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“Guess what they would make you do on this one”: The discourse of a high-stakes exam in an AP Calculus classroom The Journal of Mathematical Behavior Pub Date : 2024-02-02 Sunghwan Byun, Beth Herbel-Eisenmann
Signified by a familiar phrase, teaching to the test, the effect of high-stakes exams on mathematics instruction is widely accepted. It is, however, largely unknown how the discourse of a high-stakes exam is brought into everyday classroom interaction and shapes ways of doing mathematics in situ. This study examines details of social interaction in one Advanced Placement (AP) Calculus classroom, in
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Teaching mathematics through problem posing: Elements of the task The Journal of Mathematical Behavior Pub Date : 2024-02-02 Janaína Poffo Possamai, Norma Suely Gomes Allevato
Current research and curriculum documents from several countries have highlighted the importance of problem posing. However, some elements of this activity in mathematics classes still need to be further explored and understood. The objective of this article is to investigate how situations and problem-posing prompts affect teaching through problem posing. Three teaching cases are presented and analyzed
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Combinatorial and quantitative reasoning: Stage 3 high school students’ reason about combinatorics problems and their representation as 3-D arrays The Journal of Mathematical Behavior Pub Date : 2024-02-02 Erik S. Tillema, Andrew M. Gatza, Weverton Ataide Pinheiro
Researchers have identified three stages of units coordination that influence a range of domains of student reasoning. The primary foci of this research have been students’ reasoning in discrete, non-combinatorial whole number contexts, and with fractions, ratios, proportions, and rates represented using length quantities. This study extends this prior work by examining connections between eight high
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Attending to task variables when engaging in group problem posing for elementary level mathematics The Journal of Mathematical Behavior Pub Date : 2024-02-01 Aisling Leavy, Mairéad Hourigan
In light of the growing interest in research examining problem posing, this study explores an under-researched aspect – group problem posing. It examines the role of problem situations and prompts, introduced within a problem posing intervention, on the nature of the problems posed by groups of pre-service elementary teachers for children in two 4th grade classes. The impact of the group on the problem
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Problem-posing tasks and their influence on pre-service teachers’ creative problem-posing performance and self-efficacy The Journal of Mathematical Behavior Pub Date : 2024-01-30 Lukas Baumanns, Benjamin Rott
In problem-posing research, the influence of task variables on problem-posing outcomes is a relatively new endeavor. To systematically vary task variables, we designed eight problem-posing tasks by crossing two problem-posing situations (unstructured vs. structured) with two problem-posing prompts (open vs. closed) and two mathematical contexts (patterns vs. geometry). Using this design, we investigated
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Mathematics teachers’ specialized knowledge mobilized through problem transformation The Journal of Mathematical Behavior Pub Date : 2024-01-25 M. Montes, J. Chico, J.P. Martín-Díaz, E. Badillo
In this study we address two issues related to problem-posing tasks in teacher education: (i) the characterization of the specialized knowledge mobilized by prospective teachers when carrying out these tasks and (ii) the identification of the prospective teachers’ pedagogical intentions in making adaptations to textbook problems. We asked prospective teachers to outline their suggestions for transforming
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Variables in planning and carrying out a problem-posing task in early childhood education The Journal of Mathematical Behavior Pub Date : 2024-01-25 Enrique Carmona-Medeiro, Juan Pedro Martín-Díaz, Nuria Climent
This research focused on understanding the variables inherent in the design and implementation of a mathematical problem-posing task. We developed a single case study of a problem-posing lesson by an Early Childhood Education teacher in a classroom with 4- to 5-year-old children who were unfamiliar with such activities. The results of this study show the potential of considering five variables serving
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Do task variables of self-generated problems influence interest? Authenticity, openness, complexity, and students’ interest in solving self-generated modelling problems The Journal of Mathematical Behavior Pub Date : 2024-01-23 Janina Krawitz, Luisa Hartmann, Stanislaw Schukajlow
Problem posing—generating one’s own problems—is considered a powerful teaching approach for fostering students’ motivation such as their interest. However, research investigating the effects of task variables of self-generated problems on students’ interest is largely missing. In this contribution, we present a study with 105 ninth- and tenth-graders to address the question of whether the task variables
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Conceptualizing reasoning practices in the context of sociomathematical issues The Journal of Mathematical Behavior Pub Date : 2024-01-23 Sean Chorney, Kyle R. Evans, Megan Staples
In this conceptual paper, we explore a framework of reasoning practices for decision-making in context. We extend prior work related to socioscientific issues (SSI) (Sadler et al., 2007) to consider the applicability of this framework to sociomathematical issues, specifically using the context of fairness in political (re)districting. We illustrate the usefulness of the SSI framework for sociomathematical
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Primary students’ relational thinking and computation strategies with concrete-to-symbolic representations of subtraction as difference The Journal of Mathematical Behavior Pub Date : 2024-01-12 Karina J. Wilkie, Sarah Hopkins
Children are highly inclined to attend to the properties of numbers, operations and equality when given helpful tools for doing so. Our aim was to investigate early algebraic thinking with the compensation property of equality for subtraction. We provided 22 (9–11-year-old) students with physical blocks for building vertical towers and conducted individual interviews with them as they completed a sequence
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Demands and scaffolds for explaining the connection of multiple representations: Revisiting the bottle-filling task The Journal of Mathematical Behavior Pub Date : 2024-01-10 Katharina Zentgraf, Susanne Prediger
Explaining the connections of multiple representations can enhance students’ conceptual understanding (e.g., in the bottle-filling task for functional graphs). But it poses high discursive demands that need to be further unpacked. The design research study qualitatively investigates the potentials and demands that fourteen second-language learners face when explaining the connection between functional
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Extending the covariation framework: Connecting covariational reasoning to students’ interpretation of rate of change The Journal of Mathematical Behavior Pub Date : 2024-01-09 Franklin Yu
Research on covariational reasoning has continued to evolve as researchers learn more about how students coordinate two (or more) quantities’ values as covarying. In this study, I examine the connection between students’ covariational reasoning and how they interpret the value of a rate of change. The findings suggest that attending to students’ quantifications of a rate of change can provide insight
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From “learning to variate” to “variate for learning”: Teachers learning through collaborative, iterative context-based mathematical problem posing The Journal of Mathematical Behavior Pub Date : 2023-12-30 Nadav Marco, Alik Palatnik
Problem posing (PP) has been found to contribute to teachers’ mathematical pedagogical knowledge. However, little is known about what and how teachers learn when engaged in continuous iterative PP. We use the variation theory of learning to conceptualize what and how teachers learn during iterative PP, illustrating these processes via a case study. The main argument is that what teachers learn from
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A symbolizing activity for constructing personal expressions and its impact on a student’s understanding of the sequence of partial sums The Journal of Mathematical Behavior Pub Date : 2023-12-21 Derek Eckman, Kyeong Hah Roh
This paper reports the results from a set of exploratory teaching interviews in which students constructed individualized algebraic expressions (called personal expressions) to describe their meanings for partial sums. Our analysis focused on one student, Emily, who constructed two distinct personal expressions for partial sums, one novel and one based on her image of summation notation. Emily created
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Adidactical problem-posing as captured by scripting journeys: Investigating sums of consecutive integers The Journal of Mathematical Behavior Pub Date : 2023-12-20 Andrew Kercher, Canan Güneş, Rina Zazkis
Research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and full extent of this relationship requires detailed elaboration. This is especially true when problem-posing arises in order to facilitate problem-solving, such as during the investigation of an unfamiliar mathematical property or phenomenon. In this study, groups of participants
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“The theorem says…”: Engineering students making meaning of solutions to Ordinary Differential Equations The Journal of Mathematical Behavior Pub Date : 2023-12-15 Paul Hernandez-Martinez, Svitlana Rogovchenko, Yuriy Rogovchenko, Stephanie Treffert-Thomas
There is a need for further studies on students’ learning of Differential Equations (DEs), especially in advanced undergraduate and graduate courses. Research on the mathematical education of engineers shows a conflict between students’ demands for practical, contextualized pedagogies and the need for abstract reasoning and appropriate use of mathematical results. Few papers focus on engineering students’
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Comparing student strategies in a game-based and pen-and-paper task for linear algebra The Journal of Mathematical Behavior Pub Date : 2023-12-14 Jeremy Bernier, Michelle Zandieh
This study examines the mathematical activity involved in engaging with two tasks designed for introductory linear algebra: the Vector Unknown digital game and the pen-and-paper Magic Carpet Ride task. Five undergraduate students worked on both tasks, and we qualitatively analyzed their strategies using a modified version of a framework from prior literature. In the findings, we report on the seven
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An exploratory mixed methods study about teacher candidates’ descriptions of children’s confusion, productive struggle, and mistakes in an elementary mathematics methods course The Journal of Mathematical Behavior Pub Date : 2023-12-12 Crystal Kalinec-Craig, Anthony Rios
Recognizing and describing children's mathematical thinking in humanizing ways, especially when students engage in confusion, productive struggle, and mistakes, is a complex and challenging process. This paper describes an exploratory, mixed-methods study about how elementary teacher candidates (TCs) describe children's thinking as a right to exercise and to value their humanity when learning mathematics
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The role of topology in the construction of students’ optimization schema for two-variable functions The Journal of Mathematical Behavior Pub Date : 2023-11-30 Rafael Martínez-Planell, Maria Trigueros, Vahid Borji
This study uses Action-Process-Object-Schema theory (APOS) to examine students’ understanding of two-variable function optimization. A genetic decomposition (GD) based on the notion of Schema is proposed. This is a conjecture of mental structures and relations that students may construct to understand the optimization of these functions. The GD was tested with semi-structured interviews with eleven
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Connecting operation-choice problems by the variation principle: Sixth graders’ operational or deeper relational pathways The Journal of Mathematical Behavior Pub Date : 2023-11-28 Cristina Zorrilla, Anna-Katharina Roos, Ceneida Fernández, Salvador Llinares, Susanne Prediger
Many empirical studies documented students’ challenges with operation-choice problems, in particular for multiplication and division with rational numbers. The design principle of problem variation was suggested to overcome these challenges by engaging students in making connections between inverse operation-choice problems of multiplication and division, and between problems with natural numbers and
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Reasoning productively across algebraic contexts: Students develop coordinated notions of inverse The Journal of Mathematical Behavior Pub Date : 2023-10-19 John Paul Cook, Kathleen Melhuish, Rosaura Uscanga
The concept of inverse is threaded throughout K-16 mathematics. Scholars frequently advocate for students to understand the underlying structure: combining an element and its inverse through the binary operations yields the relevant identity element. This ‘coordinated’ way of reasoning is challenging for students to employ; however, little is known about how students might reason en route to developing
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Examining the concept of inverse: Theory-building via a standalone literature review The Journal of Mathematical Behavior Pub Date : 2023-10-14 John Paul Cook, April Richardson, Steve Strand, Zackery Reed, Kathleen Melhuish
Inverse is a critical topic throughout the K–16 mathematics curriculum where students encounter the notion of mathematical inverse across many contexts. The literature base on inverses is substantial, yet context-specific and compartmentalized. That is, extant research examines students’ reasoning with inverses within specific algebraic contexts. It is currently unclear what might be involved in productively
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Learners building conceptual understandings of mathematics: Conditions for promoting growth in understanding – A global perspective from ICME-14 The Journal of Mathematical Behavior Pub Date : 2023-10-04 Jenni Ingram, Stéphane Clivaz, Carolyn A. Maher, Louise Wilkinson
Abstract not available
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Noticing of argumentation: A comparison between pre-service and in-service secondary-school mathematics teachers The Journal of Mathematical Behavior Pub Date : 2023-09-22 Samaher Nama, Maysa Hayeen-Halloun, Michal Ayalon
This study compares pre-service mathematics teachers’ (PSMTs) and in-service mathematics teachers’ (ISMTs) noticing of argumentation at the secondary-school level. Thirty-five PSMTs and 32 ISMTs engaged in analyzing argumentation classroom situations (ACSs) using an ACS-report format emphasizing two sub-skills of noticing: attending and interpretation. Analysis of the participants’ ACS reports revealed
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Applying a new framework of connections between mathematical symbols and natural language The Journal of Mathematical Behavior Pub Date : 2023-09-12 Ulrika Wikström Hultdin, Ewa Bergqvist, Tomas Bergqvist, Lotta Vingsle, Magnus Österholm
A reader of mathematical text must often switch between reading mathematical symbols and reading words. In this study, five different categories of structural connections between symbols and language, which invite such switches, are presented in a framework. The framework was applied in a study of Swedish mathematics textbooks, where 180 randomly selected pages from different educational stages were
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Impact of prompts on students’ mathematical problem posing The Journal of Mathematical Behavior Pub Date : 2023-09-08 Jinfa Cai, Hua Ran, Stephen Hwang, Yue Ma, Jaepil Han, Faith Muirhead
This study used three pairs of problem-posing tasks to examine the impact of different prompts on students’ problem posing. Two kinds of prompts were involved. The first asked students to pose 2–3 different mathematical problems without specifying other requirements for the problems, whereas the second kind of prompt did specify additional requirements. A total of 2124 students’ responses were analyzed
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Identifying competent problem posers and exploring their characteristics The Journal of Mathematical Behavior Pub Date : 2023-09-01 Ling Zhang, Andreas J. Stylianides, Gabriel J. Stylianides
In a study involving 66 masters and 60 sixth-grade students, we conducted Principal Component Analysis to identify more-and-less competent problem posers based on performance criteria rather than, as in prior research, relying on participants’ mathematical experience or background. Also, to cast light on characteristics of competent posers, we explored possible patterns in the problem-posing process
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Middle school students at three stages of units coordination learn to make same speeds The Journal of Mathematical Behavior Pub Date : 2023-08-26 Amy J. Hackenberg, Fetiye Aydeniz-Temizer, Rebecca S. Borowski
A classroom study was conducted to understand how 18 seventh-grade students at three stages of units coordination constructed ways to make two cars travel the same speed as part of a unit on proportional reasoning co-taught by the first author and classroom teacher. Students at all three stages developed an understanding of how distance and time affected speed. However, when determining how to make
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Secondary-school teachers’ noticing of aspects of mathematics teaching talk in the context of one-day workshops The Journal of Mathematical Behavior Pub Date : 2023-08-11 Núria Planas, José M. Alfonso
In a research project with one-day teacher education workshops for secondary-school mathematics teachers, our study explores the potential of tool-supported discussions in helping them to notice important and critical aspects of mathematics teaching talk. Mathematical practices of naming and explaining in teaching talk, students’ content learning challenges, and noticing processes of identifying, interpreting
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Exploring affordances and limitations of between-group movement in elementary mathematics classrooms The Journal of Mathematical Behavior Pub Date : 2023-08-03 Tye G. Campbell, Sheunghyun Yeo, Erin Rich, Mindy Green
In this exploratory study, we examine how between-group movement, as an autonomy-promoting practice, might incentivize or disincentivize sixth-grade students’ engagement in two mathematical practices: (1) making sense of problems and persevering in solving them; and (2) constructing viable arguments and critiquing the reasoning of others. Between-group movement refers to a pedagogical strategy wherein
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Classroom interactions that shape the nature of students’ appropriation of a complex mathematical practice The Journal of Mathematical Behavior Pub Date : 2023-08-03 John Gruver, Casey Hawthorne
Scholars continue to emphasize the importance of fostering proficiency with mathematical practices as an educational outcome. As teachers attempt to support students in developing these practices, they communicate subtle messages about their nature. However, researchers lack a detailed understanding of the classroom interactions that communicate these messages. To begin to address this gap in the literature
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An inspiring career in mathematics education research: A tribute to Carolyn A. Maher The Journal of Mathematical Behavior Pub Date : 2023-07-27 Gerald Goldin, Keith Weber, Elizabeth Uptegrove
Abstract not available
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An updated conceptualization of the intuition construct for mathematics education research The Journal of Mathematical Behavior Pub Date : 2023-07-06 Jessi Lajos
To improve instruction, conduct communicable studies on student intuition, and provide an entry point for researchers interested in this area, the meaning of intuition in mathematics education needs to be addressed. This paper reviews 816 journal papers from top tier mathematics education journals to obtain an updated conceptualization of the intuition construct. Different research camps, such as a
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Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle The Journal of Mathematical Behavior Pub Date : 2023-06-30 Hollylynne S. Lee, Hamid Sanei, Lisa Famularo, Jessica Masters, Laine Bradshaw, Madeline Schellman
Assessing students’ conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by teachers to inform instruction demands the use of familiar
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Using algorithmic thinking to design algorithms: The case of critical path analysis The Journal of Mathematical Behavior Pub Date : 2023-06-13 Timothy H. Lehmann
Algorithmic thinking is emerging as an important competence in mathematics education, yet research appears to be lagging this shift in curricular focus. The aim of this generative study is to examine how students use the cognitive skills of algorithmic thinking to design algorithms. Task-based interviews were conducted with four pairs of Year 12 students (n = 8) to analyze how they used decomposition
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Geometry, groceries, and gardens: Learning mathematics and social justice through a nested, equity-directed instructional approach The Journal of Mathematical Behavior Pub Date : 2023-06-10 Francesf K. Harper, Queshonda J. Kudaisi
We addressed the call for explorations of how BIPOC students’ “experiences in secondary mathematics classrooms might advance transformative, equity-focused, pedagogical models” (Joseph et al., 2019, p. 149) by exploring how a nested, equity-directed approach created different kinds of opportunities for students to take up, shift, or resist what it means to teach, learn, and do mathematics. Specifically
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Examining and conceptualizing the relationship between teacher praise and the co-construction of mathematical competence in classrooms The Journal of Mathematical Behavior Pub Date : 2023-06-01 Kathy Liu Sun, Jennifer L. Ruef
In this study we examined how teacher praise varies across and within four middle school mathematics classrooms in relationship to mathematical competence. We then conceptualized how teacher praise contributes to the co-construction of normative identity: the class’ shared understanding of what counts as being a competent learner in a mathematics classroom. Findings revealed teachers rarely used person-based
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Students’ development of mathematical meanings while participating vicariously in conversations between other students in instructional videos The Journal of Mathematical Behavior Pub Date : 2023-05-30 Joanne Lobato, John Gruver, Michael Foster
Although interest in using videos in educational settings has surged in recent years, researchers know little about what mathematical meanings students develop from watching these videos or how they do so. To contribute to this gap in the research, we examined how two students appropriated mathematical meanings from instructional videos. In contrast to typical instructional videos, which rely heavily
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Proof construction and in-process validation – Validation activities of undergraduates in constructing mathematical proofs The Journal of Mathematical Behavior Pub Date : 2023-05-09 Katharina Kirsten, Gilbert Greefrath
Proof construction and proof validation are two situations of high importance in mathematical teaching and research. While both situations have usually been studied separately, the current study focuses on possible intersections. Based on research on acceptance criteria and validation strategies, 11 undergraduates’ proof construction processes are investigated in terms of the effective and non-effective
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Measuring interaction quality in mathematics instruction: How differences in operationalizations matter methodologically The Journal of Mathematical Behavior Pub Date : 2023-04-29 Kim Quabeck, Kirstin Erath, Susanne Prediger
Quality of interaction can enhance or constrain students’ mathematical learning opportunities. However, quantitative video studies have measured the quality of interaction with very heterogeneous conceptualizations and operationalizations. This project sought to disentangle typical methodological choices to assess interaction quality in six quality dimensions, each of them in task-based, move-based
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Prospective teachers’ unified understandings of the structure of identities The Journal of Mathematical Behavior Pub Date : 2023-04-25 Kaitlyn Stephens Serbin
United States curriculum standards advise mathematics teachers to teach students to attend to structure and understand how mathematical concepts are related. This requires teachers to have a structural perspective and a coherent, unified understanding of mathematical structures that span curricula. This study explores Prospective Secondary Mathematics Teachers’ (PSMTs) unified understandings of identities
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Describing critical statistical literacy habits of mind The Journal of Mathematical Behavior Pub Date : 2023-04-25 Nina G. Bailey, Allison W. McCulloch
Given the vast number of data representations that people encounter daily, it is imperative that people become critical consumers of the representations they will face. This requires the development of particular habits of mind. The purpose of this paper is to share the critical statistical literacy habits of mind framework. We articulate how we drew on the literature related to statistical literacy
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Leveraging interdiscursivity to support elementary students in bridging the empirical-deductive gap: the case of parity The Journal of Mathematical Behavior Pub Date : 2023-04-21 Joanne Knox, Igor’ Kontorovich
Research has recognized deductive reasoning as challenging but not impossible for young mathematics learners. In this paper, we present a learning environment developed to assist elementary-school students to bridge the empirical-deductive gap in the context of parity of numbers. Using the commognitive framework, we construe the empirical-deductive gap as part of a broader divide between two discourses
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Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning The Journal of Mathematical Behavior Pub Date : 2023-03-06 Paul Christian Dawkins, Kyeong Hah Roh, Derek Eckman
This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the relationships between predicates within the conditional statements and inference structures among various proofs (in
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Enhancing students’ fraction magnitude knowledge: A study with students in early elementary education The Journal of Mathematical Behavior Pub Date : 2023-03-05 Arthur B. Powell
The idea of magnitude is central to understanding fractional numbers. To investigate this relationship, we implemented a design research project in an urban school in the northeast of the US to examine the potential of a measuring perspective and the mathematical notion of fraction-of-quantity to enhance second-grade students’ conceptual understanding of fraction magnitude. We used ideas from the history
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Examining preservice teachers’ noticing of equity-based teaching practices to empower students engaging in productive struggle The Journal of Mathematical Behavior Pub Date : 2023-03-03 Hiroko K. Warshauer, Christin Herrera, Shawnda Smith, Christina Starkey
Our study examined ways preservice teachers (PSTs) make connections between teaching practices and use of student resources that support productive struggle and promote equity. Our research questions are: (1) How do PSTs notice and describe the equity-based mathematics teaching practice of leveraging student resources to support student struggles? and (2) In what ways do PSTs make connections to and
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A learning trajectory for university students regarding the concept of vector The Journal of Mathematical Behavior Pub Date : 2023-03-01 Armando Cuevas-Vallejo, José Orozco-Santiago, Sofía Paz-Rodríguez
This paper presents and evaluates a hypothetical learning trajectory by which students bridge the transition from elementary to university-level instruction regarding the concept of vector. The trajectory consists of an instructional sequence of five tasks and begins with a problem in context. Each task is carried out with the support of a Virtual Interactive Didactic Scenario, accompanied by exploration
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Investigating two teachers’ development of combinatorial meaning for algebraic structure The Journal of Mathematical Behavior Pub Date : 2023-02-24 Lori J. Burch
This paper reports on the results of a four-day teaching experiment that supported two algebra teachers to develop a combinatorial meaning for algebraic structure. The purpose of the teaching episodes was to support the teachers (a) to establish a combinatorial understanding for algebraic structure (Tillema & Burch, 2022) by generalizing the cubic identity, a+b3=a3+3a2b+3ab2+b3, as a symbolization
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Teachers creating mathematical models to fairly distribute school funding The Journal of Mathematical Behavior Pub Date : 2023-02-22 Hyunyi Jung, Megan H. Wickstrom
Our study aims to investigate what teachers do as they draw on their mathematical understanding and personal experiences to engage in social justice-oriented mathematical modeling. We analyze what ideas were expressed by teachers regarding their mathematical identities while they explore, wrestle with, and reconcile the underlying societal values that support mathematical models. We invited groups
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Does collaborative and experiential work influence the solution of real-context estimation problems? A study with prospective teachers The Journal of Mathematical Behavior Pub Date : 2023-02-20 C. Segura, I. Ferrando, L. Albarracín
Although it is a challenge for primary school teachers, real-context estimation problems can be used as an introduction to mathematical modeling. With this aim, we designed a two-phase activity: in the first phase, 224 prospective teachers developed individual action plans to solve a sequence of real-context estimation problems in the classroom; in the second phase, they completed the solution of the
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Spatial visualization and measurement of area: A case study in spatialized mathematics instruction The Journal of Mathematical Behavior Pub Date : 2023-02-16 Danielle Harris, Tracy Logan, Tom Lowrie
The purpose of this study was to explore the influence of spatial visualization skills when students solve area tasks. Spatial visualization is closely related to mathematics achievement, but little is known about how these skills link to task success. We examined middle school students’ representations and solutions to area problems (both non-metric and metric) through qualitative and quantitative
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Is it a function? Generalizing from single- to multivariable settings The Journal of Mathematical Behavior Pub Date : 2023-02-10 Allison Dorko
Generalizing is a hallmark of mathematical thinking. The term ‘generalization’ is used to mean both the process of generalizing and the product of that process. This paper reports on five calculus students’ generalizing activity and what they generalized about multivariable functions. The study makes two contributions. The first is a fine-grained, actor-oriented characterization of the ways undergraduates
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Values in preservice mathematics teachers’ discussions of the Body Mass Index - A critical perspective The Journal of Mathematical Behavior Pub Date : 2023-02-08 Suela Kacerja, Cyril Julie
This article explores the values that come to the fore when preservice mathematics teachers (PTs) 1 engage in critical discussions about the role of mathematical models in society. The specific model that was discussed was the Body Mass Index (BMI) 2. From the analysis of the PTs’ discussions of the BMI from a mathematical and societal point of view several mathematical and mathematics educational
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Teacher time out as a site for studying mathematical knowledge for teaching The Journal of Mathematical Behavior Pub Date : 2023-02-01 Reidar Mosvold, Kjersti Wæge, Janne Fauskanger
The special mathematical knowledge that is needed for teaching has been studied for decades but the methods for studying it have challenges. Some methods, such as measurement and cognitive interviews, are removed from the dynamics of teaching. Other methods, such as observation, are closer to practice but mostly involve an outsider perspective. Moreover, few methods tap into the tacit and often invisible
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Enhancing language-responsive meaning-making processes as an epistemic catalyst for developing multiplicative reasoning in young children The Journal of Mathematical Behavior Pub Date : 2023-01-31 Daniela Götze, Annica Baiker
Multiplicative reasoning involves the ability to coordinate bundled units on a more abstract level (“unitizing”; Lamon, 1994). As it is considered a “cutoff point” for students’ future mathematical learning, teachers must provide equitable access to mathematical conceptual understanding for all students on all mathematical achievement levels. The study presented in this paper investigates to what extent
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An examination of pre-service mathematics teachers’ ethical reasoning in big data with considerations of access to data The Journal of Mathematical Behavior Pub Date : 2023-01-25 Christian H. Andersson, Jordan T. Register
Implementations of Big Data analysis are reshaping society. The novel ways mathematics operate in society warrants new efforts for mathematics education, both in teaching the new technology and in providing an ethical and critical awareness of its implications. This interview study investigates pre-service teachers' ethical reasoning in data science contexts, focusing on aspects of access to the data
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What is the Mathematics in Mathematics Education? The Journal of Mathematical Behavior Pub Date : 2023-01-24 Eva Thanheiser
In this paper I tackle the question What is the mathematics in mathematics education? By providing three different frames for the word mathematics. 1. Frame 1: Mathematics as an abstract body of knowledge/ideas, the organization of that into systems and structures, and a set of methods for reaching conclusions. 2. Frame 2: Mathematics as contextual, ever present, as a lens or language to make sense
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The stories we tell: Why unpacking narratives of mathematics is important for teacher conocimiento The Journal of Mathematical Behavior Pub Date : 2023-01-17 Rochelle Gutiérrez, Marrielle Myers, Kari Kokka
This article articulates how mathematics (e.g., what they are, how they can be used, who they are by and for, who is able to do and understand them) are a social construct, just like racial or gender identities are social constructs. The authors describe how Political Conocimiento in Teaching Mathematics–a relational knowing that involves the entanglement of mathematics, pedagogies, students, and politics–can
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Characterizing prospective secondary teachers’ foundation and contingency knowledge for definitions of transformations The Journal of Mathematical Behavior Pub Date : 2023-01-11 Yvonne Lai, Alyson E. Lischka, Jeremy F. Strayer, Kingsley Adamoah
One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in the work of teaching. We argue that the dimensions of Rowland's (2013) Knowledge Quartet, especially Foundation and Contingency, form a fruitful framework