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Papers by Sean Yee

International Journal of Research in Undergraduate Mathematics Education

The purpose of this paper is to investigate students’ contextualization of problem solving, not t... more The purpose of this paper is to investigate students’ contextualization of problem solving, not the problems. This study draws on the naturalistic paradigm and uses a developmental perspective to explore students’ representations and metaphors used during problem solving. Students of comparable abilities employed similar representations, tended to use analogous metaphors during problem solving, and perceived solutions as outside of a problem’s context

School Science and Mathematics, 2022

The Mathematics Teacher, 2016

A three-step instructional sequence gives students authority to judge an argument's veracity ... more A three-step instructional sequence gives students authority to judge an argument's veracity by developing class-based criteria for proof.

The Journal of Mathematical Behavior, 2014

This paper investigates how students contextualize mathematical problem solving, not the actual p... more This paper investigates how students contextualize mathematical problem solving, not the actual problems. When students attempt to solve problems, what contexts (situational, cultural, or conceptual) do they evoke to describe their experiences with problem solving? The Common Core State Standards for Mathematical Practice emphasize contextualizing and decontextualizing problems, but what does this mean in practice? Middle and high school students were asked to attempt ability-appropriate problems during semi-structured interviews in this qualitative study. Situational contexts were analyzed using representation analysis (symbolic and nonsymbolic) while cultural contexts were analyzed using linguistic analysis (metaphors). The synergy of these two analyses developed a coherent and consistent conceptual contextualization for mathematical problem solving. Secondary students conceptualized problems as containers with the given information within the problem and solutions outside the problem. Thus students' representations are a means to travel from within the problem to outside of the problem.

Journal for Research in Mathematics Education, 2013

Mathematics Teacher (MT) invites classroom teachers to explore research findings in relation to t... more Mathematics Teacher (MT) invites classroom teachers to explore research findings in relation to their practice and submit manuscripts to the Connecting Research to Teaching department in MT.

School Science and Mathematics

Investigations in Mathematics Learning, 2018

Teaching methods courses are a crucial factor in the preparation of secondary mathematics teacher... more Teaching methods courses are a crucial factor in the preparation of secondary mathematics teachers. Throughout the United States, secondary methods courses have diverse curricula, including variation in the topics covered in these courses. To assess this variation, the authors identified 41 topics potentially valued by secondary methods instructors, referred to here as touchstones. The set of touchstones was revised based on peer feedback and was used as the basis of a survey administered to 116 secondary mathematics teaching methods instructors from different U.S. universities. The survey asked respondents to determine the value they placed on each touchstone. Simple means and standard deviations were calculated, and variations by instructors’ departments (mathematics or education) and levels of professorship (i.e., assistant, associate, and full) were examined using analysis of variance (ANOVA). Results indicated which touchstones were highly valued and which touchstones were not....

International Group for the Psychology of Mathematics Education, 2016

Fifty-seven students in mathematical content and secondary mathematics methods courses from four ... more Fifty-seven students in mathematical content and secondary mathematics methods courses from four U.S. universities participated in an instructional sequence to generate communal criteria defining mathematical proof within their respective classrooms. Participants completed a proof-related task before class, worked together in small groups to evaluate instructor-selected arguments, communally agreed upon criteria for evaluating a proof based on their evaluations, and then revised their original argument to meet the communal criteria after class. Similar criteria were constructed across the four classrooms. Moreover, the four authors coded and compared students’ initial and revised arguments with respect to proof schemes to identify specific shifts in students’ work after the instructional sequence. Results indicated a majority of students’ proof schemes changed in their revised argument with specific trends aligning with their class-based criteria for proof.

International Group for the Psychology of Mathematics Education, 2015

Mathematics teacher education has been criticized, both internally and externally, for failing to... more Mathematics teacher education has been criticized, both internally and externally, for failing to identify shared practices and goals within teacher preparation programs. Work has begun to address this criticism at the elementary level but less exists at the secondary level. This paper reports on a national survey with responses from 116 secondary mathematics methods course instructors from colleges and universities. The purpose of the survey was to identify those topics, or “touchstones,” in secondary methods courses that are widely valued. The survey asked participants to rank 41 potential “touchstones” of secondary mathematics methods courses on a scale from one to five according to those touchstones they value most in their methods courses. The results were quantitatively and qualitatively analyzed looking for important characteristics that would spur discussion about shared goals in secondary teacher preparation.

The purpose of this paper is to investigate students' contextualization of problem solving, not t... more The purpose of this paper is to investigate students' contextualization of problem solving, not the problems. This study draws on the naturalistic paradigm and uses a developmental perspective to explore students' representations and metaphors used during problem solving. Students of comparable abilities employed similar representations, tended to use analogous metaphors during problem solving, and perceived solutions as outside of a problem's context.

To develop graduate student instructors’ (GSIs) skills and abilities as collegiate mathematics in... more To develop graduate student instructors’ (GSIs) skills and abilities as collegiate mathematics instructors, researchers at two universities implemented a peer-mentorship model where experienced GSIs completed a 15-week professional development (PD) to learn how to mentor novice GSIs in teaching undergraduate mathematics. Using pre-survey, post-survey, and semistructured reflective interviews, we studied changes in 11 mentor GSIs’ perspectives on teaching and learning practices and what aspects of the mentor PD were deemed valuable by the mentors. Results suggest that this mentor PD, as a peer-mentorship model, helped GSIs deconstruct the dichotic mathematical paradigm of statements being true or false when discussing teaching. Moreover, mentor GSIs valued how the mentor PD helped guide them to facilitate novice GSI post-observation discussions.

Journal of Mathematics Teacher Education

Mathematics Teacher: Learning and Teaching PK-12

As mathematical patterns become more complex, students' conditional reasoning skills need to ... more As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

International Journal of Research in Undergraduate Mathematics Education

This paper presents the development and validation of the 17-item mathematics Graduate Student In... more This paper presents the development and validation of the 17-item mathematics Graduate Student Instructor Observation Protocol (GSIOP) at two universities. The development of this instrument attended to some unique needs of novice undergraduate mathematics instructors while building on an existing instrument that focused on classroom interactions particularly relevant for students’ development of conceptual understanding, called the Mathematical Classroom Observation Protocol for Practices (MCOP2). Instrument validation involved content input from mathematics education researchers and upper-level mathematics graduate student instructors at two universities, internal consistency analysis, interrater reliability analysis, and structure analyses via scree plot analysis and exploratory factor analysis. A Cronbach-Alpha level of 0.868 illustrated a viable level for internal consistency. Crosstabulation and correlations illustrate high level of interrater reliability for all but one item,...

The Journal of Mathematical Behavior

International Journal of Research in Undergraduate Mathematics Education

The purpose of this paper is to investigate students’ contextualization of problem solving, not t... more The purpose of this paper is to investigate students’ contextualization of problem solving, not the problems. This study draws on the naturalistic paradigm and uses a developmental perspective to explore students’ representations and metaphors used during problem solving. Students of comparable abilities employed similar representations, tended to use analogous metaphors during problem solving, and perceived solutions as outside of a problem’s context

School Science and Mathematics, 2022

The Mathematics Teacher, 2016

A three-step instructional sequence gives students authority to judge an argument's veracity ... more A three-step instructional sequence gives students authority to judge an argument's veracity by developing class-based criteria for proof.

The Journal of Mathematical Behavior, 2014

This paper investigates how students contextualize mathematical problem solving, not the actual p... more This paper investigates how students contextualize mathematical problem solving, not the actual problems. When students attempt to solve problems, what contexts (situational, cultural, or conceptual) do they evoke to describe their experiences with problem solving? The Common Core State Standards for Mathematical Practice emphasize contextualizing and decontextualizing problems, but what does this mean in practice? Middle and high school students were asked to attempt ability-appropriate problems during semi-structured interviews in this qualitative study. Situational contexts were analyzed using representation analysis (symbolic and nonsymbolic) while cultural contexts were analyzed using linguistic analysis (metaphors). The synergy of these two analyses developed a coherent and consistent conceptual contextualization for mathematical problem solving. Secondary students conceptualized problems as containers with the given information within the problem and solutions outside the problem. Thus students' representations are a means to travel from within the problem to outside of the problem.

Journal for Research in Mathematics Education, 2013

Mathematics Teacher (MT) invites classroom teachers to explore research findings in relation to t... more Mathematics Teacher (MT) invites classroom teachers to explore research findings in relation to their practice and submit manuscripts to the Connecting Research to Teaching department in MT.

School Science and Mathematics

Investigations in Mathematics Learning, 2018

Teaching methods courses are a crucial factor in the preparation of secondary mathematics teacher... more Teaching methods courses are a crucial factor in the preparation of secondary mathematics teachers. Throughout the United States, secondary methods courses have diverse curricula, including variation in the topics covered in these courses. To assess this variation, the authors identified 41 topics potentially valued by secondary methods instructors, referred to here as touchstones. The set of touchstones was revised based on peer feedback and was used as the basis of a survey administered to 116 secondary mathematics teaching methods instructors from different U.S. universities. The survey asked respondents to determine the value they placed on each touchstone. Simple means and standard deviations were calculated, and variations by instructors’ departments (mathematics or education) and levels of professorship (i.e., assistant, associate, and full) were examined using analysis of variance (ANOVA). Results indicated which touchstones were highly valued and which touchstones were not....

International Group for the Psychology of Mathematics Education, 2016

Fifty-seven students in mathematical content and secondary mathematics methods courses from four ... more Fifty-seven students in mathematical content and secondary mathematics methods courses from four U.S. universities participated in an instructional sequence to generate communal criteria defining mathematical proof within their respective classrooms. Participants completed a proof-related task before class, worked together in small groups to evaluate instructor-selected arguments, communally agreed upon criteria for evaluating a proof based on their evaluations, and then revised their original argument to meet the communal criteria after class. Similar criteria were constructed across the four classrooms. Moreover, the four authors coded and compared students’ initial and revised arguments with respect to proof schemes to identify specific shifts in students’ work after the instructional sequence. Results indicated a majority of students’ proof schemes changed in their revised argument with specific trends aligning with their class-based criteria for proof.

International Group for the Psychology of Mathematics Education, 2015

Mathematics teacher education has been criticized, both internally and externally, for failing to... more Mathematics teacher education has been criticized, both internally and externally, for failing to identify shared practices and goals within teacher preparation programs. Work has begun to address this criticism at the elementary level but less exists at the secondary level. This paper reports on a national survey with responses from 116 secondary mathematics methods course instructors from colleges and universities. The purpose of the survey was to identify those topics, or “touchstones,” in secondary methods courses that are widely valued. The survey asked participants to rank 41 potential “touchstones” of secondary mathematics methods courses on a scale from one to five according to those touchstones they value most in their methods courses. The results were quantitatively and qualitatively analyzed looking for important characteristics that would spur discussion about shared goals in secondary teacher preparation.

The purpose of this paper is to investigate students' contextualization of problem solving, not t... more The purpose of this paper is to investigate students' contextualization of problem solving, not the problems. This study draws on the naturalistic paradigm and uses a developmental perspective to explore students' representations and metaphors used during problem solving. Students of comparable abilities employed similar representations, tended to use analogous metaphors during problem solving, and perceived solutions as outside of a problem's context.

To develop graduate student instructors’ (GSIs) skills and abilities as collegiate mathematics in... more To develop graduate student instructors’ (GSIs) skills and abilities as collegiate mathematics instructors, researchers at two universities implemented a peer-mentorship model where experienced GSIs completed a 15-week professional development (PD) to learn how to mentor novice GSIs in teaching undergraduate mathematics. Using pre-survey, post-survey, and semistructured reflective interviews, we studied changes in 11 mentor GSIs’ perspectives on teaching and learning practices and what aspects of the mentor PD were deemed valuable by the mentors. Results suggest that this mentor PD, as a peer-mentorship model, helped GSIs deconstruct the dichotic mathematical paradigm of statements being true or false when discussing teaching. Moreover, mentor GSIs valued how the mentor PD helped guide them to facilitate novice GSI post-observation discussions.

Journal of Mathematics Teacher Education

Mathematics Teacher: Learning and Teaching PK-12

As mathematical patterns become more complex, students' conditional reasoning skills need to ... more As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.

International Journal of Research in Undergraduate Mathematics Education

This paper presents the development and validation of the 17-item mathematics Graduate Student In... more This paper presents the development and validation of the 17-item mathematics Graduate Student Instructor Observation Protocol (GSIOP) at two universities. The development of this instrument attended to some unique needs of novice undergraduate mathematics instructors while building on an existing instrument that focused on classroom interactions particularly relevant for students’ development of conceptual understanding, called the Mathematical Classroom Observation Protocol for Practices (MCOP2). Instrument validation involved content input from mathematics education researchers and upper-level mathematics graduate student instructors at two universities, internal consistency analysis, interrater reliability analysis, and structure analyses via scree plot analysis and exploratory factor analysis. A Cronbach-Alpha level of 0.868 illustrated a viable level for internal consistency. Crosstabulation and correlations illustrate high level of interrater reliability for all but one item,...

The Journal of Mathematical Behavior