Proof ability of prospective teachers on Trigonometry material is still lacking. It can be seen when they carry out trigonometry proof that does not meet the proof indicators to conduct the research. This study aimed at improving proof ability of prospective teachers with a contextual model on Trigonometry materials. The research method used was…

There is evidence that spatial thinking is malleable, and that spatial and mathematical skills are associated (Mix et al. [2016] "Journal of Experimental Psychology: General," 145, 1206; Mix et al. [2017] "Journal of Cognition and Development," 18, 465; Uttal et al. [2013] "Psychological Bulletin," 139, 352). However,…

Evidence is emerging that technology-based curricula and adaptive learning systems can personalize students' learning experiences and facilitate development of mathematical skills. Yet, evidence of efficacy in rigorous studies for these blended instructional models is mixed. These studies highlight challenges implementing the systems in…

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

This study is an investigation of elementary preservice teachers' (PSTs') exploration of model breaking points in fractions. Eighty-three PSTs at two universities in the Midwestern and Southwestern regions of the USA were asked to explore the area model of fraction addition through a series of tasks and explain their reasoning in determining its…

Disparate approaches to assessment pursue differing purposes. Clinical assessment interviews like the Australian early numeracy interview (ENI; Clarke et al. 2002) or its German version ElementarMathematisches BasisInterview (EMBI; Peter-Koop et al. 2007) can be used to gain insights into children's mathematical thinking and aim at providing a…

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN) = log (M) log (N)) with bidirectional…

The study aimed to develop and validate a test for the measurement of mathematical thinking of secondary-level students. The first-stage aspects of mathematical thinking were explored for a consolidated model in line with the curriculum of secondary-level education in Pakistan. Thirty-six items were developed and piloted in three schools. Factor…

Evidence is emerging that technology-based curricula and adaptive learning systems can personalize students' learning experiences and facilitate development of mathematical skills. Yet, evidence of efficacy in rigorous studies for these blended instructional models is mixed. These studies highlight challenges implementing the systems in…

This study aims to describe the categories of critical thinking skills of high school students in solving quadratic equation problems. The data in this study are the results of student work related to tests of critical thinking skills and the results of researchers' interviews with students. Data analysis will be carried out after giving the…

This dissertation investigates gender differences in (1) retrospective (i.e., measured after task completion) item-specific confidence judgments, and whether these judgments were warranted. Of particular interest was whether gender interacts with problem difficulty to explain confidence, calibration (speaks to the accuracy of confidence…

This paper aims to present how quantitative literacy was made a focus in a preschool classroom of threeand four-year-old children. With a focus on examining two areas of quantitative literacy, number knowledge and counting (Jordan, Kaplan, and Locuniak 2007) we seek to explore how educators, within an early childhood setting, used a project…

Offering secondary math educators an innovative holistic and process-orientated approach for implementing nonroutine problems into their curriculum, this book defines and establishes practical strategies to develop students' problem-solving skills. The text focuses on the process skills necessary to solve nonroutine problems in mathematics and…

The Home Learning Environment (HLE) focuses on everyday learning habits in families to support the development of children's early cognitive competencies. A growing number of studies have assessed the HLE by using different conceptual approaches and various assessment methods, often focusing on either the home literacy environment or the home…

This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in…