Background: Blended mathematical sensemaking in science ("MSS") involves deep conceptual understanding of quantitative relationships describing scientific phenomena. Previously we developed the cognitive framework describing proficiency in MSS across STEM disciplines, and specifically Physical Science. The framework was validated with…

This study explores how preservice secondary mathematics teachers comprehend and apply advanced mathematical concepts to the content they will teach in K-12 classrooms. Responding to student inquiries and guided by the "Mathematical Education of Teachers II" recommendations, an innovative capstone course was developed and integrated into…

Two problems, both from Gaspar Nicolas' "Tratado da Prática d'Arismética", published in 1519 are considered in this study. The tasks were carried out using pencil, paper and students from Portuguese schools. The aim was to explore the following students' performances: 1. The students were able to recognize the "error",…

As schools increasingly embrace embodied learning, there is a growing need to incorporate classroom teaching and learning activities that recognize the body's role as both an individual and collective resource for cognition and instruction. In response, we present a design for a classroom teaching sequence focused on early number learning,…

The study identified the algebraic patterns present in the cultural artifacts in the mountain ranges of northeastern Luzon, Philippines, and explored their integration into teaching mathematics. Culturally responsive teaching is a practice applied both locally and internationally, designed to strengthen the link between students' cultural context…

Instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) have shown to support students' development of reasoning about covarying quantities. However, research often neglects how this development occurs from the student point of view during the interactions with these artifacts. An analysis from this lens…

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…

The study aimed to investigate the effect of the flipped classroom strategy based on ADDIE Model on Prince Faisal College students' development of algebraic thinking skills. To achieve the goal of the study, the researchers developed a measure of development of algebraic thinking skills. The study used the quasi-experimental approach with a…

In this article, we address a call by Thompson and Carlson to directly contribute to defining the variation of students' reasoning about varying quantities. We show that students as young as in sixth grade can engage in complex forms of reasoning about multiple quantities in contexts that involve exploring science phenomena using interactive…

This qualitative case study analyzed how first year university mathematics students used words, images, and symbols to convey the same mathematical ideas. The study was located within the interpretivist paradigm and took naturalistic methodology. Twenty-six first year students were purposefully selected to participate in the study. Data was…

This study aims to investigate students' mathematical connection ability in solving the problem of mathematical and correlation between indicators of mathematical connection ability. This research is correlation research. The sample of the study is 35 girls' students in the 9th grade in a middle school in Kerman province (south-east of Iran). Data…

This article presents and analyses a didactic proposal based on manipulative material (Knobless Cylinders) used in a Montessori classroom of 3-6-year-old pre-schoolers. Choosing this material is justified in relation to the competencies/strategies/skills used during the development of mathematical patterning. Numerous studies emphasise the…

Using the tools of praxeological analysis and didactical transposition analysis, the treatments of the Fundamental Theorem of Calculus in one Norwegian, Grade 13 textbook is analysed, with a particular focus on the development of the logos block of the FTC. The terms structure, functioning and utility, first introduced by Chevallard in 2022, is…

This article is a discovery-based instructional resource for faculty to use as a capstone course or exploratory project for undergraduates who are familiar with (but not necessarily fluent in) calculus, linear algebra, complex variables, and geometry. The explorations flow from a simple change in sign: in the complex numbers a + bi, where…

Pattern is fundamental to mathematical learning yet pattern has been conspicuously low key within early mathematics curriculum guidance in England despite evidence that it predicts later attainment in mathematics overall. Whilst recent curriculum changes have seen pattern afforded enhanced status, this is within a conception of pattern that marks…