Content uploaded by E. Kazemi
Author content
All content in this area was uploaded by E. Kazemi on Nov 20, 2014
Content may be subject to copyright.
Using Designed Instructional Activities to Enable Novices to Manage Ambitious Mathematics Teaching
Abstract
If teacher education is to prepare novices to engage successfully in the complex work of ambitious instruction, it must somehow
prepare them to teach within the continuity of the challenging moment-by-moment interactions with students and content over
time. With Leinhardt, we would argue that teaching novices to do routines that structure teacher–student–content relationships
over time to accomplish ambitious goals could both maintain and reduce the complexity of what they need to learn to do to
carry out this work successfully. These routines would embody the regular “participation structures” that specify what teachers
and students do with one another and with the mathematical content. But teaching routines are not practiced by ambitious teachers
in a vacuum and they cannot be learned by novices in a vacuum. In Lampert’s classroom, the use of exchange routines occurred
inside of instructional activities with particular mathematical learning goals like successive approximation of the quotient
in a long division problem, charting and graphing functions, and drawing arrays to represent multi-digit multiplications.
To imagine how instructional activities using exchange routines could be designed as tools for mathematics teacher education,
we have drawn on two models from outside of mathematics education. One is a teacher education program for language teachers
in Rome and the other is a program that prepares elementary school teachers at the University of Chicago. Both programs use
instructional activities built around routines as the focus of a practice-oriented approach to teacher preparation.
KeywordsExchange routines–ambitious teaching–instructional activities–teacher preparation–deliberate practice
... Identifying "core," "ambitious," or "high leverage" practices has been the work of several scholars focused on supporting novice teachers in developing competence with a limited number of practices that will lead to effective student learning (Forzani, 2014;Lampert et al., 2010;McDonald et al., 2013). One such framework of core practices, Ambitious Science Teaching (AST), is designed to promote deep learning by engaging students with both science concepts and science discourse, where students learn to think and act like scientists (Hammerness et al., 2020;Stroupe & Gotwals, 2018; Thompson et al., 2013;Windschitl et al., 2012;Windschitl et al., 2018). ...
We find ourselves at a time when the need for transformation in science education is aligning with opportunity. Significant science education resources, namely the Next Generation Science Standards (NGSS) and the Ambitious Science Teaching (AST) framework, need an intentional aim of centering social justice for minoritized communities and youth as well as practices to enact it. While NGSS and AST provide concrete guidelines to support deep learning, revisions are needed to explicitly promote social justice. In this study, we sought to understand how a commitment to social justice, operationalized through culturally sustaining pedagogy (Paris, Culturally sustaining pedagogies and our futures. The Educational Forum, 2021; 85, pp. 364-376), might shape the AST framework to promote more critical versions of teaching science for equity. Through a qualitative multi-case study, we observed three preservice teacher teams engaged in planning , teaching, and debriefing a 6-day summer camp in a rural community. Findings showed that teachers shaped the AST sets of practices in ways that sustained local culture and addressed equity aims: anchoring scientific study in phenomena important to community stakeholders; using legitimizing students' stories by both using them to
... Moreover, it is thought to enable to classify teacher moves as low or high potential moves for supporting student reasoning and understand their effects on teacher and student dialogues in classroom discourse. On the other hand, Core Principles underlying the use of student mathematical thinking (National Council of Teachers of Mathematics NCTM, 2014) were taken into consideration as a theoretical construct to clarify teacher moves that support student reasoning in classroom discourse like some studies (e.g., Lampert et al., 2010;Robertson, Atkins, et al., 2016;Robertson, Scherr, et al., 2016;Stockero et al., 2022). National Council of Teachers of Mathematics NCTM (2014) explains these principles as follows: Legitimacy Principle calls for providing students opportunities to interact with mathematical ideas, considering what they are thinking, and integrating their contributions into the teaching. ...
Interest in teachers' moves to classroom discourse has started to increase since how teachers respond to students' thinking influences students' learning. The purpose of this study was to investigate the moves used by one sixth grade mathematics teacher at a public middle school in Turkey to support student reasoning in mathematics instruction and their influence on classroom discourse. Six 80‐min lessons were analyzed with particular attention to how the teacher elicits, responds to, facilitates, and extends student reasoning. The results revealed that teacher moves mainly included low‐potential moves in all categories. The teacher mainly tried to elicit student answers in the lessons and aimed to facilitate their understanding through questioning. He also tended to confirm students' answers and re‐represent their thoughts to the class, occasionally adding further information. However, the results showed that the teacher had a dominant role in classroom interactions. Besides, from time to time, the teacher did not focus on student responses and postpone the student reactions. However, the teacher moves that limit student contribution, such as ignoring students' answers and insisting on their own points of view, reduce the depth of classroom interactions and student understanding. In general, the teacher's ability to support student reasoning and facilitate productive classroom discourse was not sufficient.
... Teacher noticing is accepted as a fundamental component of teaching expertise and student-centered education (Lampert, Beasley, Ghousseini, Kazemi & Franke, 2010;Schack, Fisher & Wilhelm, 2017;Sherin, Jacobs & Philipp, 2011;van Es, 2011). As a unique way of recognizing and interpreting the important aspects of classroom interactions, "teacher noticing" became the focal point of much research (e.g., Barnhart & van Es, 2015;Star & Strickland, 2008;Sun & van Es, 2015;Ozdemir Baki & Kilicoglu, 2020;van Es & Sherin, 2002). ...
The aim of this study is to examine the error approach of middle school teachers and their noticing of their approaches. The study was designed as a case study, which is a qualitative research method, and conducted through four middle school mathematics teachers during the pandemic. The data regarding the study were gathered via in class video records and online interviews with the teachers. The videos from the lectures of middle school mathematics teachers were segmented and analysed, hence, their approaches to student errors were identified. Moreover, noticing of the participant teachers on their and their peers' approach were investigated by means of online interviews. The findings of the research indicated the participant teachers mostly opt for the intervention approaches that fall into the category of questioning, and they make delineative and explanatory comments concerning their approaches. Furthermore, it has been observed that the teachers reached deductions through the evaluation of their own approaches, however, most of the time they recommended their own error approaches to the students as an educatory proposition.
... Kuram ve uygulama arasındaki bağlantı, öğretmen eğitimi alanında önemli bir tartışma konusudur (Korthagen & Kessels, 1999;Korthagen, Loughran, & Russell, 2006). Yansıtıcı düşünmeyi destekleyen stratejiler (Dervent, 2015;Kim & Silver, 2016;Körkkö, Kyrö-Ämmälä, & Turunen, 2016), öğretmen adaylarının iş birliğine dayalı ortaklıkları, öğretme ve öğrenme ortamlarında doğrudan deneyimler kazandıran modeller (Lampert, Beasley, Ghousseini, Kazemi, & Franke, 2010) ve bazı mesleki gelişim modelleri (Cajkler, Wood, Norton, Pedder, & Xu, 2015;Huang & Shimizu, 2016) Öğrenci çeşitliliğinin artması, farklılaştırılmış öğretim ihtiyacını ortaya çıkarmıştır. Farklılaştırılmış ders tasarımı karmaşıktır ve öğretmen adaylarının bu konuda desteklenmesi gerekmektedir (Gibbs, 2022;van den Kieboom & Groleau, 2022). ...
Bu çalışma, "İşbirlikli Planlama ve Uygulama Döngüsü (IPUD)" süreci kapsamında öğretmen adaylarının deneyimlerini ve mesleki becerilerindeki gelişimi incelemeyi amaçlamaktadır. Araştırma, nitel bir durum çalışması deseni kullanarak tek bir durum ve analiz birimi üzerinde yapılmıştır. Katılımcılar, ölçüt örnekleme yöntemiyle belirlenen sınıf öğretmenliği lisans programının üçüncü sınıfındaki dört öğretmen adayıdır. Çalışmada, üç veri toplama aracı kullanmıştır: hazırlık süreci raporları, ders planları ve yansıtıcı değerlendirme raporları. Her bir araç, işbirlikli planlama ve uygulama döngüsünün aşamaları temelinde özelleştirilmiştir. Veri analizi açık kodlama, sınıflandırma ve alt kategorilere ayrıştırma adımlarıyla gerçekleştirilmiştir. Araştırmanın sonuçları, öğretmen adaylarının hazırlık çalışmalarında gereklilikleri daha detaylı ele alabilme konusunda yeterlik kazandığını göstermiştir. Adaylar tarafından geliştirilen planların çoğunun boyutların gerekliliklerine sahip olduğu görülmüştür. Adayların yansıtıcı raporları ise çeşitli kazanımlar sağladığını ortaya koymaktadır. Sonuç olarak, IPUD süreci, öğretmen adaylarının matematik öğretme becerilerini desteklemekte ve geliştirmekte etkili bir araç olarak görülmektedir. Araştırmanın bulguları, öğretmen eğitim programlarına dair öneriler sunmaktadır.
... Pre-service teachers' learning, as well as practicing teachers' professional development opportunities, used the five practices as a steppingstone leading toward change in teaching practices, also termed as ambitious instruction (Lampert et al., 2010). Yet, to the best of our knowledge, the five practices were not linked to teaching in a technological environment. ...
The slow uptake of technology by mathematics teachers is in contrast with the rapid growth in the availability of different digital resources specifically designed to help teaching and learning mathematics. We refer to platforms that were designed to permit for mathematical communication between multiple users. We seek to explore the affordances of such digital platforms to support mathematics teachers who wish to integrate technology as part of their practice, when planning and enacting technology-based mathematical activity. Specifically, we ask: What are the affordances and constraints of the platforms that may support instrumentation and instrumentalization processes leading to the development of teacher’s didactic instrument for planning and enacting a mathematical activity in a digital environment? The four platforms we chose for analysis are STEP, DESMOS, WIMS and Labomep. Our analysis shows on the one hand that the platforms afford support to the teacher while enacting technology-based mathematics activities. On the other hand, we suggest several components of didactic instrumental genesis that mathematics teachers need to develop in order to take benefit from digital platform affordances. These components include the ability to base decision-making on data gathered and visualised in dashboard embedded in learning management systems.
... Ms. Severn noted that she would use the MLRs again in her class, particularly to scaffold conversations for students. Lampert et al. (2010) noted that teaching routines are not practiced within a vacuum. In the case of our methods course, the multilingual learner core practices were practiced within the MLRs. ...
This study considered a preservice teacher’s (PST’s) attention to multilingual learner core practices within her approximations of practice of mathematics language routines during a secondary mathematics methods course. We used a framework of approximations of practice to understand how a PST enacted and developed an understanding of multilingual learner core practices. To provide a vision for what multilingual learner core practices can look like in nontraditional instructional contexts, we qualitatively analyzed four approximations of practice of mathematics language routines from a single PST during a single semester of a methods course. We share how she navigated the remote teaching context and engaged sample students in all of the multilingual learner core practices despite the challenges of the COVID-19 pandemic, providing an example of what these practices may look like in remote instruction. We also discuss how these multilingual learner core practices interact and complement one another. We consider possible implications, limitations, and future research directions.
... MPC implements ambitious teaching practices (20,26,88) (89), and additional studies (27,90,91). Many of these practices form the core of the MAA Instructional Practices Guide (20). ...
Calculus, the study of change in processes and systems, serves as the foundation for many STEM disciplines. Traditional, lecture-based calculus instruction may present a barrier for students seeking STEM degrees, limit their access to STEM professions, and block their potential to address society's challenges. A large-scale pragmatic trial with randomized student allocation was conducted to compare two calculus instruction styles: active student engagement (treatment condition) versus traditional, lecture-based instruction (control condition). A sample of 811 university students were studied across 32 sections taught by 19 instructors over three semesters at a large, US-based Hispanic-serving institution. Large effect sizes were consistently measured for student learning outcomes in the treatment condition, which demonstrates a new standard for calculus instruction and increased opportunities for completion of STEM degrees.
Field experiences are an integral part of teacher education programs because they provide preservice teachers with an opportunity to put the theory, they are learning in their university classrooms into practice. The purpose of this research study was to explore the preservice teachers’ virtual field experiences at two universities during the onset of the COVID-19 pandemic to identify the practices that inform teacher educators’ and course developers’ practices to provide effective and cohesive virtual field experiences. Twenty-seven preservice teachers participated in this study. Results of the study showed that preservice teachers identified experiences with new literacies (technologies), teacher educator’s role, video analysis, assignments, and working with a cooperating teacher (CT)as valuable in virtual field experiences.
Scholars have long assumed that institutional and cultural forces act on the work of teaching. Environmental factors such as local control, resource allocation, professional training and licensure are frequently investigated for their effects on practice. Other scholarship, however, has reversed this causal sequence by claiming that practice, not environments, is the primary independent variable. This dissertation builds on this practice-centered approach by developing a frame in which instructional practice is seen as the independent variable that acts on environments. Three dimensions of practice are particularly salient: (1) the conceptualization of problems and goals; (2) the degree of effectiveness in solving client problems; and (3) the degree of consistency in clinical method and reasoning across contexts. The resulting framework is applied to the comprehensive school reform program, America's Choice, and evaluated for its utility as an instrument of analysis. The practice-centered approach is then compared with more traditional frameworks that see the educational environment as the independent variable and practice as the dependent one. The application of the practice-centered analytic frame highlights a number of salient issues that have not appeared in past analyses. One issue is the importance of a plan for practice, or design, that structures and guides clinical work. Second, the architecture of the design for work is consequential in how it defines the nature of teaching and learning, structures the tasks of teaching, and bears on the knowledge demands of practice. Third, the knowledge demands placed on practitioners is consequential for practice and the profession as a whole, and may bear on various indicators of professionalism (e.g. state protection). The main finding of this dissertation is that while viewing practice as the chief independent variable compensates for a weakness in past research, it is still important to understand how environments affect practice. In the analysis of America's Choice, environmental factors such as local control, policy, and resource allocation were found to be integral to understanding the functioning of America's Choice. This suggests that a more complete view of the education profession must account for the way in which practice acts on environments and how environments shape practice.
As mathematics teachers, we want students to understand mathematics, not just to recite facts and execute computational procedures. We also know that allowing students to explore and have fun with mathematics may not necessarily stimulate deep thinking and promote greater conceptual understanding. Tasks that are aligned with the NCTM's curriculum standards (NCTM 1989) and that are connected to students’ lives still may not challenge students to build more sophisticated understandings of mathematics. The actions of the teacher play a crucial role.
The theoretical framework presented in this article explains expert performance as the end result of individuals' prolonged efforts to improve performance while negotiating motivational and external constraints. In most domains of expertise, individuals begin in their childhood a regimen of effortful activities (deliberate practice) designed to optimize improvement. Individual differences, even among elite performers, are closely related to assessed amounts of deliberate practice. Many characteristics once believed to reflect innate talent are actually the result of intense practice extended for a minimum of 10 years. Analysis of expert performance provides unique evidence on the potential and limits of extreme environmental adaptation and learning.
The emphasis on reasoning and discourse in mathematics education makes it a necessity to prepare preservice teachers to conduct productive mathematical discussions---no easy task given the complexity of this aspect of ambitious mathematics teaching and its unfamiliarity to many prospective teachers. In this dissertation, the author addresses the question of how pre-service teachers can be prepared to lead productive classroom mathematics discussions, assuming that they need tools to reduce some uncertainties in practice while learning to teach mathematics in intellectually responsible and responsive ways. Shc argues that the use of such tools can harness some of the complexity in practice and enable prospective teachers to attend to core tasks of teaching. The author examines the opportunities to learn about leading classroom mathematics discussions made available in the context of a secondary mathematics methods course intervention that used discourse routines to develop pre-service teachers' knowledge about leading productive mathematics discussions. She also examines how five pre-service teachers, who attended the methods course, used the discourse routines in the context of their student teaching. Using interpretive case study methodology and conversation analysis methods, the author examines the pre-service teachers' approaches to leading classroom mathematics discussions using discourse routines as embedded in an activity system comprising the community of the classroom and its prevalent social conventions. The analysis draws on data collected from classroom observations, interviews, lesson plans, and teaching reflections. Case studies are developed based on the kind of discourse patterns emerging from the analyses and the levels of appropriation of the discourse routines by the preservice teachers. Through cross-case analysis, the author finds that the pre-service teachers were able to appropriate the discourse routines at two levels: surface-level and conceptual. She finds that the pre-service teachers who appropriated the discourse routines at a surface-level promoted a contributive pattern of classroom discourse, while the one who appropriated them at a conceptual level promoted a reflective pattern of discourse. The author also examines some factors in the activity system that shaped the pre-service teachers' practice in leading classroom mathematics discussions and their levels of appropriation of the routines. Based on these findings, she discusses potential implications for the use and design of disciplined, purposeful instructional routines in professional education to scaffold the preparation of pre-service teachers for ambitious teaching.
