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Technology Integration in Mathematics

Technology Integration in Mathematics. October 9, 2007. Making Change. You have 19 coins and $1.00 worth of change in your pocket. What are the total possible combinations that you could have? Approaches?. Making Change.

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Technology Integration in Mathematics

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  1. Technology Integration in Mathematics October 9, 2007

  2. Making Change • You have 19 coins and $1.00 worth of change in your pocket. What are the total possible combinations that you could have? • Approaches?

  3. Making Change • You have 19 coins and $1.00 worth of change in your pocket. What are the total possible combinations that you could have? • Let’s explore using a spreadsheet

  4. What counts as technology?

  5. What is technology access like at your school?

  6. How is technology used in your classroom and school?

  7. What questions do you have regarding using technology?

  8. What barriers do you face using technology in your school?

  9. Laying the Groundwork • How do students learn mathematics? • What evidence shows that students have learned mathematics?

  10. What Learning Theory Tells Us What is a learning theory?

  11. Piaget’s Influence • Levels of human development • Based on age, but influenced by experience • Developed from research with thousands of students • Students progress from one stage to the next

  12. Piaget’s Influence • Mathematical Progression • Concrete: one-to-one correspondence • One object = one • Hands-on manipulatives • Representational • One object = one or another number • E.g.- 10 piece in base-10 blocks

  13. Piaget’s Influence • Mathematical Progression • Transitional • Expanded algorithms • Partial product, expanded notation • Symbolic • Computations, algorithms

  14. What Learning Theory Tells Us Theories of learning Behaviorism Cognitivism (Information Processing) Constructivism Individuals construct or form knowledge through personal experience. Individuals learn about existing knowledge through practice, rewards and punishment. Individuals construct knowledge by associating new experiences with prior knowledge (schema).

  15. Learning Theory Mathematics What do these learning theories have to do with elementary mathematics? Behaviorism Cognitivism (Information Processing) Constructivism ? ? ?

  16. How does technology fit in? Examples of mathematics technologies Behaviorism Cognitivism (Information Processing) Constructivism Virtual Base-10 Blocks AAA Math Area Explorer What similarities and differences do you notice?

  17. What the research says? • Technology improves learning (sometimes) When technology is used for… activities that focus on basic skills… activities that focus on conceptual understanding and higher-order thinking… …student achievement…. …is significantly higher than not using technology …is significantly lower than not using technology

  18. NCTM’s Position on Technology • NCTM’s position statement

  19. Calculators • When should calculators be used? • NCTM’s position statement

  20. Calculator Activities • Place Value- Wipeout • Start with the number 832,671. • Wipeout the thousands place. How? • Wipeout the hundreds place. • Wipeout the hundred thousands place. • What remaining steps would you do to end up with 0 as your final number.

  21. Calculator Activities • Expanded Notation • Build the number 43,287 by adding up five numbers. In each number every digit except for one must be a zero. • Try it with 3,196,205.

  22. Calculator Activities • Division as Repeated Subtraction • I have 123 cookies. I’m putting them into bags of 9 each. How many bags do I fill? Do I have any left over?

  23. Calculator Activities • Place Value- Wipeout • Expanded Notation • Division as Repeated Subtraction • Problem Solving tool • You are building a fence with a perimeter of 72 yards. What are the possible dimensions that have integral side lengths? What is the largest area you can build? If fencing costs $0.75 a yard how much will the materials cost?

  24. Calculator Activities • Place Value- Wipeout • Expanded Notation • Division as Repeated Subtraction • Problem Solving tool • You are building a fence with a perimeter of 72 yards. What are the possible dimensions that have integral side lengths? What is the largest area you can build? If fencing costs $0.75 a yard how much will the materials cost?

  25. Spreadsheets • Changing Rates • Who Wants to Be a Millionaire? • Planning Cruises • Renting a Car • Clothes Shopping

  26. Spreadsheets • Silver Dollar Activity • Download and save on your computer • Read the story on the first task and explore the various tabs

  27. Spreadsheets • Exploring Multiple Combinations • Making Change • Sum of the dice • Two fair six-sided die are rolled. What are the possible combinations? Which number has the highest probability of getting rolled? • What if the die were eight-sided?

  28. Spreadsheets • Geometry • Sum of Angles in Polygons • Penning for Pony • Minimum Perimeters

  29. Spreadsheets • Number Sense/Algebra • Consecutive Odds and Evens • Going Fishing • Hens and Rabbits • There are hens and rabbits in a barn. There are 52 total legs. What are the possible combinations of hens and rabbits?

  30. Spreadsheets • Data/Probability • Going Free • Taking Classes • Football Scoring • Blueberry Pancakes • You make 6 blueberry pancakes with two dozen blueberries. How many blueberries end up in each pancake? Hint: You will need a formula for the random number generator.

  31. Simulations • Lemonade Stand • Stock Market Game • Ice Cream Truck

  32. Web-based tools • Benefits • Free on the Internet • Easy to use • Targetted towards a variety of grades, topics • Drawbacks • Internet connection speed • Sometimes, they’re too open ended

  33. Early Number Manipulatives • Base-10 Blocks • Open-ended applet • Adding and Subtracting with Base-10 blocks • Pattern Blocks • Cuisenaire Rods

  34. Pre K- 2nd • Bobby Bear • Counting and Combinations • Concentration: Number and Word Form • Five (Ten) Frame: Number Sense • Pan Balance: Equality • Ladybug: Measurement, Geometry

  35. Graphing • NCES Graphing Website • Explore making each of the different types of graphs

  36. Geometry • Shape Cutter • Virtual Geoboard • Tangrams • Turtle Pond • Set- Sorting by attributes • Attribute Sorting • Transformational Golf

  37. Multiplication and Division • Factor Game • Product Game • Interactive Mutliplication Table

  38. Fractions and Decimals • Fraction Models • Adding and Subtracting Decimals • Harcourt eLab, • Base-10 Blocks Decimals on this page • Fraction Track • Fractions- Adding • Pattern Blocks- Fractional pieces

  39. Software • Ten Tricky Tiles • Zoombini’s • Tom Snyder Software • Ice Cream Truck

  40. Software • Geometer’s Sketchpad • In your Novell window, find Geometer’s Sketchpad and open it. • Dynamic geometry software • Make a square using the tools on the right.

  41. Integration issues • One computer classrooms • Education world article • Tip sheet • Come up with a list of “useful tips” to share with others

  42. Contact Information • Drew Polly • abpolly@uncc.edu

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