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Abstract
This article examines the Everyday Mathematics curriculum, developed by the University of Chicago, focusing on its original design principles and recent changes. We analyze the impact of the curriculum's spiral approach, particularly in relation to its effectiveness for students at various skill levels. The study highlights the consequences of reducing the depth of the spiral in newer versions of the curriculum and discusses implications for student learning and achievement.
Introduction
Everyday Mathematics, developed by the University of Chicago School Mathematics Project in the 1980s, was once hailed as one of the most successful mathematics curricula in the United States. Its distinctive feature was a deep spiral approach that revisited concepts across multiple grade levels, providing both reinforcement for struggling students and advanced exposure for high-achieving students. However, recent changes to the curriculum have significantly altered this approach, prompting a reevaluation of its effectiveness.
The Original Everyday Mathematics Approach
Deep Spiral Curriculum
The original Everyday Mathematics curriculum employed a deep spiral approach that spanned multiple grade levels. For example, in 4th grade:
- Content spiraled down to 2nd grade concepts for review and reinforcement
- Current grade-level content was covered comprehensively
- Content spiraled up to 6th grade, introducing advanced concepts
This approach provided several benefits:
1. Reinforcement of foundational skills for struggling students
2. Continuous review and practice opportunities
3. Exposure to advanced concepts for high-achieving students
4. Accommodation of diverse learning rates and styles
Math Boxes
A key component of the curriculum was "Math Boxes," which provided structured practice across various domains. These boxes included problems from different skill levels, reinforcing the spiral approach within daily lessons.
Recent Changes and Their Impact
Narrowed Spiral
Recent editions of Everyday Mathematics have significantly reduced the depth of the spiral:
- Content now primarily focuses on grade-level material
- Limited spiraling to previous or future grade levels
Consequences of the Narrowed Approach
1. Reduced support for below-grade-level students
- Less opportunity to revisit and master foundational skills
- Potential widening of achievement gaps
2. Limited challenge for above-grade-level students
- Decreased exposure to advanced concepts
- Possible stagnation of high achievers
3. Less flexible learning environment
- Reduced ability to accommodate diverse learning needs within a single classroom
Discussion
The original Everyday Mathematics curriculum's deep spiral approach aligned well with cognitive science principles of spaced repetition and interleaving. By revisiting concepts across multiple contexts and difficulty levels, it supported long-term retention and transfer of mathematical skills.
The narrowing of the spiral in recent versions may have been intended to align more closely with grade-level standards or to simplify implementation. However, this change potentially sacrifices the adaptability and comprehensive nature that made the original curriculum successful.
Conclusion
The evolution of Everyday Mathematics from a deeply spiraled, multi-grade approach to a more grade-level focused curriculum represents a significant shift in mathematics education philosophy. While the newer version may offer some advantages in terms of standards alignment, it appears to have lost key features that made the original curriculum exceptionally effective for diverse learners.
Further research is needed to quantify the impact of these changes on student achievement across different skill levels. Educators and curriculum developers should consider ways to reincorporate the benefits of the deep spiral approach while meeting current educational standards and practical implementation needs.
Now, let's create an example of what the 4th grade Math Boxes might have looked like in the original Everyday Mathematics curriculum:
Example: 4th Grade Math Boxes in Original Everyday Mathematics
The following is a representation of what a set of Math Boxes for 4th grade might have looked like in the original Everyday Mathematics curriculum. This example demonstrates the deep spiral approach, including problems from 2nd grade up to 6th grade concepts.
Math Box Set A
1. (2nd Grade Review) Count by 5s from 35 to 80.
_________________________
2. (3rd Grade Review) Round 678 to the nearest hundred.
Answer: __________
3. (4th Grade Current) Solve: 24 x 16 = __________
4. (4th Grade Current) Find the perimeter of a rectangle with length 7 cm and width 5 cm.
Answer: __________ cm
5. (5th Grade Preview) Express 3/8 as a decimal.
Answer: __________
6. (6th Grade Preview) If 2x + 5 = 13, what is x?
Answer: __________
Math Box Set B
1. (2nd Grade Review) Write the number 465 in expanded form.
Answer: ______ + ______ + ______
2. (3rd Grade Review) Draw hands on the clock to show 3:45.
[Clock face diagram]
3. (4th Grade Current) Find the area of a triangle with base 8 cm and height 6 cm.
Answer: __________ cm²
4. (4th Grade Current) List the factors of 24.
Answer: __________________________
5. (5th Grade Preview) Convert 2.5 km to meters.
Answer: __________ m
6. (6th Grade Preview) Simplify: 2(x + 3) + 4x
Answer: __________
Math Box Set C
1. (2nd Grade Review) Solve: 45 + ____ = 72
2. (3rd Grade Review) Identify the fraction of the shape that is shaded.
[Diagram of a circle with 3/8 shaded]
Answer: __________
3. (4th Grade Current) Find the quotient and remainder: 95 ÷ 4
Quotient: ______ Remainder: ______
4. (4th Grade Current) Measure the angle to the nearest degree.
[Diagram of a 135° angle]
Answer: __________ degrees
5. (5th Grade Preview) Order these decimals from least to greatest:
0.8, 0.08, 0.88, 0.808
Answer: __________________________
6. (6th Grade Preview) If a recipe calls for 2/3 cup of flour for 4 servings, how much flour is needed for 6 servings?
Answer: __________ cups
These Math Boxes demonstrate how the original curriculum provided:
- Review of previous grade-level concepts
- Practice of current grade-level skills
- Preview of future grade-level material
This approach allowed for reinforcement, current learning, and advanced exposure, catering to a wide range of student abilities within a single classroom setting.
These examples illustrate how the original Everyday Mathematics curriculum used Math Boxes to implement its deep spiral approach. The problems range from 2nd grade review to 6th grade preview, allowing students to reinforce previous learning, practice current skills, and get exposure to future concepts.
This structure provided several benefits:
1. Struggling students could revisit and master foundational skills.
2. On-level students received consistent practice and review.
3. Advanced students were challenged with higher-level concepts.
4. The variety of problem types helped maintain engagement and supported different learning styles.
The change to a more grade-level focused approach in newer versions of the curriculum, as you mentioned, likely impacts these benefits. Students who are below grade level may have fewer opportunities to practice foundational skills, while those above grade level may not be as challenged.
More Examples: 4th Grade Math Boxes in Original Everyday Mathematics
The following are representations of what sets of Math Boxes for 4th grade might have looked like in the original Everyday Mathematics curriculum. These examples demonstrate the deep spiral approach, including problems from 2nd grade up to 6th grade concepts, categorized according to Arizona's College and Career Ready Standards' five math domains.
Math Box Set A
1. (OA, 2nd Grade Review) Write a number sentence for: 3 groups of 4 apples.
Answer: __________
2. (NBT, 3rd Grade Review) Write 7,842 in expanded form.
Answer: ______ + ______ + ______ + ______
3. (NF, 4th Grade Current) Shade 3/4 of the rectangle below:
[Rectangle diagram]
4. (MD, 5th Grade Preview) Convert 3.5 kg to grams.
Answer: __________ g
5. (G, 6th Grade Preview) Find the area of a triangle with base 8 cm and height 6 cm.
Answer: __________ cm²
## Math Box Set B
1. (OA, 3rd Grade Review) Solve: 7 x ____ = 56
2. (NBT, 4th Grade Current) Round 3,678 to the nearest hundred.
Answer: __________
3. (NF, 5th Grade Preview) Order these fractions from least to greatest:
2/3, 5/6, 1/2, 3/4
Answer: __________________________
4. (MD, 2nd Grade Review) What time does this clock show?
[Clock face showing 4:30]
Answer: __________
5. (G, 4th Grade Current) Identify this shape:
[Diagram of a trapezoid]
Answer: __________
## Math Box Set C
1. (OA, 4th Grade Current) If 3x + 2 = 14, what is x?
Answer: __________
2. (NBT, 6th Grade Preview) What is the value of 4 in the number 241,583?
Answer: __________
3. (NF, 3rd Grade Review) What fraction of the circle is shaded?
[Circle with 1/4 shaded]
Answer: __________
4. (MD, 5th Grade Preview) Find the volume of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm.
Answer: __________ cm³
5. (G, 2nd Grade Review) How many sides does a pentagon have?
Answer: __________
## Math Box Set D
1. (OA, 5th Grade Preview) Write an expression for: 5 less than twice a number.
Answer: __________
2. (NBT, 4th Grade Current) Multiply: 23 x 16 = __________
3. (NF, 6th Grade Preview) Divide: 3/4 ÷ 1/2 = __________
4. (MD, 3rd Grade Review) Measure this line segment to the nearest centimeter:
[Line segment approximately 7.3 cm long]
Answer: __________ cm
5. (G, 4th Grade Current) Draw a line of symmetry on this shape:
[Diagram of an isosceles triangle]
## Math Box Set E
1. (OA, 2nd Grade Review) Complete the pattern: 2, 4, 6, ___, 10, ___
2. (NBT, 5th Grade Preview) Write 0.037 as a fraction.
Answer: __________
3. (NF, 4th Grade Current) Which fraction is equivalent to 2/3?
a) 3/4 b) 4/6 c) 5/8 d) 1/2
Answer: __________
4. (MD, 6th Grade Preview) If a recipe calls for 3/4 cup of sugar for 4 servings, how much sugar is needed for 6 servings?
Answer: __________ cups
5. (G, 3rd Grade Review) Classify this angle as acute, right, or obtuse:
[Diagram of a 45° angle]
Answer: __________
These Math Boxes demonstrate how the original curriculum provided:
- Review of previous grade-level concepts
- Practice of current grade-level skills
- Preview of future grade-level material
All while covering the five main domains of mathematics education:
- Operations and Algebraic Thinking (OA)
- Number and Operations in Base Ten (NBT)
- Number and Operations—Fractions (NF)
- Measurement and Data (MD)
- Geometry (G)
This approach allowed for reinforcement, current learning, and advanced exposure, catering to a wide range of student abilities within a single classroom setting.
These additional Math Boxes examples further illustrate how the original Everyday Mathematics curriculum implemented its deep spiral approach while covering all five math domains. Each set includes problems that:
1. Review concepts from earlier grades (2nd and 3rd grade)
2. Practice current 4th grade skills
3. Preview more advanced concepts (5th and 6th grade)
This structure provides several benefits:
1. Struggling students can revisit and reinforce foundational skills.
2. On-level students receive consistent practice and review of current grade-level material.
3. Advanced students are challenged with exposure to higher-level concepts.
4. The variety of problem types helps maintain engagement and supports different learning styles.
5. All five math domains are regularly practiced, ensuring a well-rounded mathematical education.
The categorization by domain (OA, NBT, NF, MD, G) also helps ensure comprehensive coverage of mathematical concepts and skills.
This approach contrasts with the newer, more grade-level focused curriculum you mentioned. The original version's deep spiral allowed for greater flexibility in addressing diverse student needs within a single classroom, potentially leading to more effective learning outcomes for students at various skill levels.
Everyday Mathematics:
1. Everyday Mathematics curriculum
2. University of Chicago math program
3. Spiral curriculum approach
4. Math education reform
5. Elementary school mathematics
6. Deep spiral learning
7. Math Boxes examples
8. 4th grade math curriculum
9. Differentiated math instruction
10. Standards-based mathematics
11. Arizona College and Career Ready Standards
12. Math domains in elementary education
13. Operations and Algebraic Thinking
14. Number and Operations in Base Ten
15. Number and Operations—Fractions
16. Measurement and Data
17. Geometry in elementary math
18. Curriculum comparison studies
19. Math education best practices
20. Scaffolding in mathematics
21. Advanced math concepts for elementary students
22. Foundational math skills reinforcement
23. Cross-grade level math instruction
24. Everyday Math curriculum changes
25. Critical analysis of math curricula
26. Spaced repetition in math education
27. Interleaving practice in mathematics
28. Cognitive science in math curriculum design
29. Math achievement gaps
30. Adaptable math learning environments
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