The current meta-analysis investigates the longitudinal association between prior and subsequent mathematics performance, involving mathematics measured at three time points, and to identify potential factors that could moderate this association, including age, time lag, and types of mathematics. Our analysis included 105 studies, comprising 111…

Calculus education research on integration is coalescing around the theme that teaching integration based on quantitative reasoning is crucial for robust understanding of and usage of integrals. This paper contributes to this International Journal for Research in Undergraduate Education special issue on the teaching and learning of definite…

This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report "why" such a model is used, "what" types of models are used, and "when" they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a…

This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications…

In this paper, we present an analytical framework for attending to reflexivity in the context of conducting teaching experiments and rationalize its components by appealing to the constructivist foundations on which the methodology is based. To illustrate the importance and utility of this framework, we discuss our analysis of recent mathematics…

The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

Describes a model of cognitive and motivational processes in mathematics learning and relates the model to Brazilian street mathematics and abacus operation. Proposes instructional strategies for motivating conceptual understanding in school mathematics learning. (RJC)

Summarizes research related to models of understanding mathematics, describes the fundamental conception of understanding mathematics, discusses basic components substantially common to the process models of understanding mathematics, and presents a theoretical framework of a process model consisting of two axes. (26 references) (MKR)

A renewal of the study of the philosophy of mathematics is encouraged and a search is made for a philosophy better attuned to the present state of the subject. (MP)

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

As of 2005, 15 states had adopted a broad-based merit aid program, providing a combined $1.2 billion for college students on the basis of academic qualifications. This represents a shift away from a long tradition of need-based aid at the state and federal levels. This article utilizes a Cox proportional hazards model to analyze states'…

Findings from prior research are drawn together to create a learning model for elementary school mathematics in the cognitive-constructivist tradition. A potential teaching/learning process consistent with the model was developed and applied in a longitudinal collaborative arrangement between university personnel and a local elementary school…

The kaleidoscope is presented as a suitable topic for a preservice mathematics teacher's first contact with a nontrivial mathematical phenomenon. Included are historical notes on the kaleidoscope, explanation of the inner mechanisms of various kaleidoscope designs, and suggestions for further student investigations. (JJK)