Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we…

This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…

Conventions play an important communicative role in mathematics. Likely due to the complex relationship between conventions and school mathematics, few education researchers have questioned or investigated the consequences of instruction and curricula that primarily, if not unquestionably, maintain conventions. Drawing on Piagetian notions of…

Current adolescent literacy rates cause concerns at the number of students who graduate high school with basic or below-basic reading skills. The Common Core State Standards promote disciplinary literacy, which presents advanced literacy skills embedded in content area instruction. Disciplinary literacy is argued as a way to raise adolescent…

Informal statistical inference has now been researched at all levels of schooling and initial tertiary study. Work in informal statistical inference is least understood in the early years, where children have had little if any exposure to data handling. A qualitative study in Australia was carried out through a series of teaching experiments with…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

Many adolescent learners have difficulty understanding the relevance of mathematics for their lives. This problem is particularly pernicious among Black and Latino adolescents who often face cultural stigma that can affect their perceived value of mathematics. The present study used concurrent nested mixed methods to explore this issue in 419…

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…

Misconceptions in geometry are an essential problem in the understanding of geometric terms by primary and pre-primary aged children. Present research shows some misconceptions in geometry demonstrated in the understanding of circles, squares, triangles and oblongs for children in the last year of kindergarten and pupils in the last year of…

In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thinking, nonverbal reasoning, and mental imagery, students in the experimental group scored significantly higher (p = 0.05) in mathematics achievement and…

This paper presents the findings of a small-scale study that investigated the issues and challenges of teaching and learning about quantitative reasoning (QR) within a project-based learning (PjBL) context. Students and teachers were surveyed and interviewed about their experiences of learning and teaching QR in that context in contrast to…

This paper uses a comparative methodology to examine the teaching of abstraction in two mathematics lessons, in Denmark and England. In doing so it aims to extend previous work by the authors, examining the effect of local, cultural issues on the form of teaching in order to understand how these also affect the subject content too. The analysis…

This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

Ratio, rate, and proportion are central ideas in the Common Core State Standards (CCSS) for middle-grades mathematics (CCSSI 2010). These ideas closely connect to themes in earlier grades (pattern building, multiplicative reasoning, rational number concepts) and are the foundation for understanding linear functions as well as many high school…