For children with persistent mathematics difficulties, research and practice espouses that an altered kind of mathematics instruction is necessary due to sustained performance differences. Yet, a critical issue in mathematics education rests in the question of why research locates the problem within these children. In this paper, we challenge a…

The aim of the study was to determine whether pre-service elementary mathematics teachers could write and use mathematical definitions. For this reason, the question sheet containing two questions, was given to 76 pre-service teachers in a public university who was taking general mathematics course. Qualitative research method was used during data…

A significant number of students receive special education services for mathematics learning disabilities, however, many additional students need mathematics intervention to support their learning in the regular education classroom. A Response to Intervention (RtI) model has been identified as effective in addressing these students' needs;…

In this study we extend our prior exploration focused on the extent to which middle school teachers appropriately identified proportional situations and whether there were relationships between attributes of the teachers and their ability to identify proportional situations. For this study, we analyzed both a larger dataset (n = 32) and two…

Talk moves simulations were used in tutorials for a mathematics education unit. Pre-service teachers (PSTs) and tutors were surveyed about their perceptions of the purposes, benefits, and drawbacks of the simulations. There was strong support from both groups for the benefits of talk moves in developing PSTs' ability to manage discussions, ask…

Interactions with technology have become a focus of education research, revealing specific constructs relevant to these interactions. Attributes of users and tools contribute to physically embodied interactions with technology and both users and tools modify attributes throughout these interactions. This study examines patterns of user-tool…

Success in math is important to all students; it provides them with college and career options in the fields of science, technology, engineering, and mathematics. In the middle grades, students build upon the critical skills taught in elementary school and prepare for entry into algebra, which is considered a gateway to later achievement in school…

Jane Watson and Lyn English use a chance activity exploring expectation and variation with coin tossing to highlight the importance of understanding the part-whole relationship embodied in percentage and its power to measure and compare for different wholes, in this case different sample sizes. The purpose of this article is to raise awareness of…

This paper proposes a setting of "exemplarity" different from the already known one, which is basically a Romanticist philosophical setting. Our general aim is to describe and explore the nature of some "exemplary themes" and "interpretive models" in advanced mathematics teaching and learning. In order to do so, we…

Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.

A certain weighted average of the rows (and columns) of a nonnegative matrix yields a surprisingly simple, heuristical approximation to its singular vectors. There are correspondingly good approximations to the singular values. Such rules of thumb provide an intuitive interpretation of the singular vectors that helps explain why the SVD is so…

In this short article, we prove an identity from which a theorem of Katsuura and two conjectures previously posed in this JOURNAL follow directly.

We discuss the motivation for dimension reduction in the context of the modern data revolution and introduce a key result in this field, the Johnson-Lindenstrauss flattening lemma. Then we leap into high-dimensional space for a glimpse of the phenomenon called concentration of measure, and use it to sketch a proof of the lemma. We end by tying…

Research affirms that pattern and structure underlie the development of a broad range of mathematical concepts. However, the concept of pattern also occurs in other fields. This theoretical paper explores pattern recognition, a neurological construct based on the world of Goldberg (2005), and pattern as defined in the field of mathematics to…

Math skills vary greatly among students enrolled in introductory chemistry courses. Students with weak math skills (algebra and below) tend to perform poorly in introductory chemistry courses, which is correlated with increased attrition rates. Previous research has shown that retention of main ideas in a peer learning environment is greater when…