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…

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the "testing effect" and "spacing effect" in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional…

This mixed-method study aims to explore the feasibility of using the game-based, multimodal representation of mathematical problems to support middle school students' practice and performance of math problem representation and solving. A three-dimensional architectural simulation game, called E-Rebuild, was developed to engage students in…

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which…

Persistent inequities in mathematics teaching and learning for specific groups of learners are a key challenge for researchers and educators. The use of ability grouping has been common practice in New Zealand mathematics classrooms. However, many researchers (e.g. Boaler and Wiliam 2001; Zevenbergen in 2003) highlight the negative effects of…

This study investigated how preschool children processed and understood critical information in Magical Garden, a teachable agent-based play-&-learn game targeting early math. We analyzed 36 children's (ages 4-6 years) real-time behavior during game-use to explore whether children: (i) processed the information meant to support number sense…

We explore student performance on True-False assessments with statements in the conditional form "If P then Q" in order to better understand how students process conditional logic and to see whether logical misconceptions impede students' ability to demonstrate mathematical knowledge. We administered an online assessment to a population…

Students' problem-solving success depends on more than their knowledge and abilities. One factor that may play a role is the teacher's expectations of students. The current study focused on how a teacher's explicitly-stated expectations influence students' ability to learn from corrective feedback during problem solving. On the one hand, setting…

Some views of elementary teacher preparation may include the idea that undergraduate mathematics courses are useful or even crucial for prospective teachers to have. This study sought to identify teacher candidates with mathematics degrees, in order to study their mathematical preparation. The identified prospective teachers were studied to…

What mathematical knowledge is required for teaching has been researched by many, with Ball et al. (J Teach Educ 59(5):389-407, 2008) and their practice-based theory of mathematical knowledge for teaching (MKT) primary among them. However, what is required in terms of mathematical knowledge for teacher educator training has been researched much…

This paper reports an ongoing effort to address the problem of instructional capacity for high school geometry from a systems improvement perspective. In an effort to understand the system that contains the high school geometry instructional capacity problem, we identified key stakeholders and conducted preliminary interviews to learn about the…

The document presents a set of categories for the analysis of the conceptualization of the congruence of polygons--a central theme in school mathematics--and details the application of the analytical tools used, derived from Grounded Theory, in this construction. This set of categories is called 'Interpretive Model of the Conceptualization of…

As the field draws to greater consensus around components of productive mathematics classrooms, the need increases to answer questions about how we operationalize and measure these components and how we can actualize such practice in classrooms. This research report shares an analysis from a larger project aimed at describing and quantifying…

This study examines pre-service teachers' (PSTs') views of tasks that engage students in mathematical argumentation. Data were collected in two different mathematics courses for elementary school education majors (n = 51 total PSTs). Analyzed were (a) written journals in which PSTs defined tasks that promote student engagement in argumentation,…

One of the main tendencies of mathematical development in 19th and 20th centuries seem to be on rigor and formalization. Rigor and formalization took place on axiomatic basis leading to more abstraction. Euclidean type of an axiomatic model became a model of mathematics even for constructively developed analysis. Even though rigor and axiomatic…