A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by…

In this study, external representations and the problems encountered related transformation process between representations towards limit concept were investigated. "Limit Representation Conversion Test" was administered to 41 preservice mathematics teachers studying at a state university in central Turkey during 2018-2019 academic…

Cognitive load can play a key role in learners' abilities to solve complex problems like mathematics. Many factors can affect the presence of cognitive load in learning including instructional strategy, task difficulty and prior knowledge. To understand the interaction of above factors and their influence on learner cognitive load and performance,…

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative…

This study questions the dominant approach in the presentation of the concept of slope in undergraduate education through mathematics textbooks. For this purpose, five mathematics textbooks, were analyzed for problems related to slope, and similarities and differences were revealed. First, the subjects related to the slope in the textbooks were…

In this study, representations used by preservice mathematics teachers in the process of solving limit problems were determined, the inter-representation transformation competence levels were investigated and the relationship between them was examined. In this context, "Limit Representation Transformation Test" with a reliability of…

This study examined secondary mathematics teachers' content knowledge for teaching the concept of function. Content knowledge, for the purpose of this study, includes the common content knowledge and specialized content knowledge domains of Ball and her colleagues' Mathematical Knowledge for Teaching (MKT) framework. Data were collected through a…

The researchers conducted a microanalysis of two purposefully sampled sessions of a tutor working with a student with a learning disability (LD) engaging with multi-step equations with and without fractions. During the tutoring sessions, the student experienced quick, independent success on equations without fractions, but struggled considerably…

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…

First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations…

Improving the algebraic concepts and skills of secondary school students with learning disabilities is critical for their success in college and in the job market. This research reviewed 12 studies to examine interventions for students with learning disabilities in relation to algebraic notions and competencies. The results indicate that in regard…

We conducted a study with introductory and upper-division level physics students in a Mexican and a Spanish university to learn how students recognize the main characteristics of the electric field in three of its more widely used representations, namely, algebraic notation, vector field plot, and electric field lines, and how the students do…

This study aims to investigate the non-algebraic solution strategies that prospective mathematics teachers use to solve word problems and their thought process while they were solving the problems. A total of 76 prospective mathematics teachers were asked to solve two word problems without using algebraic solutions and, then, clinical interviews…

We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence…

The derivative is a central concept in calculus and has applications in many disciplines. This study explored students' understanding of derivatives with a particular focus on the graphical (geometric) representation. The participants were four Mathematics Honours students from a university in Lesotho. Data were generated from the written…