The purpose of the present article is to investigate how 15-year-old Iranian students interpret the concept of equation, its solution, and studying the relation between the students' equation understanding and solving. Data from two equation-solving exercises are reported. Data analysis shows that there is a significant relationship between…

In the United States, students' learning experiences around proof is generally concentrated in the domain of high school geometry with a focus on its verification function. Thus, providing students with a limited conception of what proof entails and the role that it plays in performing mathematics. Moreover, there is a lack of U.S.-based studies…

We conducted an experimental study with 192 ninth graders in which we investigated a connection between performance and students' interest and enjoyment using task-unspecific and task-specific questionnaires. Students were randomly assigned to experimental group 1 or to experimental group 2. In group 1, they were asked about their affective…

Geometry is one of the most important branches of mathematics education, because the aim of the geometry teaching is to provide students with the ability of critical thinking, problem solving and a better understanding of the other subjects in mathematics by making the students have a high level of geometric thinking skills (Sahin, O., 2008).…

This paper reviews a few applications of the exponential function used primarily in business courses. It shows that translating time units in which queuing problems are measured can be used to overcome some apparent differences between queuing (arrival) problems and survival (decay) problems. There is a cautionary note concerning the limitations…

Data from open modelling sessions for year 10 and 11 students at an extracurricular modelling event and from a year 9 class participating in a programme of structured modelling of real situations were analysed for evidence of Niss's theoretical construct, "implemented anticipation," during mathematisation. Evidence was found for all…

This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and…

In this paper, an example is offered of a problem-solving task for senior secondary school students which was given in the context of a story. As the story unfolds, the task requires progressively more complex forms of linear programming to be applied. Coding in MATLAB is used throughout the task in such a way that it supports the increasing…

The purpose of this study is to investigate routines as guides for mathematical thinking. Four English-speaking and four Korean-speaking students were interviewed in English about the concepts of limit and infinity. Based on the communicational approach to cognition, which views mathematics as a discourse, we identified the primary characteristics…

How does one look for mathematical structure? Finding structure is a challenging yet accessible activity for all students. This article describes a lesson in which seventh graders engaged with mathematical structure. The setting was a seventh-grade prealgebra classroom in a suburban school. The classroom teacher was co-author Tatyana Finkelstein.…

The current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In…

It has been theorized that contextual tasks support student engagement and sense making. Yet, contradictory ideas exist about the role of these tasks in lessons, and further research is needed to explore how classroom interactions can help achieve their intended purposes. Through video observation of lessons in three eighth-grade classrooms using…

The prime objective of this research was to investigate whether the Montessori method of learning helped kindergarten pupils improve their mathematical proficiency, critical thinking and problem-solving skills, besides training them to be responsible learners. Quantitative, qualitative, and observational methods were employed in the investigation.…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) gives teachers access to an insightful, research-informed framework that outlines ways to promote reasoning and sense making. Specifically, as students transition on their mathematical journey through middle school and beyond, their knowledge and use of…

This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…