Teaching Cultures in California, China and Japan

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Teaching Cultures in California, China and Japan

• Tom Roby
• California State University
• Hayward, CA (near San Fran.)
• http//seki.csuhayward.edu
• troby_at_csuhayward.edu

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Outline of Talk

• Comparison of Ed. In Japan and US
• Knowledge of Chinese vs. US elementary teachers.
  (Subtraction)
• Comparison of Grade 5 standards
• Recent and upcoming changes
• Lesson Study a process of incremental
  improvement.

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References Readings

• Stigler, James W Hiebert, James. The Teaching
  Gap. NY, The Free Press, 1999.
• Ma, Liping. Knowing and Teaching Elementary
  Mathematics. Mahwal, NJ,Lawrence Ehrlbaum
  Associates, 1999.
• Stevenson, H.W. Stigler, J.W. The Learning gap
  Why our schools are failing and what we can learn
  from Japanese and Chinese education. NY, Simon
  Shuster, 1992.
• Rohlen, Thomas P. Japan's High Schools.
  Berkeley, Univ. of California Press, 1983.
• Rohlen, T.P. LeTendre, G. Teaching Learning
  in Japan.

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Conceptions of Asian Ed.

• Stress rote learning
• Lots of mechanical drill
• Passive students
• Conformity
• Homogeneous students and classes
• Others?

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Features of Ed. In Japan

• Computers and calculators are rare
• Blackboards are used, rather than Overhead
  projectors
• Egalitarian ideals imply
• Uniform standards
• No tracking until high school
• Heterogeneous classes

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Lessons in Japan

• Lessons keep students involved
• Math is taught in the morning
• More breaks to play and blow off steam
• Shorter segments
• Variety of approaches
• Multiple activities
• manipulatives
• solo problem solving
• group problem solving
• student presentations
• teacher intro wrap-up

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Statistical Comparison

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Liping Ma PUFM

• Knowing Teaching Elementary Mathematics
• In depth comparison of Chinese and American
  elementary teachers
• 11-12 years of schooling vs. 16-18
• 72 from wide range of Chinese school vs. 23
  "better than average" US
• Teacher Education and Learning to Teach (TELT)
  questions
• Subtraction with regrouping
• Two-digit multiplication
• Division of fractions
• Area vs. perimeter of closed figure

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Subtraction w/ regrouping

• Problems like 52-25 or 91-79
• Students already can do 75-12
• Many used manipulatives, but not that worked with
  the "regrouping" concept. (E.g., dinosaur eggs
  (beans), coins quarter-dime)
• Manipulatives still used in a procedural way.
• Most used the confusing term "borrow".
• "You can't take a bigger number from a smaller
  number".
• "You have to take it from the other number".

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Tr. Bernadette

• What do you think? The number, the number
  64. Can we take a number away, 46? Think about
  that. Does that make sense? If you have a
  number in the sixties, can you take away a number
  in the forties? OK then, if that makes sense
  now, then 4-6, are we able to do that? Here is
  4, and I will visually show them 4. Take away 6
  1,2,3,4. Not enough. OK, well what can we do?
  We can go to the other part of the number and
  take away what we can use, pull it away from the
  other side, pull it over to our side to help, to
  help the 4 become 14.

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Chinese Teachers

• Only 14 focused only on procedures and
  "borrowing".
• 35 gave more than one way to regroup. (No US
  teacher did.)
• Tui Yi "Decomposing a unit of higher value"
  (Abacus terms)
• Jin Yi "Composing a unit of higher value"
• RATE of composing a higher unit value (looks
  ahead to multidigit sub. alg. e.g., 2001-37, and
  to other bases)

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Tr. Mao

• What is the rate for composing a higher value
  unit? The answer is simple 10. Ask students
  how many ones there are in a 10, or ask them what
  the rate for composing a higher value unit is,
  their answers will be the same 10. However, the
  effect of the two questions on their learning is
  not the same. When you remind students that 1
  ten equals 10 ones, you tell them the fact that
  is used in the procedure. And, this somehow
  confines them to the fact. When you require them
  to think about the rate for composing a higher
  value unit, you lead them to a theory that
  explains the fact as well as the procedure. Such
  an understanding is more powerful than a specific
  fact. It can be applied to more situations.
  Once they realize that the rate of composing a
  higher value unit, 10, is the reason why we
  decompose a ten into 10 ones, they will apply it
  to other situations. You don't need to remind
  them again that 1 hundred equals 10 tens when in
  the future they learn subtraction of three-digit
  numbers. They will be able to figure it out on
  their own.

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Multiple Regrouping

• Consider the problem 53 - 26.
• 53 40 13, so add (40 - 20) (13 - 6)
• 53 40 10 3, so (40 - 20) (10 - 6) 3
• 53 40 10 3, AND 26 20 3 3
• SO (40 - 20) (10 - 3) (3 - 3)
• E.G., 56 - 7 74 - 15
• Staging "Decomposing a ten" ? "Problems within
  20" ? bigger minuends.
• Teachers understanding of what comes later
  reinforces what comes earlier they see how
  knowledge is packaged.

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Division of Fractions

• How do you solve a problem like 1 3/4 divided by
  1/2?
• Imagine that you are teaching division with
  fractions. To make this meaningful for kids,
  something that many teachers try to do is relate
  mathematics to other things. Sometimes they try
  to come up with real-world situations or
  story-problems to show the multiplication of some
  particular piece of content. What would you say
  would be a good story or model for 1 3/4 divided
  by 1/2?
• Only 43 of US teachers got the right answer
  only 52 even used the right procedure (9 got
  14/4). "Invert and multiply"
• Other US teachers knowledge was confused or
  fragmented

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US fractional knowledge

• For some reason it is in the back of my mind that
  you invert one of the fractions. Like, you know,
  either 7/4 becomes 4/7 or 1/2 becomes
• 2/1. I am not sure. (Ms. Frances)
• I would try to find, oh goodness, the lowest
  common denominator. I think I would change them
  both. Lowest common denominator, I think that is
  what it is called. I do not know how I am going
  to get the answer. Whoops. Sorry. (Tr.
  Bernadette)

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Division of fractions

• All 72 Chinese teachers got the correct answer.
  "Dividing by a number is equivalent to
  multiplying by its reciprocal" (was a
  justification, not to remind themselves of the
  algorithm).
• Most were able to explain why the rationale
  worked.
• Many used other approaches as well
• Using decimals 1.75 \div 0.5 3.5
• Using Distributive Law (1 \div 1/2) (3/4
  \div 1/2)
• Without multiplication 7/4 \div 1/2 ...

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Grade 5 Standards

• Decimals, fractions, percentages for positive
  rational numbers
• Working with all four operations, and estimation.
  
• Simple algebraic expressions and ordered pairs.
• Areas of triangles and parallelograms
• Volumes of boxes
• Graphs of points and data.

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Grade 5 differences

• California, but not Japan
• Begin working with negative integers, , -.
  J. 7th
• Prime factorization J. ?
• Japan, but not California
• Idea of ratio and "per unit US. 6th
• Area of circle, the constant pi US. 6th
• Congruence of figures, corr.sides US. 7th
• Regular polygons US. 7th
• Area of trapezoid US. 7th

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Lessons in Japan

• Lessons keep students involved
• Math is taught in the morning
• More breaks to play and blow off steam
• Shorter segments
• Variety of approaches
• Multiple activities
• manipulatives
• solo problem solving
• group problem solving
• student presentations
• teacher intro wrap-up

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Changes in Japanese 5th

• Ministry of Education describes Japanese
  education as "problem-stricken".
• New standards offer "power to live" under
  "pressure-free" education.
• Reduce classweek by an additional 1/2 day
  (eliminate Saturday classes)
• 30 cut in curriculum
• Kanji taught over 2 years (read-only in first
  year)
• Science cut hard (remove health, problem solving
  emphasis)
• Integrated studies pilot program.

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Lesson Study in Japan

• Focus on student learning
• Teachers work collaboratively
• Teachers are empowered to make improvements
• Many hours to plan one lesson
• Incremental approach to change
• Results may be shared with other teachers
• Requires standards
• Requires time for teachers to study and plan

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Lesson Study Process

• Define the problem
• Plan the lesson
• Teach it
• Evaluate Reflect
• Revise it
• Teach it again
• Evaluate the revision

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Lesson Study in US

• Some groups are trying to adopt Lesson Study in
  the US
• Pilot program in California Professional
  Development Institutes
• LessonLab Videotaping teachers and special
  software
• NSF-funded website http//www.lessonresearch.net/

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Real Life

• Give an example or real life anecdote
• Sympathize with the audiences situation if
  appropriate

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