Students' solutions of enumerative combinatorial problems may be assessed along two main dimensions: the correctness of the solution and the method of enumeration. This study looks at the second dimension with reference to the Cartesian product of two sets, and at the 'odometer' combinatorial strategy defined by English (1991). Since we are not…

This observational study used data from 270 second-grade students to investigate the association between students' strategy use for multidigit addition and subtraction and their mathematics achievement. Based on strategies they used during a mathematics interview, students were classified into the following strategy groups: (a) standard algorithm,…

We report on an international study about mathematics students' ideas of how they will use mathematics in their future study and careers. This builds on our previous research into students' conceptions of mathematics. In this paper, we use data from two groups of students studying mathematics: those who participated in an in-depth interview and…

This study examines patterns in middle-grade boys' and girls' written problem solving strategies for a mathematical task involving proportional reasoning. The students participating in this study attend a coeducational charter middle school with single-sex classrooms. One hundred nineteen sixth-grade students' responses are analyzed by gender…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

An article by Skemp (1976) on mathematical understanding describes two different types of "understanding", "relational" understanding which he initially describes simply as "knowing both what to do and why", and "instrumental" understanding which he describes in the first instance as "rules without reasons". In this article, the author highlights…

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer…

This article proposes a taxonomy of strategies for single-digit multiplication, then uses it to elucidate the nature of the learning tasks involved in multiplication. In preceding work, it has generally been assumed that much of children's strategy development is driven by changes in their general conceptual capabilities relating to number. In…

According to Kilpatrick (1987), in the mathematics classrooms problem posing can be applied as a "goal" or as a means of instruction. Using problem posing as a goal of instruction involves asking students to respond to a range of problem-posing prompts. The main goal of this article is a classification of mathematics questions created by Years 8…

Nine cooperative learning techniques are described and classified according to the following categories: (1) type of subject matter; (2) nature of student interdependence; (3) interaction among cooperative groups; (4) method of grouping students; (5) basis for evaluation and reward; and (6) practical requirements for implementation. The academic…

When students are working with hand held technology, such as graphics calculators, we usually only see the outcomes of their activities in the form of a contribution to a written solution of a mathematical problem. It is more difficult to capture their process of thinking or actions as they use the technology to solve a problem. In this paper we…

This monograph presents 13 papers dealing with various aspects of elementary problem solving. They are: (1) "Training for Effective Problem Solving" (Gary A. Davis); (2) "Patterns of Problem Solving--A Campus-Wide Course at UCLA" (Moshe F. Rubinstein, L. Robin Keller, Edward A. Kazmarek); (3) "A Taxonomy of Problem-Solving Activities and Its…