# Megan L. Franke's research while affiliated with University of California, Los Angeles and other places

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## Publications (51)

Educators, researchers, and policy makers recognize that student participation in classroom mathematics conversations, especially explaining one’s own thinking and engaging with others’ ideas, can promote students’ mathematics learning. However, precisely how participating in these ways supports learning has not often been examined in detail. Using...

Accountability mandates linked to state education standards and assessments have largely replaced play in early childhood classrooms. This approach limits educators' opportunities by preventing them from using play as a means of identifying and expanding children's diverse range of competencies. In this ethnographic case study, we explore how young...

This study is situated within efforts to embrace the challenge of preparing teacher candidates (TCs) for the complexities of teaching mathematics while creating shared opportunities for inquiry across teacher education programs. We developed a shared decomposition of leading mathematics discussions that could be used across our teacher education si...

Capturing the breadth and variety of children’s understanding is critical if studies of children’s mathematical thinking are to inform policy and practice in early childhood education. This article presents an investigation of young children’s counting. Detailed coding and analyses of assessment interviews with 476 preschoolers revealed understandi...

This vivid illustration of an instructional activity highlights the range of opportunities available for a teacher to leverage students' thinking and support rich mathematical discourse.

This paper traces the development of a program of work that seeks to understand the teacher practices that promote productive dialogue and learning in mathematics classrooms. This work originated in cooperative/collaborative learning research, with a focus on understanding group dynamics effective for student learning. Over time, it layered on incr...

Learn how teachers can use assessment data coupled with observing students' mathematical reasoning to inform instructional decisions.

Educators, researchers, and policy makers increasingly recognize that participation in classroom mathematics discussions, especially engaging with others’ ideas, can promote students’ mathematics understanding. How teachers can promote students’ high-level engagement with others’ ideas, and the challenges teachers face when trying to do so, have no...

Engaging students as active participants in mathematics classroom discussions has great potential to promote student learning. Less well understood is how teachers can promote beneficial student participation, and how teacher-student interaction relates to student achievement. This study examined how the kinds of teacher practices that may encourag...

Researchers, practitioners, and policy makers increasingly recognise that student participation in mathematical conversations, especially explaining one's thinking and engaging with other students' ideas, can promote students' mathematical understanding. How teachers can promote productive student participation is less well understood. This chapter...

This paper explores the relationships between student participation in classroom conversations, teacher practices, and student learning in elementary school mathematics classrooms. Six teachers and 111 children aged 8–10 participated in the study. Students and teachers were videotaped as they discussed how to solve mathematical problems during whol...

AERA Symposium 2014 Grossman and her colleagues argue for reimagining and redesigning teacher education so that it addresses the relational and skilled work around orchestrating instruction through approximations that focus on contingent, interactive practice (Grossman et al., 2009). We, along with a number of other teacher educators, have been red...

Research commonly finds that urban teachers bring deficit views about students of color with them into classrooms, and professional development efforts focused on this critical problem have been met with limited success. Therefore, scholars have called for work that integrates content and equity as a way to challenge teachers’ deficit views at the...

We analyze a particular pedagogy for learning to interact productively with students and subject matter, which we call “rehearsal.” Our goal is to specify a way in which teacher educators (TEs) and novice teachers (NTs) can interact around teaching that is both embedded in practice and amenable to analysis. We address two main research questions: (...

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–s...

Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students’ mathematical thinking, they struggle with how to follow up on student ideas. This study examines the classrooms of three teachers who had engaged in algebraic reasoning CGI professional development. We detail teachers’ q...

Collaborative group work has great potential to promote student learning, and increasing evidence exists about the kinds of interaction among students that are necessary to achieve this potential. Less often studied is the role of the teacher in promoting effective group collaboration. This article investigates the extent to which teachers' instruc...

mlampert@umich.edu> What might it take to support novice teachers to develop the commitment and the capacity to enact ambitious mathematics instruction? In this paper, we describe our experimentation with pedagogies in teacher education to develop novice teachers' competence in eliciting, responding to, and advancing students' mathematical thinking...

Discussion, theorising and research in the area of mathematical knowledge for teaching began by asking what level of mathematical qualification teachers need. We have moved on considerably since then, using concepts such as pedagogical content knowledge, and frameworks such as those from Deborah Ball in Michigan or, more recently, Tim Rowlands in C...

Prior research on collaborative learning identifies student behaviors that significantly predict student achievement, such as giving explanations of one’s thinking. Less often studied is the role of teachers’ instructional practices in collaboration among students. This article investigates the extent to which teachers engage in practices that supp...

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with te...

We have characterized what we callrelational thinking to include looking at expressions and equations in their entirety rather than as procedures to be carried out step by step.
For the last 8 years, we have been studying how to provide opportunities for students to engage in relational thinking in
elementary classrooms and how to use relational th...

The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work th...

This study documents how teachers who participated in a professional development program on understanding the development of students’ mathematical thinking continued to implement the principles of the program 4 years after it ended. Twenty-two teachers participated in follow-up interviews and classroom observations. All 22 teachers maintained some...

This paper presents a study of primary and secondary mathematics teachers’ changing assessment practices in the context of policy, stakeholder, and personal presses for change. Using survey and interviews, we collected teachers’ reports of their uses of three forms of assessment, one linked to traditional practice (exercises), and two linked to ref...

Investigated changes over four years for three elementary teachers participating in Cognitively Guided Instruction (CGI), which emphasized students' mathematical thinking and supported teachers through workshops, mentoring, and collaboration. Interviews and observations indicated that CGI allowed teachers to engage in ongoing practical inquiry dire...

This 3-year longitudinal study investigated the development of 82 children's understanding of multidigit number concepts and operations in Grades 1-3. Students were individually interviewed 5 times on a variety of tasks involving base-ten number concepts and addition and subtraction problems. The study provides an existence proof that children can...

This 3-year longitudinal study investigated the development of 82 children's understanding of multidigit number concepts and operations in Grades 1—3. Students were individually interviewed 5 times on a variety of tasks involving base-ten number concepts and addition and subtraction problems. The study provides an existence proof that children can...

Thirty-six first graders from 2 different school systems participated in individual interviews to determine the children's stated perceptions regarding what it means to engage in mathematics and the rationale and conditions under which they held such perceptions. These children were in classrooms that reflected the spirit of the current reform move...

Thirty-six first graders from 2 different school systems participated in individual interviews to determine the children's stated perceptions regarding what it means to engage in mathematics and the rationale and conditions under which they held such perceptions. These children were in classrooms that reflected the spirit of the current reform move...

In this article we propose that an understanding of students' thinking can provide coherence to teachers' pedagogical content knowledge and their knowledge of subject matter, curriculum, and pedagogy. We describe a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or spontaneous kn...

This study examined changes in the beliefs and instruction of 21 primary grade teachers over a 4-year period in which the teachers participated in a CGI (Cognitively Guided Instruction) teacher development program that focused on helping the teachers understand the development of children's mathematical thinking by interacting with a specific resea...

This study examined changes in the beliefs and instruction of 21 primary grade teachers over a 4-year period in which the teachers participated in a CGI (Cognitively Guided Instruction) teacher development program that focused on helping the teachers understand the development of children's mathematical thinking by interacting with a specific resea...

Seventy kindergarten children who had spent the year solving a variety of basic word problems were individually interviewed as they solved addition, subtraction, multiplication, division, multistep, and nonroutine word problems. Thirty-two children used a valid strategy for all nine problems and 44 correctly answered seven or more problems. Only 5...

Seventy kindergarten children who had spent the year solving a variety of basic word problems were individually interviewed as they solved addition, subtraction, multiplication, division, multistep, and nonroutine word problems. Thirty-two children used a valid strategy for all nine problems and 44 correctly answered seven or more problems. Only 5...

This article describes how knowledge of children’s thinking in mathematics, derived by using a cognitive science research paradigm, was used by a first-grade teacher to make instructional decisions. Children in the classroom learned mathematics to a level that exceeds what is recommended by the NCTM Standards (NCTM, 1989). The study is situated in...

what a teacher knows is one of the most important influences on what is done in classrooms and ultimately on what students learn / there is no consensus on what critical knowledge is necessary to ensure that students learn mathematics / many components of teachers' knowledge have been identified [knowledge of mathematics, knowledge of mathematical...

## Citations

... These include PD programs at different grade levels and in various forms (e.g., lesson study, video club, student interviews), such as Cognitively Guided Instruction (CGI) (Carpenter et al., 1989Carpenter & Fennema, 1992;Fennema et al., 1996;Franke et al., 2001;Steinberg et al., 2004), Mathematics Classroom Situations (Even & Markovits, 1993;Markovits & Even, 1999a, 1999b, Developing Mathematical Ideas (DMI) (Schifter, 1998(Schifter, , 2001, Integrating ...

... For a time, however, some of the aspects of these programmes remained implicit and were not theorised, even as they were essential to making the transformation possible. These included changes in the norms of a classroom discourse (McClain & Cobb, 1998), or the role that an alignment of the goals of the research programme with the school's curricular goals played (Franke, Carpenter, & Battey, 2008). Instead, the success was primarily attributed to sharing with the teachers the analysis of mathematics involved, and of how students may come to reason with it. ...

... The authors in [8,9], also perform similar kind of classification techniques with CHANGE, COMBINE, and COMPARE [8, Table 1] or with the names differ slightly [9, Table 2]. The authors in [14], first proposed a method, which includes the division-multiplication type problems along with additionsubtraction type problems. All the systems proposed by [2,10,14,15,16] can solve the arithmetic problems with all the basic four types of operations. ...

... Strategy selection models help to explain the subjective and diverse evaluation criteria used by learners in determining the appropriateness of strategies in equation solving (Franke & Carey, 1997;Star & Madnani, 2004). A previous study found that students' criteria for determining the best strategy in equation solving were quite complex. ...

... The process was supported by classroom teacher feedback. Their observations and the records of students' solutions provide convincing support for arguments that younger students can explore problems independently and invent accurate solution strategies (Cai, 2003;Carpenter et al., 1998;Hiebert & Wearne, 1998). Consideration of these younger learners lent particular weighting to the importance of context in terms of motivating student engagement and providing an appropriate match with their cultural context. ...

... Engaging young children with literacy and numeracy in a positive way is a central concern with early years' practitioners. In a play-based curriculum, children can be enabled to participate in complex literacy and numeracy practices and as Franco, Orellana, and Franke (2019) state, act as experts in ways that are often not possible within their actual social worlds. Through play they can explore the relationship between things, ideas, and symbolic representations (Vygotsky 1978), as they experiment with different forms of representation through words, pictures, objects and movement. ...

... We selected these two models because of their wide geographic influence and convergence around a similar top-level launch-explore-summarize structure. Furthermore, as part of this third generation of research, a growing body of research communicates designs for TE that oftentimes utilize one of these models as curriculum (e.g., Boerst et al., 2011;Ghousseini, 2015;Ghousseini & Herbst, 2016;Lloyd, 2005;Pang, 2016;Shaughnessy et al., 2019). As we describe in what follows, both models include phases in which the teacher selects among solutions from the class to be shared in the discussion in a particular sequence. ...

... In our proposal for using situated counting in educational programs, we follow a recent study by Johnson et al. (2019) who suggest that children are way more competent when it comes to solving mathematical problems than it is usually believed. The authors highlight that even very young preschool children can engage and make sense of sophisticated mathematical ideas in a favorable context 13 . ...

Reference: Situated Counting

... Moreover, discussions rarely occur in social studies classrooms (Barton & Avery, 2016;Ho et al., 2017;Nystrand et al., 2001;Saye & SSIRC, 2013), which limits teacher candidates' encounters with the practice in their field placements. Recent efforts have attempted to bound and specify discussion practice in ways that direct student discourse towards disciplinary learning (e.g., Grossman et al., 2019;Kloser et al., 2019), but researchers have not inquired into how candidates perceive and interpret their efforts. ...

... Critical dialogue in mathematics education should be a norm in generating new ideas and knowledge in the field within and outside the classroom through collaborative and cooperative group dynamics of students and teachers or educators (Webb et al., 2019). Such practices may help teachers and students mutually collaborate for activation, motivation, and a more significant cognitive gain in terms of meaningful learning of mathematics in the classroom (Boheim et al., 2021). ...