Models

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## Models

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**Models**• "thinker-toys" • help children explore ideas and make sense of them. • manipulatives, calculators and computers should be readily available for student use as a regular part of your classroom environment Jamar Pickreign, Ph.D. 2005**Models**• many types of models can be used to represent mathematical concepts. • concrete models, or manipulatives, are frequently used to initiate understanding in mathematics. • remember that the math is in the relationships that the learner constructs through use of representational models • learners must actively construct these relationships Jamar Pickreign, Ph.D. 2005**"Commercial" Manipulatives**• numerous commercially manufactured manipulatives available • examples: base blocks, connecting blocks, centimeter rods, various counters (colored tiles, two-sided counters, etc.), attribute blocks, pattern blocks, fraction sets, geoboards, rulers, scales, thermometers, measuring cups, play money, tangrams, pentominos, geoblocks, dice, spinners, dominos, and calculators. Jamar Pickreign, Ph.D. 2005**"Handcrafted" Manipulatives**• many manipulative models can be made by teachers and learners using commonly available material • having learners create their own manipulatives may provide a sense of ownership in the model and opportunity to gain conceptual insight Jamar Pickreign, Ph.D. 2005**"Virtual" Manipulatives**• there also exist “virtual” models or “on-line thinker tools.” • many make use of current technologies allowing users to manipulate computer generated graphics similarly to traditional models. • there are a number of these models available on the internet ( http://illuminations.nctm.org/,http://standards.nctm.org/document/eexamples/index.htm,http://matti.usu.edu/nlvm/nav/index.html) Jamar Pickreign, Ph.D. 2005**"Virtual" Manipulatives**• As with any model, care must be exercised to select those that will facilitate thinking and learning. • A good rule of thumb is to decide whether a model allows the user to think, or if it does the thinking for her or him. Jamar Pickreign, Ph.D. 2005**Using Concrete Manipulatives-Some Guidelines**• Successful use of manipulatives can be positively affected by the way they are introduced and incorporated into the classroom. • Joyner (1990) offers some simple "rules." As you plan lessons that include the use of manipulatives, think about the following: Jamar Pickreign, Ph.D. 2005**Packaging the manipulative.**• Re-sealable plastic bags, or boxes can be used to store enough of the model for an individual learner to use • ease of distribution at the start and collection when finished. • encourages learners to be responsible for their tools. Jamar Pickreign, Ph.D. 2005**Free exploration or play**• allow the learners some time to explore and familiarize themselves with the material. • they gain comfort with the material, • diminishes the novelty of the material, • can reduce the "distractibility" when using them to model mathematics concepts. Jamar Pickreign, Ph.D. 2005**Demonstrate**• Show the learners how the material can be used to model mathematics concepts. • Remember that the mathematics is not in the material; a bean is a bean, but a bean can be a model of the number one. Jamar Pickreign, Ph.D. 2005