Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in…

This study aims to identify the level of knowledge and practice on the implementation of higher-order thinking skills (HOTS) among mathematics teachers at a secondary school in the district of Terengganu. The study focused on the aspects of curriculum, pedagogy and assessment and compared them with demographic factors of the respondents. It used…

Instruction often starts with an explanation of a concept or principle before students are presented with problems to be solved. Recent research indicates that reversing this widely used tell-and-practice sequence (T&P) so that exploratory problem-solving precedes the instructional explanation (i.e., PS-I) might be more beneficial. We aimed to…

The aim of this study was to examine the working processes employed by Ghanaian senior high school students when dealing with tiling pool problem algebraically. The study employed survey design, with a total sample of 304 Senior High School Form 1 students from three Senior High Schools in the Central Region of Ghana. Data were collected through…

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

In this article, Strayer and Matuszewski present a six-phase strategy that teachers can use to help students develop a conceptual understanding of inferential hypothesis testing through simulation. As Strayer and Matuszewski discuss the strategy, they describe each phase in general, explain how they implemented the phase while teaching their…

Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008)…

Mathematical knowledge for teaching (MKT), defined by Ball ("Elementary Journal," 93, 373-397, 1993) as knowledge that is needed to teach mathematics, has been used as a framework by researchers to interrogate various aspects of teaching and learning mathematics. In this article, which draws from a larger study, we show how an in-depth…

The problem of taking a data set and separating it into subgroups, where the members of each subgroup are more similar to each other than they are to members outside the subgroup, has been extensively studied in science and mathematics education research. Student responses to written questions and multiple-choice tests have been characterised and…

This study examined the convergent and predictive validity of self-regulated learning (SRL) measures situated in mathematics. The sample included 100 eighth graders from a diverse, urban school district. Four measurement formats were examined including, 2 broad-based (i.e., self-report questionnaire and teacher ratings) and 2 task-specific…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with reform textbooks either containing the original practice problems or in which a portion of those problems were converted into…

This study examined prospective middle school mathematics teachers' problem-posing skills by investigating their ability to associate linear graphs with daily life situations. Prospective teachers were given linear graphs and asked to pose problems that could potentially be represented by the graphs. Their answers were analyzed in two stages. In…

Students' experiences with statistics and data analysis in middle school are often limited to little more than making and interpreting graphs. Although students may develop fluency in statistical procedures and vocabulary, they frequently lack the skills necessary to apply statistical reasoning in situations other than clear-cut textbook examples.…

We examined the use of balance and inverse methods in equation solving. The main difference between the balance and inverse methods lies in the operational line (e.g. +2 on both sides vs -2 becomes +2). Differential element interactivity favours the inverse method because the interaction between elements occurs on both sides of the equation for…

Metacognition encompasses knowledge and regulation that, through reflection, sustain problem solving behaviour. How metacognitive awareness is constructed from reflection on metacognitive knowledge and regulation and how these reflections enable metacognitive skills for Mathematics problem solving remain unclear. Three secondary schools…