The COVID-19 pandemic has affected student learning; according to the National Assessment of Educational Progress (2022), scores for students in the United States have shown a decline in mathematics. . One way educators can strengthen students' current mathematical knowledge and bridge to new content is through Number Talks. Number Talks are brief…

Although it is not a new idea, discourse continues to be a topic of discussion among teachers, teacher educators, and researchers in mathematics education. The National Council of Teachers (NCTM) and the Common Core State Standards for Mathematics (CCSSM 2010) describe mathematics classrooms as discourse communities in which whole-class…

The desire to persuade students to avoid strictly memorizing formulas is a recurring theme throughout discussions of curriculum and problem solving. In combinatorics, a branch of discrete mathematics, problems can be easy to write--identify a few categories, add a few restrictions, specify an outcome--yet extremely challenging to solve. A lesson…

Student learning communities (SLCs) are more than just a different way of doing group work. Like the professional learning communities they resemble, SLCs provide students with a structured way to solve problems, share insight, and help one another continually develop new skills and expertise. With the right planning and support, dynamic…

Teachers across all grade levels agree that problem solving and reasoning are areas of weakness in students. Assessments among U.S. students indicate that these weaknesses persist (NCTM 2014) in spite of repeated calls that date back more than thirty years for increased problem solving, reasoning, and sense making in our schools. The NCTM is…

Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

It is important to use rich problem-solving tasks to develop students' understanding of important mathematical ideas (NCTM 2000). Rich tasks are complex, nonalgorithmic, and nonroutine, requiring reasoning, problem solving, and communication of thinking. Evidence has shown that using rich tasks in student-centered classrooms is especially…

In this article, we provide a discussion on our revision method (termed "prescriptive tutoring") aimed at revealing students' misconceptions and misunderstandings by getting them to solve physics problems with an anonymous partner via the computer. It is currently being implemented and evaluated in a public secondary school in Singapore,…

Science centers can engage students; accommodate different learning styles and individual interests; help students become independent and confident learners; and encourage social skills among students. In this article, the author worked with third-grade students as they completed activities at learning centers during a week-long unit on simple…

This manual describes four discussion techniques that may be used in an adult education setting following a presentation by one or more resource persons. These four techniques--the huddle group, the buzz group, the chain reaction forum, and the reaction symposium--are designed to help the learner acquire information, develop skills in problem…

The Nominal Group Technique (NGT), developed by Andre Delbecq and Andrew Van de Ven at the University of Wisconsin in the 1960s, is used to enhance the generation, exploration, and communication of ideas relevant to problem-solving situations. The NGT is unlike other typical interacting group techniques in that individuals work in the presence of…

There has been much discussion recently of the effect that gender and learning style have on student performance. Educators have attempted to develop new teaching and assessment strategies that accommodate a variety of learning styles, and both males and females are becoming more aware of gender-related traits and their relationship to classroom…

This collection of papers delves into reflection as a concept and provides specific, replicable tools for professional practice. Each chapter draws on a particular school situation, demonstrating the value of teacher reflection and describing the nuts and bolts of the process, offering protocols for handling many different circumstances. After…

This booklet contains a collection of educational games that can be used by teachers to convey ideas and create discussion related to environmental protection and sustainable development. The games accommodate participants of all ages and require little preparation by the teacher, up to 30-40 players with only one operator, minimal materials (many…

Describes the Philosophy for Children program in critical thinking, its pedagogical approach involving the community of inquiry, and the sociocognitive learning theories upon which it is based. Suggests it can be used as a pedagogical model for developing collaborative learning approaches in art education, especially aesthetics. (KM)