Over the past 100 years, technology has evolved in unprecedented fashion. Calculators, computers, and smart phones have become ubiquitous, yet school mathematics experiences for many children still remain without many powerful technological tools for the exploration of mathematics. We consider the evolution of some tools as we imagine a future.
Samuel Otten and Andrew Otten
Students make strategic choices–and justify them–to solve a system of two linear equations.
Use popular culture to draw students' attention to mathematical topics.
Core content provides opportunities to focus on the structure of mathematical theory, proof, and anticipation of subsequent topics.
Marla A. Sole
Using bivariate data, students investigate the ingredients in pasta sauce.
Lynn Mitzel and Mark Spanier
When it was released in the mid-1980s, Tetris jump-started the video game craze, but many students of the current generation have never even seen this game, much less played it. Now, with the flood of mobile device applications, Tetris has made a comeback, and today's students have a chance to use it, too. We have found Tetris to be an engaging tool for high school geometry students to apply an isometry in context and to learn the composition of isometries. The game allows a player to rotate and translate moving pieces to create full rows anywhere on the screen.
A set of problems of many types.
Students analyze items from the media to answer mathematical questions related to the article.
Performance tasks provide effective ways to differentiate mathematics instruction while allowing students to be creative and to incorporate mathematics content that is suitable for their interest and readiness. A project that I have enjoyed assigning to my high school students, Algebra about Me, is designed to introduce, reinforce, and review equation-solving concepts and skills (for a customizable activity sheet, go to www.nctm.org/mt).
A t a party that I attended, the hosts gave their guests the Tower of Hanoi puzzle with alternating dark and light discs and a challenge to move the 7 discs to a new post. (I disqualified myself because I knew how to solve the challenge.) However, the hosts' son and daughter-in-law misunderstood the directions and moved the dark discs to one side post and the light discs to the other side post. I immediately wondered, “How many moves did they take, assuming that they made the most efficient moves? How can their interpretation of the problem be generalized to n discs?”