Investigating the changes in teachers\u27 pedagogical practices through the use of the Mathematics Reasoning Heuristic (MRH) approach

Our changing world needs many more mathematically literate individuals. Mathematical literacy can be defined, parallel to reading and writing literacy, as not only being able to understand the fundamental notions of mathematics, develop sophisticated mathematical models and evaluate someone else\u27s use of numbers and mathematical models but also being able to represent quantitative relations using algebraic reasoning and interpret and reflect on mathematical language patterns. In order to help students become mathematically literate, the National Council of Teachers of Mathematics (NCTM) has focused attention on students\u27 conceptual understanding of mathematics suggesting students need to be actively involved in the learning process using their experiences and prior knowledge. Along with this view on learning, understanding of teaching has also been revised in mathematics classrooms. Teachers now need to provide students with a challenging and supportive classroom environment in which they can build new knowledge by engaging in exploration of mathematical ideas by themselves. Since the publication of Curriculum and Evaluation Standards for School Mathematics in 1989, the National Council of Teachers of Mathematics (NCTM) has paid special attention on teacher change, problem solving, and, more recently, using writing in mathematics classrooms for helping students develop thorough mathematical understanding and to becoming more mathematically literate.;This change in the views of learning and teaching has placed students in the center of learning occurring in the classroom by altering students\u27 roles and requiring them to be actively involved in talking and writing in mathematics classrooms. The NCTM mandated that students at all levels should be able to use mathematical ideas in a variety of situations. For this purpose, students must have the opportunity to discuss their ideas publicly, to reflect on their thoughts and problem solving processes, and to communicate their ideas using various modes of representation (graphical, pictorial, oral, written, etc.). Writing in mathematics was emphasized in The Principles and Standards for School Mathematics (NCTM, 2000, p. 61), which said, Writing in mathematics can...help students consolidate their thinking... because it requires an active involvement of learners such that they use writing as a vehicle for learning and become the center of their own learning processes by engaging in reflection on mathematical experiences.;This study focused on examining the changes in pedagogical practices when three high school algebra teachers shift from their traditional teaching to more student-centered practices through the use of the Mathematics Reasoning Heuristic (MRH) approach. The study also looked at the performance differences on the Iowa Test of Educational Development (ITED) between the students in the control classes where the teachers engaged in their traditional instructional routines and the students in the treatment classes where the teachers used the MRH approach. The goal of the MRH approach is to help teachers improve their pedagogical practices to scaffold students\u27 understanding of mathematical concepts and their problem solving skills.;The major findings of this study are that teachers\u27 adoption of the required pedagogical practices varied as they attempted to move away from their traditional practices and that implementing a student-oriented approach such as the MRH approach which includes embedded writing-to-learn strategies does have an impact on student performance. The student performance on the standardized test was significantly enhanced for those students in the MRH classrooms compared to students who engaged in the more traditional approaches. The results from the analysis of the teachers\u27 pedagogical practices in their treatment and control classes indicate to us the importance of pedagogical skills to promote dialogical interaction during problem solving. In examining the results the researcher would suggest that there are two critical elements of the MRH approach. The first is the pedagogical approach needed and the second is the consistent use of the heuristic concept through the scaffolded writing component of the MRH approach

Matematikte Dil ve Söylem

This arcticle focuses on language and discourse in mathematics. The purpose of this article is not to discuss how to do discourse analysis. Rather, it is to argue the role of discourse and discoursive language in mathematics learning. Based on the class argumentations, it will be structurally outlined how language and discourse in mathematics converge to constitute effective communicationBu makalede matematikte dil ve söylem üzerinde durulacaktır. Bu makalenin amacı söylem analizinin nasıl yapılacağını tartışmak değildir. Daha çok, söylemin ve söylemsel dilin matematik öğrenmedeki rolünü tartışmaktır. Bunun için sınıf tartışmalarından örnekler verilerek matematikteki dil ve söylemin etkili iletişim oluşturmak için nasıl bir araya geldiği yapısal olarak şekillendirilecektir

Investigating the changes in teachers' pedagogical practices through the use of the Mathematics Reasoning Heuristic (MRH) approach

Our changing world needs many more mathematically literate individuals. Mathematical literacy can be defined, parallel to reading and writing literacy, as not only being able to understand the fundamental notions of mathematics, develop sophisticated mathematical models and evaluate someone else's use of numbers and mathematical models but also being able to represent quantitative relations using algebraic reasoning and interpret and reflect on mathematical language patterns. In order to help students become mathematically literate, the National Council of Teachers of Mathematics (NCTM) has focused attention on students' conceptual understanding of mathematics suggesting students need to be actively involved in the learning process using their experiences and prior knowledge. Along with this view on learning, understanding of teaching has also been revised in mathematics classrooms. Teachers now need to provide students with a challenging and supportive classroom environment in which they can build new knowledge by engaging in exploration of mathematical ideas by themselves. Since the publication of Curriculum and Evaluation Standards for School Mathematics in 1989, the National Council of Teachers of Mathematics (NCTM) has paid special attention on teacher change, problem solving, and, more recently, using writing in mathematics classrooms for helping students develop thorough mathematical understanding and to becoming more mathematically literate.;This change in the views of learning and teaching has placed students in the center of learning occurring in the classroom by altering students' roles and requiring them to be actively involved in talking and writing in mathematics classrooms. The NCTM mandated that students at all levels should be able to use mathematical ideas in a variety of situations. For this purpose, students must have the opportunity to discuss their ideas publicly, to reflect on their thoughts and problem solving processes, and to communicate their ideas using various modes of representation (graphical, pictorial, oral, written, etc.). Writing in mathematics was emphasized in The Principles and Standards for School Mathematics (NCTM, 2000, p. 61), which said, "Writing in mathematics can...help students consolidate their thinking..." because it requires an active involvement of learners such that they use writing as a vehicle for learning and become the center of their own learning processes by engaging in reflection on mathematical experiences.;This study focused on examining the changes in pedagogical practices when three high school algebra teachers shift from their traditional teaching to more student-centered practices through the use of the Mathematics Reasoning Heuristic (MRH) approach. The study also looked at the performance differences on the Iowa Test of Educational Development (ITED) between the students in the control classes where the teachers engaged in their traditional instructional routines and the students in the treatment classes where the teachers used the MRH approach. The goal of the MRH approach is to help teachers improve their pedagogical practices to scaffold students' understanding of mathematical concepts and their problem solving skills.;The major findings of this study are that teachers' adoption of the required pedagogical practices varied as they attempted to move away from their traditional practices and that implementing a student-oriented approach such as the MRH approach which includes embedded writing-to-learn strategies does have an impact on student performance. The student performance on the standardized test was significantly enhanced for those students in the MRH classrooms compared to students who engaged in the more traditional approaches. The results from the analysis of the teachers' pedagogical practices in their treatment and control classes indicate to us the importance of pedagogical skills to promote dialogical interaction during problem solving. In examining the results the researcher would suggest that there are two critical elements of the MRH approach. The first is the pedagogical approach needed and the second is the consistent use of the heuristic concept through the scaffolded writing component of the MRH approach.</p

A sixth grade student's geometric thinking: the van Hiele levels of geometric thought-constructivist approach to the phases of instruction

Geometric shapes around us are the initial conceptions for the mathematical thinking. Geometric thought develops throughout the interval from a concrete level of geometric understanding to an abstract level of geometric perception. Many studies have described students' geometric understanding using the van Hiele levels of geometric thinking, which help the teacher to understand his/her students' development of geometric concepts. The purpose of this case study was to explore a sixth grade student's geometric thinking based upon the van Hiele levels of geometric thought, in relation to his attitudes toward mathematics and to discuss whether or not it is a constructivist approach to use the phases of instruction of van Hiele levels of geometric thinking.</p