To support mathematics educators as they consider implications of the Common Core State Standards... more To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics is publishing a series of feature articles. In this fourth installment, authors Polly and Orrill suggest implementation strategies for grades 5 and 6. A final, cohesive article will appear in the August 2012 issue. Authored by Susan Jo Russell, the last piece concentrates on the implementation of the eight Standards of Mathematical Practice (SMP) and the constellations of Practices and Standards.
To support mathematics educators as they consider implications of the Common Core State Standards... more To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics is publishing a series of feature articles. In this fourth installment, authors Polly and Orrill suggest implementation strategies for grades 5 and 6. A final, cohesive article will appear in the August 2012 issue. Authored by Susan Jo Russell, the last piece concentrates on the implementation of the eight Standards of Mathematical Practice (SMP) and the constellations of Practices and Standards.
Learning is, at its core, about making connections between different ideas in such a way that und... more Learning is, at its core, about making connections between different ideas in such a way that underlying structures emerge (eg, Bransford et al., 1999; diSessa, 2006; Hiebert and Carpenter, 1992). To successfully make connections between and among mathematical ideas, students need scaffolding that supports connection making (eg, Franke et al., 2009). Questioning serves this scaffolding role in classrooms. Questioning allows the teacher to support students in seeing mathematics as a set of related ideas that can be drawn upon ...
Background The National Council of Teachers of Mathematics‟ standards for teaching and learning (... more Background The National Council of Teachers of Mathematics‟ standards for teaching and learning (NCTM, 2000) require teachers to have a richer understanding of mathematics than traditionally required. One topic that is particularly difficult for teachers is division of fractions. For instance, Ball (1990) asked US elementary and secondary prospective teachers to contextualize the problem 2
Table of Contents Volume 14, Number 1 Summer 2003. Full Publication EndNote | PDF. Cover PDF From... more Table of Contents Volume 14, Number 1 Summer 2003. Full Publication EndNote | PDF. Cover PDF From the Editor PDF About the Cover PDF. Guest Editorial… Do You Need a PhD to Teach K–8 Mathematics in Ways Respected by the Mathematics Education Community? PDF CHANDRA HAWLEY ORRILL. Mathematics as “Gate-Keeper” (?): Three Theoretical Perspectives that Aim Toward Empowering All Children With a Key to the Gate Abstract | PDF DAVID W. STINSON. ...
Background A nationwide shortage of teachers combined with high turnover rates in the areas of sp... more Background A nationwide shortage of teachers combined with high turnover rates in the areas of special education, mathematics and science (Ingersoll, 2001), have resulted in a practice of recruitment of teachers from non-traditional backgrounds, especially in urban areas. While the interest in research on these teachers has risen, the research in this area is still minimal with questionable results. Nonetheless, results of studies suggest alternatively certified teachers are more willing to work in the critical needs areas with low-achieving ...
The importance of the constructivist view can perhaps best be appreciated through the contrast to... more The importance of the constructivist view can perhaps best be appreciated through the contrast to more traditional views of learning. The traditional view of learning that guides most teaching today is what is known as the information processing model or more generally the “acquisition” view of learning. In this view, knowledge consists of symbols (concepts, procedures, etc) and the ability to manipulate those symbols. Learning, then, is the acquisition of these symbols while “instruction” involves finding the most efficient means of ...
In this study, we examined the reflection-on-action of four middle school mathematics teachers fr... more In this study, we examined the reflection-on-action of four middle school mathematics teachers from the perspective of Cohen and Ball's instructional triangle (1999). We addressed questions of how teachers reflect on their students' understanding differently. The four teachers were asked about their students' thinking while watching video clips taken from their lessons. Findings indicate that the teachers showed differences assessing and interpreting students' thinking, differences by teaching experiences, and changes over ...
The Learning to Teach with Technology Studio was developed in response to the needs of teachers i... more The Learning to Teach with Technology Studio was developed in response to the needs of teachers in moving beyond the first stage of technology-based professional development by engaging teachers in a directed inquiry course that leads them through the development of an inquiry-oriented, technology-enhanced product to use in their classrooms with their students. The current study considers what happens when teachers are given the opportunity to" own" their learning-that is, they are given the opportunity to select their ...
FOSTERING HIGH SCHOOL TEACHER OWNERSHIP OF CHANGE: K-12 MATHEMATICS COORDINATORS AS CHANGE AGENTS, Aug 1, 2009
79 Introduction Our world has changed significantly over the last 100 years and continues to chan... more 79 Introduction Our world has changed significantly over the last 100 years and continues to change at an ever-increasing pace. Access to information and knowledge introduced by advances in technology alone is requiring today's youth to graduate with skills and abilities very different from just one generation before (Fullan, 2001).“Our current educational system was never designed to deliver the kind of results we now need to equip students for today's world–and tomorrow's”(Wagner et al., 2006). Because of this, viewing education as part of the ...
Annual Meeting of the American Educational Research Association: Seattle, US, 2001
The increasing popularity of distance education (Gubernick & Ebeling, 1997) as well as informatio... more The increasing popularity of distance education (Gubernick & Ebeling, 1997) as well as information age educational goals such as promoting information use over information acquisition (Brown, 2000) require that careful though be given to the learning environments we create. We not only need to consider our learning goals and pedagogical approaches, but also the tools we use to support communication in these environments. This is particularly important in Problem-Based Learning (PBL) environments where much of the ...
Research in education and psychology has demonstrated that adults and children often understand s... more Research in education and psychology has demonstrated that adults and children often understand shared experiences in very different ways, but much less is known about how teachers and their students understand shared lessons or how classroom learning occurs as teachers' and students' understandings interact over sequences of lessons. In fact, research on teachers and teaching and on students and learning have rarely been conducted within the same classrooms. The research proposed here will focus on the interplay between ...
World Conference on Educational Multimedia, …, 2003
This presentation will include results of evaluation of a Web-based professional system," Le... more This presentation will include results of evaluation of a Web-based professional system," Learning to Teach with Technology Studio (LTTS)." The evaluation was conducted to examine the effectiveness and impact of the LTTS learning environment with focus on two modules designed to promote scientific inquiry. A brief overview of LTTS, theoretical framework of the evaluation, findings of the evaluation, and recommendations for designing Web-based professional development systems will be addressed.
What does it mean to align an assessment to the domain of interest? In this paper, we analyze tea... more What does it mean to align an assessment to the domain of interest? In this paper, we analyze teachers' performance on the Learning Mathematics for Teaching assessment of Proportional Reasoning. Using a mixture Rasch model, we analyze their performance on the entire assessment, then on two different subsets of items from the original assessment. We consider the affordances of different conceptualizations of the domain and consider the implications of the domain definition on the claims we can make about teacher performance. We use a single assessment to illustrate the differences in results that can arise based on the ways in which the domain of interest is conceptualized. Suggestions for test development are provided.
International Group for the Psychology of Mathematics Education, 2013
In this study, we considered how four teachers reasoned about proportional situations involving g... more In this study, we considered how four teachers reasoned about proportional situations involving geometry. We used pilot interviews conducted with in-service middle grades teachers around a set of proportional tasks. Analysis relied on a knowledge in pieces lens to uncover the resources that each teacher used in solving the tasks and which resources seemed to support the reasoning. Our findings suggest that this is an area of proportional reasoning in which multiplicative comparisons are important, but insufficient, for supporting reasoning. We also found that these teachers did not invoke the constant of proportionality in ways that supported their reasoning.
To support mathematics educators as they consider implications of the Common Core State Standards... more To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics is publishing a series of feature articles. In this fourth installment, authors Polly and Orrill suggest implementation strategies for grades 5 and 6. A final, cohesive article will appear in the August 2012 issue. Authored by Susan Jo Russell, the last piece concentrates on the implementation of the eight Standards of Mathematical Practice (SMP) and the constellations of Practices and Standards.
To support mathematics educators as they consider implications of the Common Core State Standards... more To support mathematics educators as they consider implications of the Common Core State Standards for Mathematics (CCSSM) for instruction and assessment, Teaching Children Mathematics is publishing a series of feature articles. In this fourth installment, authors Polly and Orrill suggest implementation strategies for grades 5 and 6. A final, cohesive article will appear in the August 2012 issue. Authored by Susan Jo Russell, the last piece concentrates on the implementation of the eight Standards of Mathematical Practice (SMP) and the constellations of Practices and Standards.
Learning is, at its core, about making connections between different ideas in such a way that und... more Learning is, at its core, about making connections between different ideas in such a way that underlying structures emerge (eg, Bransford et al., 1999; diSessa, 2006; Hiebert and Carpenter, 1992). To successfully make connections between and among mathematical ideas, students need scaffolding that supports connection making (eg, Franke et al., 2009). Questioning serves this scaffolding role in classrooms. Questioning allows the teacher to support students in seeing mathematics as a set of related ideas that can be drawn upon ...
Background The National Council of Teachers of Mathematics‟ standards for teaching and learning (... more Background The National Council of Teachers of Mathematics‟ standards for teaching and learning (NCTM, 2000) require teachers to have a richer understanding of mathematics than traditionally required. One topic that is particularly difficult for teachers is division of fractions. For instance, Ball (1990) asked US elementary and secondary prospective teachers to contextualize the problem 2
Table of Contents Volume 14, Number 1 Summer 2003. Full Publication EndNote | PDF. Cover PDF From... more Table of Contents Volume 14, Number 1 Summer 2003. Full Publication EndNote | PDF. Cover PDF From the Editor PDF About the Cover PDF. Guest Editorial… Do You Need a PhD to Teach K–8 Mathematics in Ways Respected by the Mathematics Education Community? PDF CHANDRA HAWLEY ORRILL. Mathematics as “Gate-Keeper” (?): Three Theoretical Perspectives that Aim Toward Empowering All Children With a Key to the Gate Abstract | PDF DAVID W. STINSON. ...
Background A nationwide shortage of teachers combined with high turnover rates in the areas of sp... more Background A nationwide shortage of teachers combined with high turnover rates in the areas of special education, mathematics and science (Ingersoll, 2001), have resulted in a practice of recruitment of teachers from non-traditional backgrounds, especially in urban areas. While the interest in research on these teachers has risen, the research in this area is still minimal with questionable results. Nonetheless, results of studies suggest alternatively certified teachers are more willing to work in the critical needs areas with low-achieving ...
The importance of the constructivist view can perhaps best be appreciated through the contrast to... more The importance of the constructivist view can perhaps best be appreciated through the contrast to more traditional views of learning. The traditional view of learning that guides most teaching today is what is known as the information processing model or more generally the “acquisition” view of learning. In this view, knowledge consists of symbols (concepts, procedures, etc) and the ability to manipulate those symbols. Learning, then, is the acquisition of these symbols while “instruction” involves finding the most efficient means of ...
In this study, we examined the reflection-on-action of four middle school mathematics teachers fr... more In this study, we examined the reflection-on-action of four middle school mathematics teachers from the perspective of Cohen and Ball's instructional triangle (1999). We addressed questions of how teachers reflect on their students' understanding differently. The four teachers were asked about their students' thinking while watching video clips taken from their lessons. Findings indicate that the teachers showed differences assessing and interpreting students' thinking, differences by teaching experiences, and changes over ...
The Learning to Teach with Technology Studio was developed in response to the needs of teachers i... more The Learning to Teach with Technology Studio was developed in response to the needs of teachers in moving beyond the first stage of technology-based professional development by engaging teachers in a directed inquiry course that leads them through the development of an inquiry-oriented, technology-enhanced product to use in their classrooms with their students. The current study considers what happens when teachers are given the opportunity to" own" their learning-that is, they are given the opportunity to select their ...
FOSTERING HIGH SCHOOL TEACHER OWNERSHIP OF CHANGE: K-12 MATHEMATICS COORDINATORS AS CHANGE AGENTS, Aug 1, 2009
79 Introduction Our world has changed significantly over the last 100 years and continues to chan... more 79 Introduction Our world has changed significantly over the last 100 years and continues to change at an ever-increasing pace. Access to information and knowledge introduced by advances in technology alone is requiring today's youth to graduate with skills and abilities very different from just one generation before (Fullan, 2001).“Our current educational system was never designed to deliver the kind of results we now need to equip students for today's world–and tomorrow's”(Wagner et al., 2006). Because of this, viewing education as part of the ...
Annual Meeting of the American Educational Research Association: Seattle, US, 2001
The increasing popularity of distance education (Gubernick & Ebeling, 1997) as well as informatio... more The increasing popularity of distance education (Gubernick & Ebeling, 1997) as well as information age educational goals such as promoting information use over information acquisition (Brown, 2000) require that careful though be given to the learning environments we create. We not only need to consider our learning goals and pedagogical approaches, but also the tools we use to support communication in these environments. This is particularly important in Problem-Based Learning (PBL) environments where much of the ...
Research in education and psychology has demonstrated that adults and children often understand s... more Research in education and psychology has demonstrated that adults and children often understand shared experiences in very different ways, but much less is known about how teachers and their students understand shared lessons or how classroom learning occurs as teachers' and students' understandings interact over sequences of lessons. In fact, research on teachers and teaching and on students and learning have rarely been conducted within the same classrooms. The research proposed here will focus on the interplay between ...
World Conference on Educational Multimedia, …, 2003
This presentation will include results of evaluation of a Web-based professional system," Le... more This presentation will include results of evaluation of a Web-based professional system," Learning to Teach with Technology Studio (LTTS)." The evaluation was conducted to examine the effectiveness and impact of the LTTS learning environment with focus on two modules designed to promote scientific inquiry. A brief overview of LTTS, theoretical framework of the evaluation, findings of the evaluation, and recommendations for designing Web-based professional development systems will be addressed.
What does it mean to align an assessment to the domain of interest? In this paper, we analyze tea... more What does it mean to align an assessment to the domain of interest? In this paper, we analyze teachers' performance on the Learning Mathematics for Teaching assessment of Proportional Reasoning. Using a mixture Rasch model, we analyze their performance on the entire assessment, then on two different subsets of items from the original assessment. We consider the affordances of different conceptualizations of the domain and consider the implications of the domain definition on the claims we can make about teacher performance. We use a single assessment to illustrate the differences in results that can arise based on the ways in which the domain of interest is conceptualized. Suggestions for test development are provided.
International Group for the Psychology of Mathematics Education, 2013
In this study, we considered how four teachers reasoned about proportional situations involving g... more In this study, we considered how four teachers reasoned about proportional situations involving geometry. We used pilot interviews conducted with in-service middle grades teachers around a set of proportional tasks. Analysis relied on a knowledge in pieces lens to uncover the resources that each teacher used in solving the tasks and which resources seemed to support the reasoning. Our findings suggest that this is an area of proportional reasoning in which multiplicative comparisons are important, but insufficient, for supporting reasoning. We also found that these teachers did not invoke the constant of proportionality in ways that supported their reasoning.
Journal for Research in Mathematics Education, 2012
Researchers have recently used traditional item response theory (IRT) models to measure mathemati... more Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called the mixture Rasch model that allows for subgroups. The model was applied to middle-grades teachers' performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic.
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