The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics--to be called TSM--that is predominant in almost all the school textbooks. By analyzing how the long…

Understanding fraction magnitudes is important for achievement and in daily life. However, adults' fraction reasoning sometimes appears to reflect whole number bias and other times reflects accurate reasoning. In the current experiments, we examined how contextual factors and individual differences in executive functioning (Experiment 1),…

Covid-19 has accelerated the speed of technocratic transformation in teaching and learning. Previous researches on whether technology enhances students' motivation towards learning or burdens them with additional layer of anxiety in learning the nitty gritty of technology itself have mixed results. The purpose of this study was to explore early…

Recent standards reform documents across the globe have called for statistical literacy by the end of high school. Thus, it is important for teachers to develop a deep understanding of the content. Despite the relatively thick literature base connecting students' content knowledge and reasoning, research on these connections among practicing…

In Spain, curricular guidelines as well as the university-entrance tests for social-science high-school students (17-18 years old) include sampling distributions. To analyse the understanding of this concept we investigated a sample of 234 students. We administered a questionnaire to them and ask half for justifications of their answers. The…

Much like one's experiences with the wonders of the world, concrete and multiperspective representations of mathematical concepts are key to understanding. Ideally, "learning environments should give students the opportunity to get to know different representations of a mathematical object in order for them to develop an appropriate…

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are…

Logical statements are prevalent in mathematics, science and everyday life. The most common logical statements are conditionals, 'If H … , then C … ', where 'H' is a hypothesis and 'C' is a conclusion. Reasoning about conditionals depends on four main conditional contexts (intuitive, abstract, symbolic or counterintuitive). This study tested a…

The purpose of this study is to reveal the concept definitions and examples of pre-service elementary mathematics teachers regarding sets. In this context, students' formal definitions, personal definitions and examples in sets were investigated. Concept of equal sets, subsets, union, intersection, compliment, and difference were considered as…

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…

Understanding fraction magnitudes is important for achievement and in daily life. However, adults' fraction reasoning sometimes appears to reflect whole number bias and other times reflects accurate reasoning. In the current experiments, we examined how contextual factors and individual differences in executive functioning (Experiment 1),…

The purpose of this guide is to provide strategies and materials for developing and implementing lessons for students who need intensive instruction in the area of place value, numeracy, and counting. Resource room teachers, math interventionists, and others working with struggling students may find this guide helpful. Within college- and…

This article demonstrates how removing algebraic representations and mathematical conventions, such as the vertical line test, and focusing on a real-world context can support students' development of essential understandings of the function concept. To do this, the authors present a lesson that engages students with a GeoGebra-based applet using…

Background: Knowledge of quantum computing is arguably inaccessible to many, with knowledge of the complex mathematics involving a particular barrier to entry, creating difficulty in terms of teaching and inclusive learning for those without a high level of mathematics. Meanwhile, it is increasingly important that the knowledge of quantum…

This paper shares findings from the study of a learning sequence designed to support prospective elementary teachers (PTs) in identifying evidence of conceptual understanding and procedural fluency. Conceptual understanding and procedural fluency are widely recognized as important to teaching and learning mathematics, and identifying evidence of…