Reasoning and Proof is one of the Process Standards set forth in National Council of Teachers of Mathematics' (NCTM) "Principles and Standards for School Mathematics." Thus, it is important to give students opportunities to build their reasoning skills and aid their understanding of the proof process. Teaching students how to do proofs is a…

How do our mental representations of number change over development? The dominant view holds that children (and adults) possess multiple representations of number, and that age and experience lead to a shift from greater reliance upon logarithmically organized number representations to greater reliance upon more accurate, linear representations.…

The interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

Children bring a wealth of mathematical knowledge from home to school. This paper describes one six/seven year old girl's home interactions over 20 weeks about measurable quantities. Almost all measurement discussions occurred when actions were not straightforward. Consequently the measurement attributes usually used to introduce measurement at…

This article describes a way toward a student-centred process of teaching arithmetic, where the content is harmonized with the students' conceptual levels. At school start, one classroom teacher is guided in recurrent teaching development meetings in order to develop teaching based on the students' prerequisites and to successively learn the…

This study examines patterns in how a group of fifth- and sixth-grade teachers evaluated and reported using different types of curriculum resources to support their teaching in relation to the mathematical concepts outlined in the Common Core State Standards for Mathematics. In particular, it explores the use of resources that were available to…

This article investigates why students reported liking a student-driven learning design better than a highly guided design despite equivalent gains in knowledge assessments in both conditions. We created two learning designs based on the distinction in the literature between student-driven and teacher-led approaches. One teacher assigned each of…

This study concentrated on the theory-practice problem in mathematics teacher education. We examined 13 student teachers' use of theory when they reflected on teaching practice in a class specifically designed to optimize the chance for theory use. We developed a Reflection Analysis Instrument with which the student teachers' use of theory could…

The authors investigated benefits of digital technology compared with traditional manipulatives in relation to preschoolers' development and learning of computational skills. The sample consisted of twenty four 4-and 5-year old children who attended a half-day prekindergarten program five times a week in a university laboratory school in the…

There is a growing need for STEAM-based (Science, Technology, Engineering, Arts, and Mathematics) knowledge and skills across a wide range of professions (Brazell 2013). Yet students often fail to see the usefulness of mathematics beyond the classroom (Kloosterman, Raymond, and Emenaker 1996), and they do not regularly make connections between…

In this report, we describe a survey of mathematics education apps in the Apple App Store, conducted as part of a research project to develop a tablet-based assessment prototype for elementary mathematics. This survey was performed with the goal of understanding the design principles and techniques used in mathematics apps designed for tablets. We…

Replication studies are extremely rare in education. This randomized controlled trial (RCT) is a scale-up replication of Fuchs et al., which in a sample of 139 found a statistically significant positive impact for Number Rockets, a small-group intervention for at-risk first graders that focused on building understanding of number operations. The…

Democracy is a most accepted form of government system and has a great importance for citizens by allowing them equal and active participation in common life. As its development and characteristics are important for all citizens of a country, each democratic country puts much emphasis on democracy education in its educational curricula. In recent…

The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multi-component fraction…