Off You Go is a PK-12 mathematical routine that leverages children's home resources and assets to help students take a concept with which they have initial or informal understanding and explore and test its boundaries to support defining or estimating with precision. The authors provide a guide for how to adapt this routine to engage students at…

In an age when distance learning has become part of the "new normal," educators know that rich remote math teaching involves more than direct instruction, online videos, and endless practice problems on virtual activity sheets. Using both personal experience and those of teachers in real K-grade 12 online classrooms, distance learning…

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…

One of the major benefits of the face-to-face teaching environment is that social interaction opportunities are a natural part of the course: Learners meet in the same room for the same allotted period of time each week. This social opportunity is not organic to online courses; therefore, to have this social interaction as a part of online classes…

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'…

Recognizing meaning in students' mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student's non-traditional strategy for dividing fractions. Six categories of…

Discusses some surprising properties of the natural numbers set such as axioms for natural numbers and mathematical induction. (ASK)

Describes the use of investigations for the purpose of assessment, teaching, and learning. Lists types of questions that can be included in investigations. Explains how to write an investigation and provides some examples. (ASK)

Presents a probability activity addressing students' misconceptions regarding the Law of Large Numbers. Provides students with better conceptual understanding of the Law of Large Numbers. (ASK)

Suggests that student writing has definite benefits for mathematics learning. Presents five activities to help teachers use writing in their mathematics classes. (ASK)

Provides practical applications of elementary coordinate geometry while discussing how mathematics is used to assess the security of systems. (ASK)

Describes some general techniques for making collapsible models, including spiral models, for all the Platonic solids except the cube. Discusses the nature of the dissections of the faces necessary for the construction of the spiral cube. (ASK)

Presents an activity on fractions and explains how students obtain different fractions having different patterns when they are represented by their decimal expansions. (ASK)

Continues analyzing some fundamental mathematical ideas on logic and proof. Provides some sample problems and their solutions. (ASK)