M. Blanton - Academia.edu (original) (raw)
Papers by M. Blanton
Teaching Children Mathematics
Helping teachers learn to identify and create opportunities for algebraic thinking as part of the... more Helping teachers learn to identify and create opportunities for algebraic thinking as part of their normal classroom instruction.
Journal for Research in Mathematics Education
This research focuses on the retention of students’ algebraic understandings 1 year following a 3... more This research focuses on the retention of students’ algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3–5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance.
Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds
Early Childhood Education Journal
The original version of this article unfortunately contained a typo in co-author name. The author... more The original version of this article unfortunately contained a typo in co-author name. The author name is "Rafael Ramírez Uclés" instead it was published incorrectly as "Rafael Ramírez Úcles". The original article has been corrected. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Early Childhood Education Journal
Infancia y Aprendizaje
In this introduction to the Special Issue Early algebraic thinking: studies from different perspe... more In this introduction to the Special Issue Early algebraic thinking: studies from different perspectives, approaches and regions we provide readers with the main motivation and interest underlying research on early algebraic thinking. We then introduce the five papers that make up this Special Issue. Each of these studies, coming from various countries around the world, has a different theoretical framework, methodological approach and perspective regarding teachers, students, instructional practices and curricula. In this introduction, we summarize some of the main themes throughout the different papers, including interviewers' practices that can promote early algebraic thinking; the kinds of practices that teachers can implement to have a positive impact on students' early algebraic thinking; and the use of physical models to explore and promote aspects of early algebraic thinking. The Special Issue also includes an additional Prospectives piece by Analúcia Schliemann and David Carraher, in which they examine the algebraic thinking research in elementary school in light of the current mathematics standards in the United States.
Educational Studies in Mathematics
Mathematical Thinking and Learning
Teaching and Learning Proof Across the Grades
ABSTRACT
Teaching Children Mathematics
The study of functions has traditionally received the most attention at the secondary level, both... more The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents—for example, the Common Core State Standards for Mathematics (CCSSI 2010) and Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM] 2000). However, the growing acceptance of algebra as a K–grade 12 strand of thinking by math education researchers and in standards documents, along with the view that the study of functions is an important route into learning algebra (Carraher and Schliemann 2007), raises the importance of developing children’s understanding of functions in the elementary grades.
Educational Studies in Mathematics, 2017
Journal For Research in Mathematics Education, 2015
This article reports results from a study investigating the impact of a sustained, comprehensive ... more This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written pre- and post-assessment that addressed their understanding of several big ideas in the area of early algebra, including mathematical equivalence and equations, generalizing arithmetic, and functional thinking. We found that the intervention group significantly outperformed the nonintervention group and was more apt by posttest to use algebraic strategies to solve problems. Given the multitude of studies among adolescents documenting students' difficulties with algebra and the serious consequences of these difficulties, an important contribution of this research is the finding that—provided the appropriate instruction—children are capable of engaging successfully with a broad and diverse set of big algebraic ideas.
National Council of Teachers of Mathematics, Apr 15, 2011
As a part of a long term district-wide study, we report on achievement test results involving stu... more As a part of a long term district-wide study, we report on achievement test results involving students in a third-grade classroom taught by a teacher in a professional development program led by the authors and directed towards the integration of algebraic reasoning with elementary school mathematics. The teacher's practice, reported upon elsewhere, embodied many of the features targeted in the professional development program, and her students' performance on a statewide standardized test for fourth graders exceeded those of a comparable control class from the same school and those of her district's fourth graders, and approximated the performance of fourth graders statewide. (Author) Reproductions supplied by EDRS are the best that can be made from the original document.
Journal for Research in Mathematics Education, 2015
This article reports results from a study investigating the impact of a sustained, comprehensive ... more This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written pre- and post-assessment that addressed their understanding of several big ideas in the area of early algebra, including mathematical equivalence and equations, generalizing arithmetic, and functional thinking. We found that the intervention group significantly outperformed the nonintervention group and was more apt by posttest to use algebraic strategies to solve problems. Given the multitude of studies among adolescents documenting students' difficulties with algebra and the serious consequences of these difficulties, an important contribution of this research is the finding that—provided the appropriate instruction—children ...
This investigation uses classroom discourse in an undergraduate mathematics course to challenge p... more This investigation uses classroom discourse in an undergraduate mathematics course to challenge preservice secondary mathematics teachers' notions about mathematical discourse, what it should resemble in the classroom, and how it can be cultivated by classroom teachers. The research setting was an upper level geometry course. Eleven preservice mathematics teachers participated. Results indicated a transition in participants' image of discourse as an active process by which students use the collective knowledge of their peers to build mathematical understanding and a development in students' ability to participate in such discourse. This awareness, along with participants' analyses of their own habits of discourse as classroom teachers, prompted shifts in their pedagogical image of the role of discourse in their future practices of teaching. Results further suggested that the undergraduate mathematics classroom (as opposed to the methods classroom) offers a powerful and unique forum in which preservice secondary teachers can practice, articulate, and collectively reflect on reform-minded ways of teaching. (Contains 27 references.) (Author/SM) Reproductions supplied by EDRS are the best that can be made from the original document. Using the Undergraduate Mathematics Classroom
Teaching Children Mathematics, 2006
Teaching Children Mathematics, 2005
Teaching Children Mathematics
Helping teachers learn to identify and create opportunities for algebraic thinking as part of the... more Helping teachers learn to identify and create opportunities for algebraic thinking as part of their normal classroom instruction.
Journal for Research in Mathematics Education
This research focuses on the retention of students’ algebraic understandings 1 year following a 3... more This research focuses on the retention of students’ algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3–5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance.
Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds
Early Childhood Education Journal
The original version of this article unfortunately contained a typo in co-author name. The author... more The original version of this article unfortunately contained a typo in co-author name. The author name is "Rafael Ramírez Uclés" instead it was published incorrectly as "Rafael Ramírez Úcles". The original article has been corrected. Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Early Childhood Education Journal
Infancia y Aprendizaje
In this introduction to the Special Issue Early algebraic thinking: studies from different perspe... more In this introduction to the Special Issue Early algebraic thinking: studies from different perspectives, approaches and regions we provide readers with the main motivation and interest underlying research on early algebraic thinking. We then introduce the five papers that make up this Special Issue. Each of these studies, coming from various countries around the world, has a different theoretical framework, methodological approach and perspective regarding teachers, students, instructional practices and curricula. In this introduction, we summarize some of the main themes throughout the different papers, including interviewers' practices that can promote early algebraic thinking; the kinds of practices that teachers can implement to have a positive impact on students' early algebraic thinking; and the use of physical models to explore and promote aspects of early algebraic thinking. The Special Issue also includes an additional Prospectives piece by Analúcia Schliemann and David Carraher, in which they examine the algebraic thinking research in elementary school in light of the current mathematics standards in the United States.
Educational Studies in Mathematics
Mathematical Thinking and Learning
Teaching and Learning Proof Across the Grades
ABSTRACT
Teaching Children Mathematics
The study of functions has traditionally received the most attention at the secondary level, both... more The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents—for example, the Common Core State Standards for Mathematics (CCSSI 2010) and Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM] 2000). However, the growing acceptance of algebra as a K–grade 12 strand of thinking by math education researchers and in standards documents, along with the view that the study of functions is an important route into learning algebra (Carraher and Schliemann 2007), raises the importance of developing children’s understanding of functions in the elementary grades.
Educational Studies in Mathematics, 2017
Journal For Research in Mathematics Education, 2015
This article reports results from a study investigating the impact of a sustained, comprehensive ... more This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written pre- and post-assessment that addressed their understanding of several big ideas in the area of early algebra, including mathematical equivalence and equations, generalizing arithmetic, and functional thinking. We found that the intervention group significantly outperformed the nonintervention group and was more apt by posttest to use algebraic strategies to solve problems. Given the multitude of studies among adolescents documenting students' difficulties with algebra and the serious consequences of these difficulties, an important contribution of this research is the finding that—provided the appropriate instruction—children are capable of engaging successfully with a broad and diverse set of big algebraic ideas.
National Council of Teachers of Mathematics, Apr 15, 2011
As a part of a long term district-wide study, we report on achievement test results involving stu... more As a part of a long term district-wide study, we report on achievement test results involving students in a third-grade classroom taught by a teacher in a professional development program led by the authors and directed towards the integration of algebraic reasoning with elementary school mathematics. The teacher's practice, reported upon elsewhere, embodied many of the features targeted in the professional development program, and her students' performance on a statewide standardized test for fourth graders exceeded those of a comparable control class from the same school and those of her district's fourth graders, and approximated the performance of fourth graders statewide. (Author) Reproductions supplied by EDRS are the best that can be made from the original document.
Journal for Research in Mathematics Education, 2015
This article reports results from a study investigating the impact of a sustained, comprehensive ... more This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written pre- and post-assessment that addressed their understanding of several big ideas in the area of early algebra, including mathematical equivalence and equations, generalizing arithmetic, and functional thinking. We found that the intervention group significantly outperformed the nonintervention group and was more apt by posttest to use algebraic strategies to solve problems. Given the multitude of studies among adolescents documenting students' difficulties with algebra and the serious consequences of these difficulties, an important contribution of this research is the finding that—provided the appropriate instruction—children ...
This investigation uses classroom discourse in an undergraduate mathematics course to challenge p... more This investigation uses classroom discourse in an undergraduate mathematics course to challenge preservice secondary mathematics teachers' notions about mathematical discourse, what it should resemble in the classroom, and how it can be cultivated by classroom teachers. The research setting was an upper level geometry course. Eleven preservice mathematics teachers participated. Results indicated a transition in participants' image of discourse as an active process by which students use the collective knowledge of their peers to build mathematical understanding and a development in students' ability to participate in such discourse. This awareness, along with participants' analyses of their own habits of discourse as classroom teachers, prompted shifts in their pedagogical image of the role of discourse in their future practices of teaching. Results further suggested that the undergraduate mathematics classroom (as opposed to the methods classroom) offers a powerful and unique forum in which preservice secondary teachers can practice, articulate, and collectively reflect on reform-minded ways of teaching. (Contains 27 references.) (Author/SM) Reproductions supplied by EDRS are the best that can be made from the original document. Using the Undergraduate Mathematics Classroom
Teaching Children Mathematics, 2006
Teaching Children Mathematics, 2005