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The impact of kinesthetic instructional strategies and manipulatives on fourth grader’s self-efficacy and self-confidence toward multiplication Mathematical Thinking and Learning (IF 1.383) Pub Date : 2024-04-15 Jennie M. Carr, Kirby Schoephoerster, Caitlin Riegel
Self-efficacy and self-confidence are listed as significant contributors to students’ general attitudes and performance in mathematics. Having negative beliefs toward mathematics is commonplace for...
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Structure recognition and generalization by second-graders in direct and inverse forms of a linear function Mathematical Thinking and Learning (IF 1.383) Pub Date : 2024-03-07 María D. Torres González, María C. Cañadas, Antonio Moreno
Within the context of the functional approach inherent in early algebra education, this paper reports the structures recognized and the generalizations shown by second-grade students (aged 7–8 year...
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Critical mathematics education Mathematical Thinking and Learning (IF 1.383) Pub Date : 2024-03-08 Laurie H. Rubel
Published in Mathematical Thinking and Learning (Ahead of Print, 2024)
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How numbers influence students when solving linear equations Mathematical Thinking and Learning (IF 1.383) Pub Date : 2024-02-21 Anna Holmlund
Most students need to learn to solve equations as a part of their education, but far from all succeed. In this study we investigate the potential impact of variation in the choice of numbers as coe...
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Does the Use of Concept Maps Affect the Defining and the Understanding of Inclusion Relationships? Mathematical Thinking and Learning (IF 1.383) Pub Date : 2024-02-05 Aehsan Haj Yahya, Areej Mahameed, Hussam Arisha Haj Yahya
The current study aimed to investigate whether teaching ninth-grade students geometrical concepts using concept maps might affect their ability to identify inclusion relationships between geometric...
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Characteristics of mathematics coaches’ suggestions to teachers Mathematical Thinking and Learning (IF 1.383) Pub Date : 2024-01-06 Julie M. Amador, Ryan Gillespie, Jeffrey Choppin, Cynthia D. Carson
We developed an analytic framework related to the suggestions coaches provided to mathematics teachers as they engaged in content-focused coaching cycles. We analyzed 712 suggestions from nine coac...
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Charles Hohensee and Joanne Lobato (Eds.). Transfer of learning: progressive perspectives for mathematics education and related fields Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-12-29 Daniel Hickey, Tripp Harris, Joshua Quick
Published in Mathematical Thinking and Learning (Ahead of Print, 2023)
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Modern mathematics: an international movement? Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-12-23 Michael N. Fried
Published in Mathematical Thinking and Learning (Ahead of Print, 2023)
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Mathematical tools for real-world applications: a gentle introduction for students and practitioners Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-12-23 Michael N. Fried
Published in Mathematical Thinking and Learning (Vol. 26, No. 2, 2024)
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Young children’s self-initiated pattern-making during free play Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-11-09 Miriam M. Lüken
Young children spontaneously create patterns during play. However, this self-initiated pattern-making has yet to be systematically researched. In particular, the extent of self-initiated pattern-ma...
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Examining the effects of an intervention on mathematical modeling in problem solving at upper elementary grades: a cluster randomized trial study Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-10-28 Yiannis Charalambous, Charalambos Y. Charalambous
Although mathematical modeling during problem solving has attracted increased scholarly interest, existing quantitative work in this field has largely concentrated on secondary and tertiary educati...
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The relationship between number talks and ambitious instruction: learning from beginning teachers Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-10-16 Byungeun Pak, Jillian M. Cavanna, Brent E. Jackson
Number talks offer one way for beginning teachers to engage in ambitious instruction (Lampert et al., 2010) that fosters students’ conceptual understanding. This paper explores: (1) features of the...
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Students’ participation in mathematics in inclusive classrooms: a study of the enacted mathematical and relational knowing of teachers Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-09-21 Malin Gardesten, Hanna Palmér
Given the need to increase equity in mathematics education, this study draws on earlier research connecting the mathematical and relational knowing of teachers to determine how such combined knowin...
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The role of contextual knowledge in noticing students’ strategies in-the-moment Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-07-24 Michael Jarry-Shore, Hilda Borko
ABSTRACT If students are to pursue the mathematical strategies they devise, teachers must be able to notice these strategies in-the-moment, attending to what a student did and interpreting what they understand. Otherwise, teachers might urge students to pursue a different approach. Novice teachers may find it particularly challenging to notice strategies in-the-moment as they have had few opportunities
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Noticing for Equity in Written Work: Exploring One Teacher’s Student Work Analysis Practices Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-06-29 Miriam S. Leshin
ABSTRACT Attending to students’ thinking and using it to inform instruction has been shown to be an effective and equitable teaching practice. Research on teachers’ noticing of thinking conceptualizes noticing as a cognitive process, while work on noticing for equity treats noticing as culturally situated but primarily focuses on participation. Drawing on theories of noticing thinking and noticing
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“Tia was the right one:” mathematical authority and trust among first graders Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-05-20 Bárbara Brizuela, Susanne Strachota, Sophia Raymond, Sofía Savid, Maria Blanton
ABSTRACT Questions regarding the construction of mathematical authority haveimplications for learning, specifically for students’ views of themselves as mathematics learners and doers with valuable contributions. We consider the ideas proposed by eight first-grade students who had the most airtime during 12 lessons of a classroom teaching experiment.We noted when ideas were proposed and how those ideas
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Counting the stars: advancing mathematical activity in a scripting journey Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-05-01 Andrew Kercher, Anna Marie Bergman, Rina Zazkis
ABSTRACT Research indicates that investigating phenomena, rather than reproducing facts, should be a core experience in the education of prospective mathematics teachers. Corresponding with its centrality to quality teacher education, there are multiple existing methodologies for analyzing the effects of investigation tasks on teachers’ mathematical development. In this study, we demonstrate the potential
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Vygotskian hybridizing of motion and mapping: Learning about geometric transformations in block-based programming environments Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-03-23 Jesús E. Hernández-Zavaleta, Corey Brady, Sandra Becker, Douglas B. Clark
ABSTRACT Research on geometric transformations suggests that early learners possess intuitive understandings grounded in motion metaphors, transitioning to mappings. The processes through which students transition between these two conceptions are not fully understood. We propose that Vygotskian hybridizing (related to Vygotsky’s articulation of everyday and scientific concepts) may provide a lens
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Promoting elements of mathematical knowledge for teaching related to the notion of assumptions Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-02-22 Gabriel J. Stylianides, Andreas J. Stylianides
ABSTRACT Although the notion of assumptions is important in mathematical activity as early as the elementary school, there is limited research on how to help elementary teachers develop mathematical knowledge for teaching related to assumptions. In this paper, we discuss the theoretical foundation and implementation of an intervention that aimed to promote three key elements of this knowledge among
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A game-based approach to promoting adaptive rational number knowledge Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-02-20 Jake McMullen, Antti Koskinen, Tomi Kärki, Antero Lindstedt, Saku Määttä, Hilma Halme, Erno Lehtinen, Minna M. Hannula-Sormunen, Kristian Kiili
ABSTRACT Adaptive expertise is a highly sought after, but difficult to achieve, outcome of mathematics education. Many teaching methods appear to support the development of adaptive expertise only in a small proportion of students. Game-based learning environments may be useful for supporting adaptive expertise. Therefore, we carried out a quasi-experimental classroom intervention to examine the possibility
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Modeling Actions Foregrounded in Whole-Class Modeling Discourse: A Case Study of a Model-Eliciting Activity and a Three-Act Task Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-02-20 Hyunyi Jung, Corey Brady
Abstract In this article, we investigated how a class engaged in whole-class discussions of modeling solutions, across two different types of modeling tasks: a Model Eliciting Activity (MEA) and a Three-Act Task. We analyzed whole-class discourse as small groups presented and responded to each other’s solutions to a MEA and a Three-Act Task. We have also analyzed how the teacher team used these tasks
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Design principles for simulation-based learning of hypothesis testing in secondary school Mathematical Thinking and Learning (IF 1.383) Pub Date : 2023-01-02 Per Nilsson, Andreas Eckert
ABSTRACT This study contributes to the call for influencing practice by increasing attention to how learning environments can be designed to support learning in statistical inference. We report on a design experiment in secondary school (students 14–16 years old), that resulted in a set of lessons with the learning goal of teaching students how to apply concepts and principles of hypothesis testing
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Editorial Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-12-01 Lyn D. English
Published in Mathematical Thinking and Learning (Vol. 25, No. 1, 2023)
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Understanding the nature of arithmetical concepts–important content for the education of primary mathematics teachers Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-10-22 Martin A. Simon
ABSTRACT For teachers to be effective in promoting understanding of mathematical concepts, they need to understand the nature of mathematical concepts. However, to date, the mathematics education literature has not focused on this important area of teacher understanding. One reason that attention to this issue has been lacking is that the term “mathematical concept” has generally been used with little
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The learning and teaching of number. Paths less travelled through well-trodden terrain Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-09-28 Anna Baccaglini-Frank
Published in Mathematical Thinking and Learning (Vol. 24, No. 4, 2022)
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Interpreting literal symbols in algebra under the effects of the natural number bias Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-09-27 Konstantinos P. Christou, Despoina Ioanna Kyrvei, Xenia Vamvakoussi
ABSTRACT In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural numbers only rather than for any rational or real
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Developing ‘deep mathematical thinking’ in geometry with 3- and 4-year-olds: a collaborative study between early years teachers and university-based mathematicians Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-09-06 Rachel Oughton, Kathryn Nichols, David S Bolden, Sarah Dixon-Jones, Sam Fearn, Sophia Darwin, Mrita Mistry, Norbert Peyerimhoff, Adam Townsend
ABSTRACT Mathematics in early years settings is often restricted to learning to count and identifying simple shapes. This is partly due to the narrow scope of many early years curricula and insufficient teacher training for exploring deeper mathematical concepts. We note that geometry is an area particularly neglected. In an innovative year-long project, a group of university-based mathematicians and
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Teacher-student interaction supporting students’ creative mathematical reasoning during problem solving using Scratch Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-07-31 Jan Olsson, Carina Granberg
ABSTRACT Studies have shown that learning mathematics through programming can be complex and that the programming itself might even hamper students’ learning. However, few studies have focused on the role of the teacher and the teacher-student interaction that aims to support students’ learning when using programming. The present study examines a didactic design in which a teacher uses well-prepared
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Third grade students’ multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-07-14 Unni Wathne, Martin Carlsen
ABSTRACT The aim of this study is to investigate Norwegian primary school students’ multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8–9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as count-all and grouping. These approaches were
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Elements of instruction that motivate students with learning disabilities to learn fractions Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-06-17 Kristie J. Newton, Amanda Jansen, Peter Puleo
ABSTRACT Despite the documented influence of motivation on mathematics learning for most students, we understand far less about this relation for students identified with learning disabilities. Based on Rogoff’s three planes of analysis (i.e., personal, community, and interpersonal), we gathered survey, interview, and video data to understand the motivations of sixth graders in a special education
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Secondary mathematics teachers’ use of students’ incorrect answers in supporting collective argumentation Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-04-26 Yuling Zhuang, AnnaMarie Conner
This study illustrates how two secondary mathematics teachers used students’ incorrect answers as they supported students’ engagement in collective argumentation. Three ways of supporting argumenta...
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Sequencing & selecting solutions in a gendered world Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-04-15 Laurie H. Rubel, Michal Ayalon, Juhaina A. Shahbari
Whole-class discussions in mathematics are envisioned as spaces for the sharing of ideas and making connections among them. We pursue how Palestinian/Arab Israeli teachers consider making use of mu...
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The complexity of supporting reasoning in a mathematics classroom of shared authority Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-04-09 Kristin Krogh Arnesen, Kirsti Rø
The paper addresses the potential relationships between shared authority in mathematics classrooms and students’ mathematical reasoning. Even though tensions and challenges related to shared author...
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Progressions in young learners’ understandings of parity arguments Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-04-08 Maria Blanton, Angela Murphy Gardiner, Ingrid Ristroph, Ana Stephens, Eric Knuth, Rena Stroud
Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characte...
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Preschool children’s repeating patterning skills: evidence of their capability from a large scale, naturalistic, Australia wide study Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-03-27 Kevin Larkin, Ilyse Resnick, Thomas Lowrie
Patterns are a fundamental component of mathematics, and the patterning ability of young children has been well researched; however, this research has largely been conducted with relatively small c...
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Differences in grade 7 students’ understanding of the equal sign Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-03-26 Lovisa Sumpter, Anna Löwenhielm
This paper studies grade 7 (age 13) students’ expressed understanding about the equal sign/notion of equivalence in order to investigate what aspects of the concept that could be seen as an establi...
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Models and Modelling: The Fine Balance between Mathematics, Practice, and Research Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-03-25 Michael N. Fried
(2022). Models and Modelling: The Fine Balance between Mathematics, Practice, and Research. Mathematical Thinking and Learning: Vol. 24, No. 2, pp. 176-180.
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Backward transfer, the relationship between new learning and prior ways of reasoning, and action versus process views of linear functions Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-02-16 Charles Hohensee, Laura Willoughby, Sara Gartland
Backward transfer is defined as the influence that new learning has on individuals’ prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that qua...
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Authenticity of elementary teacher designed and implemented mathematical modeling tasks Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-01-20 Erin E. Turner, Amy Been Bennett, Monica Granillo, Nishaan Ponnuru, Amy Roth Mcduffie, Mary Q. Foote, Julia M. Aguirre, Elzena McVicar
Mathematical modeling is a high-leverage topic; it is critical to students’ participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary lev...
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Elementary students’ fraction reasoning: a measurement approach to fractions in a dynamic environment Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-01-10 Sheunghyun Yeo, Corey Webel
In this study, we examine students’ mathematical reasoning within a technological environment designed to support understanding of relationships between quantities with adjustable measuring units. ...
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Randomness and probability: exploring student teachers’ conceptions Mathematical Thinking and Learning (IF 1.383) Pub Date : 2022-01-06 Jenni Ingram
Understanding randomness is essential for modern life, as it underpins decisions under uncertainty. It is also an essential part of both the mathematics and science curricula in schools. Yet, resea...
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Care in mathematics education: alternative educational spaces and practices Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-12-31 Tim Rowland
Published in Mathematical Thinking and Learning (Vol. 26, No. 1, 2024)
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Modeling the phenomenon versus modeling the data set Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-12-28 Gloria Ann Stillman, Jill P. Brown
ABSTRACT This paper investigates students’ mathematical modeling activity in data-rich modeling tasks. It aims at gaining insight into how students develop meaning when modeling data-rich situations and the mathematical models produced. A tendency to model a particular dataset, rather than the phenomenon that the dataset is a particular instance of, has been observed previously. Students concentrate
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Does strategic knowledge matter? Effects of strategic knowledge about drawing on students’ modeling competencies in the domain of geometry Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-12-28 Johanna Rellensmann, Stanislaw Schukajlow, Judith Blomberg, Claudia Leopold
We investigated how students’ strategic knowledge about situational (pictorial) drawings and mathematical (schematic) drawings affects drawing accuracy and modeling competencies in the domain of ge...
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Metacognition in mathematical modeling: the connection between metacognitive individual strategies, metacognitive group strategies and modeling competencies Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-12-09 Katrin Vorhölter
ABSTRACT There are several conceptualizations of modeling competencies, including among others on the one hand so-called sub-competencies, which are required to progress from one step of a modeling process to the next, and metacognitive individual and group strategies. However, the relationship between metacognitive strategies and modeling sub-competencies remains unclear, as does the influence of
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Mathematical thinking about systems – students modeling a biometrics identity verification system Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-12-08 Ana Margarida Baioa, Susana Carreira
ABSTRACT The aim of this study is to understand how students’ mathematical thinking is activated and nurtured in solving a modeling problem, where the problem situation involves the design of a system. From a STEM integrated perspective, 9th grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The theoretical framework proposes a conceptualization
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Modeling from a cognitive perspective: theoretical considerations and empirical contributions Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-12-04 Stanislaw Schukajlow, Gabriele Kaiser, Gloria Stillman
ABSTRACT Mathematical modeling and applications are an important part of curriculum and considered to be important for students’ current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the current thinking on modeling activities and
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Construction of the cardinality principle through counting: critique and conjecture Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-12-02 Martin A. Simon, Daniela Della Volpe, Arundhati Velamur
Development of the cardinality principle, an understanding that the last number-word recited in counting a collection of items specifies the number of items in that collection, is a critical milest...
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Embodied learning at a distance: from sensory-motor experience to constructing and understanding a sine graph Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-11-16 Anna Shvarts, Gitte van Helden
Educational technologies develop quickly. Which functions of face-to-face education can be substituted by technology for distance learning? One of the risks of online education is the lack of embod...
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Learning mathematics as occasioned by disturbance Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-10-24 John Mason
Published in Mathematical Thinking and Learning (Vol. 25, No. 4, 2023)
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Learning through explaining and engaging with others’ mathematical ideas Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-10-17 Noreen M. Webb, Megan L. Franke, Nicholas C. Johnson, Marsha Ing, Joy Zimmerman
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 ...
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Radford’s theory of objectification: a cultural-historical theory of learning, knowing, and becoming Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-09-29 Michael N. Fried
Published in Mathematical Thinking and Learning (Vol. 25, No. 4, 2023)
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Kindergarten students’ mathematics knowledge at work: the mathematics for programming robot toys Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-09-29 Jessica F. Shumway, Lise E. Welch, Joseph S. Kozlowski, Jody Clarke-Midura, Victor R. Lee
The purpose of this study was to explore how kindergarten students (aged 5–6 years) engaged with mathematics as they learned programming with robot coding toys. We video-recorded 16 teaching sessio...
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Professional noticing coherence: exploring relationships between component processes Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-09-22 Jonathan Thomas, David Dueber, Molly H. Fisher, Cindy Jong, Edna O. Schack
Teacher noticing and related variants have ascended in prominence among the mathematics education research community. While the component processes of such noticing (e.g., attending, interpreting a...
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Spatial training using game play in preschoolers improves computational skills Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-08-27 Sharlene D. Newman, Erin Loughery, Ambur Ecklund, Marriah Smothers, Jefney Ongeri
ABSTRACT Previous studies have found that block play results in better spatial ability which may lead to greater mathematical skills. The current study examined a specific type of block play, structured block play in which a copy of a block configuration is constructed. Structured block play is a difficult cognitive task that requires an understanding of spatial relations, hand-eye coordination, and
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Between expert and student perspectives: on the intersection of affect and heuristic-didactic discourse in the undergraduate classroom Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-08-25 Ofer Marmur, Boris Koichu
ABSTRACT This paper explores student emotion and learning experiences fostered by lecturing-style instruction in Real-Analysis problem-centered lessons. We focus on two lessons that were taught by two reputable instructors and involved challenging, mathematically-related problems the students did not understand. Nonetheless, one lesson evoked negative emotional reactions, while the other positive emotional
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Connecting mathematical modeling and social justice through problem posing Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-08-14 Hyunyi Jung, Marta T. Magiera
ABSTRACT This paper contributes to accumulating the knowledge base about prospective elementary school teachers’ (PTs’) understanding of socio-critical modeling by exploring how PTs make connections to features of mathematical modeling and social justice while posing mathematical problems and reflecting on their problem-posing. We present a conceptual framework for posing problems that connect social
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Undergraduate students’ interpretations of expressions from calculus statements within the graphical register Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-07-26 Erika David Parr
ABSTRACT The purpose of this study is to investigate how students interpret expressions from calculus statements in the graphical register. To this end, I conducted 150-minute clinical interviews with 13 undergraduate mathematics students who had completed at least one calculus course. In the interviews, students evaluated six calculus statements for various real-valued functions depicted in graphs
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A contemporary theory of mathematics education research Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-07-19 Stephen Lerman
Published in Mathematical Thinking and Learning (Vol. 25, No. 1, 2023)
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Examining how middle grade mathematics students seize learning opportunities through conflict in small groups Mathematical Thinking and Learning (IF 1.383) Pub Date : 2021-07-05 Tye Campbell
ABSTRACT Understanding how students develop learning opportunities through peer-to-peer interaction is vital for advancing research and practice on collaborative learning environments. This study investigated the discourse practices middle grade students utilized to resolve conflict in ways that promoted or inhibited learning opportunities. Seventy-seven middle grade students were audio/video recorded