Jessica Ellis | Colorado State University (original) (raw)
Papers by Jessica Ellis
International Group for the Psychology of Mathematics Education, 2014
Graduate student Teaching Assistants (GTAs) contribute to calculus instruction in two ways: as th... more Graduate student Teaching Assistants (GTAs) contribute to calculus instruction in two ways: as the primary teacher and as recitation leaders. GTAs can also be viewed as the next generation of mathematics instructors. Thus, in addition to their immediate contribution to the landscape of Calculus 1 instruction, GTAs will contribute significantly to the long-term state of calculus in their future occupations. However, their preparation for these roles varies widely and is often minimal. In this study, I first compare the mathematical beliefs, instructional practices, and student success of GTAs to other Calculus 1 instructors. I then provide rich descriptions for three GTA professional development (PD) programs that prepare graduate students as course instructors, as recitation leaders, and as future faculty. I then investigate the instructional practices and mathematical beliefs of graduate students coming from these three PD programs. I conclude this work with a description of a fram...
A substantial percentage of college students who enrol in Calculus I intending to take more calcu... more A substantial percentage of college students who enrol in Calculus I intending to take more calculus decide at the end of the semester not to continue with calculus. This represents a huge loss in terms of the need for more students to pursue a major in one of the science, technology, engineering and mathematics (STEM) disciplines. In this report we examine the characteristics of STEM intending students who begin their post secondary studies with Calculus I and either persist or switch out of the calculus sequence, and hence either remain or leave the STEM pipeline. The data used for this analysis comes from a unique, in depth national survey aimed at identifying characteristics of successful programs in college calculus.
International Journal of Research in Undergraduate Mathematics Education, 2015
We investigate the nature of Calculus I homework at five PhD-granting universities identified as ... more We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that arose as important: structure, content, and feedback. Selected universities employed more varied homework structure, included more content emphasizing skills as well as solving novel problems, and provided higher amounts of and frequency of feedback to students. Students felt positively towards conceptually driven homework, but their feelings were mixed or negative regarding the logistical aspects of online and group homework assignments. We draw on Herbst and Chazan's (ZDM-The International Journal on Mathematics Education, 44(5), 601-612, 2012) adaptation of the instructional triangle and Brousseau's (1997) notion of the didactical contract to make sense of how homework is understood as an instructional resource by instructors and by students.
ZDM, 2014
There is a clear need to increase student persistence in Science, Technology, Engineering, or Mat... more There is a clear need to increase student persistence in Science, Technology, Engineering, or Mathematics (STEM). Prior analyses have shown that students who change their Calculus II intention (a proxy for STEM intention) report being less engaged during class than students who persist onto Calculus II. This led us to ask: Are these students in different classes, or are they in the same classes but experiencing them differently? We present descriptive and univariate analyses of the relationship of calculus persistence to student demographics, background characteristics, and reported instruction for 1,684 STEM intending students and 330 non-STEM intending students enrolled in introductory calculus in Fall 2010 in the United States. We then develop regression models that control for the group effect of course enrollment to understand how perceiving low levels of various pedagogical activities within a class is associated with calculus persistence. These analyses show that different student perceptions of the frequency of a number of pedagogical activities, and thus different ways of experiencing the same class, are related to students’ decision to continue studying calculus. Specifically, among initially STEM intending students, there was a relationship between persistence and the perceived frequency of the instructor showing students how to work specific problems, preparing extra material to help students understand calculus concepts or procedures, holding a whole-class discussion, and requiring students to explain their thinking on exams. Among initially non-STEM intending students, there was a relationship between persistence and the perceived frequency of being required to explain thinking during class.
Educational Studies in Mathematics, 2016
As part of a larger study of student understanding of concepts in linear algebra, we interviewed ... more As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear transformation as related to high school function. Analysis of these data led to a characterization of student responses into three categories of mathematical structures used to discuss function: properties, computations, and a series of five interrelated clusters of metaphorical expressions. In this paper, we use this analytic framing for exploring the question: to what extent does each of the students in this study have a unified concept image of function across two mathematical contexts, high school algebra and their study of linear algebra? We found that students who expressed a unified notion of function used metaphorical language to bridge any gaps between the notion of function from high school and the notion of linear transformation from linear algebra. We conjecture that the framing of computations, properties, and metaphorical clusters could be extended to discussions of functions in contexts with other mathematical domains. Future research that further examines the extent to which undergraduate students develop a unified concept image of function could then lead to various design research efforts aimed at explicitly fostering such a unified understanding.
PLOS ONE, 2016
The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workfo... more The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that simply increasing the retention of women starting in college calculus would almost double the number of women entering the STEM workforce.
In this workshop we seek to bring together researchers from across the globe to discuss the teach... more In this workshop we seek to bring together researchers from across the globe to discuss the teaching preparation of post-graduate mathematics students tasked with teaching tertiary mathematics. In the United States, post-graduate mathematics students who are assigned teaching positions are referred to as Graduate Teaching Assistants (GTAs) and examination of their teaching-related professional development is on the rise. Current national efforts involve understanding the different ways GTAs are prepared for their mathematics teaching across the country. However, we know very little about the similarities and differences in the ways postgraduate mathematics students are involved in tertiary mathematics teaching and prepared for this teaching across the globe. A main goal of the workshop is to initiate a conversation resulting in an international overview of post-graduate mathematics student teaching preparation. We have recruited scholars who work in this area to bring to the worksho...
As part of a larger study of student understanding of concepts in linear algebra, we interviewed ... more As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear transformation as related to high school function. Analysis of these data led to a characterization of student responses into three categories of mathematical structures used to discuss function: properties, computations, and a series of five interrelated clusters of metaphorical expressions. In this paper, we use this analytic framing for exploring the question: to what extent does each of the students in this study have a unified concept image of function across two mathematical contexts, high school algebra and their study of linear algebra? We found that students who expressed a unified notion of function used metaphorical language to bridge any gaps between the notion of function from high school and the notion of linear transformation from linear algebra. We conjecture that the framing of computations, properties, and metaphorical clusters could be extended to discussions of functions in contexts with other mathematical domains. Future research that further examines the extent to which undergraduate students develop a unified concept image of function could then lead to various design research efforts aimed at explicitly fostering such a unified understanding.
International Journal of Mathematical Education in Science and Technology, 2015
Your article is protected by copyright and all rights are held exclusively by FIZ Karlsruhe. This... more Your article is protected by copyright and all rights are held exclusively by FIZ Karlsruhe. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
We investigate the nature of Calculus I homework at five PhD-granting universities identified as ... more We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that arose as important: structure, content, and feedback. Selected universities employed more varied homework structure, included more content emphasizing skills as well as solving novel problems, and provided higher amounts of and frequency of feedback to students. Students felt positively towards conceptually driven homework, but their feelings were mixed or negative regarding the logistical aspects of online and group homework assignments. We draw on Herbst and Chazan's (ZDM -The International Journal on Mathematics Education, 44(5), 601-612, 2012) adaptation of the instructional triangle and Brousseau's (1997) notion of the didactical contract to make sense of how homework is understood as an instructional resource by instructors and by students.
International Group for the Psychology of Mathematics Education, 2014
Graduate student Teaching Assistants (GTAs) contribute to calculus instruction in two ways: as th... more Graduate student Teaching Assistants (GTAs) contribute to calculus instruction in two ways: as the primary teacher and as recitation leaders. GTAs can also be viewed as the next generation of mathematics instructors. Thus, in addition to their immediate contribution to the landscape of Calculus 1 instruction, GTAs will contribute significantly to the long-term state of calculus in their future occupations. However, their preparation for these roles varies widely and is often minimal. In this study, I first compare the mathematical beliefs, instructional practices, and student success of GTAs to other Calculus 1 instructors. I then provide rich descriptions for three GTA professional development (PD) programs that prepare graduate students as course instructors, as recitation leaders, and as future faculty. I then investigate the instructional practices and mathematical beliefs of graduate students coming from these three PD programs. I conclude this work with a description of a fram...
A substantial percentage of college students who enrol in Calculus I intending to take more calcu... more A substantial percentage of college students who enrol in Calculus I intending to take more calculus decide at the end of the semester not to continue with calculus. This represents a huge loss in terms of the need for more students to pursue a major in one of the science, technology, engineering and mathematics (STEM) disciplines. In this report we examine the characteristics of STEM intending students who begin their post secondary studies with Calculus I and either persist or switch out of the calculus sequence, and hence either remain or leave the STEM pipeline. The data used for this analysis comes from a unique, in depth national survey aimed at identifying characteristics of successful programs in college calculus.
International Journal of Research in Undergraduate Mathematics Education, 2015
We investigate the nature of Calculus I homework at five PhD-granting universities identified as ... more We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that arose as important: structure, content, and feedback. Selected universities employed more varied homework structure, included more content emphasizing skills as well as solving novel problems, and provided higher amounts of and frequency of feedback to students. Students felt positively towards conceptually driven homework, but their feelings were mixed or negative regarding the logistical aspects of online and group homework assignments. We draw on Herbst and Chazan's (ZDM-The International Journal on Mathematics Education, 44(5), 601-612, 2012) adaptation of the instructional triangle and Brousseau's (1997) notion of the didactical contract to make sense of how homework is understood as an instructional resource by instructors and by students.
ZDM, 2014
There is a clear need to increase student persistence in Science, Technology, Engineering, or Mat... more There is a clear need to increase student persistence in Science, Technology, Engineering, or Mathematics (STEM). Prior analyses have shown that students who change their Calculus II intention (a proxy for STEM intention) report being less engaged during class than students who persist onto Calculus II. This led us to ask: Are these students in different classes, or are they in the same classes but experiencing them differently? We present descriptive and univariate analyses of the relationship of calculus persistence to student demographics, background characteristics, and reported instruction for 1,684 STEM intending students and 330 non-STEM intending students enrolled in introductory calculus in Fall 2010 in the United States. We then develop regression models that control for the group effect of course enrollment to understand how perceiving low levels of various pedagogical activities within a class is associated with calculus persistence. These analyses show that different student perceptions of the frequency of a number of pedagogical activities, and thus different ways of experiencing the same class, are related to students’ decision to continue studying calculus. Specifically, among initially STEM intending students, there was a relationship between persistence and the perceived frequency of the instructor showing students how to work specific problems, preparing extra material to help students understand calculus concepts or procedures, holding a whole-class discussion, and requiring students to explain their thinking on exams. Among initially non-STEM intending students, there was a relationship between persistence and the perceived frequency of being required to explain thinking during class.
Educational Studies in Mathematics, 2016
As part of a larger study of student understanding of concepts in linear algebra, we interviewed ... more As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear transformation as related to high school function. Analysis of these data led to a characterization of student responses into three categories of mathematical structures used to discuss function: properties, computations, and a series of five interrelated clusters of metaphorical expressions. In this paper, we use this analytic framing for exploring the question: to what extent does each of the students in this study have a unified concept image of function across two mathematical contexts, high school algebra and their study of linear algebra? We found that students who expressed a unified notion of function used metaphorical language to bridge any gaps between the notion of function from high school and the notion of linear transformation from linear algebra. We conjecture that the framing of computations, properties, and metaphorical clusters could be extended to discussions of functions in contexts with other mathematical domains. Future research that further examines the extent to which undergraduate students develop a unified concept image of function could then lead to various design research efforts aimed at explicitly fostering such a unified understanding.
PLOS ONE, 2016
The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workfo... more The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that simply increasing the retention of women starting in college calculus would almost double the number of women entering the STEM workforce.
In this workshop we seek to bring together researchers from across the globe to discuss the teach... more In this workshop we seek to bring together researchers from across the globe to discuss the teaching preparation of post-graduate mathematics students tasked with teaching tertiary mathematics. In the United States, post-graduate mathematics students who are assigned teaching positions are referred to as Graduate Teaching Assistants (GTAs) and examination of their teaching-related professional development is on the rise. Current national efforts involve understanding the different ways GTAs are prepared for their mathematics teaching across the country. However, we know very little about the similarities and differences in the ways postgraduate mathematics students are involved in tertiary mathematics teaching and prepared for this teaching across the globe. A main goal of the workshop is to initiate a conversation resulting in an international overview of post-graduate mathematics student teaching preparation. We have recruited scholars who work in this area to bring to the worksho...
As part of a larger study of student understanding of concepts in linear algebra, we interviewed ... more As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear transformation as related to high school function. Analysis of these data led to a characterization of student responses into three categories of mathematical structures used to discuss function: properties, computations, and a series of five interrelated clusters of metaphorical expressions. In this paper, we use this analytic framing for exploring the question: to what extent does each of the students in this study have a unified concept image of function across two mathematical contexts, high school algebra and their study of linear algebra? We found that students who expressed a unified notion of function used metaphorical language to bridge any gaps between the notion of function from high school and the notion of linear transformation from linear algebra. We conjecture that the framing of computations, properties, and metaphorical clusters could be extended to discussions of functions in contexts with other mathematical domains. Future research that further examines the extent to which undergraduate students develop a unified concept image of function could then lead to various design research efforts aimed at explicitly fostering such a unified understanding.
International Journal of Mathematical Education in Science and Technology, 2015
Your article is protected by copyright and all rights are held exclusively by FIZ Karlsruhe. This... more Your article is protected by copyright and all rights are held exclusively by FIZ Karlsruhe. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
We investigate the nature of Calculus I homework at five PhD-granting universities identified as ... more We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that arose as important: structure, content, and feedback. Selected universities employed more varied homework structure, included more content emphasizing skills as well as solving novel problems, and provided higher amounts of and frequency of feedback to students. Students felt positively towards conceptually driven homework, but their feelings were mixed or negative regarding the logistical aspects of online and group homework assignments. We draw on Herbst and Chazan's (ZDM -The International Journal on Mathematics Education, 44(5), 601-612, 2012) adaptation of the instructional triangle and Brousseau's (1997) notion of the didactical contract to make sense of how homework is understood as an instructional resource by instructors and by students.