This article describes an example of differentiating instruction (DI) involving middle school students from a five-year project funded by the National Science Foundation. In one phase of the project, a classroom teacher and the research team differentiated instruction for a class of 18 seventh-grade students during a 26-day unit on proportional…

We share our experience and lessons learned from using Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations (SIMIODE) modeling scenarios in our Differential Equations I class at Middle Tennessee State University. Specific projects with Python codes are presented. Discussions are brought forth on how to…

Research studies have found that mathematics teachers face challenges when designing technology-integrated lessons to support mathematical inquiry with authentic problems. This suggests that teachers need to develop technological pedagogical knowledge (TPACK) or their professional knowledge for technology integration. Drawing upon the concept of…

It is commonly known that mathematics is used in many subjects in physics and chemistry courses and the relations between mathematics and variables are more easily understood. These courses also comprise a number of equations that correspond to a mathematical correlation and are also called formulas. Therefore, the aim of the present study is to…

In this paper we argue that the choice of research methods reflects the theoretical framework even before these methods have been put to use in case studies. We understand the term 'case study' broadly in this paper and argue that neither thinking of them as cherry-picked cases to support preconceived ideas about mathematical practices nor…

The idea that formal learning generalizes, or is transferred, beyond the conditions of initial learning serves as a basis for our educational system. That is, educators hope students will use the learning that develops in the classroom to productively reason about situations they have yet to encounter. Researchers in psychology and mathematics…

Beliefs are known to influence learning processes and thus become relevant in the instruction of pre-service mathematics teachers with regard to the pedagogical content knowledge taught in courses of mathematics didactics at university. In exploring beliefs about mathematics didactics of pre-service teachers training for secondary school, 50…

Geometry is used in different ways in the teaching of linear algebra. In this paper, I offer a typology of these ways, which I call varieties, and address three central questions. The first question is, "What varieties of use of geometry in the teaching of linear algebra exist?" This question is addressed through an analysis of six…

We present a technique that examines handwritten equations from a student's solution to an engineering problem and from this estimates the correctness of the work. More specifically, we demonstrate that lexical properties of the equations correlate with the grade a human grader would assign. We characterize these properties with a set of features…

The simple and compound interest formulas in isolation have limited usefulness for financial planning--until the concept of a regular payment is introduced. This article presents and discusses a simple investigation given to an advanced Year 10 mathematics class, with most students looking to study Mathematical Methods in Years 11 and 12. This…

Mathematical representation has an essential role in solving mathematical problems. However, there are still many mathematics education students who have difficulty in representing ill-structured problems. Even though the ill-structured-problem-solving tasks designed to help mathematics education students understand the relevance and…

Recent years have seen increasing interest in incorporating resampling methods into introductory statistics courses and the high school mathematics curriculum. While the use of permutation tests for data from experiments is a step forward, the use of simple bootstrap methods for sampling situations is more problematical. This article demonstrates…

A maximum marginal likelihood estimation with an expectation-maximization algorithm has been developed for estimating multigroup or mixture multidimensional item response theory models using the generalized partial credit function, graded response function, and 3-parameter logistic function. The procedure includes the estimation of item…

Teachers' self-efficacy has been measured a number of ways and linked to important outcomes including teacher satisfaction, goals for students, and student achievement. However, most of these existing measures are intentionally general in their design. Given the importance of context, researchers have begun to construct more domain-specific…

Subitising, a quick apprehension of the numerosity of a small set of items, has been found to change from an individual's reliance on perceptual to conceptual processes. In this study, we utilised a constructivist teaching experiment methodology to investigate how the subitising activity of one preschool student, Amy, related to her construction…