Gerald Kulm | Texas A&M University (original) (raw)
Papers by Gerald Kulm
Journal of Mathematics Teacher Education, 2008
This case study of a first-year and an experienced teacher presents an analysis of the place and ... more This case study of a first-year and an experienced teacher presents an analysis of the place and frequency of three types of questions: probing, guiding, and factual. We examined the use of these questions in the course of five lessons, in order to study the relationship between ...
Journal of Mathematics Teacher Education, 2008
This case study of a first-year and an experienced teacher presents an analysis of the place and ... more This case study of a first-year and an experienced teacher presents an analysis of the place and frequency of three types of questions: probing, guiding, and factual. We examined the use of these questions in the course of five lessons, in order to study the relationship between ...
New ICMI Study Series, 2006
This paper outlines the nexus between developing pedagogical content knowledge and the pressures ... more This paper outlines the nexus between developing pedagogical content knowledge and the pressures for preparing preservice teachers to be successful on high stakes testing.
Page 1. THE ORIGIN AND PERSISTENCE OF MISCONCEPTIONS IN STATISTICAL THINKING Robert M. Capraro, G... more Page 1. THE ORIGIN AND PERSISTENCE OF MISCONCEPTIONS IN STATISTICAL THINKING Robert M. Capraro, Gerald Kulm, Mary Hammer, Mary Margaret Capraro Texas A&M University rcapraro@coe.tamu.edu, gkulm ...
The purpose of this paper is to describe a study we are conducting on the improvement of mathemat... more The purpose of this paper is to describe a study we are conducting on the improvement of mathematics teaching and learning at the middle school level through professional development and to discuss some of the research issues that we have encountered in conducting the study. The paper will lay out the various rationales for our initial design and for the adjustments that we made along the way. We are nearing the end of year two of a five-year study, so this is very much a work in progress. The study is not large in terms of the number of teachers involved (approximately 50 teachers and 1,000 students per year in the early stages of the study), but it is a complex study involving many interconnected elements. In Part I we lay out the design of the study, and in Part II we discuss some of the issues that we are facing as we progress through our work.
ZDM, 2009
Curriculum, as a cultural and system-specific artifact, outlines mathematics teaching and learnin... more Curriculum, as a cultural and system-specific artifact, outlines mathematics teaching and learning activities in school education. Studies of curriculum and its changes are thus important to reveal the expectations, processes, and outcomes of students' school learning experiences that are situated in different cultural and system contexts. In this article, we aim to propose a framework that can help readers to develop a better understanding of curriculum practices and changes in China and/or the United States that have been reported and discussed in articles published in this themed issue. Going beyond the selected education systems, further studies of curriculum practices and changes are much needed in helping ensure the success of educational reforms in different cultural and system contexts
ZDM, 2009
In this study, we aimed to examine mathematics teachers’ daily lesson plans and associated practi... more In this study, we aimed to examine mathematics teachers’ daily lesson plans and associated practices and thinking in lesson plan development. By focusing on teachers’ preparation for teaching fraction division, we collected and analyzed a sequence of four lesson plans from each of six mathematics teachers in six different elementary schools in China. Interviews with these teachers were also analyzed
ZDM, 2008
To make teacher preparation and professional development effective, it is important to find out p... more To make teacher preparation and professional development effective, it is important to find out possible deficiencies in teachers' knowledge as well as teachers' own perceptions about their needs. By focusing on preservice teachers' knowledge of fraction division in this article, we conceptualize the notion of pre-service teachers' knowledge in mathematics and pedagogy for teaching as containing both teachers' perceptions of their preparation and their mathematics knowledge needed for teaching. With specific assessment instruments developed for pre-service middle school teachers, we focus on both pre-service teachers' own perceptions about their knowledge preparation and the extent of their mathematics knowledge on the topic of fraction division. The results reveal a wide gap between sampled pre-service middle school teachers' general perceptions/confidence and their limited mathematics knowledge needed for teaching fraction division conceptually. The results suggest that these pre-service teachers need to develop a sound and deep understanding of mathematics knowledge for teaching in order to build their confidence for classroom instruction. The study's findings indicate the feasibility and importance of conceptualizing the notion of teachers' knowledge in mathematics and pedagogy for teaching to include teachers' perceptions. The applicability and implications of this expanded notion of teachers' knowledge is then discussed.
The Urban Review, 1995
In this paper, we describe the work by a team of university and public school mathemat-ics educat... more In this paper, we describe the work by a team of university and public school mathemat-ics educators to design mathematics assessment tasks that are effective for students who have been identified at risk in mathematics, through their failure on a state mathe-matics assessment. We ...
The Journal of Mathematical Behavior, 2012
ABSTRACT This study examined prospective middle grade mathematics teachers’ knowledge of algebra ... more ABSTRACT This study examined prospective middle grade mathematics teachers’ knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It was found that the participants had relatively limited knowledge of algebra for teaching. They also revealed weakness in selecting appropriate perspectives of the concept of function and flexibly using representations of quadratic functions. They made numerous mistakes in solving quadratic or irrational equations and in algebraic manipulation and reasoning. The participants’ weakness in connecting algebraic and graphic representations resulted in their failure to solve quadratic inequalities and to judge the number of roots of quadratic functions. Follow-up interview further revealed the participants’ lack of knowledge in solving problems by integrating algebraic and graphic representations. The implications of these findings for mathematics teacher preparation are discussed.
The Journal of Educational Research, 2007
... The 6 teachers used Connected Mathematics: Bits and Pieces I, a sixth-grade text (simply call... more ... The 6 teachers used Connected Mathematics: Bits and Pieces I, a sixth-grade text (simply called CMP ... E Delaware F 05 Middle School M 5.5 37 min 5 min 5 min 5 46 ... 3. Scaffolding questions Met What, why, and how were hierarchical questions, according to students' thinking ...
School Science and Mathematics, 2010
Journal of Research in Childhood Education, 2005
Journal of Mathematics Teacher Education, 2008
This case study of a first-year and an experienced teacher presents an analysis of the place and ... more This case study of a first-year and an experienced teacher presents an analysis of the place and frequency of three types of questions: probing, guiding, and factual. We examined the use of these questions in the course of five lessons, in order to study the relationship between the part of the lesson and types of questions asked. In addition, we interviewed the teachers to gain insights into their reasons for asking different types of questions. Both teachers asked many more factual questions than other types of questions regardless of their teaching strategies. Both asked more probing questions during the summary part of the lessons than in other parts. The first year teacher asked more probing questions overall than the experienced teacher, except in a lesson in which the experienced teacher engaged student with manipulatives. Guiding questions were rarely used by either teacher. In the interviews, both teachers said asking higher order questions was important for better students' learning, even though they asked relatively few probing or guiding questions. Using the indicators we developed for question types, we found that the two teachers were aware of the functions of questions they used. Even after a considerable amount of time had elapsed, they were able to recall the lesson from a video clip and explain why they used questions with particular students or in a specific situation
Journal of Mathematics Teacher Education, 2008
This case study of a first-year and an experienced teacher presents an analysis of the place and ... more This case study of a first-year and an experienced teacher presents an analysis of the place and frequency of three types of questions: probing, guiding, and factual. We examined the use of these questions in the course of five lessons, in order to study the relationship between ...
Journal of Mathematics Teacher Education, 2008
This case study of a first-year and an experienced teacher presents an analysis of the place and ... more This case study of a first-year and an experienced teacher presents an analysis of the place and frequency of three types of questions: probing, guiding, and factual. We examined the use of these questions in the course of five lessons, in order to study the relationship between ...
New ICMI Study Series, 2006
This paper outlines the nexus between developing pedagogical content knowledge and the pressures ... more This paper outlines the nexus between developing pedagogical content knowledge and the pressures for preparing preservice teachers to be successful on high stakes testing.
Page 1. THE ORIGIN AND PERSISTENCE OF MISCONCEPTIONS IN STATISTICAL THINKING Robert M. Capraro, G... more Page 1. THE ORIGIN AND PERSISTENCE OF MISCONCEPTIONS IN STATISTICAL THINKING Robert M. Capraro, Gerald Kulm, Mary Hammer, Mary Margaret Capraro Texas A&M University rcapraro@coe.tamu.edu, gkulm ...
The purpose of this paper is to describe a study we are conducting on the improvement of mathemat... more The purpose of this paper is to describe a study we are conducting on the improvement of mathematics teaching and learning at the middle school level through professional development and to discuss some of the research issues that we have encountered in conducting the study. The paper will lay out the various rationales for our initial design and for the adjustments that we made along the way. We are nearing the end of year two of a five-year study, so this is very much a work in progress. The study is not large in terms of the number of teachers involved (approximately 50 teachers and 1,000 students per year in the early stages of the study), but it is a complex study involving many interconnected elements. In Part I we lay out the design of the study, and in Part II we discuss some of the issues that we are facing as we progress through our work.
ZDM, 2009
Curriculum, as a cultural and system-specific artifact, outlines mathematics teaching and learnin... more Curriculum, as a cultural and system-specific artifact, outlines mathematics teaching and learning activities in school education. Studies of curriculum and its changes are thus important to reveal the expectations, processes, and outcomes of students' school learning experiences that are situated in different cultural and system contexts. In this article, we aim to propose a framework that can help readers to develop a better understanding of curriculum practices and changes in China and/or the United States that have been reported and discussed in articles published in this themed issue. Going beyond the selected education systems, further studies of curriculum practices and changes are much needed in helping ensure the success of educational reforms in different cultural and system contexts
ZDM, 2009
In this study, we aimed to examine mathematics teachers’ daily lesson plans and associated practi... more In this study, we aimed to examine mathematics teachers’ daily lesson plans and associated practices and thinking in lesson plan development. By focusing on teachers’ preparation for teaching fraction division, we collected and analyzed a sequence of four lesson plans from each of six mathematics teachers in six different elementary schools in China. Interviews with these teachers were also analyzed
ZDM, 2008
To make teacher preparation and professional development effective, it is important to find out p... more To make teacher preparation and professional development effective, it is important to find out possible deficiencies in teachers' knowledge as well as teachers' own perceptions about their needs. By focusing on preservice teachers' knowledge of fraction division in this article, we conceptualize the notion of pre-service teachers' knowledge in mathematics and pedagogy for teaching as containing both teachers' perceptions of their preparation and their mathematics knowledge needed for teaching. With specific assessment instruments developed for pre-service middle school teachers, we focus on both pre-service teachers' own perceptions about their knowledge preparation and the extent of their mathematics knowledge on the topic of fraction division. The results reveal a wide gap between sampled pre-service middle school teachers' general perceptions/confidence and their limited mathematics knowledge needed for teaching fraction division conceptually. The results suggest that these pre-service teachers need to develop a sound and deep understanding of mathematics knowledge for teaching in order to build their confidence for classroom instruction. The study's findings indicate the feasibility and importance of conceptualizing the notion of teachers' knowledge in mathematics and pedagogy for teaching to include teachers' perceptions. The applicability and implications of this expanded notion of teachers' knowledge is then discussed.
The Urban Review, 1995
In this paper, we describe the work by a team of university and public school mathemat-ics educat... more In this paper, we describe the work by a team of university and public school mathemat-ics educators to design mathematics assessment tasks that are effective for students who have been identified at risk in mathematics, through their failure on a state mathe-matics assessment. We ...
The Journal of Mathematical Behavior, 2012
ABSTRACT This study examined prospective middle grade mathematics teachers’ knowledge of algebra ... more ABSTRACT This study examined prospective middle grade mathematics teachers’ knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It was found that the participants had relatively limited knowledge of algebra for teaching. They also revealed weakness in selecting appropriate perspectives of the concept of function and flexibly using representations of quadratic functions. They made numerous mistakes in solving quadratic or irrational equations and in algebraic manipulation and reasoning. The participants’ weakness in connecting algebraic and graphic representations resulted in their failure to solve quadratic inequalities and to judge the number of roots of quadratic functions. Follow-up interview further revealed the participants’ lack of knowledge in solving problems by integrating algebraic and graphic representations. The implications of these findings for mathematics teacher preparation are discussed.
The Journal of Educational Research, 2007
... The 6 teachers used Connected Mathematics: Bits and Pieces I, a sixth-grade text (simply call... more ... The 6 teachers used Connected Mathematics: Bits and Pieces I, a sixth-grade text (simply called CMP ... E Delaware F 05 Middle School M 5.5 37 min 5 min 5 min 5 46 ... 3. Scaffolding questions Met What, why, and how were hierarchical questions, according to students' thinking ...
School Science and Mathematics, 2010
Journal of Research in Childhood Education, 2005
Journal of Mathematics Teacher Education, 2008
This case study of a first-year and an experienced teacher presents an analysis of the place and ... more This case study of a first-year and an experienced teacher presents an analysis of the place and frequency of three types of questions: probing, guiding, and factual. We examined the use of these questions in the course of five lessons, in order to study the relationship between the part of the lesson and types of questions asked. In addition, we interviewed the teachers to gain insights into their reasons for asking different types of questions. Both teachers asked many more factual questions than other types of questions regardless of their teaching strategies. Both asked more probing questions during the summary part of the lessons than in other parts. The first year teacher asked more probing questions overall than the experienced teacher, except in a lesson in which the experienced teacher engaged student with manipulatives. Guiding questions were rarely used by either teacher. In the interviews, both teachers said asking higher order questions was important for better students' learning, even though they asked relatively few probing or guiding questions. Using the indicators we developed for question types, we found that the two teachers were aware of the functions of questions they used. Even after a considerable amount of time had elapsed, they were able to recall the lesson from a video clip and explain why they used questions with particular students or in a specific situation