Big Ideas Numeracy Workshop


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Ontario Maths Curriculum - The Big Ideas and Principles of Effective Mathematics Instruction

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  • Introduce myself.
  • Big Ideas Numeracy Workshop

    1. 1. Numeracy and ‘The Big Ideas’ Grades 4-6 Aimée De Abreu
    2. 2. Aims of the Workshop <ul><li>To review principles of mathematics instruction </li></ul><ul><li>To apply the concept of ‘Big Ideas’ to the planning and instruction of Fractions. </li></ul><ul><li>To explore the numeracy teaching resources available on </li></ul>
    3. 3. “ Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.” (National Council of Teachers of Mathematics [NCTM], 2000, p. 16)
    4. 4. Reflection <ul><li>On your T-chart, jot down some recollections of an ‘AHA’ moment in your educational experiences with mathematics: </li></ul>Your AHA moment Effective Instruction of Mathematics Leave blank.
    5. 5. All teaching of mathematics should: <ul><li>foster positive mathematical attitudes; </li></ul><ul><li>focus on conceptual understanding; </li></ul><ul><li>involve students actively in their learning; </li></ul><ul><li>acknowledge and utilize students’ prior knowledge; </li></ul><ul><li>provide developmentally appropriate learning tasks; </li></ul><ul><li>respect how each student learns by considering learning styles and other factors; </li></ul><ul><li>provide a culture and climate for learning; </li></ul><ul><li>recognize the importance of metacognition; </li></ul><ul><li>focus on the significant mathematical concepts (“big ideas”). </li></ul><ul><li>‘ Principles Underlying Effective Mathematics Instruction’ A Guide to Effective Mathematics Instruction (2006) </li></ul>
    6. 6. Reflection <ul><li>Now link your AHA moment to one (or more) of the Principles Underlying Effective Mathematics Instruction. </li></ul>Your AHA moment Effective Instruction of Mathematics
    7. 7. A Big Idea is… <ul><li>A Key Mathematical Concept </li></ul>The Big Ideas for Grades 4-6 are… <ul><li>Quantity </li></ul><ul><li>Operational Sense </li></ul><ul><li>Relationships </li></ul><ul><li>Representation </li></ul><ul><li>Proportional Reasoning </li></ul>
    8. 8. Why focus on The Big Ideas? Curriculum and Instructional Planning Connections Assessment
    9. 9. Exploring the Big Ideas… <ul><li>FRACTIONS </li></ul>
    10. 10. Quantity <ul><li>Determining the ‘howmuchness’ of numbers </li></ul><ul><li>Modeling fractions as part of a whole </li></ul><ul><li>Counting fractional parts beyond one whole </li></ul>
    11. 11. Operational Sense <ul><li>Understanding addition, subtraction, multiplication and using them meaningfully to solve problems </li></ul><ul><li>Relating fractions to division </li></ul><ul><li>(e.g. “Imagine that 4 sandwiches were shared equally among 6 children. How much of a sandwich did each child eat?”) </li></ul>
    12. 12. Representation <ul><li>Mathematical symbols and language as representations of amounts, operations and concepts </li></ul><ul><li>Relating fractional symbols to their meaning (including proper and improper fractions and mixed numbers) </li></ul><ul><li>(e.g. the quantity represented by a fraction OR by the numerator and denominator) </li></ul>
    13. 13. Proportional Reasoning <ul><li>Comparison of quantities and proportions </li></ul><ul><li>Establishing part-whole relationships </li></ul><ul><li>(e.g. If this is 2/3 of the cake, what does the whole cake look like?) </li></ul><ul><li>Problem-solving with fractions </li></ul><ul><li>(e.g. If 5 girls share 2 pizzas and 7 boys share 4 pizzas, will the girls and the boys each get the same amount?) </li></ul>
    14. 14. Relationships <ul><li>“ To understand mathematics is to recognize the relationships it involves, which give it both its beauty and its utility. Seeing relationships between numbers helps students make powerful connections in mathematics, allowing them to discover new mathematics in flexible, efficient, and innovative ways.” (Guide Vol 1) </li></ul><ul><li>Relationships between decimals, fractions and percentages </li></ul><ul><li>Other relationships? </li></ul>
    15. 15. Features of eworkshop <ul><li>Guides to Effective Instruction </li></ul><ul><li>Learning Modules </li></ul><ul><li>Video workshops </li></ul><ul><li>Newsletter (this month has a fractions tip!) </li></ul><ul><li>Forum, Notebook and other features if you subscribe and create a profile </li></ul><ul><li>Other topics and resources relate to literacy, leadership, parents, healthy schools, and more </li></ul>
    16. 16. Webhunt: <ul><li>On find the following: </li></ul><ul><li>An interesting problem-solving activity in the Learning Module on Fractions </li></ul><ul><li>A teaching video that includes a useful strategy for exploring a Big Idea related to Fractions. </li></ul><ul><li>The part, most useful to you, of the Guide to Effective Instruction related to Fractions. </li></ul><ul><li>“ How might the use of this site improve/influence your teaching of Fractions and the Big Ideas?” </li></ul>
    17. 17. Sharing… <ul><li>In groups of 4-5, discuss the guiding question: </li></ul><ul><li>“ How might the use of this site improve/influence your teaching of Fractions and the Big Ideas?” </li></ul>
    18. 18. References <ul><li>“ A Guide to Effective Instruction in Mathematics Kindergarten to Grade 6. Vol 1. Retrieved July 11, 2008 from </li></ul><ul><li>National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author. </li></ul><ul><li>“ Number Sense and Numeration, Grades 4-6. Vol 1 The Big Ideas. Retrieved July 11, 2008 from </li></ul><ul><li>“ Number Sense and Numeration, Grades 4-6. Vol 5 Fractions. Retrieved July 11, 2008 from </li></ul>