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Region 11 Math and Science Teacher Center

Region 11 Math and Science Teacher Center. Equality. Session Goals :. Identify benchmarks students reach on their way to understanding equality Identify strategies students might use in solving equations Understand PLC structure you will

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Region 11 Math and Science Teacher Center

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  1. Region 11 Math and Science Teacher Center Equality

  2. Session Goals: • Identify benchmarks students reach on their way to understanding equality • Identify strategies students might use in solving equations • Understand PLC structure you will • use in your school during the • coming month

  3. Carpenter, Franke, & Levi… (2003) …contend that a “limited conception of what the equal sign means is one of the major stumbling blocks in learning algebra. Virtually all manipulations on equations require understanding that the equal sign represents a relation.” Thinking Mathematically: Integrating Arithmetic and Algebra in the Elementary School. Portsmouth, NH: Heinemann, 2003, p. 22)

  4. National Recommendation

  5. Knuth Research • The Importance of Equal • Sign Understanding in the • Middle Grades • NCTM Mathematics Teaching in the Middle School May 2008

  6. Analyze your thinking • Explore the True/False equations. • As you work, think about your own thinking. • Share your answers with a partner.

  7. Benchmark 1 BASIC NUMBER SENTENCE SENSE Students begin to understand writing number sentences and can describe their understanding of the equal sign (correctly or incorrectly). 8 + 4 = ____ + 5 Children would answer 7, 12, 17, or 12 & 17

  8. Benchmark 2 EXPERIENCE WITH A VARIETY OF EQUATIONS Students explore equations that go beyond the form of a + b = c They understand that equations in these forms might be true: 7 = 3 + 4 2 + 8 = 5 + 5 356 + 42 = 354 + 44

  9. Benchmark 3 CALCULATING EQUALITY Students recognize that the equal sign represents a balance of both sides. Students carry out calculations to determine that the two sides of an equation are equal or not equal 8 + 4 = ___ + 5 12 12 Students need to catch both sides to fill in the missing value

  10. Benchmark 4 RELATIONAL THINKING Students compare the expressions on each side of the equation and check for balance/equality by identifying relationships among numbers and reasoning instead of actually carrying out the calculations. 8 + 4 = ___ + 5 “7 is the missing number because 5 is one more than 4, so I need a number that is one less than 8.”

  11. Our Teaching Goal… • Moving students • away from the idea that the equal sign (=) • means “the answer comes next” • towardunderstanding equal as meaning • “the same (amount) on both sides” and • toward using relationships between • numbers to determine equality or inequality

  12. Observe student thinking (1.3): • How does the teaching sequence move students along in their understanding? • How does the teacher use questioning strategies to build from students’ misconceptions? • Where do you see examples of the different benchmarks in understanding equality? Where did students start out? Where did they end up?

  13. Another look: • Use observation sheet to record student thinking • Again watch for operational or relational and benchmarks for each student

  14. PLC’s: Purpose • Apply Teacher Center training ideas to your teaching; 2. Learn what to listen for to better assess student understanding; 3. Form a community to support each other.

  15. PLC Structure • Week 1: Share and record baseline assessmentstudent data • Week 2: Discuss teaching strategies • Week 3: Share student interview assessment data • Week 4: Share and record summative assessment student data

  16. PLC Structure • BaselineAssessment: How do my students compare to other classes? • Teachingstrategies: How can my teaching impact student understanding? • Student interviews: What is the range of understanding in my classroom? • Summative Assessment: What did students learn?

  17. Explore the Assessment Tools: • Do the Baseline Assessment. • With a partner: discuss the related rubric and scoring grid • Review the Student Interview • Review the Summative Assessment

  18. Summary • Equality is an equivalence relationship • Our goal is to help students think relationally about equations • Equality is a convention - students cannot discover it; you must teach it explicitly and keep coming back and reinforcing it • We can watch and listen for various benchmarks that can help us identify where students are in their thinking about equality • Students will use various strategies to solve equations on this journey toward understanding, including calculation, unwinding, and algebra

  19. Region 11 Math and Science Teacher Center Math Success: It’s In Our Hands

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