Lisa B Warner | William Paterson University (original) (raw)
Papers by Lisa B Warner
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.
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.
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.
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 ...
Foundations for the Future in Mathematics Education, 2020
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.
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.
ICERI2018 Proceedings, 2018
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.
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.
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.
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.
… mathematics education in …, 2007
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.
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.
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.
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.
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.
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.
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 ...
Foundations for the Future in Mathematics Education, 2020
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.
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.
ICERI2018 Proceedings, 2018
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.
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.
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.
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.
… mathematics education in …, 2007
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.
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.
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.