hands-on learning: using math tools in afterschool · © 2006 mcrel hands-on learning: using math...
TRANSCRIPT
![Page 1: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/1.jpg)
© 2006 McREL
Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant [email protected] Martindill, Sr. Consultant [email protected]
![Page 2: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/2.jpg)
© 2006 McREL
What are Math Tools?
Mathematical tools can be defined broadly to include concrete materials (i.e., manipulatives), symbols, pictures, drawings, and technology
![Page 3: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/3.jpg)
© 2006 McREL
Personal Knowledge of Tools Inventory
CountersCuisenaire rods/ Integer barsBase 10 blocksUnifix cubesTangramsPattern blocks
Paper MoneyGeoboardsDiceRulers & Tape MeasuresJudy ClocksCalculators & Computers
![Page 4: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/4.jpg)
© 2006 McREL
Common Math ToolsCounters
Cuisenaire Rods/Integer Bars
Unifix Cubes
PaperMoney
![Page 5: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/5.jpg)
© 2006 McREL
Common Math Tools (cont.)Tangrams Pattern
Blocks
JudyClock
Dice
![Page 6: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/6.jpg)
© 2006 McREL
Common Math Tools (cont.)Base 10Blocks
Geoboards
Calculators & ComputersRulers &
Tape Measures
![Page 7: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/7.jpg)
© 2006 McREL
Personal Knowledge of Tools Inventory
CountersCuisenaire rods/ Integer barsBase 10 blocksUnifix cubesTangramsPattern blocks
Paper MoneyGeoboardsDiceRulers & Tape MeasuresJudy ClocksCalculators & Computers
![Page 8: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/8.jpg)
© 2006 McREL
Counters & Color Tiles
PatterningEstimating numbersKeeping count during a survey and forming simple graphsSolving number riddles/ acting out word problemsAnalyzing factors and multiplesIllustrating even and odd
![Page 9: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/9.jpg)
© 2006 McREL
Cuisenaire RodsWhole numbersFractionsMeasurementRatioArea & perimeterSymmetry & congruenceThree-dimensional geometryPatterns Functions
![Page 10: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/10.jpg)
© 2006 McREL
Unifix Cubes
CountingPatternsNumber comparisonsAddition & SubtractionFractionsBeginning MeasurementProbability
![Page 11: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/11.jpg)
© 2006 McREL
Paper Money
Solving money related problems (word problems, addition, subtraction)Showing the day’s date using different combinationsExploring place value
![Page 12: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/12.jpg)
© 2006 McREL
Tangrams
Forming simple shapesExploring geometric propertiesCombining shapes to form another shapeIdentifying congruent and similar shapes
![Page 13: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/13.jpg)
© 2006 McREL
Pattern BlocksNaming and sorting shapesInvestigating relationships between shapesAnalyzing characteristics of shapesExploring patternsModeling and comparing fractionsInvestigating congruence, symmetry, tessellation, area, perimeter, angle measure
![Page 14: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/14.jpg)
© 2006 McREL
Dice
ProbabilityRandom number generatorPermutations & combinationsGames
![Page 15: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/15.jpg)
© 2006 McREL
Judy Clocks
Telling timeSolving time-related problems
![Page 16: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/16.jpg)
© 2006 McREL
GeoboardsCountingNaming, forming, comparing and making generalizations about geometric shapesIllustrating and verifying well-known formulas for finding area and perimeterNaming, forming, comparing, and generalizing about anglesExploring fractions
![Page 17: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/17.jpg)
© 2006 McREL
Base 10 Blocks
Exploring and discovering number relationshipsSolving problems that require addition, subtraction, division or multiplication of multi-digit numbersMeasuring in metric unitsModeling area of volume
![Page 18: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/18.jpg)
© 2006 McREL
Rulers & Tape Measures
MeasurementScaleRelationship between units of measurement (metric & standard)
![Page 19: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/19.jpg)
© 2006 McREL
Calculators & Computers
ComputationComplex problem solvingGraphingProgramming/GamesVirtual Manipulatives
![Page 20: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/20.jpg)
© 2006 McREL
Phases of Mathematical Understanding
AbstractConcrete Transitional
![Page 21: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/21.jpg)
© 2006 McREL
Why does the practice of using math tools work?
Tools can help students see connections among objects, symbols, language, and ideas.
Tools help students think flexibly about mathematics, use creativity to solve new mathematics problems, and explore mathematics with less anxiety.
Given the active and social aspects of afterschool, it is an ideal environment for allowing students to explore, test, build, think, talk, connect, and reason with mathematical tools.
![Page 22: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/22.jpg)
© 2006 McREL
“We remember 10% of what we hear, 30% of what we see, and
90% of what we do.”- Jean Piaget
![Page 23: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/23.jpg)
© 2006 McREL
Activity 1
Using the tools on your table, solve the following problem. Be prepared to share how you used the tool to solve the problem with the large group.
![Page 24: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/24.jpg)
Draw a 7 X 7 square on graph paper. Show how to cut the square into the least number of smaller squares. Your cuts must be along the lines of the graph paper.
Problem from : Techniques of Problem Solving: Problem Deck AAA #37© 1980 Dale Seymour Publications.
![Page 25: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/25.jpg)
© 2006 McREL
2 x 2 2 X 2
3 X 34 X 4
3 X 3
2 X 2
![Page 26: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/26.jpg)
© 2006 McREL
Activity 2
In groups of three, select a tool you would like to use to solve the problem presented to your table.Each group at your table will work with a different tool.After each group solves the problem, debrief at your table.
Why did you choose that tool?How did you solve the problem with the tool you chose?
![Page 27: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/27.jpg)
© 2006 McREL
What do you do if you want to use math tools in afterschool?
Determine what concepts and skills students are learning by talking to the day school teacher.Develop activities that students will enjoy.Provide an assortment of tools.Allow students to discuss how specific tools contributed to their thinking.
![Page 28: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/28.jpg)
© 2006 McREL
Implementation Tips
Plan for the use of mathematical toolsEnsure students have access to a variety of toolsExplore the appropriate use of mathematical toolsPlan for frequent intervention and dialogueCommunicate how the tools help children learn
![Page 29: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/29.jpg)
© 2006 McREL
Technology: Virtual Manipulatives
Sample of Tangrams online using The National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vlibrary.html
![Page 30: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/30.jpg)
© 2006 McREL
Further Details on the use of Math Tools in Afterschool
http://www.sedl.org/afterschool/toolkits/
Afterschool Training Toolkit developed by the National Partnership for Quality Afterschool Learning
![Page 31: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/31.jpg)
© 2006 McREL
“I hear and I forget. I see and I remember. I do and I
understand.”- Confucius
![Page 32: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/32.jpg)
© 2006 McREL
![Page 33: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/33.jpg)
National Partnership for Quality Afterschool Learning © McREL 2006
Hands-on Learning: Using Math Tools in Afterschool Resources
(These are just a few of the online resources available) Sites with printable templates for Manipulatives http://mason.gmu.edu/~mmankus/Handson/manipulatives.htm Provides templates for making your own manipulatives. http://math.donnayoung.org/ Provides templates for fractions, money, clocks and much more. http://mathcentral.uregina.ca/RR/database/RR.09.98/loewen2.html Provides manipulative templates & activities for upper grades. Sites with activities using manipulatives http://teacher.sholastic.com/max/index.htm Scholastic’s Max’s Math Adventures Provides activities with supplemental student pages many of which contain manipulatives. http://illuminations.nctm.org/ National Council of Teachers of Mathematics Includes activities, lessons and web links for mathematics activities using various tools. http://www.susancanthony.com/Resources/base10ideas.html Includes some ideas for using Base 10 blocks with students. Sites with Virtual Manipulatives http://matti.usu.edu/nlvm/nav/vlibrary.html National Library of Math Manipulatives http://www.arcytech.org/java Base 10 Blocks, Pattern Blocks, Integer Bars/ Cuisenaire Rods, Fraction Bars http://standards.nctm.org/document/eexamples/chap4/4.2/ Geo Board http://www.aaa.math.com/students/tools.html Provides links to online calculators, especially good for upper grades http://www.emints.org/ethemes/resources/S00000511.shtml These sites explain how to create tessellations with polygons using rotation and reflection. Also includes information about artist M.C. Escher and examples of his tessellation artwork. There are several interactive games for manipulating patterns online.
![Page 34: Hands-on Learning: Using Math Tools in Afterschool · © 2006 McREL Hands-on Learning: Using Math Tools in Afterschool Danette Parsley, Principal Consultant dparsley@mcrel.org Heather](https://reader036.vdocument.in/reader036/viewer/2022081614/5fc5559794f23c6dcd0be376/html5/thumbnails/34.jpg)
National Partnership for Quality Afterschool Learning © McREL 2006
Hands-on Learning: Using Math Tools in Afterschool References for Math Tools
Ball, D. (1992). Magical hopes: Manipulatives and the reform of math education. American Educator, 16 (1), 14-18, 46-47.
Carpenter, T.P., Fennema, E., Frank, M.L., Levi, L., & Empson, S.B. (1999). Children's Mathematics: Cognitively Guided Instruction. Portsmouth, NH: Heinemann, Reston, VA: NCTM.
Clements, D. H., & McMillen, S. (2002). Rethinking "concrete" manipulatives. In D. L. Chambers (Ed.), Putting research into practice in the elementary grades (pp. 252-263). Reston, VA: National Council of Teachers of Mathematics.
English, L., & Halford, G. (1995). Mathematics education: models and processes. Hillsdale, NJ: Lawrence Erlbaum.
Fuson, K. C. (1992). Research on whole number addition and subtraction. In D.A. Grouws (Ed.), Handbook of research on teaching and learning (pp. 243-275). Old Tappan, NJ: Macmillan.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: teaching and learning mathematics with understanding. Portsmouth, NH. Heinemann.
National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
Sowell, E. (1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20, 498-505.
Stigler, J. W., & Barnes, R. (1988). Culture and mathematics learning. In E. Z. Rothkropf (Ed.) Reveiw of research in education, 15 p. 253-306. Washington, D.C.: American Educational Research Association.
Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson Education, Inc.