Background/purpose: This research aims to classify and show the characteristics of the types of abstract thinking students use when solving mathematical problems. Materials/methods: This descriptive qualitative research was conducted in a structured manner on students of the University of Muhammadiyah Surakarta, Faculty of Teacher Training and…

The learning of multiplication facts has long been an important focus of the primary grades, but lasting mastery of facts requires a meaningful approach that develops all four components of mathematical proficiency (understanding, fluency, problem-solving, and reasoning). This article shares how visual imagery in the form of Quick Looks with dot…

In real-world settings, vision language models (VLMs) should robustly handle naturalistic, noisy visual content as well as domain-specific language and concepts. For example, K-12 educators using digital learning platforms may need to examine and provide feedback across many images of students' math work. To assess the potential of VLMs to support…

Against the backdrop of contemporary debates surrounding the public role of criminology, this article argues that a key barrier to ensuring that the next generation of criminologists is equipped with the skills necessary to engage in critical forms of citizenship, is the quantitative "skills gap" that undergraduate students possess as a…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Students may excel in computation, but their ability to apply their skills will suffer if they do not understand the math vocabulary used in instructions and story problems. This action research project examines two methods for strengthening students' ability to communicate mathematically: (1) Journal writing and peer discussion; and (2) The…

One of the most difficult topics to teach in geometry is the concept of proof. This article describes ProofBlocks as an innovative approach to helping students develop proficiency in proof. ProofBlocks is an intuitive approach to teaching proof that makes proof accessible to students without sacrificing the rigor of traditional approaches. When…

This study examined whether children with mathematical difficulties (MDs) or comorbid mathematical and reading difficulties have a working memory deficit and whether the hypothesized working memory deficit includes the whole working memory system or only specific components. In the study, 31 10-year-olds with MDs and 37 10-year-olds with both…

Examines the possibility that at times imagery might be a disadvantage in certain tasks. For example, the notion of a persistent image may be so vivid as to actually block other creative thought. Describes one calculus student's images supporting high levels of mathematical functioning which occasionally became so powerful as to obscure more than…

This book offers classroom-tested activities designed to make even the most reluctant learners crazy about math. Appealing to everyone from sports fans to readers, future fashion designers to budding musicians, the activities presented in this book offer ways to develop a deep-rooted love and appreciation of math in every student. Teachers are…

Student success in solving physics problems is related to the representational format of the problem. We study student representational competence in two large-lecture algebra-based introductory university physics courses with approximately 600 participants total. We examined student performance on homework problems given in four different…

One reason students give for attending a community college is that the mathematics requirements appear to be less rigorous. Many of the author's students have told her that they have chosen to seek an associate's degree first because they do not feel confident that they could successfully complete the mathematics requirement at a four-year…

Hypothesizes that exploring the mathematical ideas behind mathematical terms enables children to gain insight into the structure of a number system and provides a basis for powerful playing with this structure. Describes visualizing mathematical ideas for exploring aspects of mathematics. Offers rectangular numbers to link and explore structures…

Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…

The goal of this paper is to renew interest in the structural option to algebra instruction. Concern for the usual secondary school algebra curriculum related to simplifying expressions, solving equations, and rationalizing numerators and denominators is viewed from three pedagogical approaches: (1) structural approach, (2) empirical approach, and…