The purpose of this meta-analysis is to examine the effect of problem-posing on students' mathematical academic outcomes, including problem-solving skills, problem-posing skills, mathematical dispositions, and mathematics achievement. Twenty-one studies that were published between 1990 and 2019 with problem-posing as the intervention were included…

This working group continues to develop a research program on the practice of launching mathematical tasks and its resulting impact on learners. Our research agenda contains two strands of inquiry exploring (1) theory and framework building concerning effective launches and (2) empirical examination of the link between launching and opportunities…

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…

This discussion-based lesson is designed to support Year 6 students in their initial understanding of using letters to represent numbers, expressions, and equations in algebra. The three level framework is designed for: (1) making thinking explicit, (2) exploring each other's solutions, and (3) developing new mathematical insights. In each level…

There have been many recent policy and program changes in K-12 education across the United States, particularly in area of mathematics. Changes, such as the Common Core State Standards for Mathematics and standards-aligned year-end summative assessments, require an increase in student-centered, cognitively demanding activities in the classroom.…

This column presents ideas and techniques to enhance your science teaching. This month's issue shares information about a unit promoting scientific literacy and the engineering design process. The integration of engineering with scientific practices in K-12 education can promote creativity, hands-on learning, and an improvement in students'…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

Some of the most provocative problems in mathematics concern logical paradoxes. Provides a series of paradoxes for students to consider. (CCM)

Describes the Six Circle problem which consists of the numbers 1-6, six circles, and asks whether it is possible to put the numbers in the circles--which are configured in a triangle--so that the sums of the three numbers on either side are the same. (NB)

Presents a variety of mathematical games from all over the world using pen and paper, or single-board setups. (ASK)

Presents an educational game on probability that can be the starting point for an open-ended statistical project. (ASK)

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in pre-algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for…

Describes a way to assign points to the problem-solving process. Provides a rubric-scoring example. (ASK)

Discusses the use of techniques from language experiences in assisting with the learning and assessment of mathematics. Provides a mathematics activity on fractions employing story writing activities. (ASK)

Discusses the importance of writing in mathematics classrooms and offers an alternative to journal writing. Presents "Chris and Pat Writing Activities" designed to help students better understand concepts by making decisions about who has used correct skills to solve a mathematical problem. (ASK)