Teacher to Teacher Making Sense of Problem Solving Newsletter April/May 2009

Focus on Algebra in Grades K-8

Issue 5: April/May 2009
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Growing numbers of districts and states have begun requiring all students to study algebra no later than the 9th grade. However a study of 160,000 Chicago students showed that failure rates significantly increased when K-8 support systems were not in place.

The National Council of Teachers of Mathematics’ Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence (NCTM, 2006) has identified the important content that should be mastered at each grade level. The Curriculum Focal Points (CFP) call for an early emphasis on number sense and fundamental algebraic ideas in grades one through four leading to more advanced algebra beginning in grades seven and eight. Grades five and six serve as a transitional stage in which topics such as proportionality are taught. Overall this provides a rigorous curriculum that builds a bridge leading to the formal study of algebra and geometry in high school.

Fundamental algebraic ideas include:
1) functions
2) patterns and relationships
3) variables
4) generalized rules for arithmetic relationships
5) symbolic representation

The National Mathematics Advisory Panel Final Report
(March 2008) also highlighted the need for sound learning of fundamental algebraic ideas throughout the K-8 years:

“Curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. The Panel (recommends curriculum) marked by effective, logical progressions from earlier, less sophisticated topics into later, more sophisticated ones.” (p. xvii)

The NCTM Curriculum Focal Points call for more focused and rigorous curriculum, taught in the context of the NCTM Process Standards.

"A clear emphasis on the processes that Principles and Standards addressed in the Process Standards—communication, reasoning, representation, connections, and, particularly, problem solving—can provide students with a connected, coherent, ever expanding body of mathematical knowledge and ways of thinking."
(NCTM Curriculum Focal Points, 2006, p. 1)

An example of how one supplementary curriculum threads fundamental algebraic ideas throughout the grades is shown below. Teacher to Teacher’s Making Sense of Problem Solving algebra units are built around the fundamental algebraic ideas and are presented in the context of problem solving. An analysis of a small portion of the Making Sense of Problem Solving algebra units at each grade level illustrates the focus on fundamental algebraic ideas throughout the grade levels.

The numbers in the Content column correspond to the numbered list of fundamental algebraic ideas above.

Unit Number/Name	Content	Grade	Unit Number/Name	Content
A.14: A String of Beads	Extending Repeating Patterns (2)	K	A.15: How Does Your Pattern Grow?	Extending Growing Patterns (2)
B.3: Gone Fishing	Finding Unknowns (3, 5)	1	B.15: In and Out and...	Number Patterns (1, 2)
C.14: The Pelican’s Pouch	Skip Counting (2)	2	C.15: Trip to the Zoo	Foundation of Multiplication (1, 2)
D.10: Garden Patterns	Patterns w/multiplication (1, 2, 3)	3	D.11: Legs, Legs, Legs	Functional Relationships (1, 4)
E.11: Lake Oscawana	Patterns w/decimals (2, 4, 5)	4	E.2: Places Everyone	Arrays (2, 4, 5)
F.11: Jog-a-thon	Graphing lines (1, 5)	5	F.10: Soccer Snacks	Writing & solving equations (3, 5)
G.12: Coming to Terms	Rules for patterns (1, 2, 4, 5)	6	G.11: Fitness	Graphing Expressions (1, 3, 4, 5)
H.9: A Pattern Puzzle	Equations for a pattern (2, 3, 4, 5)	7	H.12: To Draw or Not to Draw	Area Models(2, 4, 5)
I.6: Meltdown	Analyzing Linear Situations (4, 5)	8	I.7: Faster, Faster	Solving Linear Equations (3, 4,5)

As we focus our K-8 math instruction to emphasize fundamental algebraic ideas, we also need to be sure that students are learning to communicate clearly, make connections between ideas, and more deeply understand meaning. Teaching algebraic content through problem solving helps students develop strength in both content and process.

"The solution to low test scores is not lower standards—it's tougher, clearer standards.”

“I’m calling on our nation’s governors and state education chiefs to develop standards and assessments that don’t simply measure whether students can fill in a bubble on a test, but whether they possess 21st century skills like problem-solving and critical thinking…”

~President Barack Obama, March 10, 2009,
Speech on education reform delivered to the Hispanic Chamber of Commerce.

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