Everyday Everyday MathematicsMathematics

Chapter 4Chapter 4

Everyday Everyday MathematicsMathematics

Chapter 4Chapter 4Gwenanne SalkindGwenanne Salkind

EDCI 856 Discussion LeadershipEDCI 856 Discussion Leadership

University of Chicago School Mathematics Project

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

(1993)

Everyday Mathematics Publication Dates

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

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.

Principles for Development5. The teacher and curriculum are

important in providing a guide for learning important mathematics

6. Mathematical questions and observations should be woven into daily classroom routines.

7. Assessment should be ongoing and should match the types of activities in which students are engaged.

8. Reforms should take into account the working lives of teachers.

Principles for Development

• Do you agree with these principles?

• Do any stand out for you in some way?

• Is there anything missing?

Studies ofEveryday Mathematics

UCSMP Studies1. The Third Grade Illinois State Test2. Mental Computation and Number Sense of Fifth

Graders3. Geometric Knowledge of Fifth- and Sixth-Grade

Students

Longitudinal Study4. Multidigit Computation in Third Grade

School District Studies5. Hopewell Valley Regional School District

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.

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

• Describe the results of the study• Consider

– Mean score comparison– Low-income populations– State goals

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)

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

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?

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

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

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?

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

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.

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?

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)

Hopewell Valley Regional School District Study (p.

102)

• What were the results of the study?

• What does Figure 4.8 tell us?

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

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.

One Final Question

• What further studies would you suggest?