This work is an exploration of upper elementary students' sense making around four conventional representations of function: equations with algebraic notation, Cartesian graphs, function tables, and natural language. The cornerstone to the empirical work is a task called the Function Puzzle, where students are given 16 cards representing four…

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students…

This investigation presents students with the challenge of determining the total number of eggs in a photograph of a stack of egg trays. The perspective of the photograph does not allow students to count all the individual eggs in the top tray but does allow them to see the number of eggs in one row and one column of the top tray. During this…

In this exploratory study we considered how one teacher's understanding of proportional reasoning related to his teaching. We relied on Knowledge in Pieces as a lens for considering the teacher's knowledge organization as a way to make sense of his understanding. We did so by collecting data from two instruments and using Epistemic Network…

The study investigated the effects of Solve-Reflect-Pose Strategy (SRP) on pre-service mathematics teachers' algebraic knowledge for teaching in Nigeria. A pre-test-post-test quasi experimental design was employed. Intact classes were used and in all, 182 pre-service mathematics teachers' participated in the study (92 in the experimental group…

Pivot Professional Learning, in consultation with the Australian Association of Mathematics Teachers, summarises their study into the characteristics of Australian mathematics teachers. The study reinforced that Australia has many excellent teachers of mathematics, but can improve by sharing excellent teaching practices of its expert teachers…

This paper explores how a group of pre-service elementary school teachers training to become mathematics teachers for elementary schools arrived at generalizations based on patterns. Two representative problems were investigated with these preservice teachers. The focus of this study was how these preservice teachers analyze and symbolize…

The purpose of this study was to investigate secondary mathematics teachers' conceptions of mathematical literacy, which are important to consider when is essential to address in designing and implementing effective approaches. Data sources included semi-structured interviews with 16 in-service mathematics teachers from different types of…

The first author's initial attempts at a whole-class mathematics discussion were woefully dysfunctional. Ten second graders showing their answers to a missing addend question about the number of children left riding a school bus did not result in the mathematical epiphany that the textbook promised. She did not give up on using mathematical…

The aim of the study is to investigate the effects of using computer for developing arithmetical skills of students with mathematics learning difficulty (MLD). The study was carried out with pre-test - post-test single subject research design. The participants of the study consist of a girl and two boys who attend 3rd grade at elementary school.…

Many students are passively engaged in mathematics content across the United States because they are in classrooms that use traditional instruction methods (i.e. lecture and guided practice). Calculus is a struggle for students because of the critical thinking, conceptual understanding, and problem solving required. Active learning has been shown…

Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

Metacognition is vital for a student's academic success. Gifted learners are no exception. By enhancing metacognition, gifted learners can identify multiple strategies to use in a situation, evaluate those strategies, and determine the most effective given the scenario. Increased metacognitive ability can prove useful for gifted learners in the…

In this article, the authors first present the Hands Together! task. The mathematics in this problem concerns the relationship of hour and minute durations as reflected in the oft-overlooked proportional movements of the two hands of an analog clock. The authors go on to discuss the importance of problem solving in general. They then consider…