This small study sought to determine students' knowledge of multiplication and division and whether they are able to use sets of bundling sticks to demonstrate their knowledge. Manipulatives are widely used in primary and some middle school classrooms, and can assist children to connect multiplicative concepts to physical representations.…

This research investigated students' sources and causes of errors and misconception in solving routine problems involving addition, subtraction, multiplication, and division of integers. This qualitative study involved observation of eight Year 7 classes and interviews with the respective classroom teachers. Sixteen Year 7 students who exhibit…

Previous research has shown knowledge, perceptions, and attitudes are essential factors during mathematics classroom instruction. The current study examined the effects of a 3-week fraction instructional unit using concrete models, problem-solving, and problem-posing to improve elementary preservice teachers' knowledge, perceptions and attitudes…

The aim of this study is to investigate how an augmented reality mobile math trails program can provide opportunities for students to engage in meaningful mathematical modelling activities. An explorative research design was conducted involving two mathematics teachers and 30 eight grades in Semarang, Indonesia. An Augmented Reality Mobile Math…

Students' interest in mathematics is important for their learning of mathematics, and the ability to accurately judge students' motivational orientation is important for mathematics teachers. The aim of this study was to answer the following research questions: (1) Is there a difference in students' interest in solving problems with and without a…

Six US first-year university students in humanities or social science degree programmes were interviewed while solving 4 tasks on continuity and asymptotes in a required mathematics course. The focus was on how the students referred to the definitions or to the concept images when solving the tasks and if partial understandings appeared. Partial…

In mathematical activities and in the analysis of mathematics teaching-learning processes, "objects," "signs", and "representations" are often mentioned, where the meaning assigned to those words is sometimes very broad, sometimes limited, other times intuitive, allusive, or not completely clear. On the other hand, as…

This article focuses on exploring students' understanding of the concept of function concerning three main aspects: secondary students' ability to (1) define the concept of function and present examples of functions, (2) solve tasks which asked them to recognize and interpret the concept of function presented in different forms of representation,…

In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

The purpose of this study was to introduce a rubric named "Rubric for the Assessment of Modeling Skills" for assessing cognitive modeling skills and explaining the rubric's development process. The dimensions of the rubric are understanding the problem, simplifying, mathematizing, working mathematically, interpreting and validating.…

We investigated how pre-service teachers (PSTs) interpret their calculations in proportional tasks. A written questionnaire was administrated to 199 PSTs and an inductive content analysis approach used for data analysis. We found that one item that asked PSTs to interpret the meaning of their results had unusually low success; open coding on the…

This article presents a checklist of 10 evidence-based practices for educators to apply in mathematics instruction for students with learning disabilities. The checklist is "actionable," meaning the items on the checklist can be put into action immediately. It provides practical strategies teachers can adopt to fit their lessons…

The researchers conducted a qualitative case study to describe the experiences of two seventh grade students with mild intellectual disability as they engaged in mathematics word problems involving proportions. The researchers analyzed student performance in large group settings and with individualized instruction to gain perspective on the…

This study aims to produce a learning trajectory using the mathematical modeling in helping students to understand the concept of algebraic operations. Therefore, the design research was chosen to meet the research aims and to give in formulating and developing local instructional theory in learning algebraic operations. Learning trajectory…