Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems. Given that current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, the purpose of this study was to evaluate the impact of a model-based…

The number line is a model that is used to measure, count, order and even operate, which requires a symbolic interpretation. Then, we investigate the conceptions of 72 in service secondary teachers, when they manage the model of the number line associated with order, spatial location and the relative position between numbers and marks. In a…

Using memorized rules and algorithms without coherence and understanding is a perennial problem for teachers and students especially in the teaching and learning of fraction operations. I present data in which prospective middle school teachers explain a commonly used rule for fraction division--keep-change-flip. I argue that using both strip…

In this study we show the models that students of administration and accounting careers built when performing an activity close to the real life, with the use of Excel. The representations and ideas exhibited by the students when they used the software are analyzed. The methodology was qualitative. The theoretical framework was the Models and…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

The aim of the paper is to provide a process model to evaluate mathematical problem solving by analogy, in order to better determine at which point and under what conditions a learner is prompted to use analogies. The model is a theoretical construct. Qualitative results of an empirical study are used to underline and illustrate core aspects of…

This paper explores the role examples play in mathematicians' conjecturing activity. While previous research has examined example-related activity during the act of proving, little is known about how examples arise during the formulation of conjectures. Thirteen mathematicians were interviewed as they explored tasks that required the development…

We analyze and discuss ways in which prospective high school teachers pose and pursue questions or problems during the process of reconstructing dynamic configurations of figures given in problem statements. To what extent does the systematic use of a Dynamic Geometry System (DGS) help the participants engage in problem posing activities…

This paper describes a model for building cognition-and-instruction-based goal trajectories (GT) in the context of a study that examines the validity of curriculum-embedded assessments. The model consists of six design processes and two constraints. The GT is constructed from curriculum-specified learning goals as well as developmental…

Math Teachers' Circles (MTCs) are an innovative, problem-solving focused approach to professional development. This model provides teachers opportunities to develop their problem solving skills as well as help them to communicate with others on classroom implementation of problem-solving activities. As with any professional development with…

Being part of a larger research project aimed at connecting mathematics and science to the world of work by promoting mathematical modeling as an inquiry based approach, the present study aimed to (a) describe parents' beliefs about inquiry-based mathematical modeling and parental engagement, and (b) explore the impact of a modeling-based learning…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…