The aim of this research is to analyse students' sense-making regarding matrix representation of geometric transformations in a dynamic geometry environment (DGE) within the perspective of semiotic mediation. In particular, the focus is on students' reasoning on the transition from the notion of function to transformation and to matrix…

A cluster randomized trial design was used to examine the effectiveness of a Grades 3 to 5 early algebra intervention with a diverse student population. Forty-six schools in three school districts participated. Students in treatment schools were taught the intervention by classroom teachers during regular mathematics instruction. Students in…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

Many engineering subjects rely on the interpretation of symbolic, numeric and graphic representations. Engineering students have challenges pertaining to their mathematical understanding of their actions with a computer algebra system (CAS). We investigated how a mathematical modelling task could mediate varied levels of mathematical…

This study measures the mathematical abilities high school graduates' in Bahrain. Mathematical abilities encompass conceptual understanding, procedural knowledge and problem-solving skills in the five content domains which are Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. While procedural understanding…

Prior to leaving middle school, students are expected to be able to solve linear equations with one unknown using multiple modes of representation, including pictorial models. Although solving these linear equations is important, many students do not have the conceptual understanding to solve these types of linear equations successfully. In this…

In this exploratory case study, the researchers conducted a qualitative analysis of six teaching sessions to describe the use of gestures and diagrams by a teacher and her students with learning disabilities when engaging in secondary level algebra (e.g., Algebra I & II content). The teacher and her students used gestures, such as pointing and…

The purpose of this research was to describe the positions and causes of students' errors in algebraic thinking based on the cognitive style. This study was qualitative research with subject consisting of twelve students. The results showed that (1) students with Field Independent type tended to make errors at the stage of comprehension,…

Whiteness is present and performed when whites are discussing race and racism. It is also working when race isn't being discussed in STEM college classrooms. As this dissertation shows, white students in college algebra participate in white racial bonding, committing racial microaggressions and what I coin "nanoaggressions" against…

Research in both the New Zealand and international contexts identifies the need for New Zealand classrooms to foster culturally responsive and mathematical practices that align with Påsifika students' cultural values, backgrounds, interests and experiences. The aim of this study was to investigate how the use of culturally responsive tasks along…

Mental models are representations of students' minds concepts to explain a situation or an on-going process. The purpose of this study is to describe students' mental model in solving mathematical patterns of generalization problem. Subjects in this study were the VII grade students of junior high school in Situbondo, East Java, Indonesia. This…

Colleges are experimenting with integrating technology into the classroom to improve student learning and reduce costs. While fully online models appear to have negative effects on student learning compared to in-person instruction, there is less evidence about models that blend elements of online and in-person instruction. In this study, I…

In this paper, we present a hypothetical learning trajectory (HLT) aimed at supporting students in developing flexible ways of reasoning about matrices as linear transformations in the context of introductory linear algebra. In our HLT, we highlight the integral role of the instructor in this development. Our HLT is based on the "Italicizing…

When establishing connections among representations of associated mathematical concepts, students encounter different difficulties and successes along the way. The purpose of this study was to uncover information about and gain greater insight into how student processes connections. Pre-calculus students were observed and interviewed while…

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…