This paper presents 'expert opinions' on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors--called 'experts' in this study--addressed the following questions: What should be on a…

This study explored how students develop meaning of functions by building on their understanding of expressions and equations. A teaching experiment using design research was conducted in a sixth-grade classroom. The data was analyzed using a grounded theory approach to provide explanations about why events occurred within this teaching episode…

Pictorial representations are often used to help children understand the situation described in a given number-sentence scheme. These static pictorial problems essentially attempt to depict a dynamic situation (e.g., one bird flies away while there are three birds still sitting on the fence). Previous research suggested that such pictorial…

This article presents a review of literature exploring five different perspectives on mathematical modeling in mathematics education. Because there is not a single agreed-on definition of what mathematical modeling is or how it should be done, a focused and extensive review of mathematical modeling is essential. The five broad classifications…

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.…

The purpose of this article is to demonstrate how exponential functions and patterns can be taught by well-structured lessons composed of classroom activities, mathematical questions, discussions, and solving problems. Sawyer (1943) used a rope-and-post system to introduce the concept of logarithms and to calculate a product by adding the…

Mathematical problems can be divided into two types, namely, process-open and process-constrained problems. Solving these two types of problems may require different cognitive mechanisms. However, there has been only one study that investigated the differences of the cognitive abilities in process-open and process-constrained problem solving, and…

The purpose of the study was to explore how contents related to sustainable development were presented in Japanese, Korean, and Singaporean elementary mathematics textbooks. For this purpose, the contents in the textbooks were analyzed at both macro and micro levels through a mixed method research. The results showed that the…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

Derivative concept is one of the essential studies in calculus, which is studied in teaching mathematics. Prospective mathematics teachers who have completed their studies and later become teachers will teach derivative concepts to their students at school. Therefore, knowledge of derivative concepts is vital in transforming knowledge to students.…

In this paper, I discuss undergraduate students' engagement in basic Python programming while solving combinatorial problems. Students solved tasks that were designed to involve programming, and they were encouraged to engage in activities of prediction and reflection. I provide data from two paired teaching experiments, and I outline how the task…

Many studies in mathematics education have emphasized the importance of attending to students' interactions, particularly, their mathematical reasoning when collaborating on solving problems. However, the question of how teachers can facilitate students' productive interactions for learning mathematics, is still a challenging one. This case study…

The mathematics standards for many countries include teaching and learning ratios, typically with efficient algorithms and strategies (Australian Curriculum: Mathematics, Assessment and Reporting Authority, 2017; National Council of Teachers of Mathematics, 2014). In the 1990s, Cramer and Post (1993) claimed that school mathematics mostly involves…

Solution representations can reveal how problem solvers communicate mathematical thinking and reasoning in problem-solving process. The present study examined the solution representations used by 20 pre-service teachers for the percentage change problems. The pre-service teachers were invited to solve a combination of simple and complex percentage…

According to the conceptual framework for K-grade 12 statistics education introduced in the 2007 Guidelines for Assessment and Instruction in Statistics Education (GAISE) report, students can be located at one of three developmental levels of statistical literacy: A, B, or C. These levels are independent of age and grade level, so, in theory,…