The Algebra Challenge

1. The Algebra Challenge Shirley Roath Mathematics Coordinator Riverside County Office of Education July 27, 2009 Algebra 1

2. Warm Up! 2 + 5 = 24 ÷ 4 = 2 • 5 = 6 • 4 = 7 - 4 = 8 + 9 = 4 • 7 = 72 ÷ 9 =

3. Top 10 Jobs From a list of200 best and worst jobs ranked by level of stress, work environment, physical demands, pay and career outlook. (Careercast.com, Jan. 2009) 1. Mathematician 2. Actuary 3. Statistician 4. Biologist 5. Software engineer 6. Computer systems analyst 7. Historian 8. Sociologist 9. Industrial design 10. Accountant

4. Quick Overview 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

5. 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

6. The State Board of Education Decides: All 8th graders will take Algebra I CST by 2011 d = r • t Algebra 1

7. d = r • t Distance Rate Time 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 Algebra 1

8. 12 11 10 CAHSEE Standards 9 8 7 Knowledge 6 5 4 3 2 1 2nd 4th 6th 8th 10th 12th Grade Level The Achievement Gap The Algebra Gap For each year of school the student only learns half a year of material (one example of a student below grade level) 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) University of Oregon, NCITE

9. 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 preparedif Algebraic reasoning has been appropriately emphasized beginning in Kindergarten and if interventions are in place.

10. 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.

11. 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.

12. Higher Order Thinking Skills • Arithmetic is doing something to numbers to get an answer. • Algebra is exploring the relationships between numbers.

13. 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

14. Algebraic Thinking Begins in Kindergarten 7 + 4 = ___ + 3 159 + 24 = ____ + 29 3x – 2 = 3 8 + 7= 10 + 5 = 15

15. Algebraic Thinking: Equality, Number and Place Value 30 v v v v 5 6 v v

16. Beginning Activities on the 100’s Chart 27 52 47 89 = 45

17. Multiply, Factor, Reduce Fractions, Equivalent Fractions, Comparing Fractions…

18. Multiplication with Meaning 47 x 23

19. Algebraic Thinking Should Continue Through High School (n2)3 = 130˚ x

20. 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. • Procedural fluency includes being flexible in choosing how, why and when to use procedures (operations and properties of numbers). • Number relationships, (more, less, equal, magnitude, estimation, composing and decomposing). • Use what students already know to our (and their) advantage. Algebra is generalized Arithmetic.

21. 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

22. The quality and rigor of instruction determines achievement, not demographics.Scores will rise as instruction improves. Don Davis ACSD Secondary Principal of the Year

23. Thank You! Shirley Roath Mathematics Coordinator Sroath@rcoe.us