Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

This study of six teachers focuses on the ways they organized the classroom discourse, attended to student thinking, and adapted complex tasks from a Standard-based middle school curriculum. The study explores Cohen's (2011) premise that the knowledge teachers develop is related to their attentiveness to student teaching. This study explores the…

The derivative of a composite function, taken with the chain rule is one of the important notions in calculus. This paper describes a study conducted in Turkey that shows that the chain rule was given with the formula in function notation and/or the Leibniz notation without relating these formulas to life-related problem situations in the…

A large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

The reality is that approximately 5-8% of school-age students have memory or other cognitive deficits that interfere with their ability to acquire, master, and apply mathematical concepts and skills (Geary, 2004). These students with Mathematical Learning Disabilities (MLD) are at risk for failure in middle school mathematics because they…

Over the past 30 years, researchers at the Freudenthal Institute in The Netherlands have developed a mathematics curriculum and a theory of pedagogy known as Realistic Maths Education (RME). This curriculum uses "imaginable" contexts to help pupils to develop mathematically, with a strong emphasis on pupils "making sense" of…

There has long been dispute in mathematics between the drill and practice orientation that focuses primarily on memorizing mathematics as meaningless rote algorithms and the approach based on understanding and making creative use of mathematics. This 25-chapter book, based on a 7-year study at the University of Illinois, seeks to explain and…

Shows by means of a mathematical example how algorithmic thinking and mathematical thinking complement each other. An algorithmic approach can lead to questions that deepen the understanding of mathematics material. (DDR)

For the purpose of promoting international cooperation in mathematics, physics, and chemistry teaching research, this first yearbook of the Finnish Association of Mathematics and Science Education Research contains articles of recent research on mathematics teaching. The contents consist of five articles in English, two in German, and one thesis…

Since the advent of reform in mathematics education, writing in mathematics courses has taken on an increasingly important role. This paper discusses what one teacher has done over time to incorporate writing into calculus classes and how the techniques employed have evolved over time. The focus is on journal writing, extended exercises, and…

As part of a larger study regarding an ideal curriculum in five subject matter domains for the elementary school, the views of seven experts in mathematics education were summarized and contrasted. Four experts were nationally and internationally known professors and researchers, and three were elementary school teachers selected by researchers…

Presents a constructivist view of mathematics, mathematics teaching, and mathematics achievement, and differentiates this view as an alternative to the typical traditional perspective of these terms. Discusses the roots of this approach in contemporary information-processing psychology. (TW)

This paper begins with a summary and analysis of Robert Glaser's arguments, presented in his paper "Education and Thinking: The Role of Knowledge," which contend there are strong interactions between structures of knowledge and cognitive processes, and that problem solving and reasoning are taught best in the context of the acquisition…