This book's 28 chapters are adapted and updated from articles published in NCTM's "Journal for Research in Mathematics Education" between 2000 and 2010. The authors have rewritten and revised their work to make it clear, understandable, and--most of all--useful for mathematics teachers today. To help teachers even more, these articles…

In 3 experiments, we examined the effects of using concrete and/or abstract visual problem representations during instruction on students' problem-solving practice, near transfer, problem representations, and learning perceptions. In Experiments 1 and 2, novice students learned about electrical circuit analysis with an instructional program that…

Children learn from a very early age what it means to get their "fair share." Whether it is candy or birthday cake, many children successfully create equal-size groups or parts of a collection or whole but later struggle to create fair shares of multiple wholes, such as fairly sharing four pies among a family of seven. Recent research suggests…

The title question has at least two natural answers, one "global" and one "local." Global: "when they can be made to coincide by a rigid motion of the whole plane;" local: "when there is a one-to-one distance preserving mapping of one onto the other." Self-evidently global implies local. We show that in fact these different notions lead to…

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…

In the past three decades, researchers have noted the limitations of a problem-solving approach that overemphasizes algorithms and quantitation and neglects student misconceptions and an otherwise qualitative, conceptual understanding of chemical phenomena. Since then, studies and lessons designed to improve student understanding of chemistry has…

This study, based on Taiwanese geographical concepts, develops a multi-touch interactive jigsaw puzzle (MIJP) to assist primary school students in solving geographical puzzles. The MIJP, which has multi-touch operating characteristics and provides two kinds of scaffolding tools, each with a different level of difficulty, can assist students in…

This paper is based on the concept that lively and interactive math classes are possible by incorporating rich tasks to meet the needs of students operating at different levels in the classrooms. A study was carried out to find out the impact on learning and motivation of using rich tasks at secondary level in the maths class by incorporating…

The learning of solving multi-step problems is a relevant aim in chemical education for engineering students. In these questions, after analyzing initial data, a complex reasoning and an elaborated mathematical procedure is needed to achieve the correct numerical answer. However, many students are able to effectively use algorithms even with a…

In 2000, the Programme for International Student Assessment (PISA) study was conducted by the Organisation for Economic Co-operation and Development (OECD). It is a worldwide study of 15-year-old students' performance in mathematics, science and reading skills. The study showed relatively poor results for German students' scientific literacy…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

The purpose of this study was to explore middle grade mathematics students' uses of scaffolding and its effectiveness in helping students solve non-routine problems. Students were given two different types of scaffolds to support their learning of sixth grade geometry concepts. First, students solved a math task by using a four square graphic…

Interactional communicative competence and higher-order thinking have been well documented as two of the biggest challenges for second/foreign language learners (EFL learners). This paper evaluates the use of digital tabletops as tools for problem-solving tasks in groups. The evaluation is based on a preliminary study of an application of the use…

Executive coaching has become increasingly commonplace in both the corporate and non-profit sectors as a means of improving professional effectiveness but there is a dearth of empirically-based protocols geared specifically toward the growth needs of school principals. This qualitative case study explores the implementation of a principal coaching…

One of the most difficult tasks that classroom teachers face is finding ways to reach all their students and match each student's level of mathematical readiness and performance to the skills they are required to teach. In classrooms and schools, current federal and state requirements have increased the emphasis on accountability for improved…