1. UPS √ Delivering Effective Problem Solving Techniques Presenter: Jesus A. Martinez Professional Development Services ABRAZO DAY 5 February 2, 2009

2. Bell Work Using two post it notes, write your definition of what is an exercise and a problem, then post them on the T-Chart.

3. SUDOKU Exercise or a Problem?  An exercise asks you to repeat a method you learned from a similar example.  A problem is usually more complex than an exercise, so it is harder to solve because you do not have a preconceived notion about how to solve it.

4. Components of a Successful Problem Solver  Practice (Exposure)  Persistence  Self Monitoring

5. Practice  To develop students’ thinking skills  To develop students’ abilities to select and use problem-solving strategies  To develop students’ abilities to find correct answers to a variety of types of problems

6. Persistence  To develop helpful attitudes and beliefs about problem solving  To develop students’ abilities to solve problems in cooperative learning situations

7. Self Monitoring  To develop students’ abilities to use related knowledge  To develop students’ abilities to monitor and evaluate their thinking

9. Types of Problems  One-Step Problems (Story Problems)  Multiple-step Problems  Process Problems  Applied Problems (Situational Problems)

10. One –Step Problems One-step problems provide experience in translating situations to a number sentence involving addition, subtraction, multiplication, or division. These are the familiar “story problems” that have always been part of school of mathematics programs. The primary strategy used to solve one-step problems is choose an operation.

11. Multiple-step Problems The difference between one-step problem and multiple-step problems is the number of operations needed to find a solution. The primary strategy used to solve multiple-step problems is to choose the operations.

12. Process Problems Process problems are solved using such strategies as guess-check-revise, draw a picture, make a table, look for a pattern, work backward, solve a simple problem, and make an organized list. The solution may involve some computation, but these problems can not be solved by the student by simple choosing the operation or operations.

13. Applied Problems Require the problem solver to collect data outside the problem statement. Many applied problems require the student to formulate a clear statement of the problem and sub-problems and identify assumptions that need to be made and the data needed for finding a solution.

14. Activities that Develop and Promote Problem Solving Skills  Problem of the Day  Sharing solutions of Problem of the Week to the whole class (Group Activity)  Summarizing and Paraphrasing the solution to a math problem (Explain your reasoning)  Create real-life word problems

15. Group Activity  Solve the problem that has been assigned to your group using METACOGNITION think about your thinking.  Follow directions for each problem.  Share your solution as a group.

16. Problem # 1 Farmer Brown had ducks and cows. One day noticed that the animals had a total of 12 heads and 32 feet. How many of the animals were ducks and how many were cows? (Find the answer using two different ways) Explain.

17. Problem # 2 Three jackals and three coyotes are on a trek across the Mokalani Plateau when they come to a river filled with carnivorous fish. There is a rowboat in sight, and the party decides to use it. However, the boat is too small for any more than two of the group at a time. So they must transverse the river in successive crossings. There is one hitch, though: The jackals must not outnumber the coyotes at any time, in any place. For example, if two jackals and only one coyote are together, the jackals will overpower, kill, and eat the coyote. It’s okay to have an equal number of each, and it’s okay to have more coyotes than jackals in a given place-neither situation poses a danger to the coyotes, and the coyotes do not pose a threat to the jackals. So, the trick here is to use the one small rowboat, a lot of sweat, and a little brainpower to ensure the coyotes’ safety while both groups cross the river. (Use the Ac It out strategy) Explain.

18. Problem # 3 A rectangle has an area measuring 120 square centimeters. Its length and width are whole numbers of centimeters. What are the possible combinations of length and width? Which possibility gives the smallest perimeter? (Use a table/List) Explain.

19. Teacher Role in Problem Solving Provide learning activities that create an environment that engages students while facilitating their development of mathematical concepts through:  Observations  Questioning Techniques  Modeling Strategies  Focus in Math language

20. Observations  Limit your observation to aspects of performance and attitude  Select only few students at a time to observe  Your observation should be focused  It is important that they learn not be distracted by your presence

21. Questioning Techniques  Stimulate mathematical thinking  Help the student to solve a problem  Example of questions (Heuristics).

22. Focus on Math Language  Symbolic This refers to mathematical notation  Content-Specific Technical words associated with abstract mathematical concepts and skills such as sum, addend, product, denominator  Academic Terms used in tests and discourse language, such as determine, simplify, predict

23. Model the Most Common Problem Solving Strategies  Acting It Out  Drawing a Picture  Making a Table  Looking for a Pattern  Making a List  Making a Model  Breaking the problem down into smaller problems

24. Group Activity  Using the TAKS booklets at your table identify the types of problems  Share your findings

25. What is problem Solving? Is an extreme complex activity. It involves the recall of facts, the use of a variety of skills and procedures, the ability to evaluate one’s own thinking and progress while solving problems, and many other capabilities

26. Success in Problem Solving….  Very much depends on the students’ interest, motivation, and self- confidence.  Involves the coordination of knowledge, previous experience, intuition, attitudes, beliefs, and various abilities.

27. Closure  The ability to coordinate skills and abilities for problem solving develops gradually over time.  This means that the ability to get correct answers will develop more slowly than the skills and abilities associated with problem solving.

28. References  How to Evaluate Progress in Problem Solving, Charles, Randall; Lester, Frank; O’Daffer, Phares. National Council of Teachers of Mathematics  The Adventures of Johnny Bunko, The Last Career Guide you’ll Ever Need by Daniel H. Pink  Problem Solving Strategies, Crossing the River with Dogs by Ken Johnson and Ted Herr  Implementing Standards-Based Mathematics Instruction, A Case Book for Professional Development by Mary Kay Stein

29. “We sometimes think of being good at mathematics as an innate ability. You either have it or you do not, but the true is that being good at math is more about attitude….” [Outliers by Malcolm Gladwell]