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Myth vs Fact: Understanding Mathematics Instruction and Learning

This presentation explores common myths and facts about mathematics instruction, emphasizing the importance of teaching a broader understanding of mathematics and promoting active student participation. It also discusses the role of mathematical reasoning and the use of learning progressions in facilitating deep mathematical understanding.

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Myth vs Fact: Understanding Mathematics Instruction and Learning

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  1. Welcome “When parents and teachers alike believe that hard work pays off and when mathematics is taught and learned by using all the strands of proficiency mathematics performance improves for all students.” Helping Children Learn Mathematics (2002) Kilpatrick and Swafford

  2. Scenario My child doesn’t know his number facts. Why aren’t we teaching the basics and teach REAL math. AISCH Parent Presentation 2012

  3. Why Has Mathematics Instruction Changed? Myths and Facts

  4. Myth Fact • Some people just can’t do math. • Every adult and every child can do mathematics. AISCH Parent Presentation 2012

  5. Myth Fact • Literacy is reading and writing. • Literacy is far broader, including an understanding of graphs, tables, statistics, probability... AISCH Parent Presentation 2012

  6. Myth Fact • Students learn math best through teacher-directed lessons. • Students learn math best when they are active participants in the learning process. AISCH Parent Presentation 2012

  7. Myth Fact • The use of calculators will have a negative impact on students’ computation skills. • When used appropriately, calculators improve computation skills. AISCH Parent Presentation 2012

  8. Myth Fact • Manipulatives are for young children. • Manipulatives help connect abstract thought to something tangible --- for learners of ALL ages. AISCH Parent Presentation 2012

  9. Myth Fact • The school program is not rigorous. • Rigor does not equate to difficulty. AISCH Parent Presentation 2012

  10. What is mathematics? Mathematics is a way of thinking about, understanding, explaining, and expressing phenomena. Mathematics is about inquiry and insight. Computation is (usually) a means to an end.

  11. Body of Knowledge Method of Thinking, Reasoning, and Explaining Collection of Skills and Procedures Language AISCH Parent Presentation 2012

  12. MATHEMATICAL PROCESSING MAKE & TEST CONJECTURES WONDER SEARCH FOR PATTERNS IMAGINATION USE INDUCTIVE REASONING CHOOSE A STRATEGY/METHOD CHOOSE REPRESENTATIONS DRAW ANALOGIES MATHEMATICALLY MODEL FORMULATE ALGORITHMS DETERMINE WHAT’S KNOWN & WHAT’S NEEDED GENERALIZE RESULTS/ ALGORITHMS JUSTIFY SPECIAL CASES EXPLORE EXAMPLES INTUITION CREATIVITY ABSTRACT PROPERTIES POSE PROBLEMS LOGICALLY DEDUCE RESULTS/ ALGORITHMS Mathematical Reasoning AISCH Parent Presentation 2012

  13. Rigor Deep mathematical understanding that allows students to: 1.) see the connections between bits of mathematical knowledge; 2.) apply mathematical thinking to formulate and execute problem-solving strategies; 3.) apply mathematics in novel situations; 4.) see and use mathematics in real world situations; 5.) communicate and collaborate mathematically.

  14. Words such as conjecture, show, explain, justify, prove, abstract, and generalize are central components of a rigorous mathematics program ─that students need to do. AISCH Parent Presentation 2012

  15. A Learning Progression Model: Learning Progression: A learning progression is a sequenced set of subskills and enabling knowledge that, it is believed, students must master en route to mastering a more remote curricular aim. (Popham 2008) AISCH Parent Presentation 2012

  16. Emerging Themes • Progressions lay out increasingly more sophisticated understandings of core concepts, principles or skill development in a domain • Progressions are based on research and conceptual analysis • Progressions describe development over an extended period of time (not necessarily in grade levels) (Heritage, 2009) AISCH Parent Presentation 2012

  17. Math Learning Progressions AISCH Parent Presentation 2012

  18. Math Learning Progressions AISCH Parent Presentation 2012

  19. Defining Math Challenge Levels • Emergent • Beginning • Transitional • Intermediate • Advanced • Social understanding of mathematics – i.e. they count in order to please • Active – construct, modify, and integrate math ideas • Extend ability to compute additively – multiplicative reasoning emerges – develops fluency AISCH Parent Presentation 2012

  20. Challenge Levels • Intermediate • Advanced • Conjectures and verifies – comprehends cause and effect, abstract reasoning and generalizing increases • More complex, algebraic expressions, new geometric perspectives, new ways to analyze data. Focus on using understanding of mathematics to solve problems. AISCH Parent Presentation 2012

  21. Grade 4 The fourth-grade students at Jackson School are going on a field trip. • There are 6 fourth-grade classes at the school. Each class has 24 students. • What is the total number of fourth-grade students at the school? • Show or explain how you got your answer. All the fourth-grade students are going on the field trip. • The students will be riding on 3 buses. The same number of students will be riding on each bus. How many students will be riding on each bus? Show or explain how you got your answer. The teachers need to collect $7 from each student for the field trip. There are 115 students who have already paid. • What is the total amount of money, in dollars, that has already been paid? Show or explain how you got your answer. • What is the total amount of money, in dollars, that the teachers still need to collect? Show or explain how you got your answer. AISCH Parent Presentation 2012

  22. Scenario Parent: How can I help my child with math? It is so different from when I went to school. AISCH Parent Presentation 2012

  23. Yes, You CanHelp Your Child You really can!

  24. Changes • Textbooks and learning materials • Types of questions posed • Types of responses needed • Assessment and grading • Uses of class time

  25. Yes, I can … Talk about math in positive ways I’m sure you will understand if you… Let’s figure it out together. I could never do the math either. Don’t worry about the math.

  26. Yes, you can … Support your child through homework challenges by listening and asking questions

  27. Yes, I can … • Allow my child to struggle through the process of problem solving. • Discuss mistakes as learning opportunities.

  28. Questions to Ask … • What do you need to find out? • Tell me what you know? • Show me what you started? • What can you try first? • Can you make a drawing or picture? • Will a list or table help?

  29. Prompts … • Ask your child to show you how he/she is finding the answer. • Share your method. • Explain to each other why your different methods are successful. Providing shortcuts for getting the answer might hinder deeper student understanding.

  30. Internet Sites … • www.nctm.org/families • www.amathdictionaryforkids.com • PTA.org/parentsguides.

  31. AISCH Parent Presentation 2012

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  34. ManipulativesandTechnologies Their Role in Teaching and Learning Mathematics AISCH Parent Presentation 2012

  35. Research … “Manipulatives support the conceptual development of important mathematical ideas for tactile and visual learners.” AISCH Parent Presentation 2012

  36. Research … • Students learn in the presence of technology. • Technology should influence the mathematics content taught and how it is taught. AISCH Parent Presentation 2012

  37. Use of manipulatives and technologies … • Engagement • Confidence • Skill development • Motivation • Relevance AISCH Parent Presentation 2012

  38. Thank You AISCH Parent Presentation 2012

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