This study investigates young students' writing in connection to mathematical problem solving. Students' written communication has traditionally been used by mathematics teachers in the assessment of students' mathematical knowledge. This study rests on the notion that this writing represents a particular activity which requires a complex set of…

Teachers have the largest school-based influence on student learning, yet there is little research on how instructional practice is systematically distributed within tracking systems. We examine whether teaching practice varies significantly across track levels and, if so, which aspects of instructional practice differ systematically. Using…

Specific acts of problem solving with rates and ratios were interpreted using a journey metaphor derived from Skemp's (1979) construct of director systems. To successfully undertake a problem solving journey a learner must recognise their starting place (present state), have a sense of destination (goal state), and co-ordinate sub-routes along the…

In this study, we examine how inservice secondary mathematics teachers working together on a contextualized problem negotiate issues arising from the ill-structured nature of the problem such as what assumptions one may make, what real-world considerations should be taken into account, and what constitutes a satisfactory solution. We conceptualize…

This dissertation targets young students' developing knowledge relevant to a fundamental practice in academic mathematics: the use of diagrams to represent idealized mathematical objects whose properties are established by definition (as in the use of drawn dots to represent zero-dimensional points and drawn lines to represent one-dimensional…

Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed…

The objectives of this research were to study and analyze the characteristics of computational thinking about the estimation of the students in mathematics classroom applying lesson study and open approach. Members of target group included 4th grade students of 2011 academic year of Choomchon Banchonnabot School. The Lesson plan used for data…

Over the course of her teaching career, this author learned to create environments in which both the teacher and learners embrace understanding. She introduced new concepts with a general question or word problem and encouraged students to find solutions with a strategy of their choice. By using this instructional method, she allowed her students…

In this article, fourth grade Upper Allen Elementary School (Mechanicsburg, Pennsylvania) teacher Jeffrey Smith describes his exploration of the Playing Basketball activity. Herein he describes how he found the problem to be an effective way to review concepts associated with the measurement of elapsed time with his students. Additionally, it…

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

Although policy documents promote teaching students multiple strategies for solving mathematics problems, some practitioners and researchers argue that struggling learners will be confused and overwhelmed by this instructional practice. In the current exploratory study, we explore how 6 struggling students viewed the practice of learning multiple…

This study is part of a larger research program aimed at studying mental mathematics with objects other than numbers. It concerns operations on functions in a graphical environment with Grade-11 students. Grounded in the enactivist theory of cognition, particularly in problem-posing, the study aims to characterize students' mathematical activity…

While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In this paper, we report findings from a classroom experiment in which Grade 7 students (aged 12-13) tackled a problem in 3D geometry that was, for them, quite challenging.…

This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical…

This journal article discusses Advanced Mathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.…