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  • The passage from Concrete is abstract thinking is the most important concept in teaching math. Without abstract thinking the student will not be able to grasp most mathematical ideas.
  • The manipulatives cannot teach the students themselves. A good teacher helps to make abstraction happen. Assumptions by Clements and McMillen.
  • quesinaire
  • The following are manipulatives used to teach algebra
  • We cannot forget about computer software
  • this is a video of Two students playing a game with dice to practice two digit addition
  • Manipulatives

    1. 1. MANIPULATIVES By: Deanna Riley and Coralisa Ford
    2. 2. Meaning of Manipulative <ul><li>A manipulative is a tool to assist students to advance from concrete novice knowledge toward more expert understanding of abstract mathematical ideas through visual and kinesthetic senses. </li></ul>
    3. 3. The Passage from Concrete to Abstract Thinking <ul><li>“ There is no single route or rate to abstraction, but research has shown that manipulatives can be important to students taking this journey.” (Driscoll, 1981) </li></ul><ul><li>It is known that the road to abstraction is not easy but manipulatives help to accelerate the student into thinking abstractly in mathematics. </li></ul><ul><li>Educational researchers like Piaget concluded that because students proceed through learning stages, that manipulatives are significant aids to learning in all four of Piaget’s stages. </li></ul>
    4. 4. Using Manipulatives <ul><li>The most important influence on the successful use of manipulatives is the quality of teacher-conducted instructions </li></ul><ul><li>Lessons with manipulatives must be carefully designed to advance students’ thinking from “naïve” to “expert.” </li></ul><ul><li>Avoid these assumptions: </li></ul><ul><li>Do not assume that the images that you see when using manipulatives are identical to those seen by your students. </li></ul><ul><li>Do not assume when students maneuver objects in specified ways that the expected mental associations automatically follow. </li></ul><ul><li>Realize that manipulatives can be used in a rote manner. </li></ul>
    5. 5. Using Manipulatives <ul><li>The effective use of manipulatives requires your thoughtful consideration to developing students’ thinking with your guidance. </li></ul><ul><li>Select manipulatives that the students all will use. </li></ul><ul><li>Select manipulatives that allow multiple applications. </li></ul><ul><li>Express the importance of proper treatment of classroom materials. Also give rules as to where they can be used and stored. </li></ul><ul><li>When introducing a topic, use one specific manipulative. Then after working and presenting that manipulative, you may allow the students to try other concrete representations. Its GOOD when they suggest them! </li></ul>
    6. 6. Types of Manipulatives: Fractions <ul><li>Fraction stacks, </li></ul><ul><li>Pattern blocks, </li></ul><ul><li>Fraction bars, </li></ul><ul><li>Fraction circles, </li></ul><ul><li>Cuisenaire rods, </li></ul><ul><li>Are all helpful with teaching fractions. Fractions difficulties are at every level of learning, even in high school. Fraction stacks have moveable segments on each tower marked with a fraction of the whole that each piece represents. Students can SEE how tower height result in given fractions. </li></ul>
    7. 7. Types of Manipulatives: Algebra <ul><li>Colored chips, </li></ul><ul><li>Base-10 blocks, </li></ul><ul><li>Balances, </li></ul><ul><li>Algebra tiles, </li></ul><ul><li>Colored beans. </li></ul><ul><li>With this simple equipment you can teach addition and subtraction of signed integers much more easily than with the traditional method. </li></ul><ul><li>Colored beans can be useful with teaching positive and negative integers with one color representing a positive integer, and another color a negative integer. </li></ul>
    8. 8. Types of Manipulatives: Geometry <ul><li>Mirrors, </li></ul><ul><li>MIRAs, </li></ul><ul><li>Patty paper, </li></ul><ul><li>Geoboards, </li></ul><ul><li>Are very useful in visualizing geometry concepts. </li></ul><ul><li>Mirrors can be used in exploring symmetry. </li></ul><ul><li>MIRA enables students to accurately construct geometric figures because of its beveled edge, which allows for a line to be drawn in the middle of the reflecting surface. </li></ul><ul><li>10x10 geoboards are very useful in exploring percentage and decimals at the secondary level. </li></ul>
    9. 9. Types of Manipulatives: Computer Software <ul><li>Computers can be used in three main ways: </li></ul><ul><li>As a tutor or instructor for students </li></ul><ul><li>As an environment for exploring mathematical concepts through interaction </li></ul><ul><li>As a helper performing calculations more quickly than a pencil, or organizing information on a spreadsheet, etc. </li></ul>
    10. 10. Let’s See How Manipulatives Work! <ul><li> </li></ul>