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The Case for Elementary Mathematics Specialists Deborah Loewenberg Ball University of Michigan Hung-Hsi Wu University of California Berkeley WebEx December 3, 2007.

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The Case for Elementary Mathematics SpecialistsDeborah Loewenberg BallUniversity of MichiganHung-Hsi WuUniversity of California BerkeleyWebEx December 3, 2007

Funded by U.S. Department of Education

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The Center on Instruction is operated by RMC Research Corporation in partnership with the Florida Center for Reading Research at Florida StateUniversity; RG Research Group; Horizon Research, Inc.: the Texas Institute for Measurement,Evaluation, and Statistics at the University of Houston; and the VaughnGross Center for Reading and Language Arts at the University of Texas at Austin.The contents of this PowerPoint were developed under cooperative agreement S283B050034 withthe U.S. Department of Education. However, these contents do not necessarilyrepresent the policy of the Department of Education, and you should notassume endorsement by the Federal Government.2007 The Center on Instruction requests that no changes be made to the content or appearance of this product.To download a copy of this document, visit www.centeroninstruction.org

Funded by U.S. Department of Education

who are we
Who are we?

We come at this question from opposite ends:

  • Deborah Ball is an elementary teacher who became interested in the mathematical problems of teaching mathematics.
  • Hung-Hsi Wu is a research mathematician who became interested in the educational problems of mathematics education.

Funded by U.S. Department of Education

and why are we interested in the possibility of elementary mathematics specialist teachers
. . . and why are we interested in the possibility of elementary mathematics specialist teachers?
  • There is a general awareness that many of our elementary teachers do not teach mathematics well, but few bother to ask why.
  • One obvious reason:
    • Our elementary teachers are being asked to do too much.

Funded by U.S. Department of Education

another more hidden reason
Another, more hidden, reason:
  • We do not prepare teachers appropriately for their job.
  • Elementary teachers have to teach all subjects in addition to being good baby sitters. To ask them to be also good at teaching something as complex as mathematics is not fair.

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the mathematics of elementary school is complex
The mathematics of elementary school is complex.
  • Some ten years ago, when the idea of creating a cadre of math specialists in the upper elementary grades first made its way to the the California legislature, a legislator asked incredulously: “All you have to do is add, subtract, multiply and divide numbers. Why do you need math specialists?”

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Before the webinar ends, you will see that the mathematics of elementary school is much more than “add, subtract, multiply and divide numbers.”

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problems with teachers mathematical preparation
Problems with teachers’ mathematical preparation
  • Unfortunately, many, or perhaps most, teacher preparation programs continue to make believe that, to teach math in K-6, all you need to do is to learn how to “add, subtract, multiply and divide numbers”.
  • This is a major reason why our elementaryteachers are not mathematically well-informed.

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An elementary teacher has to explain genuine mathematics to children in terms so simple that the children can understand.
  • Explaining mathematics is, by itself, already not easy.

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for example what does it mean to multiply 82 by 59
For example, what does it mean to multiply 82 by 59?

And why is this computation correct?

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let s try another one why do we invert and multiply to divide fractions
Let’s try another one: Why do we invert and multiply to divide fractions?

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Teaching children to flip the fraction is easy. But how to explain why they should do that, in a way that they can understand?
  • This is hard work!

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what does 7 5 2 3 mean
What does 7/5 ÷ 2/3 mean?

Write a story problem for which 7/5 ÷ 2/3 would be the appropriate computation.

Funded by U.S. Department of Education

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Another thing that teachers do is check students’ responses and verify the correctness of their texts.

Is this a correct story problem for 7/5 ÷ 2/3?

  • Wu and Deborah were racing toy cars on a roadway line. Wu’s toy car scooted to the 7/5 meters mark on the roadway. Deborah’s car went 2/3 as far as Wu’s. Where did her car stop?

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Something else teachers do is to use diagrams and representations.Which of the following could be used to represent 2 ÷ 2/3?

(b)

(a)

(d)

(c)

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what is mathematical knowledge for teaching mkt
What is “mathematical knowledge for teaching” (MKT)?
  • The mathematical knowledge, skills, and habits that are needed for the work of teaching.
  • The work of teaching includes: explaining mathematics, appraising textbook material, assessing students’ work, deciding what is important mathematically, using representations, defining terms in usable ways, asking strategic questions, choosing apt examples.

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is mkt a valid concept of the mathematics needed for teaching
Is MKT a valid concept of the mathematics needed for teaching?
  • Is mathematical knowledge
  • Special kind of mathematical understanding demanded by the work of teaching, more than common knowledge of mathematics
  • Related to the mathematical quality of instruction
  • Related to student achievement gains

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the problem
The problem
  • Lack of opportunity to learn MKT: Most professional education does not equip teachers with this sort of mathematical knowledge
  • Enormous scale: There are so many teachers out there who lack this knowledge

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understanding and solving the problem
Understanding and solving the problem
  • The long years of neglect of our elementary teachers have left us in an impossible situation. With more than two million elementary teachers out there, how can we raise the level of their content knowledge?
  • The only realistic solution is to let the mathematically knowledgeable teachers (math specialists) take over the teaching of mathematics in K-6.
  • At the same time, we can try to do intensive professional development to produce more math specialists.

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two models of math specialists
Two models of math specialists
  • Specialized teacher: The kind we have been talking about: they are classroom teachers that teaches students only mathematics.
  • Lead teacher: This kind of math specialists serve as resource persons for a school or for a district, as mentors for teachers, or as coordinators of school-wide or district-wide math programs. They no longer teach students.

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deborah s experiences
Deborah’s experiences
  • Specialist teacher in a departmentalized elementary school (1975-1977)
  • Specialist “reading helping teacher” (1980-81)
  • Specialist elementary math teacher (1984-1987)

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Final Thoughts

  • Only anecdotal evidence. Not much research done in this area.
  • Associated costs: The lead teacher specialists can be expensive because it is extra expenditure in addition to classroom teachers, but specialized teachers require no additional costs, only the willingness to change the administrative structure to accommodate their presence.
  • Availability: Lead teacher specialists are far more difficult to produce in comparison. In addition to superior content knowledge, they also need superior pedagogical knowledge and organization skills.
  • Realistically, specialized teachers are the way to go, even if the lack of solid data to back up their effectiveness prevents an all-out recommendation.

Funded by U.S. Department of Education