Understanding a graph in pairs, in a productive way, improves the comprehension of a concept. In this research, we had 2 objectives: 1) to delve deep into the behavior of 15 pairs of remedial physics students when solving a problem with a graph of velocity, 2) to understand the interchange of personal meanings during their interactions. We posed…

Reflection is an important part of teaching and needs to be considered carefully. In this study, we examined a mathematics instructor's reflections on teaching linear algebra. The research team employed Tall's (How humans learn to think mathematically: exploring the three worlds of mathematics. Cambridge University Press, Cambridge, 2013)…

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

The purpose of the current study is to examine the ways in which preservice middle school mathematics teachers (PMSMT) apply and represent algebraic reasoning in their solution processes for the problems in the concept of sets. This model provides detailed information about the reasoning made through the process of the solution of set problems.…

This study examined the relationship between students' (N = 229) concepts of size and scale and students' achievement in science and mathematics over a 3-year period. Size and scale are considered one of the big ideas in science that permeates disparate science and mathematics content areas, yet little is known about the relationship between…

Understanding fractions has been a pervasively difficult skill for struggling math learners, yet it is essential for success in secondary level mathematics skills. The present systematic review examined the evidence base of fraction interventions for elementary level students identified as struggling math learners. Twelve studies met inclusion…

The purpose of this study was to examine middle school students' proportional reasoning, solution strategies and difficulties in real life contexts in the domain of geometry and measurement. The underlying reasons of the difficulties were investigated as well. Mixed research design was adopted for the aims of the study by collecting data through…

This study characterizes the classroom mathematical practices that support the collective mathematical progress during the treatment of a quadratic function in an Introductory Calculus course comprised of 15 students from eleventh grade (from 16 to 18 years old). A teaching experiment that discussed two variational situations was designed for the…

In this article, Lindsey Fowler describes how an animal rhyme--that she shared with her fifth-grade students with the intention of assisting them with the concept of metric conversions--made fostering the Standards for Mathematical Practice (SMP) more difficult. The addition of animals, which added an extraneous element that students mistakenly…

Teachers often use number talks at the beginning of class to hear the ways that students understand mathematical topics so that they can base future instruction on student thinking. Students who engage in number talks become accustomed to thinking about mathematics in multiple ways, sharing their thoughts and critiquing the thoughts of others. The…

In this paper, I present a homework system that supports a flipped classroom environment using only a textbook for students' first contact with the material. Motivated by David Pengelley's homework system, each unit of material has four key components: Core Assignments, Conceptual Assignments, In-class Worksheets, and Follow-up Assignments. The…

In this study we investigated the relationship between urban eighth grade students' Hands-On Exposure to Algebraic Thinking (HEAT) competition performance and their subsequent performance on standardized measures of mathematics achievement (ACT Composite Score, ACT Math Scores, and Louisiana Algebra End of Course Exams). It was found that the…

Division by zero is often unclear and confusing, and teachers at various grade levels may encounter difficulties in conveying this concept to their students. The concept of dividing by zero plays a crucial role in developing an understanding of certain mathematical concepts, such as rational numbers and the relationship between multiplication and…

In the most general sense, mathematical thinking can be defined as using mathematical techniques, concepts, and methods, directly or indirectly, in the problem-solving process. In this study, efforts were made to include the Graph Theory of mathematics, which is found abundantly in physics, chemistry, computer networks, economics, administrative…