This paper examines how the Connecting Mathematics for Elementary Teachers (CMET) project is conn... more This paper examines how the Connecting Mathematics for Elementary Teachers (CMET) project is connected to the self-efficacy of preservice teachers. The primary goal of the CMET project is to connect the mathematics that preservice elementary teachers are learning in their content courses with how children learn and think about mathematics. While several studies have focused on innovative curriculum projects and their effects on preservice teachers (Hill et. al., 2004, Lloyd, 1999) and recent research has shown that preservice teachers’ efficacy can be positively influenced in methods courses and in-service teachers’ efficacy through professional development (Ross & Bruce, 2005), we ask: “Can preservice elementary teachers’ efficacy be positively influenced earlier, in mathematical content courses, through a focus on children’s mathematical thinking?” Findings Statistically significant results for students at University I on all pre- and post-efficacy items indicate that participants...
The purpose of this paper is to present results from of an ongoing design research study that exp... more The purpose of this paper is to present results from of an ongoing design research study that explores the development of early pedagogical content knowledge (PCK). Prospective elementary and secondary teachers participated in this study while enrolled in mathematics courses designed to 1) strengthen their own understanding of K-12 mathematics, 2) enhance their understanding of the strategies and models that children use in mathematics problem solving and 3) develop their capacity to be able to see the development of the big mathematical ideas in children’s work and to analyze subsequent instruction that is based on that development. These aspects of understanding of children’s thinking—critical components of PCK— were measured throughout the courses using paper and pencil measures of MPCK and participants’ reflections on video cases of students working on investigations. Results of analyses of data collected from two administrations of these measures are used to compare the differe...
Science Teacher Preparation in Content-Based Second Language Acquisition, 2016
We developed a capstone science methods course to better support preservice teachers in learning ... more We developed a capstone science methods course to better support preservice teachers in learning how both to teach science in ways attentive to English Language Learners (ELLs) and to develop an adaptive disposition to engage in reflection on their teaching of ELLs. Our course embodies three principles: (1) building from students’ funds of knowledge; (2) implementing cognitively demanding tasks; and (3) providing opportunities for rich language and literacy exposure and practice. Our methods and analysis were guided by three research questions: How did preservice science teacher participants understand the three principles of our capstone course? What successes and struggles did they identify when attempting to use these three principles to inform their classroom practice? What suggestions did they have for ways to improve the course? From our qualitative analysis of interviews with preservice science teachers, we found they were better at describing and identifying language rich opportunities for their students than at identifying ways they used their students’ funds of knowledge to inform their instruction. We also found that they felt they would benefit from knowing how to identify the needs of ELLs and how to better differentiate instruction for students. These findings make clear that we can certainly improve this capstone course. Still, our goal remains to foster the development of an adaptive disposition so that preservice science teachers can effectively work with their unique and diverse group of ELLs, not only as student teachers in a temporary placement but also as beginning teachers in their own science classrooms.
ABSTRACT We investigated six preservice secondary science teachers’ implementation of reform-base... more ABSTRACT We investigated six preservice secondary science teachers’ implementation of reform-based science, in particular, their teaching of the Next Generation Science Standards’ (NGSS) science and engineering practice of using mathematics and computational thinking. A modified version of the Task Analysis Guide in Science served as our conceptual framework: It assesses both the integration of practices and content (i.e., the kind of thinking required), and the cognitive demand of tasks (i.e., the level of thinking required) in teachers’ lessons. We used this framework to qualitatively analyze our preservice teacher participants’ edTPA (teacher performance assessment) lessons—including their written commentaries, video-recorded lesson excerpts, and student work samples—for their implementation of the NGSS using mathematics and computational thinking practice. We examined (1) the integration of the mathematical content and practices outlined in the Common Core State Standards for Mathematics within the target NGSS practice, and (2) the cognitive demand of the mathematics in relation to science and mathematical practices. We found that four of our six preservice teachers implemented lessons that were integrated and cognitively demanding: These participants used the mathematics to move students’ understanding of the science phenomena forward. However, the other two participants implemented lessons that integrated mathematical content and practices but were low in cognitive demand. We conclude with implications for how teacher education programs can better support preservice teachers’ implementation of lessons that are both integrated and cognitively demanding so as to promote students’ mathematical reasoning and scientific sensemaking.
Professional training programs strive to prepare students for success in their respective fields.... more Professional training programs strive to prepare students for success in their respective fields. Despite sustained and concentrated efforts, however, a serious gap exists between training and practice, particularly in fields requiring complex decision-making. In the field of ...
International Journal of Mathematical Education in Science and Technology, 2015
This mixed-methods study describes classroom characteristics and student outcomes from university... more This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.
This paper examines how the Connecting Mathematics for Elementary Teachers (CMET) project is conn... more This paper examines how the Connecting Mathematics for Elementary Teachers (CMET) project is connected to the self-efficacy of preservice teachers. The primary goal of the CMET project is to connect the mathematics that preservice elementary teachers are learning in their content courses with how children learn and think about mathematics. While several studies have focused on innovative curriculum projects and their effects on preservice teachers (Hill et. al., 2004, Lloyd, 1999) and recent research has shown that preservice teachers’ efficacy can be positively influenced in methods courses and in-service teachers’ efficacy through professional development (Ross & Bruce, 2005), we ask: “Can preservice elementary teachers’ efficacy be positively influenced earlier, in mathematical content courses, through a focus on children’s mathematical thinking?” Findings Statistically significant results for students at University I on all pre- and post-efficacy items indicate that participants...
The purpose of this paper is to present results from of an ongoing design research study that exp... more The purpose of this paper is to present results from of an ongoing design research study that explores the development of early pedagogical content knowledge (PCK). Prospective elementary and secondary teachers participated in this study while enrolled in mathematics courses designed to 1) strengthen their own understanding of K-12 mathematics, 2) enhance their understanding of the strategies and models that children use in mathematics problem solving and 3) develop their capacity to be able to see the development of the big mathematical ideas in children’s work and to analyze subsequent instruction that is based on that development. These aspects of understanding of children’s thinking—critical components of PCK— were measured throughout the courses using paper and pencil measures of MPCK and participants’ reflections on video cases of students working on investigations. Results of analyses of data collected from two administrations of these measures are used to compare the differe...
Science Teacher Preparation in Content-Based Second Language Acquisition, 2016
We developed a capstone science methods course to better support preservice teachers in learning ... more We developed a capstone science methods course to better support preservice teachers in learning how both to teach science in ways attentive to English Language Learners (ELLs) and to develop an adaptive disposition to engage in reflection on their teaching of ELLs. Our course embodies three principles: (1) building from students’ funds of knowledge; (2) implementing cognitively demanding tasks; and (3) providing opportunities for rich language and literacy exposure and practice. Our methods and analysis were guided by three research questions: How did preservice science teacher participants understand the three principles of our capstone course? What successes and struggles did they identify when attempting to use these three principles to inform their classroom practice? What suggestions did they have for ways to improve the course? From our qualitative analysis of interviews with preservice science teachers, we found they were better at describing and identifying language rich opportunities for their students than at identifying ways they used their students’ funds of knowledge to inform their instruction. We also found that they felt they would benefit from knowing how to identify the needs of ELLs and how to better differentiate instruction for students. These findings make clear that we can certainly improve this capstone course. Still, our goal remains to foster the development of an adaptive disposition so that preservice science teachers can effectively work with their unique and diverse group of ELLs, not only as student teachers in a temporary placement but also as beginning teachers in their own science classrooms.
ABSTRACT We investigated six preservice secondary science teachers’ implementation of reform-base... more ABSTRACT We investigated six preservice secondary science teachers’ implementation of reform-based science, in particular, their teaching of the Next Generation Science Standards’ (NGSS) science and engineering practice of using mathematics and computational thinking. A modified version of the Task Analysis Guide in Science served as our conceptual framework: It assesses both the integration of practices and content (i.e., the kind of thinking required), and the cognitive demand of tasks (i.e., the level of thinking required) in teachers’ lessons. We used this framework to qualitatively analyze our preservice teacher participants’ edTPA (teacher performance assessment) lessons—including their written commentaries, video-recorded lesson excerpts, and student work samples—for their implementation of the NGSS using mathematics and computational thinking practice. We examined (1) the integration of the mathematical content and practices outlined in the Common Core State Standards for Mathematics within the target NGSS practice, and (2) the cognitive demand of the mathematics in relation to science and mathematical practices. We found that four of our six preservice teachers implemented lessons that were integrated and cognitively demanding: These participants used the mathematics to move students’ understanding of the science phenomena forward. However, the other two participants implemented lessons that integrated mathematical content and practices but were low in cognitive demand. We conclude with implications for how teacher education programs can better support preservice teachers’ implementation of lessons that are both integrated and cognitively demanding so as to promote students’ mathematical reasoning and scientific sensemaking.
Professional training programs strive to prepare students for success in their respective fields.... more Professional training programs strive to prepare students for success in their respective fields. Despite sustained and concentrated efforts, however, a serious gap exists between training and practice, particularly in fields requiring complex decision-making. In the field of ...
International Journal of Mathematical Education in Science and Technology, 2015
This mixed-methods study describes classroom characteristics and student outcomes from university... more This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.
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Papers by Sarah Hough