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Mathematica Revisited

Mathematica Revisited. Redesigning a Math Education Museum Exhibit Nancy Daniels, Karen Jia, Nina Weber, Jim Vanides Stanford University Learning Design and Technology November 2001. Overview. Proposal Museum Observations Learning Theory Exhibit Redesign and Extensions User Feedback

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Mathematica Revisited

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  1. Mathematica Revisited Redesigning a Math Education Museum Exhibit Nancy Daniels, Karen Jia, Nina Weber, Jim Vanides Stanford University Learning Design and Technology November 2001

  2. Overview • Proposal • Museum Observations • Learning Theory • Exhibit Redesign and Extensions • User Feedback • Next Steps • Personal Reflections

  3. Proposal • Initial Proposal: “The creation of the MathMania Discovery Center where interactive hands-on learning experiences are explored in a space that cannot be duplicated in a classroom setting or software environment. • Modified: “Redesign one of the Mathematica exhibits to improve its appeal and learning impact”

  4. Mathematica Observation at the Exploratorium • Walkthrough • Discussion- selection of Multiplication Cube as focus of redesign • Visitor Observation / Photographs / Field notes • Team discussion: Where’s the Learning? • Problems with the existing design • Brainstorm ideas for redesign

  5. The Multiplication Cube

  6. Mathematica Observations • -- Children usually need guidance by adult. No • scaffolding available for just kids. • - Kids can’t see over • the controls • - Lighting sequence • doesn’t map to the • control input • --Position of the • controls not optimal • for learning

  7. Mathematica Observations --Only one child was observed reading the surrounding notes. They provide some algebraic understanding but very hard to access. -- Bulbs turn off too fast for young children to count

  8. Learning Theory: How do we get them to know? V=b•h•l Is that all? From the Mathematica exhibit

  9. interactive. multi-sensory. accessible. built on prior experience. conveyed through multiple representations. beyond just knowing a formula. What Should Learning Be?

  10. The Challenge • Language of math can be confusing. 2 +3=5 but 1/2 + 1/3= 5/6 • So much of math, relies on a solid foundation. If you miss one part, you may not get the next point. • There are many constraints in the classroom (materials, time, # of students, teaching philosophies of parents & of teachers) • “Assessment results are only estimates of what a person knows and can do.”--Knowing What Students Know, p2

  11. My experience in the classroom “ Learning entails the transformation of naïve understanding into more complete and accurate comprehension…” Knowing What Students Know, p4. • Some students just don’tget what we’re teaching • Some students really get the essence of what we’re teaching • Some students get a little bit of what we’re teaching

  12. A variety of assessments Observations Confusion Boredom Extending the activities Misbehavior How can we tell a student knows?

  13. Inspiration: Research and Theories “Not all children learn in the same way and follow the same paths to competence.” --Knowing What Students Know, p. 4. “Our knowledge can’t be a representation of that real world, but only as a key that unlocks possible paths for us.” --Ernst von Glaserfeld, p.194. “Constructivist theories assume that knowledge is actively constructed and reconstructed by the learner out of his or her experiences in the world.” --Minds in Play, p.10.

  14. Learning Theory Highlights • Ground the groundless. Make connections. • Build on what students know. Learning is recursive. • Vary the interactions by creating a multi-sensory experience: touch, hear, and see. • Think clearly about the goals before getting started. What do you want them to know?

  15. References • Knowing What Students Know: The Science and Design of Educational Assessment, Washington, DC: National Academy Press,2001. • Kafai, Yasmin. Minds in Play: Computer Game Design as a Context for Children’s Learning, New Jersey: Lawrence Erlbaum Associates, Publishers, 1995. • Klein, Elisa L. “Computer Graphics, Visual Imagery, and Spatial Thought” in New Directions for Child Development: Children and Computers, ed. E. Klein. Jossey-Bass Inc., 1985. • Novak, Joseph D. and Gowin, D. Bob. Learning how to learn. Cambridge University Press, 1984.

  16. References • Papert, Seymour. The Children’s Machine: Rethinking School in the Age of the Computer. New York: Basic Books, 1993. • Von Glaserfeld, Ernst. The Construction of Knowledge: Contributions to Conceptual Semantics. • Seeing Fractions • The Visual Arts and Early Childhood Learning, ed. C.M. Thompson. The National Art Education Association. 1995. • www.exploratorium.edu

  17. Exhibit Redesign: The Multiplication Cube • Exhibit Layout • Control Panel UI • Museum and Classroom Extensions

  18. New Exhibit Layout Reorient Exhibit to facilitate visibility Move control panel to corner Lighting sequence one dimension at a time Eliminate graphic panels Add overhead algebraic display

  19. Current Control Panel

  20. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 x x = START

  21. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 1 4 1 x x = START

  22. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 1 x x = START

  23. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 5 x x = START

  24. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 5 x x = Watch!

  25. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 1 1 = Watch!

  26. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 2 2 = Watch!

  27. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 3 = Watch!

  28. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 4 4 = Watch!

  29. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 1 4 4 x = Watch!

  30. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 2 4 8 x = Watch!

  31. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 12 x = Watch!

  32. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 1 12 x x = Watch!

  33. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 2 24 x x = Watch!

  34. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 3 36 x x = Watch!

  35. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 4 48 x x = Watch!

  36. Multiplication Machine • It will multiply the numbers you choose from these three dimensions of numbers. • press only one button in each direction • press the start button to multiply 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 2 3 4 5 6 7 8 3 4 5 60 x x = Watch!

  37. Museum and Classroom Extensions • Multiplication Activities (touchscreen) • Multiplayer Multi-Cube • Cube City (classroom) • Online Fraction Game

  38. Cube Extension Activities on Touch Screen Panels Real world application content Multiplication in context Visible problem solving process and scaffolding Downloadable simulations Examples:

  39.       Multiplication in Life Name: Rio Kenny Brian Carmen Sally Carlos Jenny # of P: 1 2 3 4 5 6 7 You’re throwing a big birthday party, and have invited seven friends. All of them are taking some additional people with them except for Rio, who will be coming by herself. The number below the name is the total number of people coming that each friend represents. How many people will be coming?

  40.       Multiplication in Life Name: Rio Kenny Brian Carmen Sally Carlos Jenny # of P: 1 2 3 4 5 6 7 1 + 7 = 8 2 + 6 = 8 Hint Hide Hint

  41. Multiplication in Work Claire’s family lives in the residential area where the school bus makes the last stop. The area is 10 miles from the school. It’s 7:00 in the morning, Claire wants to feed her dog before she leaves, but her mom is rushing her off: “Class begins at 7:30, you’ll be late!” The bus drives at ½ mile per minute. Will Claire really be late?

  42. Multiplication in Work Step 1: How far can the bus drive in 30 minutes => 0.5mile/min * 30min = 15 miles Step 2: How far does Claire live from school => 10 miles Step 3: The amount of distance left over => 15miles – 10miles = 5 miles Step 4: The amount of time left over => 5miles/.5mile/min = 10 minutes Hint Hide Hint

  43. Multiplication in Community You’re helping the city planning the green area between two administrative buildings. There are three types of trees you can plant. The big one takes 10 square feet per tree, the medium one takes 5 square feet per tree, and the small one takes 3 square feet per tree. The area to be covered is 100 square feet, and each size of tree has to be planted at least once. How can you plant the trees so that two kinds of trees get to planted only once?

  44. Multiplication in Community Step 1: If the large tree and medium tree get planted only once, then the remaining area is ð     100 – 10 – 5 = 85 Step 2: The maximum number of small trees that can be planted in the remaining area ð     85/3 = 28 1/3 => 28 Step 3: If the medium tree and small tree get planted only once, then the remaining area is ð   100 – 5 – 3 = 92 Step 4: The maximum number of large trees that can be planted in the remaining area ð     92/10 = 9 1/5 => 9 Step 5: If the large tree and small tree get planted only once, then the remaining area is ð     100 – 10 – 3 = 87 Step 6: The maximum number of large trees that can be planted in the remaining area 87/5 = 17 2/5 => 17 Hint Hide Hint

  45. Multiplayer Multiplication Cube - Objectives • Increase Mathematical Discourse and collaboration at the exhibit • Increase the cognitive challenge by providing an alternative game that works backwards from a target number • Encourage mathematical inquiry

  46. Multiplication Machine Player 1 It will multiply the numbers you and your team-mates choose from these three dimensions of numbers. Choose which game you would like to play: “Free Explore” or “Find-a-Number” Press one button from your dimension, while your team-mates pick their own numbers from their dimensions. 1 2 3 4 5 6 Free Explore 7 8 Find-a-Number x x =

  47. Multiplication Machine Player 1 Work with your team to find three numbers, that when multiplied together, equal the Challenge Number below: 1 2 Make This Total 3 60 4 5 6 7 8 Find-a-Total x x =

  48. Multiplication Machine Player 1 Work with your team to find three numbers, that when multiplied together, equal the Challenge Number below: 1 2 Make This Total 3 60 4 5 6 7 8 Find-a-Total 1 4 1 4 x x =

  49. Multiplication Machine Player 2 8 7 6 5 4 Work with your team to find three numbers, that when multiplied together, equal the Challenge Number below: 3 2 1 Make This Total 60 Find-a-Total 1 4 1 4 x x =

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