In my Keynote Address to PME-NA 45, I offer an embodied framework for naming what makes mathematics powerful for mathematicians and scientists, yet intractable for many learners. The essential claim is this: Students reside in the Real World, where math is grounded, embodied and meaningful, while mathematics resides in the ungrounded, disembodied…

Research studies are abundant in pointing at how the transition from additive to multiplicative thinking acts as a core challenge for students' understanding of proportionality. This said, we have yet to understand how this transition can be supported, and there remains significant questions to address about how students experience it. Recent work…

Prior work has established that cognitive and perceptual processes influence students' attention to notational structures in mathematical expressions, which in turn affects their problem-solving approaches and performance. Advances in educational technology provide opportunities to further investigate these processes, improve student learning, and…

The purpose of this research is to examine fourth grade students' ability to solve mathematical problems which have the same solutions but are given in three different formats as "symbolic, numerical and story (word) problem" and which require four operations. Within this frame, the students' solutions in different formats, their…

This program focused on improving mathematics content and pedagogy for Algebra I teachers, including regular classroom teachers and exceptional education teachers, as they implemented the Tennessee Mathematics Standards. Concentrating work on a few topics allowed for tightening breadth while increasing depth of content, as well as devoting study…

The aim of this study was to investigate how pictorial representations with different semiotic characteristics affect additive word problem solving by kindergartners. The focus of the study is on three categories of additive problems (change problems, combine problems and equalize problems) and on representational pictures with different semiotic…

There are opinions about approaching the proof in mathematics education need to change as providing students to understand the mathematical proof rather than developing formal mathematical proof skills. In this context, proofs without words described as informal proofs can be used in proof teaching. The purpose of this study was to investigate the…

It is known that a significant portion of the world's child population is gifted. Studies on the applications that can be used in the education of these gifted students have been given importance in recent years. In this study, the effect of differentiated instruction method on mathematics problem solving attitude and critical thinking skills of…

Due to the sudden and unexpected move to remote learning in 2020 influenced by COVID-19, both mathematics teacher educators (MTEs) and prospective elementary teachers (PTs) faced a new challenge in creating a productive remote teaching and learning environment. In this study, we used Parrish's (2014) addition strategies and Thanheiser's (2009)…

Mathematics word problems provide students with an opportunity to apply what they are learning in their mathematics classes to the world around them. However, students often neglect their knowledge of the world and provide nonsensical responses (e.g., they may answer that a school needs 12.5 buses for a field trip). This study examined if the…

This paper deals with a set of geometrical problems for mathematical problem-solving at different difficulty levels. All of these are presented as national flags and one has to investigate invariant area proportions when changing the locus of any corner of the flag. This dynamic element suggests the usage of dynamical geometry environments.…

Prior work on teachers' mathematical knowledge has contributed to our understanding of the important role of teachers' knowledge in teaching and learning. However, one aspect of teachers' mathematical knowledge has received little attention: "strategic competence for word problems." Adapting from one of the most comprehensive…

In this article, we present research on eight kindergarten and eight first-grade students' understandings of the arithmetic properties of commutativity, additive identity, and additive inverse during a classroom teaching experiment, selected from a larger study that included 88 students. In this study, we explore the students' types of…

Many primary school students have difficulties understanding mathematical equivalence with considerably poorer performance in some countries than in others. However, students' formal understanding of equivalence has significant and long-lasting effects, as it predicts arithmetic and algebra achievement throughout school years. Currently, little is…

Despite the introduction of Common Core State Standards and the National Council of Teachers of Mathematics urging educators to explore fundamental concepts in mathematics at a deeper level, the majority of mathematics education has remained aimed at initial skill acquisition. The result has led to students learning to mimic a standard set of…