Technology Takes Students Further in the Mathematical Thinking

In “Promoting Problem Solving across Geometry and Algebra by Using Technology,” [1] University of Georgia researchers make a case for teachers to use hardware and software in their classrooms (Erbas, 2005). Technology enables students to make connections between representations of numbers and operations in order to find multiple solutions to problems. Students make connections between mathematical concepts involving real life situations by using graphic calculators, geometric drafting software and spreadsheet applications. With a teacher’s encouragement, they may consider multiple answers to solve problems, evaluate plausibility of those answers, and recognize patterns for hypotheses. With spreadsheets, tables of possible answers allow students to check validity of their thinking without becoming discouraged by limited skill in solving algorithms to prove theory. Graphing calculators show relationships of the numbers and free students to consider reasonableness of their answers. Drawing software allows students to sketch accurate geometric representations of problems and connect relationships of numbers with variables. These technological tools do not release the teacher from questioning students. The teacher encourages and challenges students to use the tools to go further in their thinking, beyond one answer. The tools free students to consider their own theories and seek solutions at higher levels of learning.

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[1] Erbas, A.K. (2005). “Promoting Problem Solving Across Geometry and Algebra by Using Technology.” Mathematics Teacher, p. 599-602.

Experience Fractions Game

The Fractions Game on the Illuminations web site had decent instructions. The goal is to slide all the rulers to one by matching the fraction on the card. Individuals may play themselves by beating the previous time required to finish. The sound has to be turned on, which my be best in a classroom.  I was not clear that I had the correct equivalent by the popping sound. A card is turned over and the player has options on how to slide the markers along tracks to reach one. Six tracks are marked with fractions of halves, thirds, fourth, fifths, sixths, and 10ths of one. Players may count one part at a time to reach one, using the same denominator.  As the game progresses,  a player is forced to find an equivalent fraction as the option for using the exact denominator is no longer available. A player may reduce the fraction or multiply by one in the form of a fraction to match an available denominator. When no exact option is not available, the marker may be slid to one if the fraction on the card is larger than the space required to reach one. A weakness is that the tracks became illegible near the end faded and froze up after three rounds. Positive reinforcement was given at the end of each round.

The game builds experience with concepts about fractions. Fractions of different numbers may be equivalent. Different fractions may be added to make one. Fractions are part of one. Larger numbers in fractions do not mean they are larger parts. Numerators tell how many pieces of one. Larger denominators mean smaller pieces of one.

The game may be used with partners or individuals at the computer center. The game may be used in fourth grade after an introduction using concrete manipulative models. The teacher may model using the game on a SMART board. Students may use the representations to practice or extend their understanding about fractions. Fifth graders may need review and practice. with fractions.