In this research, our objective was to identify development enhancing features of play between pa... more In this research, our objective was to identify development enhancing features of play between parent-child (ages 26 to 39 months) dyads that may be more supportive for mathematical learning. While the adult in this research is a parent, the results can be applied to other early year settings where the adult may be an early childhood educator or caregiver. Emerging from a qualitative analysis of 23 30-minute naturalistic play sessions, three development enhancing features were identified: (1) reinforcing learning, (2) checking for understanding, or (3) advancing learning. Combinations (one or more) of these development enhancing features formed the basis of the conceptualization of “purposeful play.” Purposeful play is defined and potential implications for mathematical learning and parent-child play are discussed.
Our aim in this paper is to summarize some of the research that points to the central role that m... more Our aim in this paper is to summarize some of the research that points to the central role that mothers have, often as the primary caregivers, to young children’s mathematical learning and development. The forthcoming analysis points to the important potential of mathematically mindful mothering as a mechanism for optimizing the mathematical environment and mathematical learning potential of a young child. We define mathematically mindful as the conscious awareness and engagement of mathematical opportunities present in the environment or made possible through the environment and the conscious attention to mathematical biases. Our focus on mothering is not intended to suggest that some results are not relatable to other caregivers but rather to synthesize some important studies that involve mothers or primarily mothers. Our synthesis focuses on what mothers do mathematically in their homes, the implications of these activities on young children’s future mathematical potential, and potential beliefs or biases some mothers may hold that are noteworthy.
Canadian Journal of Math, Science & Technology …, 2005
Yerushalmy, M., Katriel, H., & Sternberg, B. Visual Math: Functions. Available: http://www.cet.ac... more Yerushalmy, M., Katriel, H., & Sternberg, B. Visual Math: Functions. Available: http://www.cet.ac.il/math/function/english/ (accessed 26 July 2005).
International Journal of Science and Mathematics …, 2010
Utilizing video study methodology where participants, as well as the researcher, analyzed their o... more Utilizing video study methodology where participants, as well as the researcher, analyzed their own video data, this research examined the nature of students talking aloud during peer collaborations in mathematics. The findings suggest that students engage in three types of talking aloud: (1) clarification of thinking (i.e. spontaneous utterances related to the mathematical task); (2) expressions of confusion (i.e. “I don’t understand!”), with the explicit intent of eliciting support from peers; or (3) a combination of (1) and (2). The findings also show that students do not perceive other students’ talking aloud as an inter-communicative gesture. This research highlights the importance emphasizing to students that talking aloud during peer collaborations should be viewed as a potential antecedent to communicative interaction and the importance of teaching students how to listen to one another.
ABSTRACT How teachers think about student thinking informs the ways in which teachers teach. By e... more ABSTRACT How teachers think about student thinking informs the ways in which teachers teach. By examining teachers’ anticipation of student thinking we can begin to unpack the assumptions teachers make about teaching and learning. Using a “mathematics for teaching” framework, this research examines and compares the sorts of assumptions teachers make in relation to “student content knowledge” versus actual “learning paths” taken by students. Groups of teachers, who have advanced degrees in mathematics, education, and mathematics education, and tenth grade students engaged in a common mathematical task. Teachers were asked to model, in their completion of the task, possible learning paths students might take. Our findings suggest that teachers, in general, had difficulty anticipating student learning paths. Furthermore, this difficulty might be attributed to their significant “specialized content knowledge” of mathematics. We propose, through this work, that examining student learning paths may be a fruitful locus of inquiry for developing both pre-service and in-service teachers’ knowledge about mathematics for teaching.
A “math congress” is a pedagogical approach in which students present their solutions from their ... more A “math congress” is a pedagogical approach in which students present their solutions from their mathematical work completed individually, in pairs, or in small groups, and share and defend their mathematical thinking. Mathematical artifacts presented during math congress remain on display as community records of practice. Math congress has four key functions: To highlight and document key mathematical concepts, to emphasize connections between different mathematical strategies, to facilitate conceptual development, and to scaffold learning by drawing attention to the efficiency of particular strategies. The goal of the research was to analyze the role of the math congress in eighth-grade students' development of mathematical thinking. Results suggest that while math congress was helpful for some students, other students articulated continued uncertainty about their mathematical thinking. Pedagogical recommendations as well as future research direction are discussed.
Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen... more Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur’s re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problem-posing in learning mathematics, as well as imagination as a cognitive space for learning.
This research compared the cognitive demand levels of mathematical tasks engaged in during classr... more This research compared the cognitive demand levels of mathematical tasks engaged in during classroom instruction to paired mathematical tasks assigned for homework. The research took place in an eighth-grade classroom over the course of one school year. In total, the cognitive demand levels of 66 mathematical tasks were evaluated using the IQA Academic Rigor: Mathematics Rubric for the Potential of the Task (Boston & Smith, 2009). Results from this research showed that approximately two thirds of the time the mathematical tasks assigned for homework differed in levels from the tasks used during classroom instruction. Implications for student learning, classroom instruction, homework, and further research are discussed.Cette étude compare le niveau d’exigence cognitive des tâches mathématiques accomplies en classe et celui des tâches mathématiques données en devoir à faire à la maison. L’étude a été réalisée au cours d’une année scolaire, dans une classe de huitième année. Au total, le niveau d’exigence cognitive de 66 tâches mathématiques a été évalué au moyen du test d’évaluation de la qualité de l’enseignement de Boston et Smith (IQA Academic Rigor: Mathematics Rubric for the Potential of the Task, 2009). Les résultats montrent que, dans environ les deux tiers des cas, les tâches mathématiques données en devoir étaient d’un niveau différent de celui des tâches accomplies en classe pendant les cours. Les implications de cet état de fait sur l’apprentissage, l’enseignement en classe, les devoirs et la recherche future sont ensuite analysées.
In this research, our objective was to identify development enhancing features of play between pa... more In this research, our objective was to identify development enhancing features of play between parent-child (ages 26 to 39 months) dyads that may be more supportive for mathematical learning. While the adult in this research is a parent, the results can be applied to other early year settings where the adult may be an early childhood educator or caregiver. Emerging from a qualitative analysis of 23 30-minute naturalistic play sessions, three development enhancing features were identified: (1) reinforcing learning, (2) checking for understanding, or (3) advancing learning. Combinations (one or more) of these development enhancing features formed the basis of the conceptualization of “purposeful play.” Purposeful play is defined and potential implications for mathematical learning and parent-child play are discussed.
Our aim in this paper is to summarize some of the research that points to the central role that m... more Our aim in this paper is to summarize some of the research that points to the central role that mothers have, often as the primary caregivers, to young children’s mathematical learning and development. The forthcoming analysis points to the important potential of mathematically mindful mothering as a mechanism for optimizing the mathematical environment and mathematical learning potential of a young child. We define mathematically mindful as the conscious awareness and engagement of mathematical opportunities present in the environment or made possible through the environment and the conscious attention to mathematical biases. Our focus on mothering is not intended to suggest that some results are not relatable to other caregivers but rather to synthesize some important studies that involve mothers or primarily mothers. Our synthesis focuses on what mothers do mathematically in their homes, the implications of these activities on young children’s future mathematical potential, and potential beliefs or biases some mothers may hold that are noteworthy.
Canadian Journal of Math, Science & Technology …, 2005
Yerushalmy, M., Katriel, H., & Sternberg, B. Visual Math: Functions. Available: http://www.cet.ac... more Yerushalmy, M., Katriel, H., & Sternberg, B. Visual Math: Functions. Available: http://www.cet.ac.il/math/function/english/ (accessed 26 July 2005).
International Journal of Science and Mathematics …, 2010
Utilizing video study methodology where participants, as well as the researcher, analyzed their o... more Utilizing video study methodology where participants, as well as the researcher, analyzed their own video data, this research examined the nature of students talking aloud during peer collaborations in mathematics. The findings suggest that students engage in three types of talking aloud: (1) clarification of thinking (i.e. spontaneous utterances related to the mathematical task); (2) expressions of confusion (i.e. “I don’t understand!”), with the explicit intent of eliciting support from peers; or (3) a combination of (1) and (2). The findings also show that students do not perceive other students’ talking aloud as an inter-communicative gesture. This research highlights the importance emphasizing to students that talking aloud during peer collaborations should be viewed as a potential antecedent to communicative interaction and the importance of teaching students how to listen to one another.
ABSTRACT How teachers think about student thinking informs the ways in which teachers teach. By e... more ABSTRACT How teachers think about student thinking informs the ways in which teachers teach. By examining teachers’ anticipation of student thinking we can begin to unpack the assumptions teachers make about teaching and learning. Using a “mathematics for teaching” framework, this research examines and compares the sorts of assumptions teachers make in relation to “student content knowledge” versus actual “learning paths” taken by students. Groups of teachers, who have advanced degrees in mathematics, education, and mathematics education, and tenth grade students engaged in a common mathematical task. Teachers were asked to model, in their completion of the task, possible learning paths students might take. Our findings suggest that teachers, in general, had difficulty anticipating student learning paths. Furthermore, this difficulty might be attributed to their significant “specialized content knowledge” of mathematics. We propose, through this work, that examining student learning paths may be a fruitful locus of inquiry for developing both pre-service and in-service teachers’ knowledge about mathematics for teaching.
A “math congress” is a pedagogical approach in which students present their solutions from their ... more A “math congress” is a pedagogical approach in which students present their solutions from their mathematical work completed individually, in pairs, or in small groups, and share and defend their mathematical thinking. Mathematical artifacts presented during math congress remain on display as community records of practice. Math congress has four key functions: To highlight and document key mathematical concepts, to emphasize connections between different mathematical strategies, to facilitate conceptual development, and to scaffold learning by drawing attention to the efficiency of particular strategies. The goal of the research was to analyze the role of the math congress in eighth-grade students' development of mathematical thinking. Results suggest that while math congress was helpful for some students, other students articulated continued uncertainty about their mathematical thinking. Pedagogical recommendations as well as future research direction are discussed.
Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen... more Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur’s re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problem-posing in learning mathematics, as well as imagination as a cognitive space for learning.
This research compared the cognitive demand levels of mathematical tasks engaged in during classr... more This research compared the cognitive demand levels of mathematical tasks engaged in during classroom instruction to paired mathematical tasks assigned for homework. The research took place in an eighth-grade classroom over the course of one school year. In total, the cognitive demand levels of 66 mathematical tasks were evaluated using the IQA Academic Rigor: Mathematics Rubric for the Potential of the Task (Boston & Smith, 2009). Results from this research showed that approximately two thirds of the time the mathematical tasks assigned for homework differed in levels from the tasks used during classroom instruction. Implications for student learning, classroom instruction, homework, and further research are discussed.Cette étude compare le niveau d’exigence cognitive des tâches mathématiques accomplies en classe et celui des tâches mathématiques données en devoir à faire à la maison. L’étude a été réalisée au cours d’une année scolaire, dans une classe de huitième année. Au total, le niveau d’exigence cognitive de 66 tâches mathématiques a été évalué au moyen du test d’évaluation de la qualité de l’enseignement de Boston et Smith (IQA Academic Rigor: Mathematics Rubric for the Potential of the Task, 2009). Les résultats montrent que, dans environ les deux tiers des cas, les tâches mathématiques données en devoir étaient d’un niveau différent de celui des tâches accomplies en classe pendant les cours. Les implications de cet état de fait sur l’apprentissage, l’enseignement en classe, les devoirs et la recherche future sont ensuite analysées.
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