Lisa B Warner | William Paterson University (original) (raw)

Papers by Lisa B Warner

Research paper thumbnail of Exploring Prospective Mathematics Teachers’ Motivating Desires during Group Problem Solving Activity

Research paper thumbnail of Working with a partner: An investigation of student engagement in an middle school math classroom

Many students work in small groups as they solve mathematical problems. In order for them to bene... more Many students work in small groups as they solve mathematical problems. In order for them to benefit from such experiences, each individual must be engaged, at least to some extent, during the problem solving session. Such engagement may take many forms, and in this paper, we focus on three closely related types of engagement, and discuss them with respect to both cognition and affect. We provide classroom examples of each, including student explanations of their mathematical ideas and reasoning. In addition, we provide qualitative descriptions of quantitative data as gathered in response to questionnaire items. Objective The purpose of this research is to analyze some of the different types of interactions that take place as small groups of students work together to solve mathematical problems. The students in this study attended an urban middle-school in which they were provided with many opportunities to solve complex problems individually and in groups. Several studies on smallgroup work in mathematics classes focus on the outcomes or performance of the students as a consequence of their peer-to-peer interactions (e.g., Cohen, 1994; Webb, 1991; Webb & Mastergeorge, 2003). These studies tend to focus on conditions that lead to more productive group work, such as group configuration (e.g., heterogeneous/homogeneous) (e.g., Hooper & Hannifin, 1988; Swing & Peterson, 1982), the nature of the interactions (e.g., what skills assisted with productive group work) (e.g.

Research paper thumbnail of From primitive knowing to formalising: The role of student-to-student questioning in the development of mathematical understanding

Research paper thumbnail of Measuring engagement structures in middle-grades urban mathematics classrooms

This paper was presented at the 2010 American Educational Research Association (AERA) Conference ... more This paper was presented at the 2010 American Educational Research Association (AERA) Conference in Denver, Colorado.

Research paper thumbnail of Extending and refining models for thinking about division of fractions

This paper was presented at the Twenty-Sixth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

Research paper thumbnail of The Non-mathematical Aspects of Mathematical Problem Solving in Urban Classrooms

You can now view the document associated with this citation by clicking on the "View Documen... more You can now view the document associated with this citation by clicking on the "View Document as HTML" link below. ... This research is part of a larger study that seeks to identify the ways in which the social context influences the mathematical problem solving of a group of ...

Research paper thumbnail of Teacher Development in a Large Urban District and the Impact on Students

Foundations for the Future in Mathematics Education, 2020

Research paper thumbnail of Rutgers University

This study builds on previous research that investigates the nature of engagement as it occurs ‘i... more This study builds on previous research that investigates the nature of engagement as it occurs ‘in the moment ’ in urban classrooms (Goldin, Epstein, Schorr, & Warner, 2011). In this article, we report on a young male student, Eric, who called out an answer in front of all his peers in response to a question posed by the teacher. Almost immediately, his peers challenged his response. Upon hearing their comments, he retorted that he “didn’t care anymore ” and withdrew from the discussion. Nonetheless, moments later he reentered the discussion, reiterating his response. In a later interview, Eric noted that he called out the answer in order to impress others, but felt disrespected when they disagreed. In this examination, we attempt to characterize his reactions with specific reference to his momentary engagement in order to discuss the implications for learning.

Research paper thumbnail of Chapter 4: Engagement Structures and the Development of Mathematical Ideas

Affect in Mathematical Modeling, 2019

We describe the relationship that exists between shifts in engagement and shifts in mathematical ... more We describe the relationship that exists between shifts in engagement and shifts in mathematical thinking, using the construct of engagement structures. The engagement structure construct (Goldin et al. 2011) is a way to account for and describe the complex dynamical interactions that recur as students solve mathematical problems. Our research is focused on a group of eighth grade students solving a problem in a group setting in an urban district. Our analysis involves video-recorded episodes, retrospective interviews and comprehensive field notes. We also document the social conditions present in the classroom that surrounded the shifts. Our findings suggest a variety of changes that can occur within an individual student, and across students in the same classroom, depending upon the social context. At times, changes in mathematical ideas preceded shifts in engagement, and vice-versa. Aside from the within student differences, our research provides an example of how, within the same classroom, students can have very different engagement and mathematical experiences.

Research paper thumbnail of Analyzing Prospective Teachers’ Motivating Desires During Mathematical Problem Solving

ICERI2018 Proceedings, 2018

Research paper thumbnail of Characterizing a middle school student's engagement in a mathematics class

This paper was presented at the Eighth Congress of European Research in Mathematics Education (CE... more This paper was presented at the Eighth Congress of European Research in Mathematics Education (CERME8) in Antalya, Turkey.

Research paper thumbnail of Responding to students’ mathematical thinking when you don’t know how to respond

This paper was presented at the Nineteenth Annual Conference of the Association of Mathematics Te... more This paper was presented at the Nineteenth Annual Conference of the Association of Mathematics Teacher Educators (AMTE), in Orlando, Florida.

Research paper thumbnail of Investigating Students' Movement to Generalization and Abstraction Using Dienes' "Learning Cycle

This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Lake Tahoe, Nevada.

Research paper thumbnail of Clinical interviews & VITAL in an elementary mathematics methods course

Research paper thumbnail of Mathematical truth and social consequences: The intersection of affect and cognition in a middle school classroom

We focus on several groups of eighth grade students in an attempt to deepen our understanding of ... more We focus on several groups of eighth grade students in an attempt to deepen our understanding of when, how, and why middle grade students engage in conceptually challenging mathematics. As part of our analysis, we have formulated the theoretical notion of engagment structures, which is a behavioral/affective/social constellation including characteristic patterns of behavior, indicative of affective pathways and models (structures) that have important cognitive interpretations and implications by the students. We report that students may be willing to abandon arguing for what they know are mathematical truths in order to avoid appearing weak or wrong in front of their peers, and this appears to be linked to the depth of their understanding and their social positioning within their groups.

Research paper thumbnail of Clinical Interviews and VITAL in an Elementary Mathematics Methods Course

Research paper thumbnail of Studying the affective/social dimension of an inner-city mathematics class

… mathematics education in …, 2007

Research paper thumbnail of Student behaviors and ways they are associated with the problem solving process

This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Lake Tahoe, Nevada.

Research paper thumbnail of Student behaviors and ways they are associated with the problem solving process

This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Lake Tahoe, Nevada.

Research paper thumbnail of Being Challenged in an Urban Classroom: A Case Study Documenting the Engagement of a Young Male Who Wanted to ‘Look Smart

Journal of Urban Learning Teaching and Research, Jan 11, 2013

This study builds on previous research that investigates the nature of engagement as it occurs 'i... more This study builds on previous research that investigates the nature of engagement as it occurs 'in the moment' in urban classrooms (Goldin, Epstein, Schorr, & Warner, 2011). In this article, we report on a young male student, Eric, who called out an answer in front of all his peers in response to a question posed by the teacher. Almost immediately, his peers challenged his response. Upon hearing their comments, he retorted that he "didn't care anymore" and withdrew from the discussion. Nonetheless, moments later he reentered the discussion, reiterating his response. In a later interview, Eric noted that he called out the answer in order to impress others, but felt disrespected when they disagreed. In this examination, we attempt to characterize his reactions with specific reference to his momentary engagement in order to discuss the implications for learning.

Research paper thumbnail of Exploring Prospective Mathematics Teachers’ Motivating Desires during Group Problem Solving Activity

Research paper thumbnail of Working with a partner: An investigation of student engagement in an middle school math classroom

Many students work in small groups as they solve mathematical problems. In order for them to bene... more Many students work in small groups as they solve mathematical problems. In order for them to benefit from such experiences, each individual must be engaged, at least to some extent, during the problem solving session. Such engagement may take many forms, and in this paper, we focus on three closely related types of engagement, and discuss them with respect to both cognition and affect. We provide classroom examples of each, including student explanations of their mathematical ideas and reasoning. In addition, we provide qualitative descriptions of quantitative data as gathered in response to questionnaire items. Objective The purpose of this research is to analyze some of the different types of interactions that take place as small groups of students work together to solve mathematical problems. The students in this study attended an urban middle-school in which they were provided with many opportunities to solve complex problems individually and in groups. Several studies on smallgroup work in mathematics classes focus on the outcomes or performance of the students as a consequence of their peer-to-peer interactions (e.g., Cohen, 1994; Webb, 1991; Webb & Mastergeorge, 2003). These studies tend to focus on conditions that lead to more productive group work, such as group configuration (e.g., heterogeneous/homogeneous) (e.g., Hooper & Hannifin, 1988; Swing & Peterson, 1982), the nature of the interactions (e.g., what skills assisted with productive group work) (e.g.

Research paper thumbnail of From primitive knowing to formalising: The role of student-to-student questioning in the development of mathematical understanding

Research paper thumbnail of Measuring engagement structures in middle-grades urban mathematics classrooms

This paper was presented at the 2010 American Educational Research Association (AERA) Conference ... more This paper was presented at the 2010 American Educational Research Association (AERA) Conference in Denver, Colorado.

Research paper thumbnail of Extending and refining models for thinking about division of fractions

This paper was presented at the Twenty-Sixth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

Research paper thumbnail of The Non-mathematical Aspects of Mathematical Problem Solving in Urban Classrooms

You can now view the document associated with this citation by clicking on the "View Documen... more You can now view the document associated with this citation by clicking on the "View Document as HTML" link below. ... This research is part of a larger study that seeks to identify the ways in which the social context influences the mathematical problem solving of a group of ...

Research paper thumbnail of Teacher Development in a Large Urban District and the Impact on Students

Foundations for the Future in Mathematics Education, 2020

Research paper thumbnail of Rutgers University

This study builds on previous research that investigates the nature of engagement as it occurs ‘i... more This study builds on previous research that investigates the nature of engagement as it occurs ‘in the moment ’ in urban classrooms (Goldin, Epstein, Schorr, & Warner, 2011). In this article, we report on a young male student, Eric, who called out an answer in front of all his peers in response to a question posed by the teacher. Almost immediately, his peers challenged his response. Upon hearing their comments, he retorted that he “didn’t care anymore ” and withdrew from the discussion. Nonetheless, moments later he reentered the discussion, reiterating his response. In a later interview, Eric noted that he called out the answer in order to impress others, but felt disrespected when they disagreed. In this examination, we attempt to characterize his reactions with specific reference to his momentary engagement in order to discuss the implications for learning.

Research paper thumbnail of Chapter 4: Engagement Structures and the Development of Mathematical Ideas

Affect in Mathematical Modeling, 2019

We describe the relationship that exists between shifts in engagement and shifts in mathematical ... more We describe the relationship that exists between shifts in engagement and shifts in mathematical thinking, using the construct of engagement structures. The engagement structure construct (Goldin et al. 2011) is a way to account for and describe the complex dynamical interactions that recur as students solve mathematical problems. Our research is focused on a group of eighth grade students solving a problem in a group setting in an urban district. Our analysis involves video-recorded episodes, retrospective interviews and comprehensive field notes. We also document the social conditions present in the classroom that surrounded the shifts. Our findings suggest a variety of changes that can occur within an individual student, and across students in the same classroom, depending upon the social context. At times, changes in mathematical ideas preceded shifts in engagement, and vice-versa. Aside from the within student differences, our research provides an example of how, within the same classroom, students can have very different engagement and mathematical experiences.

Research paper thumbnail of Analyzing Prospective Teachers’ Motivating Desires During Mathematical Problem Solving

ICERI2018 Proceedings, 2018

Research paper thumbnail of Characterizing a middle school student's engagement in a mathematics class

This paper was presented at the Eighth Congress of European Research in Mathematics Education (CE... more This paper was presented at the Eighth Congress of European Research in Mathematics Education (CERME8) in Antalya, Turkey.

Research paper thumbnail of Responding to students’ mathematical thinking when you don’t know how to respond

This paper was presented at the Nineteenth Annual Conference of the Association of Mathematics Te... more This paper was presented at the Nineteenth Annual Conference of the Association of Mathematics Teacher Educators (AMTE), in Orlando, Florida.

Research paper thumbnail of Investigating Students' Movement to Generalization and Abstraction Using Dienes' "Learning Cycle

This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Lake Tahoe, Nevada.

Research paper thumbnail of Clinical interviews & VITAL in an elementary mathematics methods course

Research paper thumbnail of Mathematical truth and social consequences: The intersection of affect and cognition in a middle school classroom

We focus on several groups of eighth grade students in an attempt to deepen our understanding of ... more We focus on several groups of eighth grade students in an attempt to deepen our understanding of when, how, and why middle grade students engage in conceptually challenging mathematics. As part of our analysis, we have formulated the theoretical notion of engagment structures, which is a behavioral/affective/social constellation including characteristic patterns of behavior, indicative of affective pathways and models (structures) that have important cognitive interpretations and implications by the students. We report that students may be willing to abandon arguing for what they know are mathematical truths in order to avoid appearing weak or wrong in front of their peers, and this appears to be linked to the depth of their understanding and their social positioning within their groups.

Research paper thumbnail of Clinical Interviews and VITAL in an Elementary Mathematics Methods Course

Research paper thumbnail of Studying the affective/social dimension of an inner-city mathematics class

… mathematics education in …, 2007

Research paper thumbnail of Student behaviors and ways they are associated with the problem solving process

This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Lake Tahoe, Nevada.

Research paper thumbnail of Student behaviors and ways they are associated with the problem solving process

This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the ... more This paper was presented at the Twenty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education in Lake Tahoe, Nevada.

Research paper thumbnail of Being Challenged in an Urban Classroom: A Case Study Documenting the Engagement of a Young Male Who Wanted to ‘Look Smart

Journal of Urban Learning Teaching and Research, Jan 11, 2013

This study builds on previous research that investigates the nature of engagement as it occurs 'i... more This study builds on previous research that investigates the nature of engagement as it occurs 'in the moment' in urban classrooms (Goldin, Epstein, Schorr, & Warner, 2011). In this article, we report on a young male student, Eric, who called out an answer in front of all his peers in response to a question posed by the teacher. Almost immediately, his peers challenged his response. Upon hearing their comments, he retorted that he "didn't care anymore" and withdrew from the discussion. Nonetheless, moments later he reentered the discussion, reiterating his response. In a later interview, Eric noted that he called out the answer in order to impress others, but felt disrespected when they disagreed. In this examination, we attempt to characterize his reactions with specific reference to his momentary engagement in order to discuss the implications for learning.