Kristin Lesseig | Washington State University (original) (raw)

Papers by Kristin Lesseig

Investigations in Mathematics Learning

Despite the recognized importance of mathematical proof in secondary education, there is a limite... more Despite the recognized importance of mathematical proof in secondary education, there is a limited but growing body of literature indicating how preservice secondary mathematics teachers (PSMTs) view proof and the teaching of proof. The purpose of this survey research was to investigate how PSMTs in Australia and the United States perceive of proof in the context of secondary mathematics teaching and learning. PSMTs were able to outline various mathematical and pedagogical aspects of proof, including: purposes, characteristics, reasons for teaching, and imposed constraints. In addition, PSMTs attended to differing, though overlapping, features of proof when asked to determine the extent to which proposed arguments constituted proofs or to decide which arguments they might present to students

Journal of pedagogical research, Apr 20, 2022

The goal of this paper is to share an analytic framework for understanding Students" Ways of Thin... more The goal of this paper is to share an analytic framework for understanding Students" Ways of Thinking (SWoT) in STEM-rich learning environments. Before revealing our refined coding framework, we detail the nature of our collaborations and the various analytic decisions that led to its formation. These collaborations supported our collective ability to make sense of SWoT and produce a more coherent perspective that can be operationalized in STEM contexts. Our analytic framework foregrounds student claim-making and the related evidence and reasoning used in support. Specific commentary about the development and application of each coding category is provided, including examples of student data and rationale for related coding decisions. Our analytic framework, and discussion of its formation, can help educators, curriculum makers, and policymakers make use of SWoT in the development of meaningful and effective STEM education.

School Science and Mathematics, 2021

AERA Online Paper Repository, Apr 30, 2017

Research in Mathematics Education, 2022

International Journal of Mathematical Education in Science and Technology, 2021

Despite the recognized importance of mathematical proof in secondary education, there is a limite... more Despite the recognized importance of mathematical proof in secondary education, there is a limited but growing body of literature indicating how preservice secondary mathematics teachers (PSMTs) view proof and the teaching of proof. The purpose of this survey research was to explore PSMTs' knowledge and beliefs about proof and proof teaching in the context of secondary mathematics teaching and learning. Six cases (PSMTs' survey responses) were purposively selected from an entire data set comprising participants from the United States and Australia. Using a situative learning perspective as the theoretical framework, the authors developed a sensible belief system (Leatham, 2006) for sampled PSMTs and inductively conceptualized how their knowledge of and orientations toward proof acted as a function of their teaching and learning contexts. Furthermore, an analysis of data revealed that PSMTs' knowledge and beliefs about proof are multifaceted, dynamic and evolving as they engage with proof in their various contexts.

2017 IEEE Frontiers in Education Conference (FIE), 2017

This work-in-progress studies empathy in middle-school engineering design pedagogy. A model of em... more This work-in-progress studies empathy in middle-school engineering design pedagogy. A model of empathy in engineering as a core skill, as a practice orientation and a professional way of being that can be taught in university programs has been proposed [1]. Does an emotional intelligence model of empathy need to be taught earlier than at the university level? The engineering design process has been included in the science standards for k-12 schools since 2013[2]. One of the purposes of this inclusion is the ability to reach a diverse population of students by applying real world problems in their curriculum. The design process typically includes the steps of defining the engineering problem, developing solutions and optimizing the design. Although the word “empathy” is not used, these problems are defined from an empathetic perspective as “situations people want to change” of “social and global significance.” However, the standards do not discuss how to define a problem or how to teach empathy. In the winter of 2016 a study was conducted to evaluate the influence of empathy-based lessons on girls' interest in science, technology, engineering and mathematics (STEM). Some information is known about empathy in lessons. Girls may be more interested if lessons are altered to include an element of caring [3]. Other studies indicate children's empathy increases with type of media provided in lesson (computer versus robot) [4]. The study in this article was a qualitative case study of 50 children, grades 6, 7, and 8, boys and girls in an after-school 4-H Science Club. The lessons were conducted once per week. The lessons were previously conducted in an all-girls after-school STEM program with similar available inexpensive materials. Both schools had similar demographics. The students and coordinators(instructors) were observed, pre- and post-surveys were conducted, and interviews of both students and coordinators were audio and/or video-taped. Although responses varied by lesson, initial results indicate many students and coordinators did not understand the meaning of empathy situated in engineering design.

Proof is too abstract for this age group 0 3 3 T-KNOW Teachers may not have the knowledge and ski... more Proof is too abstract for this age group 0 3 3 T-KNOW Teachers may not have the knowledge and skills necessary to teach proof 1 2 3 Part II Proof Evaluation The purpose of Part II in the survey was to determine the extent to which PSMTs felt that proposed arguments constituted a proof, and ascertain the features of proof to which PSMTs attended. Participants attended to a variety of features in describing why they felt a proposed argument constituted a proof or identifying what they felt was missing in the argument. The most common rationales provided were in relation to whether (or not) the arguments proved the statement in general (i.e. they covered all cases within the domain), were based on accepted statements or theorems, and followed a logical structure, aligning with the top five characteristics of proof outlined in Part I of the survey. To a lesser degree, participants argued (in the affirmative or the negative) that the proofs were error-free and were easy to follow or unde...

This study documents teachers' productions of algebraic generalizations and justification... more This study documents teachers' productions of algebraic generalizations and justification that draw on specialized content knowledge (SCK) for teaching. Examining the entailments of teachers' productions developing SCK in professional development (PD) is essential to advance research on teacher knowledge used in teaching. Twenty teachers' productions of two tasks were analyzed. Results show that teachers' productions examined mathematical relationships and structures to explain generalizations that were both mathematically valid and beyond reproach in the teacher community. Further, productions elaborated key mathematical practices drawing on and developing SCK. Implications of this research are ways of working in PD to advance teachers' SCK.

The Journal of Effective Teaching, 2012

This study describes the development and validation of an instrument to measure graduate teaching... more This study describes the development and validation of an instrument to measure graduate teaching assistants’ (GTAs) learning about teaching during professional development. In the pilot study, exploratory factor analysis of data from 239 graduate students indicates a single factor structure. The second study, involving 177 science, technology, engineering, and mathematics (STEM) GTAs, confirms the single factor structure of the instrument. The instrument is highly reliable with both populations. The instrument is correlated to the hours STEM GTAs spend in professional development and their self-efficacy in teaching. It is sensitive to departmental differences between GTAs perceptions of their professional development. This instrument has multiple possible users including university faculty involved in GTA professional development as well as educational researchers. University faculty can use it for needs assessment during GTA program development, comparisons among departmental prog...

Research suggests that the enhanced role of proof in mathematics classrooms presented in current ... more Research suggests that the enhanced role of proof in mathematics classrooms presented in current standards and reform policy poses great challenges for teachers and will require substantial teacher learning. However, to date there is little research detailing what mathematical knowledge might be useful for teaching proof or how professional development might afford such learning. This paper presents a framework for Mathematical Knowledge for Teaching Proof that couples research on justification and proof in mathematics and mathematics education with Ball and colleagues' (2008) conceptualization of Mathematical Knowledge for Teaching (MKT). An empirical study of teachers' proof-related activity in professional development demonstrates the utility of this framework and provides further insights into mathematical knowledge for teaching proof.

In the era of standards-based reforms, informal teacher leadership is a critical factor in realiz... more In the era of standards-based reforms, informal teacher leadership is a critical factor in realizing instructional improvement. In this paper, we report on data from a one-year study of four early career mathematics teachers engaging in professional development around Common Core mathematical practices and leadership. Our findings highlight how the professional development structure supported the development of early career teachers’ leader identity. Through iterative opportunities to participate in two communities of practice (within the professional development setting and in school-based professional learning communities) early career teachers were able to engage in collegial conversations and imagine themselves taking on new roles and responsibilities in order to support the learning of the teachers with whom they worked.

International Journal for mathematics teaching and learning, 2016

The purpose of this study was to detail teachers’ proving activity and contribute to a framework ... more The purpose of this study was to detail teachers’ proving activity and contribute to a framework of Mathematical Knowledge for Teaching Proof (MKT for Proof). While working to justify claims about sums of consecutive numbers, teachers searched for key ideas and productively used examples to make, test and refine conjectures. Analysis of teachers’ mathematical activity revealed knowledge of the proving process that would be useful for and useable in the teaching of proof. This includes knowledge of the interconnections among empirical exploration, conjecturing, generalizing, and justifying as well as an understanding of the characteristics of examples and conjectures that could support the proving process. The central premise of this paper is that delineating aspects of teacher knowledge is a first step to supporting teachers’ efforts to engage all students in fundamental mathematical practices of conjecturing, generalizing and justifying.

Mathematics Teacher Education and Development, 2016

Calls to advance students’ ability to engage in mathematical reasoning practices including conjec... more Calls to advance students’ ability to engage in mathematical reasoning practices including conjecturing, generalizing and justifying (CGJ) place significant new demands on teachers. This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote them in the classroom. Findings demonstrate how CGJ readings and focused discussions, coupled with repeated cycles of collaborative lesson planning, observation and debrief, supported the development of teacher knowledge, professional community, and teaching resources. In addition, this paper explores the role school leadership played in facilitating Math Studio to ensure these learning opportunities were realized. Documenting how Math Studio features and participants contributed to teachers’ ability to implement CGJ focused lessons not only provides insights into the difficulties teachers have shifting instruction, but also adds to our un...

International Group for the Psychology of Mathematics Education, 2019

We explore the epistemological issues that arise when considering STEM as a curricular and instru... more We explore the epistemological issues that arise when considering STEM as a curricular and instructional construct. Our approach is somewhat unique in that we are not focused on the curricular or instructional boundaries of STEM education, but consider the nature of the cognitive activity at play during STEM-focused activity, with an emphasis on mathematical thinking. We focus specifically on the epistemological underpinnings of mathematics and other STEM disciplines, and the possibility of an epistemology of STEM as a curricular construct. The im lica ion on den STEM a of hinking (SWoT) a e di c ed in de ail f om a theoretical and empirical lens. Future research directions are identified.

for the learning of mathematics, 2020

Mathematics Teacher Education and Development, 2018

This study examined proposed teacher responses to students’ work to investigate how they respond,... more This study examined proposed teacher responses to students’ work to investigate how they respond, what characteristics of a good response are more difficult than others to achieve, and whether particular student error types are more difficult to respond to appropriately. Sixteen preservice secondary mathematics teachers’ proposed responses to five students’ work to solve linear equations were analysed based on four characteristics of a good response: work toward student learning objective, draw on presented student thinking, draw on research on students’ mathematical development, and leave space for student’s future thinking. The preservice teachers’ responses consistently met the last characteristic, but their skill at meeting the other characteristics differed markedly based on the type of student error in the work sample. An implication is the need to help preservice teachers learn how to address conceptual issues in their responses rather than solely focusing on procedural error...

Investigations in Mathematics Learning

Despite the recognized importance of mathematical proof in secondary education, there is a limite... more Despite the recognized importance of mathematical proof in secondary education, there is a limited but growing body of literature indicating how preservice secondary mathematics teachers (PSMTs) view proof and the teaching of proof. The purpose of this survey research was to investigate how PSMTs in Australia and the United States perceive of proof in the context of secondary mathematics teaching and learning. PSMTs were able to outline various mathematical and pedagogical aspects of proof, including: purposes, characteristics, reasons for teaching, and imposed constraints. In addition, PSMTs attended to differing, though overlapping, features of proof when asked to determine the extent to which proposed arguments constituted proofs or to decide which arguments they might present to students

Journal of pedagogical research, Apr 20, 2022

The goal of this paper is to share an analytic framework for understanding Students" Ways of Thin... more The goal of this paper is to share an analytic framework for understanding Students" Ways of Thinking (SWoT) in STEM-rich learning environments. Before revealing our refined coding framework, we detail the nature of our collaborations and the various analytic decisions that led to its formation. These collaborations supported our collective ability to make sense of SWoT and produce a more coherent perspective that can be operationalized in STEM contexts. Our analytic framework foregrounds student claim-making and the related evidence and reasoning used in support. Specific commentary about the development and application of each coding category is provided, including examples of student data and rationale for related coding decisions. Our analytic framework, and discussion of its formation, can help educators, curriculum makers, and policymakers make use of SWoT in the development of meaningful and effective STEM education.

School Science and Mathematics, 2021

AERA Online Paper Repository, Apr 30, 2017

Research in Mathematics Education, 2022

International Journal of Mathematical Education in Science and Technology, 2021

Despite the recognized importance of mathematical proof in secondary education, there is a limite... more Despite the recognized importance of mathematical proof in secondary education, there is a limited but growing body of literature indicating how preservice secondary mathematics teachers (PSMTs) view proof and the teaching of proof. The purpose of this survey research was to explore PSMTs' knowledge and beliefs about proof and proof teaching in the context of secondary mathematics teaching and learning. Six cases (PSMTs' survey responses) were purposively selected from an entire data set comprising participants from the United States and Australia. Using a situative learning perspective as the theoretical framework, the authors developed a sensible belief system (Leatham, 2006) for sampled PSMTs and inductively conceptualized how their knowledge of and orientations toward proof acted as a function of their teaching and learning contexts. Furthermore, an analysis of data revealed that PSMTs' knowledge and beliefs about proof are multifaceted, dynamic and evolving as they engage with proof in their various contexts.

2017 IEEE Frontiers in Education Conference (FIE), 2017

This work-in-progress studies empathy in middle-school engineering design pedagogy. A model of em... more This work-in-progress studies empathy in middle-school engineering design pedagogy. A model of empathy in engineering as a core skill, as a practice orientation and a professional way of being that can be taught in university programs has been proposed [1]. Does an emotional intelligence model of empathy need to be taught earlier than at the university level? The engineering design process has been included in the science standards for k-12 schools since 2013[2]. One of the purposes of this inclusion is the ability to reach a diverse population of students by applying real world problems in their curriculum. The design process typically includes the steps of defining the engineering problem, developing solutions and optimizing the design. Although the word “empathy” is not used, these problems are defined from an empathetic perspective as “situations people want to change” of “social and global significance.” However, the standards do not discuss how to define a problem or how to teach empathy. In the winter of 2016 a study was conducted to evaluate the influence of empathy-based lessons on girls' interest in science, technology, engineering and mathematics (STEM). Some information is known about empathy in lessons. Girls may be more interested if lessons are altered to include an element of caring [3]. Other studies indicate children's empathy increases with type of media provided in lesson (computer versus robot) [4]. The study in this article was a qualitative case study of 50 children, grades 6, 7, and 8, boys and girls in an after-school 4-H Science Club. The lessons were conducted once per week. The lessons were previously conducted in an all-girls after-school STEM program with similar available inexpensive materials. Both schools had similar demographics. The students and coordinators(instructors) were observed, pre- and post-surveys were conducted, and interviews of both students and coordinators were audio and/or video-taped. Although responses varied by lesson, initial results indicate many students and coordinators did not understand the meaning of empathy situated in engineering design.

Proof is too abstract for this age group 0 3 3 T-KNOW Teachers may not have the knowledge and ski... more Proof is too abstract for this age group 0 3 3 T-KNOW Teachers may not have the knowledge and skills necessary to teach proof 1 2 3 Part II Proof Evaluation The purpose of Part II in the survey was to determine the extent to which PSMTs felt that proposed arguments constituted a proof, and ascertain the features of proof to which PSMTs attended. Participants attended to a variety of features in describing why they felt a proposed argument constituted a proof or identifying what they felt was missing in the argument. The most common rationales provided were in relation to whether (or not) the arguments proved the statement in general (i.e. they covered all cases within the domain), were based on accepted statements or theorems, and followed a logical structure, aligning with the top five characteristics of proof outlined in Part I of the survey. To a lesser degree, participants argued (in the affirmative or the negative) that the proofs were error-free and were easy to follow or unde...

This study documents teachers' productions of algebraic generalizations and justification... more This study documents teachers' productions of algebraic generalizations and justification that draw on specialized content knowledge (SCK) for teaching. Examining the entailments of teachers' productions developing SCK in professional development (PD) is essential to advance research on teacher knowledge used in teaching. Twenty teachers' productions of two tasks were analyzed. Results show that teachers' productions examined mathematical relationships and structures to explain generalizations that were both mathematically valid and beyond reproach in the teacher community. Further, productions elaborated key mathematical practices drawing on and developing SCK. Implications of this research are ways of working in PD to advance teachers' SCK.

The Journal of Effective Teaching, 2012

This study describes the development and validation of an instrument to measure graduate teaching... more This study describes the development and validation of an instrument to measure graduate teaching assistants’ (GTAs) learning about teaching during professional development. In the pilot study, exploratory factor analysis of data from 239 graduate students indicates a single factor structure. The second study, involving 177 science, technology, engineering, and mathematics (STEM) GTAs, confirms the single factor structure of the instrument. The instrument is highly reliable with both populations. The instrument is correlated to the hours STEM GTAs spend in professional development and their self-efficacy in teaching. It is sensitive to departmental differences between GTAs perceptions of their professional development. This instrument has multiple possible users including university faculty involved in GTA professional development as well as educational researchers. University faculty can use it for needs assessment during GTA program development, comparisons among departmental prog...

Research suggests that the enhanced role of proof in mathematics classrooms presented in current ... more Research suggests that the enhanced role of proof in mathematics classrooms presented in current standards and reform policy poses great challenges for teachers and will require substantial teacher learning. However, to date there is little research detailing what mathematical knowledge might be useful for teaching proof or how professional development might afford such learning. This paper presents a framework for Mathematical Knowledge for Teaching Proof that couples research on justification and proof in mathematics and mathematics education with Ball and colleagues' (2008) conceptualization of Mathematical Knowledge for Teaching (MKT). An empirical study of teachers' proof-related activity in professional development demonstrates the utility of this framework and provides further insights into mathematical knowledge for teaching proof.

In the era of standards-based reforms, informal teacher leadership is a critical factor in realiz... more In the era of standards-based reforms, informal teacher leadership is a critical factor in realizing instructional improvement. In this paper, we report on data from a one-year study of four early career mathematics teachers engaging in professional development around Common Core mathematical practices and leadership. Our findings highlight how the professional development structure supported the development of early career teachers’ leader identity. Through iterative opportunities to participate in two communities of practice (within the professional development setting and in school-based professional learning communities) early career teachers were able to engage in collegial conversations and imagine themselves taking on new roles and responsibilities in order to support the learning of the teachers with whom they worked.

International Journal for mathematics teaching and learning, 2016

The purpose of this study was to detail teachers’ proving activity and contribute to a framework ... more The purpose of this study was to detail teachers’ proving activity and contribute to a framework of Mathematical Knowledge for Teaching Proof (MKT for Proof). While working to justify claims about sums of consecutive numbers, teachers searched for key ideas and productively used examples to make, test and refine conjectures. Analysis of teachers’ mathematical activity revealed knowledge of the proving process that would be useful for and useable in the teaching of proof. This includes knowledge of the interconnections among empirical exploration, conjecturing, generalizing, and justifying as well as an understanding of the characteristics of examples and conjectures that could support the proving process. The central premise of this paper is that delineating aspects of teacher knowledge is a first step to supporting teachers’ efforts to engage all students in fundamental mathematical practices of conjecturing, generalizing and justifying.

Mathematics Teacher Education and Development, 2016

Calls to advance students’ ability to engage in mathematical reasoning practices including conjec... more Calls to advance students’ ability to engage in mathematical reasoning practices including conjecturing, generalizing and justifying (CGJ) place significant new demands on teachers. This case study examines how Mathematics Studio provided opportunities for a team of U.S. middle school teachers to learn about these practices and ways to promote them in the classroom. Findings demonstrate how CGJ readings and focused discussions, coupled with repeated cycles of collaborative lesson planning, observation and debrief, supported the development of teacher knowledge, professional community, and teaching resources. In addition, this paper explores the role school leadership played in facilitating Math Studio to ensure these learning opportunities were realized. Documenting how Math Studio features and participants contributed to teachers’ ability to implement CGJ focused lessons not only provides insights into the difficulties teachers have shifting instruction, but also adds to our un...

International Group for the Psychology of Mathematics Education, 2019

We explore the epistemological issues that arise when considering STEM as a curricular and instru... more We explore the epistemological issues that arise when considering STEM as a curricular and instructional construct. Our approach is somewhat unique in that we are not focused on the curricular or instructional boundaries of STEM education, but consider the nature of the cognitive activity at play during STEM-focused activity, with an emphasis on mathematical thinking. We focus specifically on the epistemological underpinnings of mathematics and other STEM disciplines, and the possibility of an epistemology of STEM as a curricular construct. The im lica ion on den STEM a of hinking (SWoT) a e di c ed in de ail f om a theoretical and empirical lens. Future research directions are identified.

for the learning of mathematics, 2020

Mathematics Teacher Education and Development, 2018

This study examined proposed teacher responses to students’ work to investigate how they respond,... more This study examined proposed teacher responses to students’ work to investigate how they respond, what characteristics of a good response are more difficult than others to achieve, and whether particular student error types are more difficult to respond to appropriately. Sixteen preservice secondary mathematics teachers’ proposed responses to five students’ work to solve linear equations were analysed based on four characteristics of a good response: work toward student learning objective, draw on presented student thinking, draw on research on students’ mathematical development, and leave space for student’s future thinking. The preservice teachers’ responses consistently met the last characteristic, but their skill at meeting the other characteristics differed markedly based on the type of student error in the work sample. An implication is the need to help preservice teachers learn how to address conceptual issues in their responses rather than solely focusing on procedural error...