Eye tracking is getting increasingly popular in mathematics education research. Studies predominantly rely on the so-called eye-mind hypothesis (EMH), which posits that what persons fixate on closely relates to what they process. Given that the EMH was developed in reading research, we see the risk that implicit assumptions are tacitly adopted in…

The current paper aims to identify the mathematical connections activated by 10 Mexican high school students while solving mathematical tasks that involve the exponential and logarithmic function. We used the Expanded Mathematical Connections Model (EMCM) and the OntoSemiotic Approach of Cognition and Mathematical Instruction (OSA) as theoretical…

One of the factors associated with the less than positive mathematics performance of American students could be poorly designed textbooks that fail to facilitate the development of critical mathematical ideas. This study examined two reform-based textbooks (Go math! and Investigations) in reference to essential, mathematical big ideas emphasized…

Ability of solving mathematical non-routine problems among Malaysian students remains at a low level, therefore there is a need to introduce a new and effective teaching strategy for the teaching and learning of mathematical problem solving. This study aims to determine the effectiveness of Mayer's problem solving Model with Visual Representation…

While school performance suggests students with learning disabilities require intervention to demonstrate mathematics proficiency, little is known about how they approach problem solving in secondary geometry. Think aloud protocols highlight the higher order thinking skills underlying complex academic tasks. We conducted an exploratory descriptive…

Compelling research evidence shows benefits for student learning from explaining one's ideas and engaging with the ideas of others. However, whether certain patterns of group interaction may engender this productive student participation is unknown. Using data from two third grade mathematics classrooms, and over the course of six days during a…

This study presents a teaching experiment in which second-grade primary school students compared a city and a town according to population estimates. The activities were presented to them as Fermi problems and required an analysis of the reality to identify sub-problems that students could deal with. The students' products were analyzed from the…

This research is motivated by the importance of developing ways of thinking (WoT) in geometry learning at the Sambas District Elementary School, West Kalimantan, Indonesia. In general, this study aims to describe realistic mathematics teaching to WoT elementary school students in completing geometry material related to the design of the Sambas…

Implementation support strategies such as professional development (PD) are pivotal in guaranteeing the assistance that teachers need to enact mathematics teaching innovations and to secure lasting change. Within large-scale efforts an important issue for researchers is to understand how to design and put into effect these implementation support…

Cognitive difficulty arises from two types of cognitive processes: treatments; within the same, conversions; between different types of representational registers. Conversions are difficult since they ask for understanding of two representations. Direction and the choice of first register could be a threshold for the student. Wasan geometry is…

The acquisition of procedural and conceptual knowledge is imperative for the development of problem solving skills in mathematics. However, while there are mixed research findings on the relationship between the two domains of knowledge in some branches of mathematics, the relationship between learners' procedural and conceptual knowledge of…

This paper reports on a project that sought to enhance problem-solving practices within a cluster of primary schools. In-service teachers' description of their approach to problem-solving suggested it was treated as an isolated practice that occurred after concepts had been taught; often focusing on teaching particular problem-solving strategies…

Numbers and variables often follow the same principles of arithmetic operations, yet numbers can be computed to a value whereas variables cannot. We examined the effect of symbols--numbers versus variables--on middle school students' problem-solving behaviors in a dynamic algebra notation system by presenting problems in numbers (e.g., 3+5-3) or…

Teachers in kindergarten, primary, and secondary schools use hands-on manipulatives to help students grasp concepts in areas such as numbers, operations, geometry, algebra, measurement, data analysis, and probability. These manipulatives and interactive games are essential for fostering mathematical understanding, enabling students to build,…

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…