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Everyday Math Algorithms This isn’t how we learned math!

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Thank you for being here and for supporting your student’s math education!

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Dr. Kimberly Kappler Hewitt kapplerhewitt.kim@oakwoodschools.org 937-297-7801 kapplerhewitt.kim@oakwoodschools.org

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Objectives Introduce parents to Everyday Math’s use of standard and alternative algorithms. Teach parents the EM alternative algorithms. Answer parent questions.

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EM Algorithm Resources EM online suite: –Email kapplerhewitt.kim@oakwoodschools.org to get an account for the Everyday Math online suite:kapplerhewitt.kim@oakwoodschools.org –Suite includes: Computation games Interactive Student Reference Book Algorithms videos at http://everydaymath.uchicago.edu/educators/computation/. http://everydaymath.uchicago.edu/educators/computation/ Algorithms videos on Youtube. Parent EM resources at: http://www2.oakwood.k12.oh.us/~cia/CIA/Everyday_Mat h_Resources.html http://www2.oakwood.k12.oh.us/~cia/CIA/Everyday_Mat h_Resources.html

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EM Computation Algorithms Background: –Math fact fluency is imperative –Algorithm: step-by-step procedure to fulfill an objective Societal context: –Changing role of computation algorithms –Changing role of math Algorithms abound! (e.g. different algorithms have been favored in different time periods and nations)

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EM Computation Algorithms Example: Varying multiplication algorithms: –Sunzi multiplication algorithms (400 AD) with rod calculus –Lattice multiplication (AKA sieve multiplication) (1202) –Peasant or binary multiplication (ancient Egypt) –Quarter square multiplication (2000-1600 BC Babylon; 1817 Voisin) –Karatsuba multiplication (1960) for large numbers; used in some computer systems –Expanded notation (AKA partial products) –Algebraic notation method

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EM Computation Algorithms Traditional algorithms fail a significant # of students –e.g., 60% US 10-year olds & 56% of Japanese 3rd graders mastered standard subtraction “borrowing” algorithm –Overemphasis on procedure over conceptual understanding leads to “bugs” (common, difficult-to- break habits of incorrect procedures) –EM introduces algorithms that are conceptually friendlier and algorithms that capitalize on students’ “natural” approaches to problems (e.g. solving left-to- right) –“that’s just how you do it” explanation promotes math myths

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EM Computation Algorithms Students learn to compute using mental math, paper and pencil, and technology Students learn to find exact and approximate results Students are expected to attain mastery of one or more algorithms for each operation Students use: –Invented procedures –Alternative algorithms –US standard algorithms –Focus algorithms: Partial-sums Trade-first subtraction Partial-products multiplication Partial-quotients Distributed (spaced) practice is emphasized (v. massed)

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EM Algorithms Partial sums Partial differences Lattice method of multiplication Partial product multiplication Partial quotient division

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Questions?

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Learning Mathematics for Teaching Presented by Donna McLeish, IMI Staff To IMI Cohort III Kindergarten and Grade One Teachers September 29-30, 2004.

Learning Mathematics for Teaching Presented by Donna McLeish, IMI Staff To IMI Cohort III Kindergarten and Grade One Teachers September 29-30, 2004.

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