Welcome to Episode One – The Road Sign Problem – Introduction

Welcome to a new approach towards teaching and learning math with technology. I could call this approach lessons or activities but I prefer to call them adventures because I hope that each adventure will bring a new perspective on learning math with technology. This idea has been on my back burner for a long time and it’s finally ready to go. Keep in mind that this is also a learning experience for me so  I also call it a work in progress. So let’s begin with the road sign adventure.

Back in 1992, the Wall Street Journal in an article entitled Reinventing Math (Active learning promises radical changes, as teachers say the rote appproach doesn’t add up) posed this problem: There are 26 sheep and 10 goats on a ship. How old is the captain? When researchers asked 41 second-graders on a math test […], about 90% of the children gave the same answer: 36. This is a surprising answer. According to David Pleaser’s A Student’s Guide to Problem Solving the children should have subtracted 10 from 36 to get the answer. (See Pleacher’s Post.) This, of course, is meant to tickle one’s funny bone, but the reality of it all may be quite surprising. Try the Road Sign problem in your class. It doesn’t matter what the grade level, it never seems to fail.

Click on image above.

Doing Dynamic Math & Tech Adventures

Helping students to improve their problem solving ability is one of the major goals of mathematics education. The dynamic math approach is intended to help facilitate that ability.

Preliminaries

  • Students should be organized for small groups activity. Each group chooses a “captain” who will be responsible for sharing his groups decisions.
  • Room arranged appropriately for group activity.
  • Computer and projection device setups are ready to go. 

  • Since you want to facilitate “conversation” try calling on students rather than responding to hand raises. This will give you better leverage in leading the group discussion and minimize the calling out of answers. When you do call on a student with his or her hand raised try to get another student to respond. Remember your goal is to encourage good mathematical conversation between you and the students and the students with each other.
  • Go over the rules (see below) with them. Make sure they understand each of them.

Setting the stage

  • Pose the problem to the students in an interesting manner. 
  • Hand out recording sheets.

Note: Before you let the students start working on the problem, make sure everyone understands by asking a student (or two) to restate the problem in his or her own words. Look around to make sure everyone understands. If not, let a student explain it to the student or students who still don’t understand.

  • Ask the class if there are any final clarification questions. If not, you can ask them to begin.

Doing the activity

The students should discuss the problem in their groups. You should listen in on their conversations and help them in appropriate ways. If you are using a time limit, remind them how much time left they have. Reinforce that their responses must be written clearly on the activity sheet. Though only one person may be writing, the result represents the group’s consensus on the solution. Once the time for the activity is over, the students should not be doing any more writing.

Debriefing

Have each captain share his or her group’s results by standing up and saying or reading what they wrote. Ask the other groups what they think the score (0 to 5) for their response should be.

Assessment Rubric

Use a scoring rubric to assign the group a score for the problem.