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Teacher beliefs and the reform movement in mathematics education
... This suggests that teachers may be caught amid a paradigm shift, when they implement multicultural education in class. When considering that an official curriculum is enacted through a teacher's interpretation, teachers' belief is an essential part of teaching competency for curricular reform (Battista, 1994;Cross, 2009;Handal & Herrington, 2003;Voss, et al., 2013). Therefore, it is important to understand the nature of teachers' beliefs for the successful implementation of multicultural reform of school curricula. ...
... In particular, knowledge and skill without multicultural awareness are not enough to change teaching practice because teachers' belief system conditions their expectation and judgment in class (Riegle-Crumb & Humphries, 2012;Rubie-Davis, 2009). Mathematics teachers' beliefs can either facilitate or inhibit curricular reform depending on whether they are compatible with the educational values of the reform (Battista, 1994;Cross, 2009;Handal & Harrington, 2003;Thompson, 1992). This suggests that teachers' beliefs constitute an essential part of multicultural teaching competency (Gay, 2002;Voss, et al., 2013). ...
... In this perspective, there has been an increasing concern about teachers' beliefs because of their influence in the enactment of curricular reform (Battista, 1994;Cross, 2009;Handal & Harrington, 2003;Philipp, 2007;Skott, 2015;Thompson, 1992). Belief is not a clear and welldefined psychological construct due to the lack of cohesion (Leder, et al., 2002). ...
As schools have become ethnically, culturally, and linguistically diversified, multicultural mathematics education is emerging as the paradigm of school mathematics reform. When considering that an enacted curriculum is a set of beliefs put into action by a teacher, it is important to understand teachers’ beliefs for the successful implementation of multicultural mathematics education. From this perspective, this research analyzed mathematics teachers’ narratives to describe the multicultural transformation of their beliefs about mathematics as a school subject in the context of a multicultural mathematics teacher education course. The analysis shows that through the course participation, the teachers came to see mathematics as a cultural construct and challenged the Eurocentric perspective of mathematics. This change facilitated the teachers to seek ways to make school mathematics inclusive and equitable. The analysis also revealed the teachers’ contradicting beliefs, which led them to engage in dialogues for collective reflection to nurture their narratives of multicultural mathematics education. The results of this research imply that a multicultural teacher education program should be extended into a community to support teachers’ lifelong learning within a collaborative network of sharing and nurturing their narratives by integrating theory and practice about multicultural mathematics education.
... Taken together, pieces from Pajares (1992) and Battista (1994) provided a backdrop to the literature around PTs' beliefs in mathematics and aided in understanding why shifting PTs' beliefs towards reform is challenging. Much of the research on teacher beliefs referenced Pajares' (1992) in which he asserted that while one must examine the content and teacher thinking that impacts reform movements, what teachers believe and the ways they believe must also be examined. ...
... However, researchers do agree that all teachers hold beliefs about the role, thus understanding beliefs is important to future initiatives. Battista's (1994) work established a background for research on teacher beliefs within the context of mathematics. Historically, mathematics was seen as computation, so teaching mathematics meant providing students with a set of skills and learning mathematics meant remembering and progressing through set skills. ...
... Reform-based mathematics asks that students do mathematics through problem solving and sense making instead of through rote memorization. Battista (1994) felt that teachers holding traditional beliefs around mathematics T Prospective Teachers' Beliefs about Mathematics: An Overview teaching and learning were "robbing their students of opportunities to 'do' mathematics" (p.467). However, like Pajares (1992), Battista acknowledged that beliefs are difficult to shift. ...
The Mathematics Enthusiast Special Issue (2014) presented an extensive review of the literature around the content knowledge of prospective elementary teachers (PTs). The issue excluded articles around PTs’ beliefs. Understanding research around PTs’ beliefs is important to understanding how to design and support their teaching preparation. Attending to PTs’ beliefs helps to ensure their content knowledge and instructional methods are aligned with reform-based mathematics. This article highlights a literature review that addressed the omission of beliefs and explored how teacher preparation might address PTs’ held beliefs.
... Consequently, teachers' viewswhich include what teachers know, value, and care about, as well as how they interpret instructional resources, institutional regulations, and demandsare of interest only in terms of how these may influence the intended students' engagement with the resource. Frequently, teachers' views are regarded as "beliefs" and used as explanatory constructs for why the learning that the resource was expected to produce did not take place (Battista 1994;Francis et al. 2014;Handal and Herrington 2003). Explorations of how to bring about the teacher beliefs that would benefit the resource use become of considerable research interest (Lloyd 2002;Swan 2007). ...
... Such descriptions could be challenged by alternative interpretations of implementation events, or of the teachers involved. The implementation outcomes could be attributed to differences in teachers' and designers' beliefs about student mathematical learning (Battista 1994;Francis et al. 2014;Handal and Herrington 2003). We hasten to clarify that rather than aiming for a description of reality, we use the terms relevance and clarity to the teacher as tools for analysis and modification of the resource that is being designed. ...
In this handbook chapter, we suggest that in designing resources for mathematics education, it is important that the designers explicitly contemplate whether and how the resources contribute to teaching. We guide the readers in considering how instructional design practices and the resulting resources always convey a specific positioning of the teacher within the educational process and expectations of teaching as a profession at large. We draw on conceptualizations of teaching as a complex endeavor in proposing that designing for supporting mathematical learning directly is insufficient. We then discuss two design research examples in which designing for teaching was overtly taken as a goal, and where digital resources played a role. We use these examples to derive three types of design tasks that, we propose, characterize designing for teaching: designing for resource relevance and clarity to the teacher and for resource viability in the teacher’s classroom. We comment on contributions of digital resources to these tasks.
................................................................................................... Višňovská, J., Cortina, J. L., & Eckert, A. (2024). Resource design for re-sourcing teaching. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of digital resources in mathematics education (pp. 1029-1053). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-031-45667-1_39
... Consequently, teachers' viewswhich include what teachers know, value, and care about, as well as how they interpret instructional resources, institutional regulations, and demandsare of interest only in terms of how these may influence the intended students' engagement with the resource. Frequently, teachers' views are regarded as "beliefs" and used as explanatory constructs for why the learning that the resource was expected to produce did not take place (Battista 1994;Francis et al. 2014;Handal and Herrington 2003). Explorations of how to bring about the teacher beliefs that would benefit the resource use become of considerable research interest (Lloyd 2002;Swan 2007). ...
... Such descriptions could be challenged by alternative interpretations of implementation events, or of the teachers involved. The implementation outcomes could be attributed to differences in teachers' and designers' beliefs about student mathematical learning (Battista 1994;Francis et al. 2014;Handal and Herrington 2003). We hasten to clarify that rather than aiming for a description of reality, we use the terms relevance and clarity to the teacher as tools for analysis and modification of the resource that is being designed. ...
In this handbook chapter, we suggest that in designing resources for mathematics education, it is important that the designers explicitly contemplate whether and how the resources contribute to teaching. We guide the readers in considering how instructional design practices and the resulting resources always convey a specific positioning of the teacher within the educational process and expectations of teaching as a profession at large. We draw on conceptualizations of teaching as a complex endeavor in proposing that designing for supporting mathematical learning directly is insufficient. We then discuss two design research examples in which designing for teaching was overtly taken as a goal, and where digital resources played a role. We use these examples to derive three types of design tasks that, we propose, characterize designing for teaching: designing for resource relevance and clarity to the teacher and for resource viability in the teacher’s classroom. We comment on contributions of digital resources to these tasks.
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Višňovská, J., Cortina, J.L., Eckert, A. (2023). Resource Design for Re-Sourcing Teaching. In: Pepin, B., Gueudet, G., Choppin, J. (eds) Handbook of Digital Resources in Mathematics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-030-95060-6_39-1
... Numerous scholars believe that understanding the beliefs of teachers is essential to improving teachers' professional preparation and their practice (e.g., Beswick, 2005;Muis & Foy, 2010;Pajares, 1992). Changing teachers' beliefs and practice is a major challenge in implementing reforms (Battista, 1994;Prawat, 1992). Therefore, teacher education and professional development programmes need to focus on changing teachers' beliefs rather than only focusing on methodology (Cross, 2009). ...
... Today, there is a growing body of research that suggest that mathematical understanding is built as the outcome of an active process, and teaching and learning is considered as a social interaction (Ben-Hur, 2006;Prawat, 1992;Voigt, 1994). This approach to teaching and learning provides students with knowledge that is more meaningful and useful for reallife contexts (Battista, 1994;Clements & Ellerton, 1996;Yackel, 1995). ...
Recent reforms in mathematics education have been influenced by such theoretical perspectives as constructivism, which have reconceptualised teaching and learning. Mismatches between teachers' beliefs about teaching and learning, and ideas underpinning reform are often viewed as major obstacles to implementing educational reforms. This study examined the mathematical beliefs and practices, and factors affecting practices, of eight primary teachers selected from four schools in two different regions of the Maldives. The research used a multiple case study approach within a qualitative methodology. A questionnaire, semi-structured interviews, and observations were used to collect data about teachers' beliefs and practice. Teachers' lesson notes, worksheets, samples of student work, and test papers were used to understand teachers' practice. Data were analysed within and across cases using a thematic approach. Teachers demonstrated a range of beliefs that included both constructivist and traditional elements to different degrees. In general, teachers' observed practice was more traditional than their beliefs about teaching and learning mathematics. The teachers' practice showed some consistency with their beliefs about the nature of mathematics, mathematics teaching and learning; however, the degree of consistency between beliefs and practice differed from teacher to teacher. Overall, the findings indicated there are several factors affecting teachers' practice, including methods of assessment, teacher accountability for students' results, limited time to cover the curriculum, lack of resources, and parental pressure to use textbooks. National assessment practices, affecting many factors found to limit practice, emerged as being particularly influential on the teachers' instructional behaviour. The study suggests the need to change the nature of national assessment, and remove other barriers if teachers are to be best placed to implement their constructivist beliefs and the Maldives mathematics curriculum. The findings also have implications for professional development and teacher education programmes.
... As explained by different scholars (e.g. Battista, 1994;Hewson & Hewson, 1987;Loughran, 2010), student-teachers bring with them mature beliefs about teaching and learning that tend to be more congruent with their past experiences than with the views we are asking them to consider. In other words, a student-teacher who have gone through traditional teaching practice at lower education level tend to consider the teacher as source of knowledge and believe that his/her role is to convey information to his/her students. ...
... Strengthening this, previous studies (e.g. Applefield et al., 2001;Battista, 1994;Darling-Hammond, 2006;Holt-Reynolds, 1992;Russell, 2005;Struyven et al., 2010;Yerrick & Hoving, 2003) have reported that student-teachers educated by means of lectures fail to adopt the techniques that have been advocated rather it strengthened the student-teachers" existing traditional belief of teaching and learning and carry out their instructional practices in support of their beliefs. Yerrick and Hoving (2003) identified such student-teachers as "reproducers" who continued to hold traditional views of teaching and learning and prefer to teach as they had been taught. ...
The purpose of this study was to examine teacher-educators’ instructional beliefs and practice and its influence on student-teachers’ future teaching approach preference. To this end, a concurrent mixed research design was employed. More specifically pre-experimental one group pretest posttest design was employed in order to examine student-teachers’ entry behaviors and changes, if any, at the end of the program. Descriptive Survey method was also used to examine teacher-educators’ beliefs about teaching and learning and their classroom practice. Data were collected using different questionnaires (i.e. Approaches to Teaching Inventory (ATI), Conception of Teaching and Learning Questionnaire (CTLQ), and Revised Two-factor Study Process Questionnaire (R-SPQ-2F), interview, and classroom observation. Whereas two public universities were selected using convenient sampling, 350 student-teachers in Post-Graduate Diploma in Teaching (PGDT) program in the 2016/2017 academic year were selected using stratified and simple random sampling. Thirty-three teacher-educators offering courses in the PGDT program were also participated in the study. The data from the interview and classroom observation were analyzed using qualitative content analysis techniques. The data from the questionnaire were analyzed using means, Pearson correlation coefficient, independent and paired samples t-tests, and structural equation modeling. The quantitative data revealed that teacher-educators’ beliefs and practice found to be compatible with the reform initiatives. Though they demonstrated strong commitments to constructivism in the interview and self-reported questionnaire, their actual teaching practice reflected a strong reliance over teacher-centered approach. Regarding student-teachers, the results indicated that they have joined the PGDT program with behaviorist orientation. Significant relationships were also found between likewise conceptions and teaching approach preference. The posttest results also indicated that student-teachers’ entry characteristics remained unchanged. The predominantly teacher-centered approach observed in the PGDT classrooms has influenced the student-teachers to retain their entry characteristics. Based on these findings, it was concluded that teacher educators have absorbed, rather than being reformed, elements of constructivism and continue echoing the old adage “do as I say, not as I do” principle which has been proved to bring about “no change” on student-teachers’ teaching approach preferences. Based on the conclusion made, implications are discussed.
... Changing only the teaching program, however, is not sufficient to improve the quality of the activities on teaching and education (Çanakçı, 2008). For, besides the reforms that are made, it is required that the individuals who will be the operators of those reforms have positive beliefs, and show no resistance to innovation and change (Battista, 1994). It is important thus, that teachers, the operators of the reforms on teaching and education, refresh themselves and keep up with the changing conditions. ...
... It is important thus, that teachers, the operators of the reforms on teaching and education, refresh themselves and keep up with the changing conditions. The quality of the education given in the institutions that train the teachers who play a key role in the actualization of the reforms play a crucial role (Battista, 1994;Rogers and Steele, 2016). ...
In this study, it was tried to determine teaching activities that elementary preservice mathematics teachers exhibited in a micro teaching session. Preservice teachers are required to prepare and later present a sample micro teaching session. First of all, they were advised to freely select a topic (or an attainment) of their own intention within 5-8 middle school mathematics subjects. Then, every one of them planned their own special session. While they were planning the sessions, they were advised to take into account of all perspectives and practices of the theoretical subjects covered via the course of Special Teaching Methods 1 and the experiences that they gained during the other courses of the mathematics teacher education program. After that, each one performed tasks in the classroom environment related to their own planning. No intervention was made to the preservice mathematics teachers by the lecturer during the sessions. After each session, the remaining candidates and the lecturer made critique about the candidate’s performance. The study was conducted with 50 preservice teachers who take Special Teaching Methods II course. A systematic observation form has been prepared and used for data collection. Descriptive analysis and content analysis based on observations were used as mixed methods in the study. Findings show that preservice mathematics teachers have some misconceptions regarding the lectured subject, besides the deficiencies and mistakes in the course planning and performance.
... The reason for such inconsistency is that beliefs in student-teachers are mainly a construct resulting from their previous experiences in K-12 schooling and quite possibly in university. As explained by different scholars (e.g., Battista, 1994;Hewson & Hewson, 1987;Loughran, 2010), student-teachers bring with them mature beliefs about teaching and learning that tend to be more congruent with their past experiences than with the views we are asking them to consider. In other words, a student-teacher who have gone through traditional teaching practice at lower education level tend to consider the teacher as source of knowledge and believe that his/her role is to convey information to his/her students. ...
... Supporting this argument, Kaufman (1996) has underlined that student-teachers have to be exposed to constructivist learning environment in order to construct or reconstruct their conception about teaching and learning. Strengthening this, previous studies (e.g., Applefield et al., 2001;Battista, 1994;Darling-Hammond, 2006;Holt-Reynolds, 1992;Russell, 2005;Struyven et al., 2010;Yerrick & Hoving, 2003) have reported that student-teachers educated by means of lectures fail to adopt the techniques that have been advocated rather it strengthened the student-teachers' existing traditional belief of teaching and learning and carry out their instructional practices in support of their beliefs. Yerrick and Hoving (2003) identified such student-teachers as "reproducers" who continued to hold traditional views of teaching and learning and prefer to teach as they had been taught. ...
This study investigated the change in pre-service teachers’ conceptions of teaching and learning and teaching approach preference over the course of a teacher education program. One group pretest-posttest design was employed. Conceptions of Teaching and Learning Questionnaire (CTLQ) and Approaches to Teaching Inventory (ATI) were used for data collection. Two hundred ninety three (293) randomly selected pre-service secondary student-teachers admitted to Post Graduate Diploma in Teaching (PGDT) program in two Universities were participated in the study. Participants didn’t exhibit significant changes in their teaching approach preference and beliefs about teaching and learning – participants favored teacher-dominated teaching approach and more traditional in beliefs about teaching and learning. At the end of the nine-month-long teacher preparation program, the student-teachers seemed to view learning as recalling and absorbing as much information as possible and teaching as simply telling, presenting or explaining the subject matter. Their teaching approach preference was also found to be consistent with their conceptions of teaching and learning.
... Over time, the definition of effective elementary math and science teaching has evolved (e.g., Battista, 1994;Dana et al., 1997). In response, teacher education has adjusted practices for preparing and supporting future teachers' learning. ...
Preservice teachers (PSTs) enter teacher education programs with years of experience as students in the classroom (Lortie, Schoolteacher: A sociological study, University of Chicago, Chicago, 1975). Teacher educators aim to understand PSTs’ unique experiences and support their learning of pedagogy within and across various contexts, including content methods coursework and clinical experiences. Research indicates that coherence between these contexts is crucial (Cochran-Smith & Zeichner, Studying teacher education: The report of the AERA panel on research and teacher education, Routledge, 2009). Our study examined how PSTs conceptualized pedagogical approaches using animation and whether the approach enacted changed across content methods coursework and clinical experiences. The results reveal a discrepancy in teaching approaches, highlighting the influence of clinical experience on PST learning and underscoring the pivotal role of teaching beliefs in shaping views on teaching mathematics and science.
... Wallace and Priestly (2011) found that teachers' beliefs can positively contribute to the implementation of an educational innovation and conclude that congruency between teachers' beliefs and the philosophy behind any curriculum reform is a key to its enactment in classrooms. Many studies have also found that a mismatch between teachers' beliefs about teaching and learning mathematics and the goals of the curriculum reform can be problematic, negatively affecting the success of the reform (Battista, 1994;Handal & Herrington, 2003;Maaß, 2011). It is therefore important that discrepancies between teachers' opinions and the ideas underpinning a curriculum reform are identified and addressed if the reform is to be effective (Handal & Herrington, 2003). ...
Over the past two decades there has been significant reform to the post-primary mathematics curriculum in Ireland. The introduction of Project Maths in 2010 placed an increased emphasis on problem-solving within the curriculum and encouraged teachers to adopt problem-solving approaches to the teaching and learning of mathematics. A further reform at Junior Cycle again stressed the importance of problem-solving within mathematics and introduced classroom-based assessments, one of which is explicitly focused on problem-solving. Despite these extensive reforms, there is little evidence that much has changed in post-primary classrooms and teachers have expressed concerns regarding the reform and the new pedagogical approaches promoted within them (Berry et al., 2021; Byrne & Prendergast, 2020; Jeffes et al., 2013). This suggests that learners may not be experiencing the types of learning environments that build their capacities as problem-solvers.
This research aims to support young learners to become proficient and confident problem solvers by working with their teachers to develop and strengthen their problem-solving pedagogy. If teachers are struggling to enact the changes to their practices as envisaged by the reform, it is important to understand why so that appropriate support can be offered. The first phase of this research therefore investigated teachers’ perceptions of problem-solving and concerns related to incorporating it in the classroom. Data from semi-structured interviews with teachers show that teachers need clear guidance on how to enact problem-solving approaches in their classroom along with opportunities to understand how their role as a teacher is impacted, and to critically reflect on their current practices and beliefs around the teaching and learning of mathematics. In addition, teachers expressed a desire for more collaboration with colleagues and for suitable resources to use with problem-solving in their classrooms. These findings informed the second phase of the research. A professional development intervention was developed which comprised specifically designed educative curriculum materials alongside lesson study. A case-study was conducted to explore the impact of this professional development intervention on teachers’ knowledge, beliefs, and practices related to problem-solving. Findings from the case-study revealed that engagement with the educative curriculum materials and lesson study impacted on teachers mathematical problem-solving knowledge for teaching, in particular their knowledge of Structured Problem Solving practices. Moreover, it supported the teachers in their journeys of teacher change, through surfacing tensions in their practice, encouraging reflection on tensions, and assisting them in seeking resolutions to these tensions.
... Our study was grounded in research from Pajares [17] on teachers' beliefs about education and teaching, and from Battista [2] on beliefs specifically related to mathematics education. Pajares [17] acknowledged a challenge to researching beliefs is the varied definitions of what beliefs are and what they entail. ...
... Moreover, teachers' beliefs, attitudes, content knowledge, and pedagogical expertise significantly influence both learning and teaching. In particular, their beliefs play a pivotal role in shaping not only what they teach but also how they teach (Battista, 1994). Pajares (1992) emphasizes the importance of focusing on the beliefs of teachers and prospective teachers, advocating that this issue should be central to educational research. ...
... For many years, mathematics educators have sought to conceptualize what might be the fundamental elements of a mathematics teaching practice that are more likely to generate success than traditional teaching practices. This search has led to different conceptualizations by various authors, such as reform teaching (Battista, 1994;Simon & Tzur, 1997), ambitious teaching (Lampert et al., 2013), inquiry-based mathematics teaching (Artigue & Blomhøj, 2013) and structured problem solving (Fujii, 2016). In Portugal, an approach along these lines has been theorized for 20 years as exploratory approach (Ponte, 2005). ...
Este artigo aborda um intercâmbio entre futuros professores de duas universidades brasileiras e uma portuguesa envolvidos em Estudos de Aula na formação inicial de professores de Matemática. O seu objetivo é conhecer como os futuros professores desenvolvem a sua compreensão de uma aula seguindo a abordagem exploratória, focando-se na natureza das tarefas, na estrutura da aula e na discussão coletiva, no contexto das discussões promovidas no intercâmbio. O estudo é de natureza qualitativa e interpretativa, desenvolvido em três aulas virtuais gravadas e degravadas. Os dados foram recolhidos, também, de formulários respondidos pelos futuros professores. Para fins de análise, optamos por assumir os pontos de maior discussão entre os futuros professores, entendendo-os como conflituosos ou de difícil compreensão sobre a abordagem exploratória. Como resultados, obteve-se que o intercâmbio contribuiu para melhor compreensão do ensino exploratório pelos futuros professores a partir das discussões realizadas.
... (Clark, 2012, p. 81) Many studies (i.e. Battista, 1994;Prawat, 1992;Thompson, 1992) have shown that the attitudes and beliefs teachers hold towards mathematics have a strong influence on their performance and preparation in the classroom. Philippou and Christou (1998) set out to show that adding content based on the history of mathematics to both content and methods courses in a mathematics education program could change pre-service teachers' attitudes towards mathematics. ...
Many scholars have written about using the history of mathematics in the teaching of preservice mathematics teachers. For this study, preservice mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the Mathematics History Journal was to help measure the mathematics content knowledge and pedagogical content knowledge of the preservice mathematics teachers for accreditation purposes. Results of the study indicated that by allowing preservice teachers to investigate and present topics in the history of mathematics, preservice teachers believed they strengthened their mathematics content knowledge and were introduced to a new avenue for teaching secondary students about mathematics.Keywords: History, Preservice Teachers, Secondary Mathematics, Teacher Knowledge
... They found that beliefs about mathematics learning have statistically significant effect on mathematics anxiety. Thus, it is important to know pre-service teachers' beliefs about mathematics (Battista, 1994). Finally Zelzy Sahar and Muhamad Suhaimi present their study on the acquisition of Jawi and its curriculum in primary school in Brunei Darussalam. ...
This introductory Volume I presents six chapters of articles related to research in education, in particular North Borneo from the three countries: Malaysia, Indonesia and Brunei Darussalam. It is essential that the focus of research in education is to improve practice in the teaching and learning (Mohd. Zaki, 2009) in any curriculum. The practice is not only, about content knowledge, but also, issues related to pedagogy, psychology, sociology, and assessment. Other than practice, Millar (2003) emphasizes the importance of insights that a teacher can see the familiar in a new way, by sharpening thinking, by directing attention to important issues, by clarifying problems, challenging established views, encouraging debate and stimulating curiosity. The focus, practice and insights, are reflected in these six articles.
... Therefore, this study aimed to investigate the degree of conformity between teacher and student beliefs concerning mathematics related to Higher Order Thinking (1992), and Thompson (1992). Meanwhile, the teacher beliefs survey were items adapted from Battista (1994), Hart (2002), Perry et al. (1999), Peterson et al. ...
Teacher beliefs play a fundamental role in mathematics teaching and learning, as they will ultimately influence the teacher's classroom practices. Student beliefs on a subject matter also hold equal importance as they will be reflected in how the students approach the learning and related issues to the subject. The importance of research on teachers' beliefs stems from the possible relationship between teacher beliefs and student beliefs. This descriptive quantitative study aimed to measure the degree of conformity between teacher and student beliefs concerning mathematics related to Higher Order Thinking (HOT) and Lower Order Thinking (LOT). The population was all Year 9 students in Aceh, Indonesia, and the samples were 1135 Year 9 students and 46 Year 9 mathematics teachers from 25 schools selected through stratified random sampling. Data collection was obtained through teacher and student questionnaires, and data were analyzed descriptively by SPSS 20. The finding of this study revealed that teacher beliefs concerning mathematics related to HOT were highly positive (83%). While the percentage of students who hold highly positive beliefs concerning mathematics related to HOT was just over 50%, indicating the discrepancy between teacher and student beliefs. However, regarding the beliefs concerning mathematics related to LOT, teacher and student beliefs conformed; they had somewhat positive beliefs (68% and 71.30%, respectively). This study implies that teachers need to promote HOTS in mathematics teaching at schools to foster students’ positive beliefs toward HOT.
... Beliefs have taken a central role in education research due to their theorized importance in guiding decisionmaking (e.g., Bandora, 1986;Bryan, 2012;Dewey, 1933). Researchers have been concerned that teachers hold beliefs that may be incompatible with recommendations for reform (Battista, 1994). Beliefs might be resistant to intervention because researchers have found evidence that beliefs are formed over time through experiences (Raymond, 1997;Nespor, 1987). ...
Background
The growing understanding of the oppressive inequities that exist in postsecondary education has led to an increasing need for culturally relevant pedagogy. Researchers have found evidence that beliefs about the nature of knowledge predict pedagogical practices. Culturally relevant pedagogy supports students in ways that leverage students’ own cultures through three tenets: academic success, cultural competence, and sociopolitical consciousness. If STEM practitioners believe that their disciplines are culture-free, they may not enact culturally relevant pedagogy in their courses. We investigated how and in what forms 40 faculty from mathematics, physics, chemistry, and biology departments at Hispanic-Serving Institutions enacted culturally relevant pedagogy. We used the framework of practical rationality to understand how epistemological beliefs about the nature of their discipline combined with their institutional context impacted instructors’ decision to enact practices aligning with the three tenets of culturally relevant pedagogy.
Results
In total, 35 instructors reported using practices that aligned with the academic success tenet, nine instructors with the cultural competence tenet, and one instructor with the sociopolitical consciousness tenet. Instructors expressed and even lauded their disciplines’ separation from culture while simultaneously expressing instructional decisions that aligned with culturally relevant pedagogy. Though never asked directly, six instructors made statements reflecting a “culture-free” belief about knowledge in their discipline such as “To me, mathematics has no color.” Five of those instructors also described altering their teaching in ways that aligned with the academic success tenet. The framework of practical rationality helped explain how the instructors’ individual obligation (to the needs of individual students) and interpersonal obligation (to the social environment of the classroom) played a role in those decisions.
Conclusions
Instructors’ ability to express two contradictory views may indicate that professional development does not have to change an instructor’s epistemological beliefs about their discipline to convince them of the value of enacting culturally relevant pedagogy. We propose departmental changes that could enable instructors to decide to cultivate students’ cultural competence and sociopolitical consciousness. Our findings highlight the need for future research investigating the impacts of culturally relevant pedagogical content knowledge on students’ experiences.
... Limitations of the TSE measurement involve the method of measuring self-efficacy (Shawer, 2013), the lack of focus on culturally responsive self-efficacy items (Siwatu et al., 2016), and the nature and definition of TSE itself (Wyatt, 2014). Consequently, strengthening TSE has become an important component of both teacher education and educational reform in the past decades (Battista, 1994;Goddard, 2002;Goddard et al., 2000). The international comparative studies showed that teachers' self-efficacy in the Western countries is frequently higher than teachers in East or Southeast Asian countries such as Hong Kong (Ho & Hau, 2004), Singapore (Klassen et al., 2009), and the Republic of Korea (Vieluf et al., 2013). ...
Using the Teaching and Learning International Survey (TALIS) 2018, this study examines U.S. and Japanese new teachers’ initial teacher preparation (ITP), feelings of preparedness, motivations, and self-efficacy. The analysis of 355 U.S. and 433 Japanese new secondary teachers provided several findings. First, ITP in the U.S. more often included teaching in mixed-ability and multicultural settings, cross-curricular skills, and technology than Japan, and U.S. teachers felt more prepared than Japanese teachers in every category of preparation. Second, Japanese teachers were more likely to declare teaching as their first career choice and reportedly scored significantly higher on motivations to become a teacher of personal utility value, while U.S. new teachers scored higher on social utility value. Third, there were no significant differences in self-efficacy between U.S. and Japanese new teachers. This study contributes to the gap of large-scale, comparative literature between the U.S. and Japanese initial teacher preparation. Implications for practice and directions for future research are discussed.
... For example, if a teacher believes that mathematics involves memorization and regurgitation of facts and procedures they would not be inclined to spend time on problems that do not require the application of a known procedure. Aligned to this, Sakshaug and Wohlhuter (2010) reported that teachers tend to teach in like manner as they were taught (Battista, 1994;Oleson & Hora, 2014), and the way that they were taught often differs considerably from teaching through problem solving. ...
This research (the second part of a 2-part study) sought to investigate selected high school teachers' knowledge and use of a problem solving approach to mathematics teaching and learning. It also examined the challenges that they experienced in implementing this pedagogical approach. A survey research design was used for this research whereby data were collected using a questionnaire with closed-and open-ended items. Thirty-one high school teachers from Jamaica participated in the study. The findings indicated that the teachers generally used a problem solving approach during instruction very regularly and felt extremely competent when using the approach. Some of the most frequently reported challenges included students' lack of interest and tenacity in solving problems; teachers' heavy workload; and the time consuming nature of the approach. One key recommendation to address the challenges raised is implementation of professional development for teachers to guide them in effectively incorporating problem solving as a teaching/ learning approach in the mathematics classroom.
... Research findings suggest that teachers' beliefs significantly influence their practice and are difficult to change (Buehl & Beck, 2015;Kagan, 1992;Lumpe et al., 2000) and that they are not always consistent with literature about best practices in teaching (Battista, 1994;Fetters et al., 2002;Haney et al., 1996). The extant literature examining the relationship between teachers' beliefs and their practice looks mainly at teachers' beliefs and math instruction (e.g., Stipek et al., 2001), science instruction (e.g., Milner et al., 2012), and technology integration (e.g., Kim et al., 2013). ...
The children and youth of today will need social-emotional competence to help them navigate the challenges of an uncertain future. School-based social and emotional learning (SEL) programs have been shown to be effective in helping youth develop these vital, malleable skills, and that the positive outcomes endure. However, achieving these positive outcomes requires quality implementation by classroom teachers. There are many factors that contribute to teachers’ motivation, readiness, and ability to deliver an SEL program as intended. Using data collected in four experimental evaluations of SEL programs, two studies were conducted to explore the relationship between program implementation quality and teacher factors such as teaching efficacy, stress, job satisfaction, and beliefs about SEL. Study 1 explored relations of teachers’ (N = 32) pre-implementation factors including SEL experience, job satisfaction, and SEL beliefs, to program implementation quality.
... Science education reforms across the globe strive to achieve high-quality elementary science teaching (Australian Curriculum, 2015;National Curriculum in England, 2015;Newfoundland & Labrador, Department of Education, 2016;NGSS Lead States, 2013). And, teachers play a critical role (Battista, 1994) as "the decisive component" in implementing any science education reform (Bybee, 2014, p. 144). Despite the calls and systemic reform initiatives to improve science teaching in elementary classrooms (AAAS, 1993;NRC, 2012;No Child Left Behind, 2000; van Driel, Beijaard & Verloop, 2001), anecdotal evidence from the recent surveys in the United States and Canada suggest that fewer elementary teachers felt prepared to teach science Rowell & Ebbers, 2004;Trygstad, Smith, Banilower, & Nelson, 2013), and sometimes tend to avoid teaching science altogether (Appleton & Kindt, 2002). ...
teachers’ science teaching beliefs and explain how these beliefs influence the way these teachers interpret their science teaching and learning experiences. Supported by the theoretical underpinnings of teacher beliefs and drawings as a tool to investigate teacher beliefs, this research utilized qualitative (written science autobiographies and reflections) and quantitative (Draw-a-Science-Teacher-Test-Checklist as a pre and post measure) data collection techniques. A total of 55 preservice elementary teachers participated from two public universities located in the United States and Canada. Quantitative analysis revealed positive shifts in science teaching beliefs of preservice elementary teachers largely in two ways: A small shift representing small positive difference or a large shift representing large positive difference between the pre- to post-course DASTT-C scores. Qualitative data analysis for the two sub-groups of participants (small shift and large shift) provided evidence that preservice teachers’ beliefs were linked to their personal histories and were influenced by their prior science experiences. Preservice teachers’ beliefs and their self-images changed as they participated in the field teaching experiences in elementary classrooms and engaged with elementary learners, during the science methods course. Implications for preservice teacher education programs, science teacher education, and research are included.
... Depending on the ever-changing and renewed social life, new developments are taking place in education and training environments according to the needs of the society. The key variable of achieving success in these reform movements certainly is the teachers (Battista, 1994). The teachers strive to create environments to maximize learning of the student, day to day attending classes (Nussbaum, 1992). ...
The aim of this study is to determine the teaching activities of pre-service teachers in the course of mathematics teaching methods. All of the pre-service teachers have selected an attainment content from the primary (1-4) mathematics education curriculum at the beginning of the semester in the scope of mathematics teaching methods course. Data collection tools include prepared lesson plans and presentation notes by the students, as well as field notes of the researchers in addition to an observation form. According to the results obtained with descriptive statistics and content analysis, while the pre-service teachers were successfully performed in timing and taking into account of curriculum requirements, they were not adequately performed in problem posing and problem solving and also using alternative and appropriate evaluation methods.
... Specifically, males perform higher than females in problem solving (Battista, 1990;Lindberg et al., 2010), spatial visualization (Battista, 1994), and mathematical application problems (Vermeer, Boekaerts, & Seegers, 2000). Females perform better in basic mathematics computation and conceptual understanding. ...
The purpose of this study was to investigate the interactive effects of gender, learning motivations, and pedagogy (Project-Based Learning [PBL] and conventional) on secondary mathematics learning. In order to measure their academic achievement and learning motivations, 165 secondary students were given a state standardized mathematics test and the Motivated Strategies for Learning Questionnaire. Study results indicated that pedagogy and gender had no impact on academic achievement. Pedagogy played a stronger role in rehearsal, peer learning, and task value. Gender played a stronger role in test anxiety, organization, help seeking, and control of learning. PBL students seemed to value and actively engage in the mathematics more than did the conventional students.
... In any major educational reform effort, teachers are critical to ensuring success 19 . However, teachers may operate with beliefs about learning and instruction that are incompatible with central principles of the reform effort 20,21 . The pool of engineers in the United States is neither large enough nor diverse enough to meet the needs of a growing, high-tech economy 22 . ...
... It also requires teaching students the strategies needed for the successful completion of such tasks. Teachers who believe that their role in the classroom is the provision of subject content may find it difficult to agree with the proposition of SRL that learning depends on what students do to learn and that teachers can best help their students by influencing their knowledge about learning and the strategies they use to learn (Battista 1994;Calderhead 1996;Lane 2015;Perry et al. 2015;Torff and Sternberg 2001). ...
It is proposed that the transition from secondary to higher education can be facilitated by improving secondary school students’ capabilities for independent, self-directed, and self-regulated learning (SRL). University learning places high demands on students for complex and independent learning, namely learning that requires the ability to plan, monitor and evaluate one’s work and to control one’s motivation and emotion. A major stream of educational research has shown the beneficial impact of self-regulated learning on student motivation and has concluded that self-regulation is a significant source of achievement differences among students. However, many secondary school students lack the skills of an independent and self-regulated learner when they enter higher education, something that contributes to considerable student attrition during the first year of university study. In this article I argue that more attention should be paid to the promotion of self-regulated learning in secondary schools. This can be achieved by helping teachers understand how to enrich students’ knowledge about learning and strategies to manage it. Some exemplary practices developed at secondary schools are discussed as a means of providing examples of effective learning environments for SRL.
... The academic performance demonstrated by the students in the first semester can be attributed to the strong connection between the mathematics curriculum content covered in the first semester and school mathematics curriculum content. Battista (1994) argues that students are not achieving their fullest potential in mathematics for various reasons, but it is clear that improvement in the quality of mathematics teaching needs to occur in order to combat low student achievement. Other researchers such as Karp et al. (2011) are of the view that some students are not given ample opportunities to learn important mathematics while other students are not challenged by the curriculum, and yet other students do not actively engage in the mathematics. ...
... Educational curriculum based on the constructivist approach was introduced in Turkey after 2005 (Çiftçi, Sünbül, and Köksal, 2013;Bukova-Güzel & Alkan, 2005). Battista (1994) stated that teachers played a key role in the success of curriculum changes. However, he noted that the beliefs most teachers have about mathematics are incompatible with the ideas underlying the reform attempts. ...
In this study, we aimed at introducing to prospective primary school teachers how to present a
pattern of numbers through designing a mobile game according to the Theory of Didactical Situations
(TDS). Additionally, the games developed by teacher candidates were examined. In our study, the case
study method was used, which is one of the qualitative research methods. The participants were 17
prospective primary school teachers (9-females, 8-males). The data were collected through video
cameras, audio recorders, and files that include game designs of prospective teachers. In data analysis, the
actions concerning mobile gaming experiences of prospective teachers were conducted according to the
TDS stages. The games designed by prospective teachers were examined in terms of basic gamification
criteria. Findings of the study; it was demonstrated that mobile games designed according to TDS support
the prospective teachers in many aspects, such as developing a milieu for using gamification in teaching
math, internalizing processes of reflecting gamification criteria to the game, and positively influencing the
affective characteristics. Moreover, concerning gamification criteria, it was determined that some
prospective teachers are successful at gamification of mathematical knowledge; however, most of them
have difficulties in game designing, particularly in giving feedbacks about games.
... It can be said that teachers has the greatest mission on this matter. They play a crucial role in implementing ongoing innovations (Battista, 1994). This gives significance to education and training processes of the teachers that they pass to succeed in their professional life. ...
... Some of these studies before 1990 (e.g., Grant, 1984;Nespor, 1987;Peterson, Fennema, Carpenter, & Loef, 1989;Rokeach, 1968;Stonewater & Oprea, 1988;Thompson, 1984) emphasize the description and existence of different beliefs without a focus on change of beliefs. Other studies from 1990 to 2000 (e.g., Battista, 1994;Brosnan, Edward, & Erickson, 1996;Brown & Baird, 1993;Jones, 1991;Kagan, 1992;Perry, Howard, & Tracey, 1999;Quinn, 1998a;Quinn, 1998b;Richardson, 1996;Schmidt & Kennedy, 1990;Tillema, 1995;Witherspoon & Shelton, 1991) seem to focus on the measurement of teacher beliefs using belief scales. These studies did not elaborate on the reasons for different beliefs. ...
This paper aimed to discuss the meanings, dimensions, and categories of teacher beliefs about teaching and learning mathematics. I reviewed the relevant literature about teacher beliefs in general, beliefs about mathematics, and beliefs about mathematics teaching and learning in particular. Based on the review of the literature, I outlined the meanings of teacher beliefs and conceptualized three dimensions of teacher beliefs-affective dimension, cognitive dimension, and pedagogical dimension. Then, I discussed three viewpoints to observe teacher beliefs-relational, institutional, and praxis lenses. I utilized these lenses to categorize belief constructs into three classes of beliefs about mathematics, teaching mathematics, and learning mathematics. These classes' included-instrumentalist, constructivist, and integral beliefs. I addressed the pedagogical implications of these categorical beliefs in the end.
... And also they have vital importance in gaining the targeted skills (Borko & Putnam, 1996). This situation causes many results, which could affect teacher education and causes major changes in prospective teachers' knowledge (Battista, 1994;Putnam & Borko, 2000;Szydlik, Szydlik, & Benson, 2003). However, teachers' efforts to change their PK and practices are usually not reflected on their tendencies at skill-based applications in the targeted curriculum (Anderson, White, & Wong, 2012). ...
Realistic Mathematics Education (RME) is based on the idea that mathematics is a human activity; and its main principle is to ensure the transition from informal knowledge to formal knowledge through contextual problems. This study aims at revealing how RME is configured in the minds of prospective mathematics teachers and their cognitive competency in that sense. For that purpose, at the end of the process, in which the approaches used in mathematical education including RME are examined and interpreted, 32 prospective teachers were asked various open-ended questions. Moreover, they were expected to pose contextual problems that could be used in RME. After analysing the obtained data via qualitative research techniques, it is seen that the majority of the prospective teachers possesses theoretical knowledge on RME. However, it is also observed that their ability to present its differences and similarities with other approaches and to pose contextual problems suitable to RME has been decreased.
... Preservice teachers who believe that subject matter knowledge consists of certain facts and that the main task of teachers is the transmission of these facts to students, will find it difficult to simultaneously agree that the most important task for teachers is to influence what students do to learn (Ambrose et al. (2010)). SRL theory places less emphasis on role of the teacher as a simple dispenser of subject matter information and more on the teacher teaching students learning strategies that will help them to construct knowledge effectively (Battista, 1994;Calderhead, 1996;Lane, 2015;Perry, Brenner, & MacPherson, 2015;Torff & Sternberg, 2001). Another set of beliefs that might be inconsistent with SRL theory is that learning is quick, that it is an innate or fixed ability, and therefore that it cannot be taught. ...
Pre-service teachers’ belief systems regarding the self-regulation of learning were investigated from a conceptual change perspective. Four hundred and twenty nine pre-service teachers answered a 6-point Likert scale Beliefs about Learning and Teaching (BALT) questionnaire. The results confirmed that beliefs theoretically consistent with SRL were be positive predictors of beliefs in the importance of teaching students SRL strategies. Beliefs inconsistent with SRL were found to be negative predictors of beliefs in the importance of teaching students SRL strategies. The SEM modeling also revealed that the participants’ belief systems contained internally inconsistent beliefs about teaching. The implications for the design of SRL interventions and future research are discussed.
... Teachers with traditional beliefs describe mathematics as a collection of fixed and reliable concepts and skills (Romberg, 1992). Teachers who view mathematics as following set procedures invented by others that should be simply accepted and learned will have difficulty making sense out of mathematics (Battista, 1994). On the other hand, teachers with constructivist beliefs encourage students to construct their mathematical knowledge and help their students like mathematics by allowing them to be creative through hands-on experiences and other strategies. ...
This study investigated Jordanian pre-service teachers’ beliefs about the learning and
teaching of mathematics. One aim of the study was to identify possible explanations for why Jordanian students score much lower than many of their global counterparts on international mathematics tests. On the 2007 Trends in International Mathematics and Science Study (TIMSS), Jordanian eighth-graders’ average score was 427, far below the TIMSS scale average of 500. Jordan ranked 31st out of the 48 participating countries. On the 2011 TIMSS, Jordanian eighth-graders’ average dropped to 406, and Jordan’s overall ranking was 49th out of 56 participating countries and education systems.
In addition to investigating Jordanian pre-service teachers’ beliefs, the findings were
compared to the findings from a similar study in South Korea (Kim, 2009), the top
performing country in mathematics in 2011 and second overall in 2007 on the TIMSS
assessments. The participants in this study were 441 pre-service teachers enrolled in 5 universities in Jordan, four public and one private. Participants’ data were collected using a questionnaire survey, the same instrument that was used in the Korean study of 2009.
Nearly 95% of the Jordanian participants believed in the existence of a mathematical
mind indicating that they view mathematics ability as fixed or stable. Other strong beliefs
were about the importance of memorization, gender, and mathematics ability. Specifically, 65% of the participants believed that the best way to learn mathematics was to memorize all the formulas, and nearly 70% believed that math ability was not associated with a specific gender.The comparison between Jordanian and Korean pre-service teachers produced significant results about the necessity for memorization and the belief in multiple methods for doing mathematics. Jordanian pre-service teachers believed strongly in the need to memorize in mathematics and in the existence of a single correct way to do mathematics. These are beliefs are not held by Korean pre-service teachers.
... Within mathematics education research, the resistance of teaching to reformers' ideas has been conceptualized as a matter of teacher beliefs (e.g., Battista, 1994;Bray, 2011;Cross, 2009;Fang, 1996;Leder, Pehkonen, & Törner, 2003;Philipp, 2007;Thompson, 1992). In this line of reasoning, teachers are often portrayed as not understanding or appreciating reasons for moving away from procedures to problem solving. ...
Many research studies have sought to explain why NCTM's vision for mathematics classrooms has not had greater impact on everyday instruction, with teacher beliefs often identified as an explanatory variable. Using instructional exchanges as a theoretical construct, this study explores the influence of teachers' institutional positions on the solving of equations in algebra classrooms. The experimental design uses surveys with embedded rich-media representations of classroom interaction to surface how teachers appraise correct solutions to linear equations where some solutions follow suggested textbook procedures for solving linear equations and others do not. This paper illustrates the feasibility of studying teaching with rich-media surveys and suggests new ways to support changes in everyday mathematics teaching. © National Council of Teachers of Mathematics. All rights reserved.
... In primary school every teacher teaches Mathematics, but not all of them are prepared for this task [3]. Some of teacher related barriers of modern approach for teaching Mathematics are teachers' negative attitude towards Mathematics based on their previous experiences, teachers' lack of mathematical or methodological knowledge. ...
Teachers' beliefs about teaching Mathematics influence their teaching practice. The aim of the paper
is to present a research on pre-service primary school teachers' opinions about teaching Mathematics.
The research sample was a group of second years Primary and Preschool Pedagogy specialization
students from Babes-Bolyai University. The research tool was an online questionnaire with multiplechoice
and open questions. The data was quantitatively and qualitatively processed. The results show
that students consider developing pupils' number sense, calculation skills, and problem solving
competencies, and evolving a positive attitude towards Mathematics the main goals of teaching
Mathematics in primary school. They don't consider learning mathematical notions, experimenting
Geometry, and learning special word problem solving methods/algorithms important at this age.
Students think that developing positive attitude towards Mathematics can be done by using games
and hands-on activities; by giving tasks according each pupils' competencies, and encouraging them.
They also consider teacher's positive attitude important. Only half of the students think that hand-on
activities help learning Mathematics. In their opinion these activities contribute to a deeper
understanding and a better illustration; but they are time consuming, they need financial effort, and in
some cases pupils become addicted to them and they can't make abstraction from the concrete
objects.
Mathematics teaching and learning are crucial to the future of Kenya’s knowledge economy and deserve a special focus in our education system. The objective of the study was to determine the effectiveness of using Grapes and GeoGebra on students’ learning of graphs as compared to the traditional approach. This study was guided by Technology Acceptance Model (Davis, 1989). Technology Acceptance Model (TAM) explains computer-usage behavior that relates to reasons why some people use computers and their attitudes towards them. This study adopted Solomon four group experimental research design. The respondents were selected using both stratified and simple random sampling. Data was collected through the use of students’ questionnaires, pre-test and post-test. Analysis of data was done using both descriptive and inferential statistics. For descriptive statistics, frequency tables, means and percentages were used. Anova, t-test and Multiple Regression Analysis were employed for the inferential statistics. The study found out that the students who were taught using Grapes and GeoGebra performed much better than those who were taught using the conventional method. It is recommended that ICT integration in the teaching of Mathematics should be included in the curriculum of pre-service teachers at the university level.
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Bu araştırmanın amacı yeni nesil matematik sorularına ilişkin ortaokul matematik öğretmenlerinin yaklaşımlarının incelenmesidir. Bu amaç doğrultusunda araştırmacı ve bir alan uzmanı tarafından altı adet açık uçlu sorunun yer aldığı veri toplama aracı uzman görüşü alınarak oluşturulmuştur. Araştırmanın katılımcı grubunu 2019-2020 eğitim öğretim yılında Gaziantep il merkezi, ilçeleri ve köylerinde MEB’e bağlı ortaokullarda görev yapan 208 ortaokul matematik öğretmeni oluşturmaktadır. Katılımcılar kolay erişilebilirlik ve gönüllük esasına dayalı olarak belirlenmiştir. Veri toplama aracı zümre whatsapp gruplarına Google form aracılığıyla gönderilerek katılımcıların veri toplama aracını cevaplamaları istenmiştir. Araştırma nitel betimsel olarak desenlenmiştir. Araştırmadan elde edilen veriler içerik analizine tabi tutularak kod ve kategoriler oluşturulmuştur. Araştırma sonucunda öğretmenlerin bir kısmının soruların dış görünüşüne odaklanarak bu soruları yapısal / şekilsel olarak ele aldıkları tespit edilmiştir. Öğretmenlerin diğer kısmının ise ağırlıklı olarak bu soruları; beceri temelli olan ve kavramsal ve işlemsel öğrenmeyi sağlayan sorular olarak kavramsallaştırdıkları görülmüştür. Bununla beraber katılımcıların bir kısmı bu soruların uzunluğuna dikkat çekerek bu soruların aşırı zor olduğuna vurgu yapmıştır. Diğer taraftan yeni nesil matematik sorularının öğrencilerin becerilerini geliştirdiği ve öğrencilere becerileri kazandırdığı ağırlıklı olarak vurgulanmıştır.
The aim of this chapter is to present and discuss the theoretical framework “Personalized Mathematics and Mathematics Inquiry” (PMMI) which supported the design and development of the Cyprus Mathematics Textbooks. The PMMI framework involves a set of Personalized Mathematics practices in which students actively set mathematics goals, engage, reason, discuss, create, make connections, solve problems, and reflect on mathematical content. Mathematics instruction, within this framework, seeks to actively involve students in authentic and personally relevant learning experiences. Mathematics Inquiry is at the core of the PMMI framework and evolves in three learning phases, “romance,” “precision,” and “generalization.” Mathematics Inquiry consists of challenging problems, namely explorations and investigations, which capture students’ curiosity and invite them to make hypotheses and pursue their hunches. The goal of an exploration, at the beginning of each chapter, is to elicit motivation, which will ignite students’ personal inquiry. Inevitably, students bring their own experiences in these explorations, and thus, differentiation and personal learning are facilitated. Each exploration is followed by an investigation. Investigations, however, are more closed and guided than explorations. To respond to these investigations, students often need to analyze, form hypotheses, and work systematically with various strategies, using different mathematical tools, manipulatives, and applets. During these investigations, the teachers’ role is to facilitate students to control their own learning. At this stage, new mathematical concepts and vocabulary are introduced. The application of the PMMI framework is exemplified through examples taken from the mathematics textbooks.KeywordsMathematics inquiryPersonalized mathematicsExplorationInvestigationTextbooks
The work of teaching includes many in-the-moment decisions for teachers to make. In this study, we focused on the decisions prospective teachers made within the elementary context specific to shared teaching practice in mathematics and science instruction – elicit and use evidence of student thinking. Within a qualitative multisite case study, we analyzed data for how PTs took up student thinking within instructional decisions, and the nature of responsive moves enacted within an animated context once student thinking had been elicited. Findings reveal PTs were responsive to elicited student thinking. Most commonly, PTs’ instructional decisions involved asking additional questions or inviting students to test their ideas. However, PTs’ pedagogical moves varied across mathematics and science disciplines. Our findings guide teacher educators to focus on what moves best support PTs’ development to use evidence of student thinking across disciplines in the elementary classroom. The consistency of asking questions within mathematics and science begins to inform the quest for shared core practices. Results highlight the benefit of using technology (i.e. animations) as a tool to support PTs’ learning of instructional decisions and pedagogical moves to uncover the nuances of the teaching practice elicit and use evidence of student thinking.
This chapter describes the design of integrated learning spaces (ILS) for prospective teachers (PSTs) to support PSTs' learning about reform-based teaching by helping them experience, think about, understand, and position mathematical argumentation in their future classrooms. Drawing on a longitudinal research program that explored PSTs' learning about argumentation in elementary and middle school mathematics, the authors discuss the design of ILS in the context of mathematics and pedagogy with field experience courses in a teacher education program. The authors also share the visions of mathematical argumentation as a teaching-learning practice that PSTs developed in the ILS context. Finally, this chapter poses questions for future research that might explore design principles for creating effective ILS in teacher education programs and examine how PSTs' learning in the ILS context supports their content and pedagogical knowledge development. This chapter also poses questions about ongoing support that future teachers might need to implement and sustain instructional reform.
Science, technology, engineering, and mathematics (STEM) education is important to producing students prepared for problem solving, critical analysis, and collaborative approaches to address the needs of the 21st century. For meaningful and intentional STEM instruction to occur, teachers need support and professional development. This paper presents a case study of a year-long professional learning project connecting the school’s environmental science focus to improving mathematics instruction. A whole school agreement bounds this particular case. The school faculty initiated the project and included developing a mathematics trail to connect with their nature trail, garden, and an outdoor amphitheater. The quantitative and qualitative data reveal significant changes in mathematics practices and teachers’ beliefs about the teaching and learning of mathematics. Since this case study revealed that whole school professional development in STEM could improve the teaching and learning of mathematics, implications for practice and research are discussed.
Research indicates that teachers’ mathematical beliefs and mathematical knowledge for teaching impacts practices in the classroom. Research also suggests that success in Algebra I is the gatekeeper to higher-level mathematics. With the increased number of certification pathways in some states, it is important to identify those Algebra I teachers’ beliefs and knowledge of algebra for teaching. A study of current Algebra I teachers revealed that regardless of certification pathway, mathematical beliefs are not significantly different. Additionally, significant differences did exist in regards to the certification pathway and Knowledge of Algebra for Teaching (KAT) levels.
With an increasing focus on STEM (DES, 2017) and mathematics education (DES, 2011) in Irish preschool education contexts, this paper reports on the findings of a qualitative study which explored the beliefs and self-reported practices of eight early childhood educators in relation to mathematics in preschool settings. This paper focuses in particular on the answers of participants to questions focusing on educator ‘noticing’: educator recollections of observations of mathematical concepts in children’s free play and their responses to them. Findings show that while participants could recall mathematical aspects of children’s free play or interests, these were not always responded to, or if responded to were responded to in a non-mathematical way. These findings align to those in international research and contribute to the gap in the research context in relation to mathematics in Irish preschool settings.
Ideally, mathematical concepts must be justified rather than simply stated. This study examined the reasoning expressed by pre-service elementary teachers when asked to describe how they would introduce the concept of multidigit subtraction to their students. The sample consisted of 230 pre-service elementary teachers from six Philippine universities located in various regions of the country. The reasoning in each response was classified to be of high- or low-quality, on the basis of whether they were anchored to intrinsic mathematical properties. Repeating phrases were also identified and were analysed qualitatively. The findings show that more than 90% of the reasoning produced by teachers relied heavily on rules and procedures, without connections to the quantities involved in the problem. The existence of responses that were repeated across a large number of participants also suggests that the pre-service teachers’ reasoning’s were influenced by a ‘cultural script’ they learned over a lifetime of participation in rule-dominated classrooms. The paper concludes by offering recommendations and future directions.
This working group will discuss mathematics teacher leaders and the assessment and evaluation of programs for their professional development. Mathematics teacher leaders (MTLs) are school-based, teacher leaders who are responsible for supporting other teachers with mathematics teaching and learning. Mathematics teacher leaders learn to lead professional development, coach other teachers, and work on school-level initiatives for mathematics. The challenge is that understanding of the role is still evolving as are the areas in which they need the most professional development. Many programs focus on developing their mathematical content knowledge for teaching, but they also need to learn about curriculum, assessment, pedagogy, and leadership for school change. This working group will start by discussion of existing tools and resources for documenting the work and development of MTLs. The discussion will continue with setting an agenda for research about their professional development.
This chapter continues to follow three secondary biology teachers and reveals their Personal Practice Assessment Theories (PPATs)—those constructs based on beliefs, values, forms of knowledge, mental model of learning, experiences, and assessment goals that undergird their decision making. These PPATs are placed in an Assessment Development Model (ADM) that serves as a theoretical framework for analysis of the dynamic interactions between PPATs and contextual elements and their impact on the purpose, planning, implementation, and reflection on assessment practices. Forms of knowledge, whether propositional, theoretical, or strategic, served as an internally constructed contextual element that played a significant role in the teachers’ ability to translate theory into practice. Other constraining and facilitating contextual elements are discussed as well.
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