Hidden Numbers Computer Game
The purpose of this game is to develop the skill of ordering decimal numbers and to raise discussion about decimal misconceptions. (The interviews in the Case Studies show how revealing this game can be.) The computer version can be played individually or in small groups, or in a teacher-led discussion.
This computer game presents children with two decimal numbers (generally of different lengths) with the digits hidden behind "doors". They have to select the larger number. Students begin with a certain amount of money and have to pay to open the doors to see the digits. The diagrammatic screen above shows a game in which the student has opened 4 doors and has $1900 remaining. If they correctly identify the larger number they win money.
This game directly confronts misconceptions such as longer decimals are always larger or smaller. It also identifies whether good students are using the most efficient decimal ordering strategy (i.e. left to right comparison of digits). As with all good mathematical games, there can be an element of luck - expert students will begin to make shrewd guesses.
When students make errors, the next questions are accompanied by help. As students uncover the digits behind the doors, lines of appropriate length appear. Students can then examine the lengths of the lines on the screen to see why one number is greater than the other. For example, if a hidden number is 0.423 and the student opens the 2, then the 3 and then the 4, lines of length proportional to 2 hundredths, then 3 thousandths, then 4 tenths appear. When all doors are opened, this makes a line of total length representing 0.423.