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.
Proceedings of the 42nd ACM technical symposium on Computer science education, 2011
A popular approach to introducing students to computer science is to involve middle-school studen... more A popular approach to introducing students to computer science is to involve middle-school students in engaging programming activities. One challenge in such a program is attracting students who are not already positively predisposed to computing. In order to attract a diverse audience, we developed a summer program based on culturally-relevant themes that appealed to our two target audiences, females and Latina/os. This paper describes our success in developing and implementing a computing curriculum and recruiting materials for a 2-week summer camp integrating two themes, animal conservation and Mayan culture. Scratch programming was used to engage students in creating animations about animals and Mayan culture, allowing them an interdisciplinary experience that combined programming, culture, biology, art, and storytelling. Our recruiting efforts resulted in an application pool that was 73% female and 67% Latina/o, with only 6.5% in neither group. We had 34 students complete the program. Preand post-surveys showed that the number of students citing computer science as their top choice for a career doubled and interest in computer science as a career more than tripled.
The purpose of this study was to explore teachers' growth in understanding of algebra using conce... more The purpose of this study was to explore teachers' growth in understanding of algebra using concept maps. The study was set in the context of a five-year National Science Foundation funded teacher retention and renewal professional development project. In this project both beginning and experienced teachers are supported as they increase their understanding about mathematics, their ability to implement effective mathematics practices in their classrooms, and their knowledge of working with English Learners. Results indicate that teachers' algebraic knowledge structures became more complex and connected as a result of their professional development. In addition, they were able to adapt their knowledge networks to incorporate important aspects of algebra into them. Concept maps are recommended to other leaders of mathematics professional development as a means of assessing change.
... As can be seen in table 3 above, all four groups of PETs generalized the strategy that they u... more ... As can be seen in table 3 above, all four groups of PETs generalized the strategy that they used in Maggie's Farm to use in Mikki's Chocolate Box whereas only the one group of PSTs that worked in context did. ... Level 0: Sees the congress in Miki's second congress as a share out ...
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 ...
The purpose of session is twofold: To discuss project CASELINK? S model of professional developme... more The purpose of session is twofold: To discuss project CASELINK? S model of professional development which utilizes interactive, web-based learning modules that are based on a constructivist view of the learner and a problem-based learning pedagogy; and to present research from an ongoing study that examines CASELINKS impact on teacher learning during a pilot test of a module. Project CASELINKS is a research and development project whose impetus was a question: How can traditional academic knowledge and the ...
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...
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.
Preservice elementary teachers' mathematical knowledge and beliefs about teaching and the lea... more Preservice elementary teachers' mathematical knowledge and beliefs about teaching and the learning of mathematics can be developed by focusing on how children learn and think about mathematics in content courses. This mathematical knowledge entails an understanding of the conceptual nature of procedures such as standard algorithms—understanding why they work, making sense of children's unique self generated algorithms for computation, and having the mathematical knowledge to explain procedures and concepts (Feikes & Schwingendorf, 2004). Teachers' beliefs about how children learn mathematics and how to teach children mathematics impacts teaching and might also be more fully developed by focusing on how children learn mathematics. A goal of the NSF supported (DUE 0341217) Connecting Mathematics for Elementary Teachers (CMET) project is to develop the beliefs and knowledge of preservice teachers in mathematics content courses. This approach is unique in that these are typically freshmen level mathematical content courses rather than professional development with practicing teachers (Hill, Rowan & Ball, 2005). CMET attempts to help preservice elementary teachers connect the mathematics they are learning in content courses with how children learn and think about mathematics thus tying research on children's learning of mathematics with practice. To this end, a supplement was developed that parallels the typical mathematics content course topics. The intent in helping preservice teachers make these types of connections is that they will both improve their own understanding of mathematics and eventually improve their future teaching of mathematics to children. The CMET materials primarily consist of descriptions, written for prospective elementary teachers, on how children think about, misunderstand, and come to understand mathematics. These descriptions are based on current research, and some of the connections include: how children come to know number, addition as a counting activity, and the importance of concept image in understanding geometry. Methods Evaluation of the CMET project is ongoing and considers multiple areas besides the focus of this paper including: teacher self-efficacy, teaching, and parents' use of these materials. For the study, 168 Likert survey questions were developed to correspond with the typical content in the mathematical content courses for elementary teachers. An analysis of the most popular textbooks for these courses was done to determine the content of CMET and the survey questions. The Likert questions were developed by two team members and two different members suggested revisions and verified the reversed worded questions. The control group
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.
To prepare preservice secondary science teachers to teach English learners (ELs), teacher educati... more To prepare preservice secondary science teachers to teach English learners (ELs), teacher education programs must provide sustained coursework and experiences in principles and strategies found effective in supporting ELs' learning 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.
Proceedings of the 42nd ACM technical symposium on Computer science education, 2011
A popular approach to introducing students to computer science is to involve middle-school studen... more A popular approach to introducing students to computer science is to involve middle-school students in engaging programming activities. One challenge in such a program is attracting students who are not already positively predisposed to computing. In order to attract a diverse audience, we developed a summer program based on culturally-relevant themes that appealed to our two target audiences, females and Latina/os. This paper describes our success in developing and implementing a computing curriculum and recruiting materials for a 2-week summer camp integrating two themes, animal conservation and Mayan culture. Scratch programming was used to engage students in creating animations about animals and Mayan culture, allowing them an interdisciplinary experience that combined programming, culture, biology, art, and storytelling. Our recruiting efforts resulted in an application pool that was 73% female and 67% Latina/o, with only 6.5% in neither group. We had 34 students complete the program. Preand post-surveys showed that the number of students citing computer science as their top choice for a career doubled and interest in computer science as a career more than tripled.
The purpose of this study was to explore teachers' growth in understanding of algebra using conce... more The purpose of this study was to explore teachers' growth in understanding of algebra using concept maps. The study was set in the context of a five-year National Science Foundation funded teacher retention and renewal professional development project. In this project both beginning and experienced teachers are supported as they increase their understanding about mathematics, their ability to implement effective mathematics practices in their classrooms, and their knowledge of working with English Learners. Results indicate that teachers' algebraic knowledge structures became more complex and connected as a result of their professional development. In addition, they were able to adapt their knowledge networks to incorporate important aspects of algebra into them. Concept maps are recommended to other leaders of mathematics professional development as a means of assessing change.
... As can be seen in table 3 above, all four groups of PETs generalized the strategy that they u... more ... As can be seen in table 3 above, all four groups of PETs generalized the strategy that they used in Maggie's Farm to use in Mikki's Chocolate Box whereas only the one group of PSTs that worked in context did. ... Level 0: Sees the congress in Miki's second congress as a share out ...
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 ...
The purpose of session is twofold: To discuss project CASELINK? S model of professional developme... more The purpose of session is twofold: To discuss project CASELINK? S model of professional development which utilizes interactive, web-based learning modules that are based on a constructivist view of the learner and a problem-based learning pedagogy; and to present research from an ongoing study that examines CASELINKS impact on teacher learning during a pilot test of a module. Project CASELINKS is a research and development project whose impetus was a question: How can traditional academic knowledge and the ...
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...
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.
Preservice elementary teachers' mathematical knowledge and beliefs about teaching and the lea... more Preservice elementary teachers' mathematical knowledge and beliefs about teaching and the learning of mathematics can be developed by focusing on how children learn and think about mathematics in content courses. This mathematical knowledge entails an understanding of the conceptual nature of procedures such as standard algorithms—understanding why they work, making sense of children's unique self generated algorithms for computation, and having the mathematical knowledge to explain procedures and concepts (Feikes & Schwingendorf, 2004). Teachers' beliefs about how children learn mathematics and how to teach children mathematics impacts teaching and might also be more fully developed by focusing on how children learn mathematics. A goal of the NSF supported (DUE 0341217) Connecting Mathematics for Elementary Teachers (CMET) project is to develop the beliefs and knowledge of preservice teachers in mathematics content courses. This approach is unique in that these are typically freshmen level mathematical content courses rather than professional development with practicing teachers (Hill, Rowan & Ball, 2005). CMET attempts to help preservice elementary teachers connect the mathematics they are learning in content courses with how children learn and think about mathematics thus tying research on children's learning of mathematics with practice. To this end, a supplement was developed that parallels the typical mathematics content course topics. The intent in helping preservice teachers make these types of connections is that they will both improve their own understanding of mathematics and eventually improve their future teaching of mathematics to children. The CMET materials primarily consist of descriptions, written for prospective elementary teachers, on how children think about, misunderstand, and come to understand mathematics. These descriptions are based on current research, and some of the connections include: how children come to know number, addition as a counting activity, and the importance of concept image in understanding geometry. Methods Evaluation of the CMET project is ongoing and considers multiple areas besides the focus of this paper including: teacher self-efficacy, teaching, and parents' use of these materials. For the study, 168 Likert survey questions were developed to correspond with the typical content in the mathematical content courses for elementary teachers. An analysis of the most popular textbooks for these courses was done to determine the content of CMET and the survey questions. The Likert questions were developed by two team members and two different members suggested revisions and verified the reversed worded questions. The control group
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.
To prepare preservice secondary science teachers to teach English learners (ELs), teacher educati... more To prepare preservice secondary science teachers to teach English learners (ELs), teacher education programs must provide sustained coursework and experiences in principles and strategies found effective in supporting ELs' learning of
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