Teaching Math to Students With Exceptional Needs

1. Teaching Math to Students With Exceptional Needs Jennifer Kosiak kosiak.jenn@uwlax.edu www.uwlax.edu/faculty/kosiak/projects/index.html Jon Hasenbank Hasenban.jon@uwlax.edu

2. A tale of the gifted and talented.

3. Gifted Student Gifted students are properly challenged when they are asked to move beyond computation into higher-order mathematical thinking processes such as applying computational skills to everyday problems, problem solving, problem posing, and crating new mathematics (Shelffield, 2003)

4. Mathematics Investigation Centers • To provide enrichment activities that generally fit into the theme that the whole class is working on. These activities focus on processes of mathematics rather than computation skills in attempt to proved depther rather than breadth.

5. MIC & TIC MIC for a given unit consists of nine activities dept in separate folders in a box with any necessary manipulatives. The reason for nine = tic tac toe.

6. MIC & TIC MIC for a given unit consists of nine activities dept in separate folders in a box with any necessary manipulatives. The reason for nine = tic tac toe.

7. Ten Criteria • The activity is investigative and will require some initiative and discovery on the student’s part. • The activity can be approached in different ways. • The activity is complex and will require a variety of mathematical skills to solve. • The activity is structured so that gifted students of a variety of abilities can begin the problem at their own level. • The activity will provide practice of insight into the skills being presented in the regular mathematics unit.

8. Ten Criteria • The activity is engaging. • The activity is structured so that it can be worked on individual or in small groups. • The activity is structured to encourage reasoning and communication about mathematical ides • For each unit, attention will be given to different learning style. • For each unit, attention will be given to Bloom’s taxonomy.

9. Example MIC Write a letter to the president telling him which system of measurement (metric or U.S. customary) Americans should use and why. • Problem Solving (Logic): A Horse Has Got to Eat Build a fence for your hungry horse that lets him eat the most grass.

10. Math Activity VII:All Mathematics Tasks are not Created Equally Martha’s Carpeting Task: Martha was re-carpeting her bedroom, which is 15 feet ling and 10 feet wide. How many square feet of carpeting will she need to purchase?

11. 1996 National Performance Results If both the square and the triangle above have the same perimeter, what is the area of the square? • 16 • 25 • 35 • 49

12. Math Activity VII:All Mathematics Tasks are not Created Equally A Horse Has Got to Eat! • Introduction: You love horses, and your parents have just bought you one. Your neighbor has agreed to let you build a fence in her field to let your horse graze. You have only one piece of electric fence wire 100 feet long, and you have as many stakes as you need to hold the fence wire. Because the fence is electric, assume that you need just on strand of fence all the way around your horse. Build a fence around your horse with this wire. • Draw a picture of your fence on a piece of graph paper. Make sure your picture shoes that you wire is 100 feet long. • What shape is the fence you made? • How can you use the string to represent the 100 feet of wire? • Your horse is very hungry. Experiment with different shapes to solve this problem so that when you build the fence around your horse, the horse is able to eat the most grass. • What shapes are your fences. • Draw pictures of your fences that show how you now that your horse will eat the most grass in the fenced area you drew. • Is this problem similar to another kind of problem you have worked on before? Explain the similarity.

13. Lange’s Pyramid

14. Level 1: Reproduction, procedures, concepts and definitions • Responses to a question labeled Level 1 often require knowledge of facts, definitions and routine procedures that have been memorized and have been practiced during previous lessons

15. Level 2: Connections and integration for problem solving. • On this level of competence, students have to choose their own strategies and choose their own mathematical tools. Problems on this level more often can be solved in several correct ways. Sometimes a student solves a problem in an informal way, where he already has been taught more formal ways. This provides important information about the level of students thinking.

16. Level 2: Connections and integration for problem solving. • On a copying machine you can enlarge or reduce the size of a drawing. Nathan used the machine to make a copy of a drawing, reducing the size to 60%. He was not satisfied with the result so he took the copy and made a new one at 140%. He assumed that now he would have the original measurements again. Was Nathan right? Explain your answer.

17. Level 3:Mathematization, mathematical thinking and reasoning, generalization and insight. • Uncle Peter brought a large bag of marbles for the three of us. “Share fairly”, he said. How would you do that? • Mathematize a situation

18. Level 3:Mathematization, mathematical thinking and reasoning, generalization and insight. Which is the best bargain: 3 pieces for $10 or $4 a piece and a 15% discount? Recognize and extract the mathematics embedded in the situation,

19. Level 3:Mathematization, mathematical thinking and reasoning, generalization and insight. Explain why you can be sure the white part of this drawing is larger than the shaded part. Choose mathematical tools to solve more complicated problems.

20. Task Sorting Activity • Sort the tasks according to Lange’s triangular prism.