NCTM's "Principles to Actions: Ensuring Mathematical Success for All" (2014), outlines eight teaching practices for effective teaching and learning mathematics. One of them, facilitate meaningful mathematical discourse, states, "Effective teaching of mathematics facilitates discourse among students to build shared understanding of…

How can teachers engage students in learning essential mathematics? The National Council of Teachers of Mathematics recommends using "contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations" (NCTM 2006, p. 11). Understanding the Process Standards (NCTM 2000) enables teachers…

Children build foundations for mathematical thinking in early play and exploration. During the preschool years, children enjoy exploring mathematical concepts--such as patterns, shape, spatial relationships, and measurement--leading them to spontaneously engage in mathematical thinking during play. Block play is one common example that engages…

Presents a word problem designed to encourage students to create systematic methods for counting and develop probability concepts. Involves sharing eight cookies between three people. (KHR)

Presents activities to incorporate Polya's four-step problem-solving process. (KHR)

Discusses a problem that appeared in the September, 1999 issue of this journal and presents solutions from students in grades 2-6. The question involved using colored cubes rearranged to make different stacked towers. (KHR)

Introduces a problem that can be used to help children develop graph sense. Involves two graphs of which students must determine which one applies to which situation. (KHR)

Provides a model for teachers to engage children in understanding problems and communicating their solutions in order to lead them toward becoming mathematically powerful learners. (Author/NB)

Presents solutions to the Pumpkin Puzzler problem that appeared in the October 2001 issue of this journal. (Author/NB)

Presents solutions to the Football Frenzy problem that appeared in the November 2001 issue of this journal. (Author/NB)

Describes a problem that appeared in the April, 1999 issue of this journal and analyzes student responses and misconceptions. The problem concerns exponential progressions. (KHR)

Poses the Fractionberry Pie problem to teach students fractions. (Author/NB)

Presents solutions to the Have a Heart problem that appeared in the February 2002 issue of this journal. (Author/NB)

Presents the March Mathness problem which allows students to mathematically analyze familiar situations. Uses sports as the analogy. (Author/NB)

Presents the Shopping Spree problem to teach students the concept of estimation. (Author/NB)