumfangs und des Zusammenhangs zwischen Schulmerkmalen und der Nutzung unterschiedlicher Fortbildungsthemen. Darüber hinaus wird ein Vergleich zwi-schen den beiden Angebotsformaten hinsichtlich des jeweiligen Anteils an thematischen Fortbildungsveranstaltungen vorgenommen. Hierzu wurden Daten der Fortbildungsdatenbank des Landes Brandenburg ausgewertet. Neben der Untersuchung der Fortbildungsteilnahme im Zusammenhang mit administrativen Vorgaben und der Nutzung des schulinternen Fortbildungsangebots auf Schulebene wurde zur Bearbeitung der übergeordneten Forschungsfrage der vorliegenden Arbeit in der Studie IV darüber hinaus eine Untersuchung des Einsatzes von Professionalisierungsmaßnahmen im Rahmen schulischer Personalentwicklung durchgeführt. Durch die qualitative Studie IV wurde ein vertiefender Einblick in die schulische Praxis ermöglicht, um die Kenntnisse aus den quantitativen Studien I bis III zu ergänzen. Im Rahmen einer qualitati-ven Interviewstudie wurde der Frage nachgegangen werden, wie Schulleitungen ausgezeichneter Schulen Personalentwicklung auffassen, welche Informationsquellen sie hierbei mit einbeziehen und welche Maßnahmen sie nutzen und in diesem Sinne Personalentwicklung als ein Instrument für Organisationsentwicklung einsetzen. Im abschließenden Kapitel der vorliegenden Arbeit werden die zentralen Ergebnisse der durchgeführten Studien zusammenfassend diskutiert. Die Ergebnisse der Arbeit deuten insgesamt darauf hin, dass Akteure auf den jeweiligen Ebenen direkte und indirekete Steuerungsinstrumente mit dem Ziel einsetzen, die Nutzung des zur Verfügung stehenden Angebots zu erhöhen, allerdings erzielen sie mit den genutzten Instrumenten nicht die gewünschte Steuerungswirkung. Da sie weder mit beruflichen Sanktionen noch mit Anreizen verknüpft sind, fehlt es den bestehenden Steuerungsinstrumenten an Durchsetzungsmacht. Außerdem wird das Repertoire an möglichen Steuerungsinstrumenten von den beteiligten Akteuren nicht ausgeschöpft. Die Ergebnisse dieser Arbeit bieten somit die Grundlage für anknüpfende Forschungsarbeiten und geben Anreize für mögliche Implikationen in der Praxis des Fortbildungssystems und der Bildungspolitik.
This study investigates the nature of pedagogical expertise by comparing the planning, teaching, and postlesson reflections of three student teachers (two secondary and one elementary) with those of the cooperating teachers with whom they were placed. Participants were observed teaching mathematics for 1 week of instruction and were interviewed prior to and following each lesson. Differences in the thinking and actions of these experts and novices were analyzed by perceiving teaching both as a complex cognitive skill and as improvisational performance Novices showed more time-consuming, less efficient planning, encountered problems when attempts to be responsive to students led them away from scripted lesson plans, and reported more varied, less selective postlesson reflections than experts. These differences were accounted for by the assumptions that novices' cognitive schemata are less elaborate, interconnected, and accessible than experts' and that their pedagogical reasoning skills are less well developed. We offer several recommendations for student teaching based on this analysis.
This article presents the findings of a study designed to determine the relationship between teachers' beliefs about the teaching of reading comprehension and their classroom practices. The study, dealing with teachers from grades 4, 5, and 6, uses a beliefs interview technique borrowed from anthropology. Predictions about teaching practices were made from the belief interviews of 39 teachers and were related to practices observed in their classrooms. The study demonstrates that the beliefs of teachers in this sample relate to their classroom practices in the teaching of reading comprehension. A case study explores a situation in which the teacher's beliefs did not relate to her practices. This case suggests that the teacher was in the process of changing beliefs and practices, but that the changes in beliefs were preceding changes in practices.
This essay posits a problem of fit among five streams of reform and prevailing configurations of teachers’ professional development. It argues that the dominant training-and-coaching model—focused on expanding an individual repertoire of well-defined classroom practice—is not adequate to the conceptions or requirements of teaching embedded in present reform initiatives. Subject matter collaboratives and other emerging alternatives are found to embody six principles that stand up to the complexity of reforms in subject matter teaching, equity, assessment, school organization, and the professionalization of teaching. The principles form criteria for assessing professional development policies and practices.
This paper addresses two questions: What is involved in bringing about significant and worthwhile change in teaching practices? How can or should research aid in this process? In order to do so, two related literatures will be explored—teacher change and learning to teach. These literatures will be used to develop a third perspective, which will be grounded in examples from a teacher change research project which is funded by the Office of Educational Research and Improvement (OERI), U.S. Department of Education. This perspective suggests that empirical premises derived from research (Fenstermacher, 1986) be considered as warranted practice, which, in combination with teachers's practical knowledge, become the content of reflective teacher change. It also suggests that practice should be viewed as activity embedded in theory. The paper concludes with suggestions for ways of approaching the introduction of research into teachers' ways of thinking.
In this article we propose that an understanding of students' thinking can provide coherence to teachers' pedagogical content knowledge and their knowledge of subject matter, curriculum, and pedagogy. We describe a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or spontaneous knowledge about students' mathematical thinking. Our major thesis is that children enter school with a great deal of informal or intuitive knowledge of mathematics that can serve as the basis for developing much of the formal mathematics of the primary school curriculum. The development of abstract symbolic procedures is characterized as progressive abstractions of students' attempts to model action and relations depicted in problems. Although we focus on one facet of teachers' pedagogical content knowledge, we argue that understanding students' thinking provides a basis for teachers to reconceptualize their own knowledge more broadly.
This article explores two forms of research on practice: formal research and practical inquiry. Formal research is undertaken by researchers and practitioners to contribute to an established and general knowledge base. Practical inquiry is undertaken by practitioners to improve their practice. It is suggested that practical inquiry is more likely than formal research to lead to immediate classroom change; that these two forms of research are fundamentally different; and that both are useful to practice, but in different ways.
Reforming schools depends on the interplay between research and local knowledge. This article uses examples from a multiyear project to improve reading achievement of Spanish-speaking children. Achieving changes was partially dependent on local action and understanding of the local school culture. It could not be done exclusively through reference to research knowledge, no matter how compellingly documented in the national literature.
Characterizes teaching as a complex cognitive skill amenable to analysis in a manner similar to other skills described by cognitive psychology. A formal model of the process of instruction in elementary mathematics is presented and examined in light of empirical data from 8 expert and 4 novice teachers. The model's perspective is that teaching skill rests on 2 fundamental knowledge systems: lesson structure and subject matter. Instructional segments were analyzed to clarify the nature of instructional action and goal systems that support competence. The expert teachers were shown to be characterized by use of well-practiced routines, effective application of guided or monitored practice, methods of obtaining feedback on the performance of all children, and efficient presentation of material. Analyses of specific teaching episodes are presented. (23 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This research examines the role of teachers' content knowledge during the implementation of mathematics education reform. Current mathematics education reform efforts require teachers to learn in the act of teaching. I claim that this learning occurs as teachers negotiate among 3 areas of their content knowledge: their understanding of the subject matter, view of the curriculum materials, and knowledge of student learning. The data for this study come from observations and videotapes of 2 teachers implementing a reform-based linear-functions unit in a high school algebra class. The focus of the article is a detailed analysis of 1 lesson that illustrates the process through which these negotiations occur and the learning that takes place as a result.
This study examined changes in the beliefs and instruction of 21 primary grade teachers over a 4-year period in which the teachers participated in a CGI (Cognitively Guided Instruction) teacher development program that focused on helping the teachers understand the development of children's mathematical thinking by interacting with a specific research-based model. Over the 4 years, there were fundamental changes in the beliefs and instruction of 18 teachers such that the teachers' role evolved from demonstrating procedures to helping children build on their mathematical thinking by engaging them in a variety of problem-solving situations and encouraging them to talk about their mathematical thinking. Changes in the instruction of individual teachers were directly related to changes in their students' achievement. For every teacher, class achievement in concepts and problem solving was higher at the end of the study than at the beginning. In spite of the shift in emphasis from skills to concepts and problem solving, there was no overall change in computational performance. The findings suggest that developing an understanding of children's mathematical thinking can be a productive basis for helping teachers to make the fundamental changes called for in current reform recommendations.
the goal of many research and implementation efforts in mathematics education has been to promote learning with understanding / drawing from old and new work in the psychology of learning, we present a framework for examining issues of understanding / the questions of interest are those related to learning with understanding and teaching with understanding / what can be learned from students' efforts to understand that might inform researchers' efforts to understand understanding
the framework we propose for reconsidering understanding is based on the assumption that knowledge is represented internally, and that these internal representations are structured / point to some alternative ways of characterizing understanding but argue that the structure of represented knowledge provides an especially coherent framework for analyzing a range of issues related to understanding mathematics (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This study examined changes in the beliefs and instruction of 21 primary grade teachers over a 4-year period in which the teachers participated in a CGI (Cognitively Guided Instruction) teacher development program that focused on helping the teachers understand the development of children's mathematical thinking by interacting with a specific research-based model. Over the 4 years, there were fundamental changes in the beliefs and instruction of 18 teachers such that the teachers' role evolved from demonstrating procedures to helping children build on their mathematical thinking by engaging them in a variety of problem-solving situations and encouraging them to talk about their mathematical thinking. Changes in the instruction of individual teachers were directly related to changes in their students' achievement. For every teacher, class achievement in concepts and problem solving was higher at the end of the study than at the beginning. In spite of the shift in emphasis from skills to concepts and problem solving, there was no overall change in computational performance. The findings suggest that developing an understanding of children's mathematical thinking can be a productive basis for helping teachers to make the fundamental changes called for in current reform recommendations.
Twenty primary teachers were interviewed who, three or four years earlier, had participated in in-service workshops on Cognitively Guided Instruction (CGI). Three patterns of CGI use seemed related to the meanings teachers constructed for CGI itself. Teachers who reported developing their use of CGI until it formed the mainstay of their mathematics teaching saw CGI conceptually. They also reported learning mainly through their interactions with students and other teachers and developing beliefs about the conceptual nature of mathematics, the constructivist nature of learning, and the students' central role in that learning. Teachers who reported never having used CGI more than supplementally saw CGI as a group of procedures and espoused more traditional beliefs in these areas. Teachers who reported using CGI more at first, but less currently, showed a marked incongruity between their espoused beliefs and reported practices. The authors ask whether additional reseacher support, collegial interaction, or perhaps prescriptiveness in the intervention might have helped teachers in this third group enact their conceptually based beliefs.
This study investigated 40 first-grade teachers' pedagogical content knowledge of children's solutions of addition and subtraction word problems. Most teachers could identify many of the critical distinctions between problems and the primary strategies that children used to solve different kinds of problems. But this knowledge generally was not organized into a coherent network that related distinctions between problems, children's solutions, and problem difficulty. The teachers' knowledge of whether their own students could solve different problems was significantly correlated with student achievement.
SummerMath for Teachers, an inservice program which combined coursework with ongoing support in the classroom, was designed to stimulate teachers' development of a constructivist view of learning to serve as a basis for mathematics instruction. While almost all teachers adopted new classroom techniques, project researchers were particularly concerned about the impact of the program on the epistemological perspectives that informed teachers' instructional decision making. This paper describes the development of an assessment tool used to evaluate program effectiveness along this latter dimension.
This study investigated teachers' use of knowledge from research on children's mathematical thinking and how their students' achievement is influenced as a result. Twenty first grade teachers, assigned randomly to an experimental treatment, participated in a month-long workshop in which they studied a research-based analysis of children's development of problem-solving skills in addition and subtraction. Other first grade teachers (n = 20) were assigned randomly to a control group. Although instructional practices were not prescribed, experimental teachers taught problem solving significantly more and number facts significantly less than did control teachers. Experimental teachers encouraged students to use a variety of problem-solving strategies, and they listened to processes their students used significantly more than did control teachers. Experimental teachers knew more about individual students' problem-solving processes, and they believed that instruction should build on students' existing knowledge more than did control teachers. Students in experimental classes exceeded students in control classes in number fact knowledge, problem solving, reported understanding, and reported confidence in their problem-solving abilities.
We analyzed cases of restructuring experiments in three elementary schools, each with ethnically diverse populations, located in large urban school districts in different parts of the United States. Over 2 years, we gathered data on views and classroom writing practices of two teachers in each school through on-site interviews and observations. We also interviewed the principal and other support personnel. We found that these three schools did successfully restructure; changes included new student grouping patterns, new ways of allocating time for subject matter, teachers meeting together as a whole school or in teams, and access to new ideas through professional development opportunities. Through close analyses of teachers' classroom practices, we learned that changing teachers' practice is primarily a problem of learning, not a problem of organization. While school structures can provide opportunities for learning new practices, the structures, by themselves, do not cause the learning to occur.
Historical perspectives and developments in the teaching and learning of elementary school science and the continuing calls for reform in science education provide the context for this article. Key influences on science teaching and on teacher education primarily since 1955 are examined and offered as a foundation for the development of a new paradigm for elementary science teacher education. Citing contemporary practices and scholarship, we build a case for theoretical constructs that can inform policy and programs in science teacher education. Three theoretical bases for the reform of science teacher education are elaborated: constructivism, reflection, and professional community. The complex tasks involved in learning and understanding science concepts and science-specific pedagogy suggest the need for teacher education and development that span preservice and in-service education throughout the professional lifetime.
The purpose of this case study was to examine teacher’s learning in the setting of the classroom. In an ongoing mathematics research project based on constructivist views of learning and set in a second-grade classroom, the teacher changed in her beliefs about learning and teaching. These alterations occurred as she resolved conflicts and dilemmas that arose between her previously established form of practice and the emphasis of the project on children’s construction of mathematical meaning. The changes that occurred as the teacher reorganized her practice were analyzed and interpreted by using selected daily video recordings of mathematics lessons along with field notes, open-ended interviews, and notes from project meetings. The analyses indicated that changes occurred in her beliefs about the nature of (a) mathematics from rules and procedures to meaningful activity, (b) learning from passivity to interacting and communicating, and (c) teaching from transmitting information to initiating and guiding students’ development of knowledge.
This paper posits that, as educators' attention turns to elementary mathematics as preparation for algebra, it is important to begin by examining the kind of elementary mathematics content teaching that is aligned with reform. The paper calls for a close examination of students' development of operation sense. The role of children's engagement with the four basic operations in their preparation for algebra is also discussed. One method of data collection used in this study is episode writing. Six of the scenarios presented in this paper are taken from episodes written by teachers in a National Science Foundation teacher-enhancement project known as Teaching To the Big Ideas. Although the question of how elementary education can prepare students for algebra is addressed here, teachers at other levels still need to be prepared to help their students begin to make meaning of the language of algebra. Implications of this work include the idea that other notional systems such as diagrams, graphs, and tables in written and electronic forms are important for students to understand. Contains 62 references. (DDR)
This collection of articles focuses on the practice and policy of staff development in terms of recent developments in teacher learning. Following an introduction by the editors, the book is divided into five parts. Part 1: New Perspectives on Practice contains three chapters: (1) "Reconceptualizing Teaching: Moving toward the Creation of Intellectual Communities of Students, Teachers, and Teacher Educators" (B. S. Nelson and J. K. Hammerman); (2) "Teaching the Way Children Learn" (B. Falk); and (3) "Constructivism and School Reform" (M. G. Brooks and J. Grennon Brooks). Part 2: A New Lens on Traditional Roles contains three chapters: (4) "Of Regularities and Reform: Navigating the Subject-Specific Territory of High Schools" (P. Grossman); (5) "Improving Classroom Practice: Ways Experienced Teachers Change after Supervising Student Teachers" (E. S. Tatel); and (6) "Assessment as a Heuristic for Professional Practice" (K. Jamentz). Part 3: New Structures for Learning and Change contains three chapters: (7) "Networks for Educational Change: Powerful and Problematic" (A. Lieberman and M. W. McLaughlin); (8) "Rethinking Restructuring: Building Habits of Effective Inquiry" (M. Szabo); and (9) "Communities for Teacher Research: Fringe or Forefront?" (M. Cochran-Smith and S. L. Lytle). Part 4: New Roles for Traditional Structures has five chapters: (10) "The Role of Teachers' Organizations: Reflections on Educational Policy Trust Agreements" (C. T. Kerchner); (11) "Text and Context for Professional Development of New Bilingual Teachers" (S. Dalton and E. Moir); (12)"Preparing Teachers for Multicultural, Inner-City Classrooms: Grinding New Lenses" (K. Tellez and M. D. Cohen); (13) "Problem-Based Learning: A Promising Approach to Professional Development" (E. Bridges and P. Hallinger); and (14) "School-University Partnership: Getting Broader, Getting Deeper" (L. Miller and C. O'Shea). Part 5: An Emergent Paradigm for Practice and Policy contains two chapters: (15) "Practices That Support Teacher Development: Transforming Conceptions of Professional Learning" (A. Lieberman); and (16) "Policies That Support Professional Development in an Era of Reform" (L. Darling-Hammond and M. W. McLaughlin). A list of participants at the July 1993 Pew Forum on Educational Reform is appended. (Contains extensive references.) (ND)
Investigated changes over four years for three elementary teachers participating in Cognitively Guided Instruction (CGI), which emphasized students' mathematical thinking and supported teachers through workshops, mentoring, and collaboration. Interviews and observations indicated that CGI allowed teachers to engage in ongoing practical inquiry directed at understanding their students' thinking, thus helping them to engage in self-sustaining, generative growth. (SM)
This paper discusses teaching science to language minority students and describes work with linguistic minority children and their teachers. A key goal of this work is to create scientific sense-making communities in the classroom that parallel science as it is practiced in the world. Following a critique of current practice in science education, the paper explores what conditions are necessary to create classroom communities of scientific sense-making. This is followed by a look at a new approach to teacher development based on the belief that the teacher, whether bilingual, English-As-A-Second-Language, or science specialist, is critical to creating communities of scientific sense-making. Also discussed is the role of discourse appropriation in teacher development, with an example of teachers and students reviewing a homework assignment on acids and bases. A case study of one teacher's experience of learning science in order to teach science illustrates the nature and complexity of the learning process that undergirds the creation of classroom communities. A conclusion brings the issues together and emphasizes that in their reflective practice, teachers can construct a view of science as a socially constituted, meaning-making activity that includes rather than excludes linguistic minority children. (Contains 62 references.) (JB)
describe the theoretical bases of an instructional program, Fostering Communities of Learners (FCL) / set in the inner city elementary schools, FCL is designed to promote the critical thinking and reflection skills underlying multiple forms of higher literacy: reading, writing, argumentation, technological sophistication / although billed as a thinking curriculum . . . the FCL program is embedded in deep disciplinary content / a major part of [the authors'] research agenda has been to contribute to a theory of learning that can capture and convey the essential features of the learning environments that [they] design / aspects of the design, implementation, and evaluation of the FCL program, from its inception to the present day, have been guided by the development of a situated learning theory, one grounded in the day-to-day milieu of regular schools / this theory, or more precisely, set of learning principles . . . has evolved over the course of the project
the components of FCL: the simple system / FCL: activity structures that support the system [research activities, children teaching children, sharing information, the consequential task] / principles of learning [systems and cycles, a metacognitive environment, the centrality of discourse, deep content knowledge, distributed expertise, instruction and assessment, community of practice] (PsycINFO Database Record (c) 2012 APA, all rights reserved)
address . . . how knowledge & beliefs change over time as novice teachers learn to teach and experienced teachers attempt to make changes in their teaching practices / selected studies to be representative of research approaches and of various aspects of our conceptual framework / that framework incorporates key assumptions underlying a cognitive psychological perspective on learning to teach, and a model of domains of teachers' knowledge and beliefs / review research on how pre-service and in-service teachers learn to teach / conclude with a set of recommendations for helping novice and experienced teachers expand and elaborate their professional knowledge base (PsycINFO Database Record (c) 2012 APA, all rights reserved)
A constructivist perspective provided the basis for a four stage intervention with teachers. The intervention which combined intensive summer courses with ongoing support in the classroom was designed to stimulate teachers' development of a constructivist view of learning to serve as a basis for their instructional decision-making. Impact of the intervention was studied through analysis of teachers' writings and the use of an interview-based instrument developed by the researchers. The results indicated that this intervention had an important effect on teachers' beliefs about learning which in turn affected the decisions that they made in the classroom.
This article focuses on the process of change experienced by a group of third grade teachers and the factors that facilitated and impeded that process, during their participation in the University of Colorado Assessment Project. The project's purpose was to help teachers design and implement classroom-based performance assessments compatible with their instructional goals in mathematics and literacy. We examined the change process in mathematics by analyzing conversations between teachers and researchers during workshops conducted throughout the school year and interviews conducted at the beginning, middle, and end of the year. Results are organized around five themes: (1) Situating the change process in the actual contexts where new ideas will be implemented is an effective strategy for helping teachers change their practice; (2) Group discussions can be an effective tool for the social construction of new ideas; (3) Staff development personnel can facilitate change by introducing new ideas based on teachers' current levels of interest, understanding, and skill; (4) When teachers' beliefs are incompatible with the intentions of the staff development team and are not challenged, the teachers are likely to either ignore new ideas or inappropriately assimilate them into existing practice; and (5) Time is a major obstacle to changing classroom practice.
Incl. biographical notes on the authors, bibliographical references, index We also have:The meaning of educational change,1st ed. (1982) and 2nd ed.(1991)
Rousing minds to life
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Reconstructing mathematics education: Stories of teachers meeting the challenge of reform
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teachers meeting the challenge of reform. New York: Teachers College Press.
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Using case discussions to promote changes in beliefs among mathematics teachers
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