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Piaget Schemes Activities push toward rearranging and adding information about ordering fractions

Common Mathematic M isconception : “The fraction with the largest denominator is always the greatest fraction.”. Developmental Level Targeted : Upper Elementary Level (Students in grades 3-5 ) Why the private theory? Prior experience with integers Example: 3>2 So, it seems that 1/3>1/2.

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Piaget Schemes Activities push toward rearranging and adding information about ordering fractions

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  1. Common Mathematic Misconception:“The fraction with the largest denominator is always the greatest fraction.”

  2. Developmental Level Targeted:Upper Elementary Level(Students in grades 3-5)Why the private theory? Prior experience with integersExample: 3>2So, it seems that 1/3>1/2

  3. Cognitive development theories:Woolfolk, Anita. Educational Psychology. 11th ed. Upper Saddle River: Merrill, 2010. Print. • Vgotsky • Psychological tools • Working with signs and symbols • Co-constructed process • Students will be working with partners • Cultural tools • Activities are web-based • Zone of proximal development • Working with material that is nearly mastered • Scaffolding • Teacher will be available for assistance • Students are learning on their own • Piaget • Schemes • Activities push toward rearranging and adding information about ordering fractions • Equilibration • Students will be searching for balance • Assimilation • Accommodation • Seriation • Working with ordering and comparing fractions

  4. Assessment of Knowledge & Quest for Private Theory • Students use this site to compare fractions with like and unlike numerators and denominators • Multiple-choice answers using words, signs, and numbers • Uses multiple shapes to model fractions • Gives explanation for wrong answers • Keeps track of number of problems attempted and score • Source: http://www.ixl .com/math/practice/grade-4-compare-fractions

  5. Theoretical ContributionsWoolfolk, Anita. Educational Psychology. 11th ed. Upper Saddle River: Merrill, 2010. Print. • Vgotsky • Private speech • Students will be responding to correct or incorrect answers • Students will be conversing • Co-constructed • Students will be answering /working out questions together Piaget • Schemes • Activity works toward evaluating students’ perception and experience with comparing fractions

  6. Connect to Private Theories & Work in the Zone of Proximal Development • Students use the “Fraction Pieces” activity individually • Manipulatives of different size fractions • Able to put one on top of another to compare • Source: • http://nlvm.usu.edu/en/nav/grade_g_2.html

  7. Theoretical ContributionsWoolfolk, Anita. Educational Psychology. 11th ed. Upper Saddle River: Merrill, 2010. Print. • Vgotsky • Psychological tools • Working with signs and symbols • Zone of Proximal Development • Working with material that is nearly mastered • Scaffolding • Teacher will be available for assistance • Students are learning on their own • Piaget • Schemes • Visually represented fractions enable obvious comparison

  8. Move Past Egocentric Learning & Scaffold Through Collaborative Learning • Students create two fractions at one time and they are placed on a number line • Actually see the order on number line • Source: • http://shodor.org/interactive/activities/FractionSorter/

  9. Theoretical ContributionsWoolfolk, Anita. Educational Psychology. 11th ed. Upper Saddle River: Merrill, 2010. Print. • Vgotsky • Scaffolding • Teacher present • Students working individually and actively • Piaget • Schemes • Visual representations make for better recollection later • Assimilation • Accommodation

  10. Reflection on How Internet Interventions Help Create Adequate Conception • These interventions will help students to visually compare modeled fractions while also prompting them to think about symbolic relationships. • Students will also be able to talk problems out with others and have interactive practice with the material

  11. Summary of Theoretical Support Woolfolk, Anita. Educational Psychology. 11th ed. Upper Saddle River: Merrill, 2010. Print. • Vgotsky • Psychological tools • Co-constructed process • Cultural tools • Zone of proximal development • Scaffolding • Piaget • Schemes • Equilibration • Assimilation • Accommodation • Seriation

  12. Conclusion I feel that this intervention would be successful in altering student this misconception because: • It allows them to interact with one another and to manipulate the fractions to compare them. • The students are getting organized practice with comparing and ordering fractions, which usually leads to at least a small increase in comfort and understanding of the material. • The activities are supported by Piaget and Vgotskys’ viewpoints.

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