Teaching and Learning Mathematics

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Teaching and Learning Mathematics

• How did we get to where we are?

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Sputnik -- 1957

• Led to the Woods Hole Conference
• Chaired by Jerome Bruner
• Sooner is Better!!
• Clashed with Piaget

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History after Woods Hole

• 1960 Meaningful Math (New Math)
• Not only do we need to know math, we need to
  be fluent math theorists!
• 1980 Back to the Basics
• Test scores have fallen, its a direct result
  of a lack of understanding the basics

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History continued

• 1989 National Council of Teachers of Mathematics
  (NCTM) Standards
• Teaching, Curriculum, Assessment
• Adopted Constructivism
• reasoning,
• problem solving,
• communication,
• representation

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The Time Line of Mathematics Instruction

• 1900 1930 1960 1970 1980 1990
  2000
• ____________________________________________
  gt
• lt---Behaviorism--gtlt-Bruner-gtlt-Piaget---gtltInfo
  Processinggt
• Drill practice, Meaningful New
  Constructivism
• learning assoc- math math,
• iations Spiral
• Curriculum

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Timss Trends in International Math and Science
Study

• 13-year-olds from the U.S. are scoring
  substantially lower in mathematics than students
  from Korea, Ireland, Spain, and the United
  Kingdom
• second International Assessment of Education
  Progress -1991, U.S. Students were outperformed
  by Korean, Swiss, and Taiwanese students in every
  area of mathematics

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TIMMS continued

• U.S. students are outperformed by French and
  Hungarian students in four out of five areas
  tested.
• 13-year-old American students outperformed only
  Luxembourg, Nigeria, and Swaziland
• 2006 data no change

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NAEP National Assessment of Education Progress
Since 1969

• 1 in 5 4th and 8th Graders is proficient in
  mathematics
• 1/3 of 4th graders are below basic (lowest level)
• 1 of 8th graders were proficient in Algebra,
  Geometry and basic functions

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No Child Left Behind

• 1) to institute high academic standards for all
  students, and
• 2) to insure that there are 'highly qualified'
  teachers in every U.S. classroom

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NCLB cont.

• Content Standards.
• Annual Testing. Ninety-five percent of all
  students in grades 3 8 must undergo annual
  testing in mathematics and reading.

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NCLB cont.

• Every Childs Test Score. NCLB requires that
  every student be tested (only very minor
  exceptions exist for severe mentally or
  physically handicapped students) and that every
  child reach proficiency by 2014. (if subgroup
  fails, the whole school fails)

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NCLB cont.

• Sanctions. By 2014 every American student who is
  tested (100) must demonstrate Adequate Yearly
  Progress (AYP) in reading and mathematics After
  five years of inadequate test score gains, a
  school falls into the reconstitution category.
  Such a fate results in dismissing the schools
  teachers and administration and closing the
  school.

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NCLB cont.

• Highly Qualified Teachers
• Licensed in the area they teach
• Understand the content
• Gifted teachers

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What do we need to do in order to compete in math
internationally?

• Look at mathematics differently
• Teach it Differently
• Require students to solve problems to learn
  algorithms
• Focus on Problem solving not mechanics

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NCTM 2000 Six Features of the New Standards - 2000

1. Equity high expectations for all students to
   study and learn mathematics
2. Curriculum coherent, well-organized learning
   that integrates mathematics ideas
3. Teaching understanding what students know and
   need to learn and using effective pedagogical
   strategies

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• 4. Learning actively building conceptual
  understanding and proficiency
• 5. Assessment ongoing and routine enhancement
  of student learning and teacher instruction
• 6. Technology normal and expected support for
  effective mathematics teaching and learning