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The Example-Conclusion Map is used to learn basic rules. The idea is for the instructor to develop and provide three examples of the application of a rule (without giving the specific rule to students). Students are asked to try to find a pattern based on the examples, which is basically a verbalization of the rule in the students own words. Students are then asked to prepare their own example to verify their findings.
The Example-Conclusion Map is used to learn basic rules. When using this map, the instructor develops and provides three examples of a rule without explicitly stating the rule. Students then look for a pattern based on the examples and state the applicable rule in their own words. As a final step, students prepare their own example to verify their findings. |
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Once students have learned the basic rules related to the specific topic, teachers can use the Multi-Rule Map (see figure 2) to attack multi-rule problems. The problem is written in the initial point and then a rule (learned with the previous map) is used to move the problem to the next step. The rule is written in the cloud next to the box. The process is repeated by picking a new rule until the problem is completed. Once students have mastered the basic rules, the Multi-Rule map can be used. With this map, the problem is written as the initial point, then students write a previously-learned rule in the cloud next to the point box. Students apply the rule to the problem and write the next step of the problem in the second box (step 1). This sequence is repeated until the problem is solved. |
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The last Problem Solving Map is the Math-Breaker Map. There is not a specific template for this tool because it depends on the problem being solved but the basic idea of the tool is depicted in figure 3. The map breaks down the problem into smaller steps. Each step is given in a box that contains instructions and blank spaces for the student to do that step. The arrows represent prerequisites, a step with the arrow pointing to it means that all previous steps must be completed first. Examples of problems that can be presented using this map include, long formulas (such as the quadratic equation), structured processes (e.g. solving systems of equations), and word problems.
The final map is the Math-Breaker Map. This map is broadly applicable and can be customized to different problems. Students use a series of boxes is used to show rules that apply to each step. Each box contains space for writing a rule and for completing the step. The boxes are connected by arrows indicating which parts should be solved first. This map is ideal for complex formulas, structured processes, and word problems. |
