| Use the Right Materials | | | | you know that is true?"o "Who can explain |
| 1. Forget the textbook approach. You know, | | | | why?"o "Who disagrees?"o "Who agrees?"o "Will |
| "Students, open up to page...." The textbook | | | | this always work?"o "Who can explain this in |
| writers did not write the test your students will | | | | another way?"o "What is another way to |
| face. If you have administered the test YOU | | | | approach this problem?"o "Find someone who |
| know what students have to know to perform | | | | used another method." |
| well on this test. Look for materials that teach | | | | 11. You get the idea. Push further and dig deeper. |
| this. | | | | Just because students can arrive at a correct |
| 2. Think in terms of units and big major concepts. | | | | answer doesn't mean they understand the |
| Use the MAP Level Descriptors as your guide. If | | | | concept or process. They are often guessing or |
| you want to develop Level 4 and % students, | | | | using misinformation that coincidentally works. If |
| teach what is described in Level 4 and 5. | | | | they can't explain it, don't be satisfied that they |
| 3. Laminate the formulas sheet and refer to it at | | | | have learned anything. |
| appropriate opportunities. | | | | 12. Never explain or demonstrate anything that a |
| 4. Use manipulatives to introduce each concept. | | | | student can explain. Never say anything that a |
| Move student understanding from concept, to | | | | student can say. |
| connecting, to symbolic.o At the concept level | | | | 13. Encourage students to find multiple solutions |
| students use concrete materials to explore | | | | and use multiple strategies on the same problem. |
| concepts. No symbolic representations of the | | | | 14. Always collect all the answers before deciding, |
| concept is introduced. At this level, it is important | | | | "which one is right." |
| that students interact with a concept in a variety | | | | 15. Make it a routine to identify where wrong |
| of ways, using a variety of materials.o At the | | | | answers came from. |
| connecting level, the concept, as concretely | | | | Teacher Strategies |
| experienced by the student, is connected to the | | | | 1. Reward creativity. |
| mathematical symbolization that represents the | | | | 2. Value alternative methods. Do not require |
| concept. The teacher guides students through | | | | problems only be done "your" way. |
| discussion, encouraging students to use their own | | | | 3. Ask students to "show their thinking" and |
| language and then expanding their vocabulary and | | | | "provide the work that shows how you arrived at |
| developing their ability to represent their verbal | | | | your answer." |
| expressions symbolically. But the students must | | | | 4. Give additional credit for working a problem in |
| already have a firm grasp of the concept for this | | | | more than one way. |
| to be meaningful.o At the symbolic level, the | | | | 5. Use calculators routinely in class. Teach them to |
| students themselves write the mathematical | | | | use the calculator as a tool. Teach them how to |
| symbols to represent the concepts they have | | | | use it, including all functions. Require them to look |
| learned. They may still sell concrete materials; | | | | back and check that the answer is reasonable. |
| they will drop them when they are ready. The | | | | Keep a class chart or poster of "calculator |
| symbols are not the vehicle for teaching the | | | | mistakes" to make a point that the calculator is |
| concept or solving a problem. They are used for | | | | only a tool that works as well as the person who |
| recording concepts that have already been | | | | employs it. |
| internalized to understanding. | | | | 6. Use multiple-choice tests in this different way: |
| 5. Collect and use Sample MAP-like problems | | | | Students are not allowed to work any problem:) |
| every day and as assessments. Have students | | | | They get points for every answer they can |
| create their own that are modeled after the ones | | | | eliminate with correct justification. |
| they have encountered on pretests and through | | | | Tackle the Myths |
| daily classwork. | | | | 1. Only certain kinds of people are "good at math." |
| Require Students to THINK. | | | | 2. You have to be taught how. This is learned |
| 6. Practice accountable talk as a prelude to | | | | helplessness. |
| accountable problem solving. | | | | 3. When in doubt, ask the teacher. More |
| 7. Start with problems designed for lower grade | | | | helplessness. |
| levels. Don't tell students what grade level they | | | | 4. Math is mostly knowing how to calculate. |
| were designed for this develops success and | | | | 5. If you don't know "the basics," you can't do |
| motivation. | | | | anything else. |
| 8. Use brainteasers. Lots of good books and | | | | 6. The calculator is smarter than a fifth grader. |
| websites are available for this. | | | | 7. The most important thing in math is "getting |
| 9. Model your thinking by "thinking out loud" during | | | | the right answer." |
| demo problems. | | | | Address these myths and any others you notice |
| 10. Always ask students to explain why. These | | | | whenever they rear their ugly heads. Teach |
| following should become part of your routine | | | | students that these myths are not true and that |
| discussions:o "Tell us why you think so."o "How do | | | | they are merely self-limiting misbeliefs. |