Mathematics education at the high school level is not working for many students. Although there has been steady improvement in mathematics learning at the elementary and middle school levels across the United States, for the past decade, student achievement has remained essentially flat at the high school level (NCES 2015, 2016). One possible…

Most prospective secondary mathematics teachers complete a course in real analysis, yet view the content as unrelated to their future teaching. We leveraged a theoretically motivated instructional model to design modules for a real analysis course that could inform secondary teachers' pedagogy, focusing on how this model was implemented in a…

Despite the fact that mathematics is present and necessary in any area of daily life, students have little interest in developing mathematical skills. Hence, the aim of the study is to check whether the variables motivation, usefulness, anxiety, confidence, and liking are determining in their attitude towards mathematics. The present research is…

Number sense has been considered as one of the most important mathematical notions to be addressed in school mathematics in the 21st century. In this paper, we identify how students of a public middle school, located in a rural area in Mexico, showed several aspects of number sense by performing tasks involving arithmetic operations in a shopping…

This paper is centred around a framework for studying teaching--Mediating Primary Mathematics (MPM)--developed in the context of the teaching of Whole Number Arithmetic (WNA) in South Africa. Findings from the analysis of four WNA lessons are used to illustrate how the application of the MPM framework can measure nuanced differences in the…

At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

The Board on Science Education and the Board on Mathematical Sciences and Analytics of the National Academies of Sciences, Engineering, and Medicine convened the Workshop on Increasing Student Success in Developmental Mathematics on March 18-19, 2019. The Workshop explored how to best support all students in postsecondary mathematics, with…

Mathematics requirements are a significant barrier to completing a college credential for many college students. In an effort to change the tide, colleges across the country are working to implement mathematics pathways, which encourages all students to enroll in one of several college-level mathematics courses that best aligns with their chosen…

Trends in International Mathematics and Science Study (TIMSS) data reveal that setting high standards for the overall mathematics curriculum and ensuring teachers adhere to these standards may not necessarily lead to better learning outcomes for students. There are significant gaps between the intended and implemented grade 8 mathematics curricula…

In this article, we question the prevalent assumption that teaching and learning mathematics should always entail movement from the concrete to the abstract. Such a view leads to reported difficulties in students moving from manipulatives and models to more symbolic work, moves that many students never make, with all the implications this has for…

Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory…

The rules of indices, e.g. a[superscript n] b[superscript n] = (ab)[superscript n], are a particularly important part of elementary algebra. This paper reports results from a textbook analysis which examined how the shift from integer to rational exponents in the rules of indices is discussed in school textbooks. The analysis also considered…

This study examined the genre of undergraduate mathematical proof writing by asking mathematicians and undergraduate students to read 7 partial proofs and identify and discuss uses of mathematical language that were out of the ordinary with respect to what they considered conventional mathematical proof writing. Three main themes emerged: First,…

Growth in two subscales, Informal and Formal Mathematics Skills, of the "Test of Early Mathematics Abilitity-3" (TEMA-3) was explored in a sample of 281 children. Children were identified as either typically developing (TYP; n = 205) or having mathematics difficulties (MD; n = 76) based on their total TEMA-3 score at the end of…

This paper describes a research project implemented in a course of Real Analysis II. The aim of this project is to analyse students' comprehension of the limiting behaviour of a function from "R"[superscript 2] to "R" at a point "P"[subscript 0] focusing on the formal definitions. Alternative definitions and other…