Hollylynne Lee - Academia.edu (original) (raw)
Papers by Hollylynne Lee
Contemporary Issues in Technology and Teacher Education, 2000
In the Principles and Standards of School Mathematics the National Council of Teachers of Mathema... more In the Principles and Standards of School Mathematics the National Council of Teachers of Mathematics (NCTM) identified the "Technology Principle" as one of six principles of high quality mathematics education (NCTM, 2000). This principle states: "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning" (p. 24). There is widespread agreement that mathematics teachers, not technological tools, are the key change agents to bringing about reform in mathematics teaching with technology (Kaput, 1992; NCTM 1991, 2000). Yet, preparing teachers to use technology appropriately is a complex task for teacher educators (Mergendoller, 1994). Waits and Demana (2000) argue that adoption of technology by teachers requires professional development that focuses on both conceptual and pedagogical issues, ongoing support in terms of "intensive start-up assistance and regular follow-up activit...
Assessment in Mathematics Education Contexts, 2019
We observed eight beginning secondary mathematics teachers’ classrooms to investigate which they ... more We observed eight beginning secondary mathematics teachers’ classrooms to investigate which they organized students for learning, uses of instructional methods, and how these may differ based on the level of course being taught. We found that beginning teachers frequently organize their students to learn collaboratively – either in small groups or as a whole class – coupled with an abundance of teacher directed instruction. Differences in organizations, teaching methods, and associated learning opportunities between course levels also exist. Implications for supporting practicing teachers and preparing prospective teachers to establish collaborative learning environments and utilize student centered teaching methods are discussed.
With online learning becoming a more viable and attractive option for students and teachers aroun... more With online learning becoming a more viable and attractive option for students and teachers around the world, we discuss how one effort in the U.S. is focused on designing, implementing, and evaluating MOOCs designed for professional development of mathematics teachers. We share design principles and learning opportunities, as well as discuss specific impacts participants report for changes to teaching practices and how these MOOCs have impacted engagement of educators.
With online learning becoming a more viable option for teachers to develop their expertise, our r... more With online learning becoming a more viable option for teachers to develop their expertise, our report shares one such effort focused on improving the teaching of statistics. We share design principles and learning opportunities, as well as discuss specific impacts evident in classroom teachers’ course activity concerning changes to their beliefs and perspectives about statistics. Specific course experiences that served as triggers for critical reflection are discussed.
Contemporary Issues in Technology and Teacher Education, 2012
Simulation approaches to inference have gained prominence in statistics education. In this paper ... more Simulation approaches to inference have gained prominence in statistics education. In this paper we combine a theoretical analysis of the ways researchers and curriculum developers have represented models of simulation processes with an empirical analysis of the ways teachers represent models of the process they believe would be helpful to students. Our results cumulate in suggestions for a more explicit framework for using a simulation approach to inference.
Teaching Children Mathematics
How third graders worked together to investigate relationships between fractions and percents usi... more How third graders worked together to investigate relationships between fractions and percents using a spreadsheet tool. Highlights a student's creative approach to a proportion task.
STATISTICS EDUCATION RESEARCH JOURNAL
We examined how middle school students reason about results from a computer-simulated die-tossing... more We examined how middle school students reason about results from a computer-simulated die-tossing experiment, including various representations of data, to support or refute an assumption that the outcomes on a die are equiprobable. We used students’ actions with the software and their social interactions to infer their expectations and whether or not they believed their empirical data could be used to refute an assumption of equiprobable outcomes. Comparisons across students illuminate intricacies in their reasoning as they collect and analyze data from the die tosses. Overall, our research contributes to understanding how students can engage in informal hypothesis testing and use data from simulations to make inferences about a probability distribution. First published May 2010 at Statistics Education Research Journal: Archives
STATISTICS EDUCATION RESEARCH JOURNAL
Repeated sampling approaches to inference that rely on simulations have recently gained prominenc... more Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization and sampling processes. We explicate the role of probability in this approach and draw upon a models and modeling perspective to support the development of teachers’ models for using a repeated sampling approach for inference. We explicate the model development task sequence and examine the teachers’ representations of their conceptualizations of a repeated sampling approach for inference. We propose key conceptualizations that can guide instruction when using simulations and repeated sampling for drawing inferences. First published November 2016 at Statistics Education Research Journal Archives
STATISTICS EDUCATION RESEARCH JOURNAL
This study examined a random stratified sample (n=62) of teachers’ work across eight institutions... more This study examined a random stratified sample (n=62) of teachers’ work across eight institutions on three tasks that utilized dynamic statistical software. We considered how teachers may utilize and develop their statistical knowledge and technological statistical knowledge when investigating a statistical task. We examined how teachers engaged in transnumerative activities with the aid of technology through representing data, using dynamic linking capabilities, and creating statistical measures and augmentations to graphs. Results indicate that while dynamic linking was not always evident in their work, many teachers took advantage of software tools to create enhanced representations through many transnumerative actions. The creation and use of such enhanced representations of data have implications for teacher education, software design, and focus for future studies. First published May 2014 at Statistics Education Research Journal Archives
Journal of Statistics and Data Science Education
As the demand for skilled data scientists has grown, university level statistics and data science... more As the demand for skilled data scientists has grown, university level statistics and data science courses have become more rigorous in training students to understand and utilize the tools that their future careers will likely require. However, the mechanisms to assess students' use of these tools while they are learning to use them are not well defined. As such, a framework to assess statistical computing actions was created. Using task-based interviews of students who completed a second course in statistics, the framework was used to determine the ways in which students utilize statistical computing tools, specifically R, while going through problem solving phases. Patterns that emerged are discussed. Supplementary materials for this article are available online.
2003 Annual Conference Proceedings
Engineering faculty are often discouraged by the challenges of participating in distance learning... more Engineering faculty are often discouraged by the challenges of participating in distance learning, or incorporating on-line learning approaches in their courses. A particularly important challenge is the time-, skill-, and resource-intensive endeavor of producing web-based content for students. This is particularly true in engineering and scientific and mathematically-based disciplines, where much of the content involves representing concepts through diagrams and equations. While the tools for electronic production of text-based content are well-developed and very easy to use, the production of more technologically sophisticated content needed to represent engineering concepts is much more challenging. For example, suppose a student in an introductory circuits course is having trouble conceptualizing reducing a circuit to its Thevenin equivalent. With pencil and paper during face-to-face interaction, the instructor could illustrate and explain the problem solving process. In contrast, producing a web-based resource to accomplish the same purpose would be a very time-consuming ordeal, typically requiring skill with sophisticated software tools.
Online Learning
With online learning becoming a more viable option for teachers to develop their expertise, our r... more With online learning becoming a more viable option for teachers to develop their expertise, our report shares one such effort focused on improving the teaching of statistics. We share design principles and learning opportunities in an online course developed specifically to serve as a wide-scale online professional development opportunity for educators, thus deemed as a massive open online course for educators (MOOC-Ed). In this report we focus on a subset of 412 participants who identified themselves as classroom teachers. We use multiple data sources, quantitative and qualitative, to characterize changes in teachers’ beliefs and perspectives about statistics and identify triggers in the course that appear to influence teachers’ sense making about issues related to teaching statistics. Implications about specific course experiences that served as triggers for critical reflection and change are discussed.
ZDM
Three MOOCs for Educators (MOOC-Eds) were designed for mathematics and statistics teachers based ... more Three MOOCs for Educators (MOOC-Eds) were designed for mathematics and statistics teachers based on principles of effective online professional development that include: self-directed learning, learning from multiple voices, job-connected learning, and peer-supported learning (Kleiman et al., in: Kim (ed) Massive Open Online Courses: the MOOC Revolution, Routledge, New York, 2015). We examined how these design principles were enacted in the development of the MOOC-Eds and how they influenced the engagement of 5767 participants. We also analyzed opportunities the MOOC-Eds provided for participants to develop their knowledge of, beliefs about, and attitudes towards teaching mathematics and statistics. The Interconnected Model of Professional Growth (Clarke and Hollingsworth in Teach Teach Educ 18(8):947–967, 2002) was used to guide analysis of click data, discussion forum posts, and interviews to consider the ways in which elements of the external domain influenced the personal domain...
Journal of Statistics Education
One of the main goals of statistics is to use data to provide evidence in support of an argument.... more One of the main goals of statistics is to use data to provide evidence in support of an argument. This article will discuss some popular forms of writing assessments currently in use, to demonstrate the differences between the methods for structuring the students' learning to support their arguments with evidence. We share a model, which was originally created to assess students in introductory statistics and has been adapted for the second course in statistics, which takes a unique approach toward assessing the students' understanding of statistical concepts through writing. In this model, students are expected to answer prompts that required them to (1) take a stance on an argument, (2) defend their position with facts given in the prompt, (3) discern the implications that those facts implied, and (4) give a proper conclusion to their argument. We provide examples of a few of the writing assignment prompts used in the course, their intended assessment purpose, and common answers that students gave to these assignments. Supplementary materials for this article are available online.
Journal of Psychoeducational Assessment
Recently adopted state standards for middle grades and high school mathematics content have an in... more Recently adopted state standards for middle grades and high school mathematics content have an increased emphasis on statistical topics. With this change, teacher education programs may need to adapt how they prepare preservice secondary mathematics teachers (PSMTs) to teach statistics and require measures related to statistics teaching to assess the impact of programmatic changes and track teacher growth. Using responses from a sample of 290 PSMTs from 20 institutions across the United States, this study presents validity and reliability evidence for the high school version of the Self-Efficacy to Teach Statistics (SETS-HS), which could be used to assess statistics teaching efficacy. Confirmatory factor analysis results via Rasch modeling support the use of three subscales, which exhibit adequate reliabilities and correspond to the three levels in the Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education endorsed by the American Statistical Association. Item an...
Computers & Education
Abstract While many studies describe the use of technology in the mathematics classroom, few expl... more Abstract While many studies describe the use of technology in the mathematics classroom, few explore the factors that influence teacher decisions around its use. The participants in this study were 21 early career secondary mathematics teachers who had completed an undergraduate mathematics teacher preparation program in the USA with a strong emphasis on the use of technology to teach mathematics. In this qualitative study, interview data were collected and analyzed with attention toward why teachers choose to use technology to teach mathematics, what tools they chose to use and why, as well as the general factors they consider when selecting particular technology tools. Findings indicate that one of the most important factors when deciding whether to use technology was how well it aligned with the goals of a lesson. The range of technology used spanned mathematical action tools, collaboration tools, assessment tools, and communication tools. When selecting particular tools teachers most heavily considered ease of use for both themselves and their students. These findings suggest that when considering how to infuse technology into teacher education programs we suggest that it is important to focus more broadly on types of tools, ways teachers can position them, and how particular activities align with specific mathematics learning objectives.
Contemporary Issues in Technology and Teacher Education, 2000
In the Principles and Standards of School Mathematics the National Council of Teachers of Mathema... more In the Principles and Standards of School Mathematics the National Council of Teachers of Mathematics (NCTM) identified the "Technology Principle" as one of six principles of high quality mathematics education (NCTM, 2000). This principle states: "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning" (p. 24). There is widespread agreement that mathematics teachers, not technological tools, are the key change agents to bringing about reform in mathematics teaching with technology (Kaput, 1992; NCTM 1991, 2000). Yet, preparing teachers to use technology appropriately is a complex task for teacher educators (Mergendoller, 1994). Waits and Demana (2000) argue that adoption of technology by teachers requires professional development that focuses on both conceptual and pedagogical issues, ongoing support in terms of "intensive start-up assistance and regular follow-up activit...
Assessment in Mathematics Education Contexts, 2019
We observed eight beginning secondary mathematics teachers’ classrooms to investigate which they ... more We observed eight beginning secondary mathematics teachers’ classrooms to investigate which they organized students for learning, uses of instructional methods, and how these may differ based on the level of course being taught. We found that beginning teachers frequently organize their students to learn collaboratively – either in small groups or as a whole class – coupled with an abundance of teacher directed instruction. Differences in organizations, teaching methods, and associated learning opportunities between course levels also exist. Implications for supporting practicing teachers and preparing prospective teachers to establish collaborative learning environments and utilize student centered teaching methods are discussed.
With online learning becoming a more viable and attractive option for students and teachers aroun... more With online learning becoming a more viable and attractive option for students and teachers around the world, we discuss how one effort in the U.S. is focused on designing, implementing, and evaluating MOOCs designed for professional development of mathematics teachers. We share design principles and learning opportunities, as well as discuss specific impacts participants report for changes to teaching practices and how these MOOCs have impacted engagement of educators.
With online learning becoming a more viable option for teachers to develop their expertise, our r... more With online learning becoming a more viable option for teachers to develop their expertise, our report shares one such effort focused on improving the teaching of statistics. We share design principles and learning opportunities, as well as discuss specific impacts evident in classroom teachers’ course activity concerning changes to their beliefs and perspectives about statistics. Specific course experiences that served as triggers for critical reflection are discussed.
Contemporary Issues in Technology and Teacher Education, 2012
Simulation approaches to inference have gained prominence in statistics education. In this paper ... more Simulation approaches to inference have gained prominence in statistics education. In this paper we combine a theoretical analysis of the ways researchers and curriculum developers have represented models of simulation processes with an empirical analysis of the ways teachers represent models of the process they believe would be helpful to students. Our results cumulate in suggestions for a more explicit framework for using a simulation approach to inference.
Teaching Children Mathematics
How third graders worked together to investigate relationships between fractions and percents usi... more How third graders worked together to investigate relationships between fractions and percents using a spreadsheet tool. Highlights a student's creative approach to a proportion task.
STATISTICS EDUCATION RESEARCH JOURNAL
We examined how middle school students reason about results from a computer-simulated die-tossing... more We examined how middle school students reason about results from a computer-simulated die-tossing experiment, including various representations of data, to support or refute an assumption that the outcomes on a die are equiprobable. We used students’ actions with the software and their social interactions to infer their expectations and whether or not they believed their empirical data could be used to refute an assumption of equiprobable outcomes. Comparisons across students illuminate intricacies in their reasoning as they collect and analyze data from the die tosses. Overall, our research contributes to understanding how students can engage in informal hypothesis testing and use data from simulations to make inferences about a probability distribution. First published May 2010 at Statistics Education Research Journal: Archives
STATISTICS EDUCATION RESEARCH JOURNAL
Repeated sampling approaches to inference that rely on simulations have recently gained prominenc... more Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization and sampling processes. We explicate the role of probability in this approach and draw upon a models and modeling perspective to support the development of teachers’ models for using a repeated sampling approach for inference. We explicate the model development task sequence and examine the teachers’ representations of their conceptualizations of a repeated sampling approach for inference. We propose key conceptualizations that can guide instruction when using simulations and repeated sampling for drawing inferences. First published November 2016 at Statistics Education Research Journal Archives
STATISTICS EDUCATION RESEARCH JOURNAL
This study examined a random stratified sample (n=62) of teachers’ work across eight institutions... more This study examined a random stratified sample (n=62) of teachers’ work across eight institutions on three tasks that utilized dynamic statistical software. We considered how teachers may utilize and develop their statistical knowledge and technological statistical knowledge when investigating a statistical task. We examined how teachers engaged in transnumerative activities with the aid of technology through representing data, using dynamic linking capabilities, and creating statistical measures and augmentations to graphs. Results indicate that while dynamic linking was not always evident in their work, many teachers took advantage of software tools to create enhanced representations through many transnumerative actions. The creation and use of such enhanced representations of data have implications for teacher education, software design, and focus for future studies. First published May 2014 at Statistics Education Research Journal Archives
Journal of Statistics and Data Science Education
As the demand for skilled data scientists has grown, university level statistics and data science... more As the demand for skilled data scientists has grown, university level statistics and data science courses have become more rigorous in training students to understand and utilize the tools that their future careers will likely require. However, the mechanisms to assess students' use of these tools while they are learning to use them are not well defined. As such, a framework to assess statistical computing actions was created. Using task-based interviews of students who completed a second course in statistics, the framework was used to determine the ways in which students utilize statistical computing tools, specifically R, while going through problem solving phases. Patterns that emerged are discussed. Supplementary materials for this article are available online.
2003 Annual Conference Proceedings
Engineering faculty are often discouraged by the challenges of participating in distance learning... more Engineering faculty are often discouraged by the challenges of participating in distance learning, or incorporating on-line learning approaches in their courses. A particularly important challenge is the time-, skill-, and resource-intensive endeavor of producing web-based content for students. This is particularly true in engineering and scientific and mathematically-based disciplines, where much of the content involves representing concepts through diagrams and equations. While the tools for electronic production of text-based content are well-developed and very easy to use, the production of more technologically sophisticated content needed to represent engineering concepts is much more challenging. For example, suppose a student in an introductory circuits course is having trouble conceptualizing reducing a circuit to its Thevenin equivalent. With pencil and paper during face-to-face interaction, the instructor could illustrate and explain the problem solving process. In contrast, producing a web-based resource to accomplish the same purpose would be a very time-consuming ordeal, typically requiring skill with sophisticated software tools.
Online Learning
With online learning becoming a more viable option for teachers to develop their expertise, our r... more With online learning becoming a more viable option for teachers to develop their expertise, our report shares one such effort focused on improving the teaching of statistics. We share design principles and learning opportunities in an online course developed specifically to serve as a wide-scale online professional development opportunity for educators, thus deemed as a massive open online course for educators (MOOC-Ed). In this report we focus on a subset of 412 participants who identified themselves as classroom teachers. We use multiple data sources, quantitative and qualitative, to characterize changes in teachers’ beliefs and perspectives about statistics and identify triggers in the course that appear to influence teachers’ sense making about issues related to teaching statistics. Implications about specific course experiences that served as triggers for critical reflection and change are discussed.
ZDM
Three MOOCs for Educators (MOOC-Eds) were designed for mathematics and statistics teachers based ... more Three MOOCs for Educators (MOOC-Eds) were designed for mathematics and statistics teachers based on principles of effective online professional development that include: self-directed learning, learning from multiple voices, job-connected learning, and peer-supported learning (Kleiman et al., in: Kim (ed) Massive Open Online Courses: the MOOC Revolution, Routledge, New York, 2015). We examined how these design principles were enacted in the development of the MOOC-Eds and how they influenced the engagement of 5767 participants. We also analyzed opportunities the MOOC-Eds provided for participants to develop their knowledge of, beliefs about, and attitudes towards teaching mathematics and statistics. The Interconnected Model of Professional Growth (Clarke and Hollingsworth in Teach Teach Educ 18(8):947–967, 2002) was used to guide analysis of click data, discussion forum posts, and interviews to consider the ways in which elements of the external domain influenced the personal domain...
Journal of Statistics Education
One of the main goals of statistics is to use data to provide evidence in support of an argument.... more One of the main goals of statistics is to use data to provide evidence in support of an argument. This article will discuss some popular forms of writing assessments currently in use, to demonstrate the differences between the methods for structuring the students' learning to support their arguments with evidence. We share a model, which was originally created to assess students in introductory statistics and has been adapted for the second course in statistics, which takes a unique approach toward assessing the students' understanding of statistical concepts through writing. In this model, students are expected to answer prompts that required them to (1) take a stance on an argument, (2) defend their position with facts given in the prompt, (3) discern the implications that those facts implied, and (4) give a proper conclusion to their argument. We provide examples of a few of the writing assignment prompts used in the course, their intended assessment purpose, and common answers that students gave to these assignments. Supplementary materials for this article are available online.
Journal of Psychoeducational Assessment
Recently adopted state standards for middle grades and high school mathematics content have an in... more Recently adopted state standards for middle grades and high school mathematics content have an increased emphasis on statistical topics. With this change, teacher education programs may need to adapt how they prepare preservice secondary mathematics teachers (PSMTs) to teach statistics and require measures related to statistics teaching to assess the impact of programmatic changes and track teacher growth. Using responses from a sample of 290 PSMTs from 20 institutions across the United States, this study presents validity and reliability evidence for the high school version of the Self-Efficacy to Teach Statistics (SETS-HS), which could be used to assess statistics teaching efficacy. Confirmatory factor analysis results via Rasch modeling support the use of three subscales, which exhibit adequate reliabilities and correspond to the three levels in the Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education endorsed by the American Statistical Association. Item an...
Computers & Education
Abstract While many studies describe the use of technology in the mathematics classroom, few expl... more Abstract While many studies describe the use of technology in the mathematics classroom, few explore the factors that influence teacher decisions around its use. The participants in this study were 21 early career secondary mathematics teachers who had completed an undergraduate mathematics teacher preparation program in the USA with a strong emphasis on the use of technology to teach mathematics. In this qualitative study, interview data were collected and analyzed with attention toward why teachers choose to use technology to teach mathematics, what tools they chose to use and why, as well as the general factors they consider when selecting particular technology tools. Findings indicate that one of the most important factors when deciding whether to use technology was how well it aligned with the goals of a lesson. The range of technology used spanned mathematical action tools, collaboration tools, assessment tools, and communication tools. When selecting particular tools teachers most heavily considered ease of use for both themselves and their students. These findings suggest that when considering how to infuse technology into teacher education programs we suggest that it is important to focus more broadly on types of tools, ways teachers can position them, and how particular activities align with specific mathematics learning objectives.