Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…

Problem solving and reasoning are two key components of becoming numerate. Reports obtained from international assessments show that Australian students' problem solving ability is in a long-term decline. There is little evidence that teachers are embracing problem solving as part of the classroom routine. In this study, we analyse 598 Year 7 to…

This study was guided by the question, how do we understand the multiplicative reasoning of upper high school students and use that to give insight to their performance on a standardized test? After administering a partial ACT assessment to a class of high school students, we identified students to make comparisons between low and high scoring…

In this brief article, the author illustrates the flaws of FOIL (multiply the First, Outer, Inner, and Last terms of two binomials) and introduces the box method. Much like FOIL, the box method can become easy to use. Unlike FOIL, however, the box method is a more direct and visible link to using the distributive property to determine area, a…

Students in upper secondary education encounter difficulties in applying mathematics in physics. To improve our understanding of these difficulties, we examined symbol sense behavior of six grade 10 physics students solving algebraic physic problems. Our data confirmed that students did indeed struggle to apply algebra to physics, mainly because…

The student's criterion for being diagnosed with MLD (Mathematics Learning Disabilities) can be classified as low arithmetic skills and poor working memory. The goal of this research is to understand students' process of thinking through the Polya stages when tackling arithmetic problems, as it has been expounded by Dr. Polya For students who have…

Originally written 30 years ago, this paper is an analysis of the central challenge of schooling--that of engaging fully the powers of students' minds in classroom learning. This challenge maintains its relevance today. The work of engaging what John Dewey referred to as students' "inner attention" becomes the focus of an investigation…

This article focuses on learners' understanding and their descriptions of the concepts of area and perimeter, how learners solve problems involving area and perimeter and the relationship between them and misconceptions, and the causes of these misconceptions as revealed by learners when solving these problems. A written test was administered to…

The purpose of this study is to explore Grade 9 learners' understanding of ratio and proportion. The sample consists of a group of 30 mathematics learners from a rural school in the province of KwaZulu-Natal, South Africa. Data were generated from their responses to two missing value items, adapted from the Concepts in Secondary Mathematics and…

To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students…

South Africa participated in TIMSS from 1995 to 2015. Over these two decades, some positive changes have been reported on the aggregated mathematics performance patterns of South African learners. This paper focuses on the achievement patterns of South Africa's high-performing Grade 9 learners (n = 3378) in comparison with similar subsamples of…

We examined the effects of the Concrete-Representational-Abstract Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the…

Research on teaching high school mathematics shows that the topic of percentages often causes learning difficulties. This article describes a method of teaching percentages that the authors used in university bridging courses. In this method, the information from a word problem about percentages is presented in a two-way table. Such a table gives…