Being a cognitive strategy instruction model called 'Solve It!' involves cognitive and metacognitive elements. The model was developed by Montague (1992) as one of the process-based teaching strategies. The purpose of 'Solve It!' strategy is to teach the following seven cognitive strategy steps: read, paraphrase, visualize, hypothesize, predict,…

Previous studies of integral calculus have mainly explored students' conceptual and procedural knowledge; only a few have focused on students' metacognition in relation to integral calculus. The study reported here explored students' metacognitive knowledge of integral calculus by interviewing nine first-year university and eight Year 13 students.…

This paper reports on the evaluation results of the implementation of the Parallel Curriculum Model (PCM) in a Singapore secondary school for Grades 7-10. PCM was adopted by the school in 2016 to provide a comprehensive framework for designing the school's curriculum around the core, connections, practice, and identity. Two years into the…

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance,…

Mind maps are usually employed by teachers from all the educational levels as powerful learning strategies. This use enables important pedagogic achievements, but they do not exceed their maximum level, due to the dogmatic use of Tony Buzan's mind map (1996). Situation that would be different if it were entirely internalized, understand and…

Fluency is an important aspect of mathematics learning and plays a major role in developing proficiency as students are required to use skills and apply knowledge. This paper draws upon findings from a large project that aimed to explore primary students' mathematical fluency. Data from 160 primary students (K-6) from a NSW Departmental school…

Background: Base-ten thinking (BTT) -- children's ability to reason in tens and ones is a crucial measure of Foundation Phase learners' mathematical performance in South Africa. Aim: The study looks at the six learners using BTT to solve additive tasks through two different assessments. Setting: Six purposely selected Grade 3 learners in…

Background & aims: In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been…

Prior work exploring preschool-aged children's reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children's growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern…

The purpose of this study is to investigate a mathematically gifted student's self-regulation behaviours while constructing and consolidating mathematical knowledge. However, the objective is to determine which self-regulation strategies influence this student's mathematical abstraction process. The case study method was used in the research. As…

A mixed-methods study investigated the relationship between teachers within urban Title I elementary schools (e.g., high versus low performing) and their mathematics problem-solving beliefs in six constructs ("perseverance," "procedural," "conceptual," "importance," "effort," and…

Feedback in educational technologies can teach and engage students in math, but questions remain on how to present failure feedback that supports positive learning behaviors. We explore how error- and reward-based feedback influenced students' choices to replay completed problems in "From Here to There!," a math game-based educational…

We examined the influences of pre-solving pause time, algebraic knowledge, mathematics self-efficacy, and mathematics anxiety on middle-schoolers' strategy efficiency in an algebra learning game. We measured strategy efficiency using (a) the number of steps taken to complete a problem; (b) the proportion of problems completed on the initial…

Many Grade 9 mathematics learners face difficulties in solving number-pattern problems due to insufficient exposure to strategies in solving such problems. The aim of this exploratory qualitative study was to investigate Grade 9 mathematics learners' strategies in solving number-pattern problems. The problem-solving conceptual framework of Singer…

Although students' nonstandard strategies have great importance in understanding students' thinking and creating effective mathematics classrooms, much remains unexplored in the literature. This study investigated 22 middle school teachers' reasoning about a student's nonstandard strategy for the division of fractions. The data were collected…