Manipulative presentation
- 1. Manipulatives at the Middle Grades Level(Chapter 3)Katherine Anthony & Kate Collishaw
- 2. What is a manipulative?“A manipulative is a tool to assist students to advance from concrete knowledge toward more expert understanding of abstract mathematics ideas through visual and kinesthetic senses.” - pg 71in other words…Objects that can be handled or touched by students that represent concrete mathematical ideas leading to understanding of significant abstract ideas.
- 3. What does NCTM say?“Principles and Standards for School Mathematics names technology as one of the six main principles for mathematics; it influences the mathematics that is taught and enhances students’ learning” – NCTM 2000
- 4. Important Information About ManipulativesPiaget’s research says that symbolic representations have meanings for students only if they are closely tied to concrete representations.The objects/representations cannot teach – teacher-conducted instruction must be high quality.Students will see representations differently than you (the teacher).Manipulatives are a means, NOT an end, to developing students’ thinking with your guidance.
- 5. Suggestions for Effective/Appropriate UseSelect manipulatives that the students ALL will useSelect manipulatives that allow multiple applicationsImpress proper treatmentGive general rulesAllow exploration timeUse one specific manipulative when introducing a topic
- 6. Suggestions cont.Encourage students to use manipulatives when they feel it would assist learningRemember students advance at different ratesBe certain all students have an opportunity to manipulate the objectsConsider appropriateness of manipulative to students’ ageOrganize in transparent bags/boxes/containers
- 7. Manipulatives!Fraction StacksCuisenaire RodsColored ChipsBalancesPatty PaperGeoboardsCalculators
- 8. Virtual ManipulativesHands on MathAlgebra ToolkitGeometry ToolkitGeometer Sketchpad
- 9. Classroom Changes with TechnologyStudents learn because they can see multiple examples quickly to see patternsEngagementNo more slow hand calculations (good for younger students)Students process information differently because they are “digital natives”.
- 10. “I hear, and I forget. I see, and I remember. I do, and I understand.” – Chinese proverb