Everyday Mathematics Chapter 4

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Everyday MathematicsChapter 4

• Gwenanne Salkind
• EDCI 856 Discussion Leadership

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University of Chicago School Mathematics Project

• Amoco Foundation (1983)
• GTE Corporation
• Everyday Learning Corporation
• National Science Foundation (1993)

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Everyday Mathematics Publication Dates

• 1987 Kindergarten
• 1989 First Grade
• 1991 Second Grade
• 1992 Third Grade
• By 1996 Fourth-Sixth Grade

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Principles for Development (p. 80)

1. Children begin school with a great deal of
   mathematical knowledge.
2. The elementary school mathematics curriculum
   should be broadened.
3. Manipulatives are important tools in helping
   students represent mathematical situations
4. Paper-and-pencil calculation is only one strand
   in a well-balanced curriculum.

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Principles for Development

1. The teacher and curriculum are important in
   providing a guide for learning important
   mathematics
2. Mathematical questions and observations should be
   woven into daily classroom routines.
3. Assessment should be ongoing and should match the
   types of activities in which students are
   engaged.
4. Reforms should take into account the working
   lives of teachers.

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Principles for Development

• Do you agree with these principles?
• Do any stand out for you in some way?
• Is there anything missing?

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Studies ofEveryday Mathematics

• UCSMP Studies
• The Third Grade Illinois State Test
• Mental Computation and Number Sense of Fifth
  Graders
• Geometric Knowledge of Fifth- and Sixth-Grade
  Students
• Longitudinal Study
• Multidigit Computation in Third Grade
• School District Studies
• Hopewell Valley Regional School District

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The Third-Grade Illinois State Test (p. 84)

• Illinois public schools (26 schools from 9
  suburban districts)
• All third grade students who had used EM
• Illinois Goal Assessment Program (IGAP)
• Compared mean test scores to mean state scores
  and mean Cook County scores.

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The Third-Grade Illinois State Test (p. 86)

• Describe the results of the study
• Consider
• Mean score comparison
• Low-income populations
• State goals

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Mental Computation and Number Sense of Fifth
Graders (p. 86)

• 78 students in four fifth-grade classes who were
  using EM
• Had used EM since kindergarten
• 3 suburban, 1 urban
• Compared to 250 students from a mental math study
  by Reys, Reys, Hope (1993)

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Mental Computation and Number Sense of Fifth
Graders (p. 88)

• 25 items
• Range of mathematical operations and
  computational difficulty
• Problems read orally or presented visually on an
  overhead
• Calculations done mentally
• 8 seconds to record answers on a narrow strip of
  paper

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Mental Computation and Number Sense of Fifth
Graders (p. 89)

• Look at table 4.1
• Which questions were missed the most? Why? How
  would you solve the problems?
• Which problems showed the greatest discrepancy
  between the two groups? Why? How would you solve
  the problems?

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Geometric Knowledge of Fifth-and Sixth-Grade
Students (p. 90)

• 6 classes using sixth-grade EM
• 4 classes using fifth-grade EM
• from 6 districts (4 Illinois, 1 Pennsylvania, 1
  Minnesota)
• 3 suburban, 2 rural, 1 urban
• All students used EM since K

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Geometric Knowledge of Fifth-and Sixth-Grade
Students (p. 90)

• Ten comparison classes
• 6 at sixth grade
• 4 at fifth grade
• Matched the EM schools on location and
  socioeconomic status
• Used traditional texts

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Geometric Knowledge of Fifth-and Sixth-Grade
Students (p. 93)

• Looking at Figure 4.6 on page 93. Notice that EM
  fifth-grade students outperformed the comparison
  sixth-grade students on both the pretest and the
  posttest.
• Why do you think this occurred?

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Longitudinal Study (p. 95)

• Commissioned by NSF (1993)
• Northwestern University
• Began with 496 first-grade students who were
  using EM
• Five school districts (Urban suburban Chicago,
  Rural district in Pennsylvania)
• Schools planned on adopting EM K-5

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Longitudinal Study (p. 96)

• In the second year of the study EM second-grade
  students scored lower on standard computational
  problems when compared to Japanese second-grade
  students.
• So, the researchers looked at multidigit
  computation in third grade the following year.

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Longitudinal StudyMultidigit Computation in
Third Grade

• Look at Table 4.3 on page 98.
• Why do you think the EM group did not show a
  significantly higher difference on the standard
  computational problems when compared with the
  NAEP group? (Problems 3, 5, 6, 7)
• What else do you notice about the results?

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Hopewell Valley Regional School District Study
(p. 99)

• 500 students in three schools
• Compared fifth-grade students (1996) who had
  never used EM to fifth-grade students (1997) who
  had used EM since second grade
• Two standardized tests
• Comprehensive Testing Program (CTP III)
• Metropolitan Achievement Test (MAT7)

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Hopewell Valley Regional School District Study
(p. 102)

• What were the results of the study?
• What does Figure 4.8 tell us?

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Conclusions

• EM students perform as well as students in more
  traditional programs on traditional topics such
  as fact knowledge and paper-and-pencil
  computation.
• EM students use a greater variety of
  computational solution methods
• EM students are stronger on mental computation

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Conclusions

• EM students score substantially higher on
  non-traditional topics such as geometry,
  measurement, and data.
• EM students perform better on questions that
  assess problem-solving, reasoning, and
  communication.

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One Final Question

• What further studies would you suggest?