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Hands-on LeUsing Math TAfterschool
Danette Parsley, Principal [email protected]
Heather Martindill, Sr. Cons
McREL
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What are Math Tools?
Mathematical tools can be definto include concrete materials (i
manipulatives), symbols, picturdrawings, and technology
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Personal Knowledge of Tools
Counters
Cuisenaire rods/Integer bars
Base 10 blocks
Unifix cubes
Tangrams
Pattern blocks
Paper M
Geoboar
Dice
Rulers &Measure
Judy Clo
CalculatoCompute
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Common Math To
CountersCuisenaireInteger Bar
UnifixCubes
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Common Math Tools
Tangrams
Dice
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Common Math Tools Geoboards
Rulers &Tape Measures
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Personal Knowledge of Tool
Counters
Cuisenaire rods/
Integer bars Base 10 blocks
Unifix cubes
Tangrams
Pattern blocks
Paper M
Geoboa
Dice Rulers &
Measur
Judy Cl
CalculaComput
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Counters & Color Tiles
Patterning
Estimating numbers
Keeping count during a
survey and formingsimple graphs
Solving number riddles/acting out word problems
Analyzing factors and
multiples Illustrating even and odd
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Cuisenaire Rods
Whole num Fractions Measurem
Ratio Area & pe Symmetry Three-dim
geometry
Patterns Functions
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Unifix Cubes
Counting
Patterns
Number c
Addition &
Fractions
Beginning
Probabilit
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Paper Money
Solving mrelated p(word pro
addition,
Showingdate usincombina
Exploring
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Tangrams
Forming shapes
Exploringpropertie
Combiniform ano
Identifyinand simi
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Pattern Blocks
Naming an
Investigatinbetween sh
Analyzing cshapes
Exploring p
Modeling afractions
Investigatinsymmetry, area, perimmeasure
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Dice
Probability
Random numbergenerator
Permutations &combinations
Games
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Judy Clocks
Telling ti
Solving tproblems
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Geoboards
Counting
Naming, forming,comparing and makinggeneralizations about
geometric shapes Illustrating and verifying
well-known formulas forfinding area and perimeter
Naming, forming,
comparing, andgeneralizing about angles
Exploring fractions
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Base 10 Blocks
Exploring and discoveringnumber relationships
Solving problems that
require addition,subtraction, division ormultiplication of multi-digitnumbers
Measuring in metric units
Modeling area of volume
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Rulers & Tape Measure
Measurement
Scale
Relationship betweenunits of measurement(metric & standard)
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Calculators & Computer
Computa
Complexsolving
Graphing
Program
Virtual M
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Phases of Mathematical Unde
Concrete Transitional
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Why does the practice of u
math tools work? Tools can help students see connectio
objects, symbols, language, and ideas
Tools help students think flexibly aboumathematics, use creativity to solve nemathematics problems, and explore mwith less anxiety.
Given the active and social aspects ofis an ideal environment for allowing stexplore, test, build, think, talk, connecwith mathematical tools.
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We remember 10% of hear, 30% of what we s
90% of what we d
-
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Activity 1
Using the tools on your table, sfollowing problem.
Be prepared to share how you tool to solve the problem with thgroup.
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Draw a 7 X 7 squareon graph paper. Showhow to cut the square
into the least numberof smaller squares.Your cuts must be
along the lines of thegraph paper.
Problem from : TeProblem Deck AA
1980 Dale Seym
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2 x 2 2 X 2
3 X 34 X 4
3 X 3
2 X 2
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Activity 2
In groups of three, select a tool youuse to solve the problem presented
Each group at your table will work wtool.
After each group solves the problemyour table.
Why did you choose that tool? How did you solve the problem with th
chose?
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What do you do if you wan
math tools in afterschool? Determine what concepts and s
students are learning by talking
school teacher. Develop activities that students
Provide an assortment of tools
Allow students to discuss how stools contributed to their thinkin
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Implementation Tips
Plan for the use of mathematical to
Ensure students have access to a vtools
Explore the appropriate use of mathtools
Plan for frequent intervention and d
Communicate how the tools help ch
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Technology: Virtual Manip
Sample of Tangrams online using The National LibraManipulatives http://nlvm.usu.edu/en/nav/vlibrary
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Further Details on the useTools in Afterschoo
http://www.sedl.org/afterschoo
Afterschool Training Toolkit developed byPartnership for Quality Afterschool Learni
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I hear and I forget. I s
remember. I do an
understand.- Con
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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
Scholastics Maxs 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 areseveral interactive games for manipulating patterns online.
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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.