Johnna Bolyard - Academia.edu (original) (raw)
Papers by Johnna Bolyard
Canadian journal of science, mathematic and technology education/Canadian journal of science, mathematics and technology education, Feb 3, 2024
The purpose of this phenomenological research study was to examine the phenomenon of living throu... more The purpose of this phenomenological research study was to examine the phenomenon of living through struggle while learning mathematics on the part of pre-service elementary teachers. We elicited lived-experience descriptions and interviews from 46 participants enrolled in an elementary teacher education program over the course of two years. We chose to focus on struggle, as one of the research-based teaching practices recommends that teachers of mathematics engage their students in "productive" struggle. We argue that opening up an understanding of the variant ways struggle manifests in learning informs the work of teacher educators; namely, it supports our understanding of how these lived-struggle moments may influence subsequent perspectives of mathematics and mathematics teaching and learning preservice teachers may bring with them. We end by considering the ways in which teacher educators can leverage this understanding of lived-struggle to support continued growth, such as drawing on these experiences to engage pre-service teachers in a critical examination of mathematics teaching and learning.
... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... R... more ... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... Recommended Citation. Bolyard, JJ, & Moyer, PS (2003). Investigations in algebra with virtualmanipulatives. ON-Math, Online Journal of School Mathematics, 2(2), 1-10. ...
The purpose of this phenomenological research study was to examine the phenomenon of living throu... more The purpose of this phenomenological research study was to examine the phenomenon of living through struggle while learning mathematics on the part of pre-service elementary teachers. We elicited lived-experience descriptions and interviews from 46 participants enrolled in an elementary teacher education program over the course of two years. We chose to focus on struggle, as one of the research-based teaching practices recommends that teachers of mathematics engage their students in "productive" struggle. We argue that opening up an understanding of the variant ways struggle manifests in learning informs the work of teacher educators; namely, it supports our understanding of how these lived-struggle moments may influence subsequent perspectives of mathematics and mathematics teaching and learning preservice teachers may bring with them. We end by considering the ways in which teacher educators can leverage this understanding of lived-struggle to support continued growth, such as drawing on these experiences to engage pre-service teachers in a critical examination of mathematics teaching and learning.
Choice Reviews Online, 2011
ON-Math, Online …, 2003
... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... R... more ... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... Recommended Citation. Bolyard, JJ, & Moyer, PS (2003). Investigations in algebra with virtualmanipulatives. ON-Math, Online Journal of School Mathematics, 2(2), 1-10. ...
Proceedings of the 2020 AERA Annual Meeting
Professional Development in Education
This study analysed elementary mathematics specialists’ stories of work to examine how these disc... more This study analysed elementary mathematics specialists’ stories of work to examine how these disciplinary-specific teacher leaders engage in their practice. This paper examines the ways in which el...
Mathematics Teaching in the Middle School, 2012
An analysis of food choices becomes a rich data-driven lesson set in a real-world context.
Abstract: This mixed method study compared mathematics achievement and conceptual understanding i... more Abstract: This mixed method study compared mathematics achievement and conceptual understanding in 6 sixth-grade classrooms. A total of 99 students learned integer addition and subtraction concepts using one of three different virtual manipulatives designed for integer instruction. The ...
Journal for Research in Mathematics Education, 2019
Past experiences as mathematics learners play a critical role in the way mathematics teachers con... more Past experiences as mathematics learners play a critical role in the way mathematics teachers consider what it means to know, do, and teach mathematics. Thus, understanding past experiences and ways to work with them in teacher education is a critical concern. Using phenomenological inquiry, we investigated moments of shift that occur along one's mathematics journey. The study draws on 30 prospective teachers' experiences in the form of lived-experience writing and interview data. Findings show that prospective teachers' shifts manifest in relations with others, across different time frames, and through material relations with mathematics. Most salient was the tentative and mutable nature of shifts, showing that shift might be better viewed as a possibility rather than a single event.
Proceedings of the 2022 AERA Annual Meeting
Mathematics Teaching in the Middle School, 2013
Students access the THINK framework that involves prompts exploring talk, how, identify, notice, ... more Students access the THINK framework that involves prompts exploring talk, how, identify, notice, and keep.
This study was a comprehensive examination of the use of mathematics manipulative materials by a ... more This study was a comprehensive examination of the use of mathematics manipulative materials by a group of K-8 teachers identified as knowledgeable and experienced mathematics manipulative users. Because the teachers in this study were knowledgeable and experienced, the inquiry focused what mathematics materials the teachers chose to use. Analysis of over 500 lesson summaries from 116 K-8 teachers indicated that there were three common mathematics materials used by K-8 teachers who are knowledgeable and experienced manipulative users (dice, pattern blocks and snap cubes). The results support previous research showing that frequency of manipulative use declines from grades K through 8. In addition, the results revealed that the variety of manipulative used by teachers in this project also decreased across grades K through 8. An additional difference among the grade-specific groups was the way that teachers used the mathematics materials in their lessons, with Grades K-2 and 3-4 teache...
Contemporary Issues in …, 2008
This study examined teachers' uses of virtual manipulatives across grades K-8 after particip... more This study examined teachers' uses of virtual manipulatives across grades K-8 after participating in a professional development institute in which manipulatives and technology were the major resources used throughout all of the activities. Researchers analyzed 95 lesson ...
This study was a comprehensive examination of the use of mathematics manipulative materials by a ... more This study was a comprehensive examination of the use of mathematics manipulative materials by a group of K-8 teachers identified as knowledgeable and experienced mathematics manipulative users. Because the teachers in this study were knowledgeable and experienced, the inquiry focused what mathematics materials the teachers chose to use. Analysis of over 500 lesson summaries from 116 K-8 teachers indicated that there were three common mathematics materials used by K-8 teachers who are knowledgeable and experienced manipulative users (dice, pattern blocks and snap cubes). The results support previous research showing that frequency of manipulative use declines from grades K through 8. In addition, the results revealed that the variety of manipulative used by teachers in this project also decreased across grades K through 8. An additional difference among the grade-specific groups was the way that teachers used the mathematics materials in their lessons, with Grades K-2 and 3-4 teache...
From their earliest arithmetic experiences, students develop mental models conducive to algebraic... more From their earliest arithmetic experiences, students develop mental models conducive to algebraic thinking. Teachers can nourish this development by providing well-structured activities that use visual and tactile clues and cues to promote thinking. Experiences that allow students to recognize patterns and to represent and communicate their thinking through a variety of forms—verbal, concrete, pictorial, virtual, and symbolic—set the stage for later, more sophisticated representations such as tables, graphs, and equations. Using the algebraic concept of direct variation, this paper (a) describes how developmentally appropriate activities can be used across the grades to help students arrive at and communicate mental models, (b) provides specific examples of these investigations along a developmental continuum, and (c) discusses how this concept translates among various representational forms. Developing Algebraic Thinking through Representation From students’ earliest experiences in...
The purpose of this instrumental case study was to examine pre-service teachers’ (PSTs) reflectio... more The purpose of this instrumental case study was to examine pre-service teachers’ (PSTs) reflections on mathematics teaching and learning as it relates to the practice of supporting productive struggle. The research team created a framework aligning instructional features/teacher strategies that support productive struggle with related perspectives, organizing these by classroom culture/environment, treatment of content, and communication to support reasoning. The current analysis reports on PSTs perspectives related specifically to classroom culture/environment. Findings show the variant ways in which PSTs perspectives are both aligned and misaligned as well as considerations for leveraging these perspectives in mathematics teacher education.
Canadian journal of science, mathematic and technology education/Canadian journal of science, mathematics and technology education, Feb 3, 2024
The purpose of this phenomenological research study was to examine the phenomenon of living throu... more The purpose of this phenomenological research study was to examine the phenomenon of living through struggle while learning mathematics on the part of pre-service elementary teachers. We elicited lived-experience descriptions and interviews from 46 participants enrolled in an elementary teacher education program over the course of two years. We chose to focus on struggle, as one of the research-based teaching practices recommends that teachers of mathematics engage their students in "productive" struggle. We argue that opening up an understanding of the variant ways struggle manifests in learning informs the work of teacher educators; namely, it supports our understanding of how these lived-struggle moments may influence subsequent perspectives of mathematics and mathematics teaching and learning preservice teachers may bring with them. We end by considering the ways in which teacher educators can leverage this understanding of lived-struggle to support continued growth, such as drawing on these experiences to engage pre-service teachers in a critical examination of mathematics teaching and learning.
... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... R... more ... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... Recommended Citation. Bolyard, JJ, & Moyer, PS (2003). Investigations in algebra with virtualmanipulatives. ON-Math, Online Journal of School Mathematics, 2(2), 1-10. ...
The purpose of this phenomenological research study was to examine the phenomenon of living throu... more The purpose of this phenomenological research study was to examine the phenomenon of living through struggle while learning mathematics on the part of pre-service elementary teachers. We elicited lived-experience descriptions and interviews from 46 participants enrolled in an elementary teacher education program over the course of two years. We chose to focus on struggle, as one of the research-based teaching practices recommends that teachers of mathematics engage their students in "productive" struggle. We argue that opening up an understanding of the variant ways struggle manifests in learning informs the work of teacher educators; namely, it supports our understanding of how these lived-struggle moments may influence subsequent perspectives of mathematics and mathematics teaching and learning preservice teachers may bring with them. We end by considering the ways in which teacher educators can leverage this understanding of lived-struggle to support continued growth, such as drawing on these experiences to engage pre-service teachers in a critical examination of mathematics teaching and learning.
Choice Reviews Online, 2011
ON-Math, Online …, 2003
... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... R... more ... TEaL Faculty Publications. Title. Investigations in Algebra with Virtual Manipulatives. ... Recommended Citation. Bolyard, JJ, & Moyer, PS (2003). Investigations in algebra with virtualmanipulatives. ON-Math, Online Journal of School Mathematics, 2(2), 1-10. ...
Proceedings of the 2020 AERA Annual Meeting
Professional Development in Education
This study analysed elementary mathematics specialists’ stories of work to examine how these disc... more This study analysed elementary mathematics specialists’ stories of work to examine how these disciplinary-specific teacher leaders engage in their practice. This paper examines the ways in which el...
Mathematics Teaching in the Middle School, 2012
An analysis of food choices becomes a rich data-driven lesson set in a real-world context.
Abstract: This mixed method study compared mathematics achievement and conceptual understanding i... more Abstract: This mixed method study compared mathematics achievement and conceptual understanding in 6 sixth-grade classrooms. A total of 99 students learned integer addition and subtraction concepts using one of three different virtual manipulatives designed for integer instruction. The ...
Journal for Research in Mathematics Education, 2019
Past experiences as mathematics learners play a critical role in the way mathematics teachers con... more Past experiences as mathematics learners play a critical role in the way mathematics teachers consider what it means to know, do, and teach mathematics. Thus, understanding past experiences and ways to work with them in teacher education is a critical concern. Using phenomenological inquiry, we investigated moments of shift that occur along one's mathematics journey. The study draws on 30 prospective teachers' experiences in the form of lived-experience writing and interview data. Findings show that prospective teachers' shifts manifest in relations with others, across different time frames, and through material relations with mathematics. Most salient was the tentative and mutable nature of shifts, showing that shift might be better viewed as a possibility rather than a single event.
Proceedings of the 2022 AERA Annual Meeting
Mathematics Teaching in the Middle School, 2013
Students access the THINK framework that involves prompts exploring talk, how, identify, notice, ... more Students access the THINK framework that involves prompts exploring talk, how, identify, notice, and keep.
This study was a comprehensive examination of the use of mathematics manipulative materials by a ... more This study was a comprehensive examination of the use of mathematics manipulative materials by a group of K-8 teachers identified as knowledgeable and experienced mathematics manipulative users. Because the teachers in this study were knowledgeable and experienced, the inquiry focused what mathematics materials the teachers chose to use. Analysis of over 500 lesson summaries from 116 K-8 teachers indicated that there were three common mathematics materials used by K-8 teachers who are knowledgeable and experienced manipulative users (dice, pattern blocks and snap cubes). The results support previous research showing that frequency of manipulative use declines from grades K through 8. In addition, the results revealed that the variety of manipulative used by teachers in this project also decreased across grades K through 8. An additional difference among the grade-specific groups was the way that teachers used the mathematics materials in their lessons, with Grades K-2 and 3-4 teache...
Contemporary Issues in …, 2008
This study examined teachers' uses of virtual manipulatives across grades K-8 after particip... more This study examined teachers' uses of virtual manipulatives across grades K-8 after participating in a professional development institute in which manipulatives and technology were the major resources used throughout all of the activities. Researchers analyzed 95 lesson ...
This study was a comprehensive examination of the use of mathematics manipulative materials by a ... more This study was a comprehensive examination of the use of mathematics manipulative materials by a group of K-8 teachers identified as knowledgeable and experienced mathematics manipulative users. Because the teachers in this study were knowledgeable and experienced, the inquiry focused what mathematics materials the teachers chose to use. Analysis of over 500 lesson summaries from 116 K-8 teachers indicated that there were three common mathematics materials used by K-8 teachers who are knowledgeable and experienced manipulative users (dice, pattern blocks and snap cubes). The results support previous research showing that frequency of manipulative use declines from grades K through 8. In addition, the results revealed that the variety of manipulative used by teachers in this project also decreased across grades K through 8. An additional difference among the grade-specific groups was the way that teachers used the mathematics materials in their lessons, with Grades K-2 and 3-4 teache...
From their earliest arithmetic experiences, students develop mental models conducive to algebraic... more From their earliest arithmetic experiences, students develop mental models conducive to algebraic thinking. Teachers can nourish this development by providing well-structured activities that use visual and tactile clues and cues to promote thinking. Experiences that allow students to recognize patterns and to represent and communicate their thinking through a variety of forms—verbal, concrete, pictorial, virtual, and symbolic—set the stage for later, more sophisticated representations such as tables, graphs, and equations. Using the algebraic concept of direct variation, this paper (a) describes how developmentally appropriate activities can be used across the grades to help students arrive at and communicate mental models, (b) provides specific examples of these investigations along a developmental continuum, and (c) discusses how this concept translates among various representational forms. Developing Algebraic Thinking through Representation From students’ earliest experiences in...
The purpose of this instrumental case study was to examine pre-service teachers’ (PSTs) reflectio... more The purpose of this instrumental case study was to examine pre-service teachers’ (PSTs) reflections on mathematics teaching and learning as it relates to the practice of supporting productive struggle. The research team created a framework aligning instructional features/teacher strategies that support productive struggle with related perspectives, organizing these by classroom culture/environment, treatment of content, and communication to support reasoning. The current analysis reports on PSTs perspectives related specifically to classroom culture/environment. Findings show the variant ways in which PSTs perspectives are both aligned and misaligned as well as considerations for leveraging these perspectives in mathematics teacher education.