the algebra challenge shirley roath mathematics coordinator riverside county office of education...
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The Algebra ChallengeShirley Roath
Mathematics Coordinator
Riverside County Office of Education
July 27, 2009
Algebra 1
Warm Up!
2 + 5 = 24 ÷ 4 =2 • 5 = 6 • 4 =7 - 4 = 8 + 9 =4 • 7 = 72 ÷ 9 =
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Algebra 1 has been the implied course of study in 8th grade since the 1999 release of the Mathematics Framework
In 2000 we began accountability measures using API. SAT-9 is High Stakes Test, No Penalty for 8th grade general math.
In 2002 First AYP Math CSTs, Algebra 1 and General Math in 8th Grade. Penalty for General Math in 8th for API, None for AYP
Quick Overview
Last year California is “called” on the discontinuity between standards
and testing in 8th Grade.According to NCLB we must test grade level standards
and since there is no “8th grade math” Algebra 1 is grade level for 8th grade.
The General Math CST is comprised of 6th and 7th grade standards.
California was told to fix this problem by either Making Algebra 1 the sole CST for 8th grade or by creating a second Algebra CST, (Algebra Lite) that addresses over 50% of the Algebra 1 standards
The State Board of Education Decides:
All 8th graders will take Algebra I CST by 2011
Algebra 1
d = r • t
d = r • tDistance Rate Time
Algebra 1
Current 7th graders to proficiency by end of this school year.(49% of these students scored basic or below on their 5th grade CST.)
1 year to proficient or above + 1 year of Algebra
Knowledge
Grade Level
1
2
3
4
5
6
7
89
10
11
12
2nd 4th 6th 8th 10th 12th
The Achievement Gap
CAHSEEStandards
The CAHSEE is given in the 10th thru 12th grade but only counts for AYP in the 10th grade.
One year of knowledge growth for each year in school (where students should be)
For each year of school the student only learns half a year of material (one example of a student below grade level)
University of Oregon, NCITE
The Algebra Gap
How do we get on the Train?Materials for the current adoption
were written with 8th grade Algebra 1 as the normal course of study. Students should be prepared if Algebraic reasoning has been appropriately emphasized beginning in Kindergarten and if interventions are in place.
The National Panel Final Report 2008
Key Findings• Math knowledge is cumulative from Kindergarten through
Algebra.• The structure of mathematics itself requires teaching a
sequence of major topics (from whole numbers to fractions, from positive numbers to negative numbers, and from the arithmetic of rational numbers to algebra) and an increasingly complex progression from specific number computations to symbolic computations.
• Algebra Proficiency sits on top of 8 years of math instruction, and every year matters.
The National Panel Final Report 2008
Key Findings• The goal of K – 7 mathematics instruction should be to build
“algebraic thinking” and not just “arithmetic thinking”.• Our task is to prepare our students to be Proficient in
Algebra and not be content with simply placing them into Algebra.
• The Panel recommends that struggling students receive some explicit mathematics instruction regularly. Some of this time should be dedicated to ensuring that these students possess the foundational skills and conceptual knowledge for understanding the mathematics they are learning at their grade level.
Higher Order Thinking Skills
• Arithmetic is doing something to numbers to get an answer.
• Algebra is exploring the relationships between numbers.
The depressing thing about arithmetic badly taught is that it destroys a child’s intellect and, to some extent, his integrity. Before they are taught arithmetic, children will not give their assent to utter nonsense; afterwards they will. Instead of looking at things and thinking about them, they will make wild guesses in the hopes of pleasing a teacher. The essential quality for a Mathematician is the habit of thinking things out for oneself. That habit is usually acquired in childhood. It is hard to acquire later.
--- W. W. Sawyer
Algebraic Thinking Begins in Kindergarten
7 + 4 = ___ + 3
159 + 24 = ____ + 29
3x – 2 = 3
8 + 7= 10 + 5 = 15
Algebraic Thinking: Equality, Number and Place Value
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v5 6
30
vv
v
Beginning Activities on the 100’s Chart
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
47
27
52
89
= 45
Multiply, Factor, Reduce Fractions, Equivalent Fractions, Comparing
Fractions…Multiplication Table
1 2 3 4 5 6 7 8 9 10
2 4 6 8 10 12 14 16 18 20
3 6 9 12 15 18 21 24 27 30
4 8 12 16 20 24 28 32 36 40
5 10 15 20 25 30 35 40 45 50
6 12 18 24 30 36 42 48 54 60
7 14 21 28 35 42 49 56 63 70
8 16 24 32 40 48 56 64 72 80
9 18 27 36 45 54 63 72 81 90
10 20 30 40 50 60 70 80 90 100
Multiplication with Meaning
47x 23
Algebraic Thinking Should Continue Through High
School
(n2)3 =
130˚ x
Three Considerations for Classroom Instruction
We need to transition from practices of traditional “arithmetic” instruction to the kinds of knowledge that students need to learn algebra with understanding.
1. Procedural fluency includes being flexible in choosing how, why and when to use procedures (operations and properties of numbers).
2. Number relationships, (more, less, equal, magnitude, estimation, composing and decomposing).
3. Use what students already know to our (and their) advantage. Algebra is generalized Arithmetic.
Understandings for Teaching…Teaching for Understanding
Effective teachers have high expectations for their students… a teacher’s expectations about students and the mathematics they are able to learn can powerfully influence the tasks the teacher poses, the questions they ask…and the encouragement they give their students. Adding It Up
The quality and rigor of instruction determines
achievement, not demographics.
Scores will rise as instruction improves.
Don Davis ACSD Secondary Principal of the Year
