Exploring Problem Based Learning in Mathematics

1. Exploring Problem Based Learning in Mathematics Heartland Convention 2012 Kaitlin Troost ValorieZonnefeld

2. Teacher-Centered The sage on the stage

3. Student-Centered Guide on the Side, not the sage on the stage A Danger of Social Constructivism

4. Content-Centered Allows God’s absolute truth in mathematics to speak for itself Uses many of the same pedagogies as student-centered

5. What is the center of your classroom? The next classroom observation, have someone draw arrows on your seating chart for all discourse that occurs. Are all questions directed to you? Do you repeat student questions?

8. Logical Thinkers Problem Solvers

9. Problem-Based Learning World

16. Pi Activity Any comments or questions? Reinforce the next day with a Frisbee and tape measure

17. Pattern Blocks Given the three block patterns, identify how the pattern is growing from Case 1 to Case 3. Represent this growth

18. Pattern Blocks How did you approach this?

19. Four Levels of Cognitive Demand Memorization Procedures Without Connections Procedures With Connections Doing Mathematics Stein, Smith, Henningsen, and Silver 2000, p. 16

20. Four Levels of Cognitive DemandMemorization Reproducing a fact learned from memory Not ambiguous No connection to concepts or underlying meaning 2 + 7 = Represent ¼ as a decimal and a fraction

21. Four Levels of Cognitive DemandProcedures without Connections A recipe to follow Low cognitive demand Little ambiguity Focused on the answer, not the process Davis wants to tile his rectangular room which is 8 feet by 10 feet. How many square feet of tile will he need to purchase?

22. Four Levels of Cognitive DemandProcedures WITH Connections Focus on the procedure to create deeper understanding A path to follow may be suggested Often multiple representations are used Requires mental effort Using base-ten blocks, show that .17 is less than .2

23. Four Levels of Cognitive DemandDoing Math Complex thinking N0 path or recipe to follow Students need to access necessary knowledge Cognitively demanding In my bag of candy ½ of the pieces are red, 1/3 are blue, the remaining 21 are white. How many pieces are in the bag?

24. Four Levels of Cognitive Demand Memorization Procedures Without Connections Procedures With Connections Doing Mathematics How would you categorize the pi activity? How about the pattern block activity

25. Four Levels of Cognitive Demand Memorization Procedures Without Connections Procedures With Connections Doing Mathematics Can Differentiate Instruction based on the question Students who perform best on project-based problem solving were in classrooms in which tasks were implemented at high levels of cognitive demand Leutzinger, L. ICTM Journal, 2010 Good teaching demands a blend of all four levels

26. Ideas • What could you do with newspapers • Work with place value –Find • Purchase car • Give students a large amount of frequent flier miles to plan a trip around Europe with. • What topics could you cover with this? • What can you do with census data? Kristin Kanaskie 2011 Fall ICTM Journal p. 4

27. Ideas • Visit a creek • Estimate depth • Estimate water flow (Math’s Teacher, May 2012) • A bag of oranges • Volume • Peel it to find surface area (Math’s Teacher, Oct. 2011) • Stack oranges for space

28. Ideas

29. Ideas • Turning everyday living activities into math • Have students record, survey, analyze, and collect data: • number of texts send/received a day • hours of sleep • hours of T.V. • hours of favorite activity... • Students can collect data in a journal and expand using graphs and calculations

30. Ideas • How much water do you use in the shower? • How long does it takes to fill up a gallon • Average amount of time spent in the shower (Dan Meyer) • Exploring surface area using cheese blocks of same volume but different surface areas • Which takes longest to melt in the microwave (Dan Meyer) • Using a bike to look at speed, gears for ratio and proportion. • Using plastic cups... how many cups will you have to stack to be the height of your teacher (Dan Meyer) • Three doors with a prize, stay with your same choice or switch? The Monty Hall problem

31. Ideas Design a mini-golf course Pull up Hy-Vee’s on-line add

32. Book Resources • What’s Math Got to Do With It? By Joe Boaler • Fostering Geometric thinking: A guide for teaching by Mark Driscoll • Applications of Secondary School Mathematics: Readings from the Mathematics Teacher by the NCTM • Problem-Based Learning for Math and Science: Integrated Inquiry and the Internet by Diane L. Ronis • The Essentials of Mathematics, Grades 7-12 by Kathy Checkley

33. Online Resources • yummymath.com • www.khanacademy.org • blog.mrmeyer.com • www.nctm.org • www.coolmath.com

34. Activity Sheets

35. Resources • Make Learning Real • God wrote creation in the language of mathematics • PBL allows concepts to be taught in context - an avenue for integration of faith • Dan Meyer • Presentation is posted at • Bored student photo • http://www.google.com/imgres?q=bored+student&um=1&hl=en&safe=active&client=safari&sa=N&rls=en&biw=1191&bih=604&tbm=isch&tbnid=8umVDWkckUyetM:&imgrefurl=http://ecodesignproject4th.blogspot.com/2011/11/lethargic-students.html&docid=-MNFWsymC6V7mM&imgurl=http://1.bp.blogspot.com/_dR2248KTLUs/TKX6gG7ZJII/AAAAAAAABCE/bFbK8cCNaI4/s1600/bored%252Bstudent.jpg&w=283&h=424&ei=Y4-VT8W7F-nh0QGEhOjmBw&zoom=1&iact=hc&vpx=270&vpy=190&dur=1465&hovh=275&hovw=183&tx=151&ty=123&sig=108937824454470224396&page=1&tbnh=122&tbnw=86&start=0&ndsp=21&ved=1t:429,r:15,s:0,i:101 • Work force picture • http://www.opttek.com/OptForce