Journal of Psychoeducational Assessment, May 2, 2019
Understanding students' readiness for precalculus and calculus at the community college level is ... more Understanding students' readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC) was designed to investigate community college students' quantitative reasoning abilities and conceptual understanding in algebra. The present study investigates the psychometric properties of the APCR-CC instrument using item response theory based on a sample of intermediate and college algebra students from six community colleges collected in a pretest (N = 1,131) and posttest (N = 772) setting. We examine unidimensionality, item fit, local item independence, measurement invariance, and sensitivity to instruction. Our findings suggest that the APCR-CC instrument is sufficiently characterized by one underlying construct, local dependence does not seem to be an issue, and 80% of the items in the APCR-CC instrument are sensitive to instruction.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Moving from the anecdote to evidence: The need for a research agenda in community college mathema... more Moving from the anecdote to evidence: The need for a research agenda in community college mathematics education Mathematics education research has, until recently, focused primarily on issues of teaching and learning in K-12 mathematics. A decade ago, RUME was founded to "foster research on learning and teaching undergraduate mathematics." Although community college mathematics intersects both K-12 and undergraduate mathematics, there are phenomena unique to community college mathematics that remain largely under investigated. For example, community college mathematics teachers often find themselves re-teaching content that students have encountered in previous mathematics courses, yet little is known about how students arrive at an understanding when they re-learn the material. Other issues, such as how adult students learn the content compared to students who are reviewing the content, are largely unknown. Furthermore, Science, Technology, Engineering, and Mathematics (STEM) majors at community colleges are as capable as their counterparts at four-year colleges and universities, but their transition to university mathematics after several years at a community college presents unique challenges. Research questions within the context of community college mathematics certainly overlap with other research in mathematics education, but the community college context presents itself as a unique setting in which most of what we know is contested. Currently, national attention on community colleges has provided a necessary spotlight for investigating mathematics education. President Obama's recent White House Summit on Community Colleges was preceded by a flurry of papers related to community college mathematics (e.g.
This work has been funded in part by the National Science Foundation through award DRL 0745474. O... more This work has been funded in part by the National Science Foundation through award DRL 0745474. Opinions are those of the author. Special thanks to the members of the Teaching Mathematics in Community Colleges research group and the Junior Faculty at the University of Michigan and to all the reviewers of the many drafts of this document.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022
In this paper we investigate how experienced community college mathematics faculty, taking part i... more In this paper we investigate how experienced community college mathematics faculty, taking part in an item-writing camp designed to generate items to assess mathematical knowledge for teaching college algebra, thought about student thinking and the work of teaching in this context. We conceived of the participants' knowledge as practice-based professional learning. By analyzing video records of item development sessions, drafts of items produced, feedback sessions on the items, and selfreports of their learning during the camp, we identified four major themes related to participants' work highlighting the possible advantages of engaging faculty in item-writing: understanding mathematical knowledge for teaching, understand the item writing process, drawing on their teaching experience in the item-writing process, and noticing the complexity of writing MKT items. These themes make salient the advantages of engaging classroom-based faculty in item-writing.
International Journal of Mathematical Education in Science and Technology, Dec 13, 2021
In this paper we present an exploratory analysis of differences in the performance of two differe... more In this paper we present an exploratory analysis of differences in the performance of two different samples of teachers-high school practicing teachers and community college faculty-on an instrument that assesses mathematical knowledge for teaching algebra 1. To better understand the variance in the performance within and between the two groups of teachers, we examine the relationships between the measured knowledge and teachers' educational and teaching background. Highlighting the positive effect of algebra-based teaching experience on the knowledge, we discuss the implications regarding the extent to which the instrument captures the construct it seeks to assess.
Two‐year college mathematics teaching has interesting challenges, and it helps to have a national... more Two‐year college mathematics teaching has interesting challenges, and it helps to have a national organization representing the profession that provides professional development, issues position statements on relevant topics, and cultivates leaders. This chapter illustrates how the AMATYC organization provides these services.
This dissertation study describes a case study investigating a secondary mathematics teacher'... more This dissertation study describes a case study investigating a secondary mathematics teacher's ways of thinking as he worked through a collection of activities related to the concept of exponential function. The research instruments were designed to explore his ...
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
As part of a large-scale study of algebra instruction at two-year post-secondary institutions in ... more As part of a large-scale study of algebra instruction at two-year post-secondary institutions in the United States, we have developed a qualitative video analysis framework, Evaluating the Quality of Instruction in Post-secondary Mathematics (EQIPM). In this paper, we present two of twelve characteristics used to describe instruction (Instructors Making Sense of Procedures, and Student Mathematical Reasoning and Sense Making), which describe students and instructors engaging with mathematics so their ideas or ways of thinking are evident. We use examples taken from our corpus of videos to exemplify these two characteristics of instruction and how they contribute to its quality. We also offer suggestions for professional development activities.
Moving from the anecdote to evidence: The need for a research agenda in community college mathema... more Moving from the anecdote to evidence: The need for a research agenda in community college mathematics education Mathematics education research has, until recently, focused primarily on issues of teaching and learning in K-12 mathematics. A decade ago, RUME was founded to "foster research on learning and teaching undergraduate mathematics." Although community college mathematics intersects both K-12 and undergraduate mathematics, there are phenomena unique to community college mathematics that remain largely under investigated. For example, community college mathematics teachers often find themselves re-teaching content that students have encountered in previous mathematics courses, yet little is known about how students arrive at an understanding when they re-learn the material. Other issues, such as how adult students learn the content compared to students who are reviewing the content, are largely unknown. Furthermore, Science, Technology, Engineering, and Mathematics (STEM) majors at community colleges are as capable as their counterparts at four-year colleges and universities, but their transition to university mathematics after several years at a community college presents unique challenges. Research questions within the context of community college mathematics certainly overlap with other research in mathematics education, but the community college context presents itself as a unique setting in which most of what we know is contested. Currently, national attention on community colleges has provided a necessary spotlight for investigating mathematics education. President Obama's recent White House Summit on Community Colleges was preceded by a flurry of papers related to community college mathematics (e.g.
Understanding students’ readiness for precalculus and calculus at the community college level is ... more Understanding students’ readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC) was designed to investigate community college students’ quantitative reasoning abilities and conceptual understanding in algebra. The present study investigates the psychometric properties of the APCR-CC instrument using item response theory based on a sample of intermediate and college algebra students from six community colleges collected in a pretest ( N = 1,131) and posttest ( N = 772) setting. We examine unidimensionality, item fit, local item independence, measurement invariance, and sensitivity to instruction. Our findings suggest that the APCR-CC instrument is sufficiently characterized by one underlyin...
This work has been funded in part by the National Science Foundation through award DRL 0745474. O... more This work has been funded in part by the National Science Foundation through award DRL 0745474. Opinions are those of the author. Special thanks to the members of the Teaching Mathematics in Community Colleges research group and the Junior Faculty at the University of Michigan and to all the reviewers of the many drafts of this document.
Understanding the concept of exponential functions and multiplicative rate of change is critical ... more Understanding the concept of exponential functions and multiplicative rate of change is critical for students as they progress through mathematics. Not only are exponential growth and decay topics encountered in our everyday world, these functions are embedded in the sciences as well as mathematics, and they provide a model for representing multiplicative growth and decay patterns for real world phenomena. The National Council of Teachers of Mathematics Principles and Standards (NCTM, 2000) advocate for high school and college mathematics curricula to include the topic of exponential functions and emphasize the importance of developing this functional understanding and multiplicative behavior conceptually through the use of real world contexts. Research has shown that students experience difficulty developing a profound and robust understanding of exponential functions (Confrey & Smith, 1995; Weber, 2002). However, irrespective of these findings, more research is needed to investiga...
Journal of Psychoeducational Assessment, May 2, 2019
Understanding students' readiness for precalculus and calculus at the community college level is ... more Understanding students' readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC) was designed to investigate community college students' quantitative reasoning abilities and conceptual understanding in algebra. The present study investigates the psychometric properties of the APCR-CC instrument using item response theory based on a sample of intermediate and college algebra students from six community colleges collected in a pretest (N = 1,131) and posttest (N = 772) setting. We examine unidimensionality, item fit, local item independence, measurement invariance, and sensitivity to instruction. Our findings suggest that the APCR-CC instrument is sufficiently characterized by one underlying construct, local dependence does not seem to be an issue, and 80% of the items in the APCR-CC instrument are sensitive to instruction.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 1, 2017
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Moving from the anecdote to evidence: The need for a research agenda in community college mathema... more Moving from the anecdote to evidence: The need for a research agenda in community college mathematics education Mathematics education research has, until recently, focused primarily on issues of teaching and learning in K-12 mathematics. A decade ago, RUME was founded to "foster research on learning and teaching undergraduate mathematics." Although community college mathematics intersects both K-12 and undergraduate mathematics, there are phenomena unique to community college mathematics that remain largely under investigated. For example, community college mathematics teachers often find themselves re-teaching content that students have encountered in previous mathematics courses, yet little is known about how students arrive at an understanding when they re-learn the material. Other issues, such as how adult students learn the content compared to students who are reviewing the content, are largely unknown. Furthermore, Science, Technology, Engineering, and Mathematics (STEM) majors at community colleges are as capable as their counterparts at four-year colleges and universities, but their transition to university mathematics after several years at a community college presents unique challenges. Research questions within the context of community college mathematics certainly overlap with other research in mathematics education, but the community college context presents itself as a unique setting in which most of what we know is contested. Currently, national attention on community colleges has provided a necessary spotlight for investigating mathematics education. President Obama's recent White House Summit on Community Colleges was preceded by a flurry of papers related to community college mathematics (e.g.
This work has been funded in part by the National Science Foundation through award DRL 0745474. O... more This work has been funded in part by the National Science Foundation through award DRL 0745474. Opinions are those of the author. Special thanks to the members of the Teaching Mathematics in Community Colleges research group and the Junior Faculty at the University of Michigan and to all the reviewers of the many drafts of this document.
HAL (Le Centre pour la Communication Scientifique Directe), Feb 2, 2022
In this paper we investigate how experienced community college mathematics faculty, taking part i... more In this paper we investigate how experienced community college mathematics faculty, taking part in an item-writing camp designed to generate items to assess mathematical knowledge for teaching college algebra, thought about student thinking and the work of teaching in this context. We conceived of the participants' knowledge as practice-based professional learning. By analyzing video records of item development sessions, drafts of items produced, feedback sessions on the items, and selfreports of their learning during the camp, we identified four major themes related to participants' work highlighting the possible advantages of engaging faculty in item-writing: understanding mathematical knowledge for teaching, understand the item writing process, drawing on their teaching experience in the item-writing process, and noticing the complexity of writing MKT items. These themes make salient the advantages of engaging classroom-based faculty in item-writing.
International Journal of Mathematical Education in Science and Technology, Dec 13, 2021
In this paper we present an exploratory analysis of differences in the performance of two differe... more In this paper we present an exploratory analysis of differences in the performance of two different samples of teachers-high school practicing teachers and community college faculty-on an instrument that assesses mathematical knowledge for teaching algebra 1. To better understand the variance in the performance within and between the two groups of teachers, we examine the relationships between the measured knowledge and teachers' educational and teaching background. Highlighting the positive effect of algebra-based teaching experience on the knowledge, we discuss the implications regarding the extent to which the instrument captures the construct it seeks to assess.
Two‐year college mathematics teaching has interesting challenges, and it helps to have a national... more Two‐year college mathematics teaching has interesting challenges, and it helps to have a national organization representing the profession that provides professional development, issues position statements on relevant topics, and cultivates leaders. This chapter illustrates how the AMATYC organization provides these services.
This dissertation study describes a case study investigating a secondary mathematics teacher'... more This dissertation study describes a case study investigating a secondary mathematics teacher's ways of thinking as he worked through a collection of activities related to the concept of exponential function. The research instruments were designed to explore his ...
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
As part of a large-scale study of algebra instruction at two-year post-secondary institutions in ... more As part of a large-scale study of algebra instruction at two-year post-secondary institutions in the United States, we have developed a qualitative video analysis framework, Evaluating the Quality of Instruction in Post-secondary Mathematics (EQIPM). In this paper, we present two of twelve characteristics used to describe instruction (Instructors Making Sense of Procedures, and Student Mathematical Reasoning and Sense Making), which describe students and instructors engaging with mathematics so their ideas or ways of thinking are evident. We use examples taken from our corpus of videos to exemplify these two characteristics of instruction and how they contribute to its quality. We also offer suggestions for professional development activities.
Moving from the anecdote to evidence: The need for a research agenda in community college mathema... more Moving from the anecdote to evidence: The need for a research agenda in community college mathematics education Mathematics education research has, until recently, focused primarily on issues of teaching and learning in K-12 mathematics. A decade ago, RUME was founded to "foster research on learning and teaching undergraduate mathematics." Although community college mathematics intersects both K-12 and undergraduate mathematics, there are phenomena unique to community college mathematics that remain largely under investigated. For example, community college mathematics teachers often find themselves re-teaching content that students have encountered in previous mathematics courses, yet little is known about how students arrive at an understanding when they re-learn the material. Other issues, such as how adult students learn the content compared to students who are reviewing the content, are largely unknown. Furthermore, Science, Technology, Engineering, and Mathematics (STEM) majors at community colleges are as capable as their counterparts at four-year colleges and universities, but their transition to university mathematics after several years at a community college presents unique challenges. Research questions within the context of community college mathematics certainly overlap with other research in mathematics education, but the community college context presents itself as a unique setting in which most of what we know is contested. Currently, national attention on community colleges has provided a necessary spotlight for investigating mathematics education. President Obama's recent White House Summit on Community Colleges was preceded by a flurry of papers related to community college mathematics (e.g.
Understanding students’ readiness for precalculus and calculus at the community college level is ... more Understanding students’ readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC) was designed to investigate community college students’ quantitative reasoning abilities and conceptual understanding in algebra. The present study investigates the psychometric properties of the APCR-CC instrument using item response theory based on a sample of intermediate and college algebra students from six community colleges collected in a pretest ( N = 1,131) and posttest ( N = 772) setting. We examine unidimensionality, item fit, local item independence, measurement invariance, and sensitivity to instruction. Our findings suggest that the APCR-CC instrument is sufficiently characterized by one underlyin...
This work has been funded in part by the National Science Foundation through award DRL 0745474. O... more This work has been funded in part by the National Science Foundation through award DRL 0745474. Opinions are those of the author. Special thanks to the members of the Teaching Mathematics in Community Colleges research group and the Junior Faculty at the University of Michigan and to all the reviewers of the many drafts of this document.
Understanding the concept of exponential functions and multiplicative rate of change is critical ... more Understanding the concept of exponential functions and multiplicative rate of change is critical for students as they progress through mathematics. Not only are exponential growth and decay topics encountered in our everyday world, these functions are embedded in the sciences as well as mathematics, and they provide a model for representing multiplicative growth and decay patterns for real world phenomena. The National Council of Teachers of Mathematics Principles and Standards (NCTM, 2000) advocate for high school and college mathematics curricula to include the topic of exponential functions and emphasize the importance of developing this functional understanding and multiplicative behavior conceptually through the use of real world contexts. Research has shown that students experience difficulty developing a profound and robust understanding of exponential functions (Confrey & Smith, 1995; Weber, 2002). However, irrespective of these findings, more research is needed to investiga...
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