1. A Secondary Mathematics
Acceleration Pathway
Diana Kolhoff
Mathematics Education Consultant
K-12 Instructional Coach

2. Why do we accelerate?
Pathway to Advanced Mathematics Parental Request ~ “Honors” Part of NYSED Regulations Increase Graduation Rate International Baccalaureate Appropriate for the Student

3. Low Achieving – On Level – High Achieving
Who do we accelerate?
Research on hetero vs homogeneous grouping
Low Achieving – On Level – High Achieving

4. True or False: Some people are naturally good at math, some are not.
Certain students have more math potential than others due to their innate abilities.
A student’s math potential can be determined at an early age.
Students must learn and do math quickly to be successful in math.

5. Truth:
There is no such thing as a “math gene”. Anyone can learn math at high levels with the right experiences and mindset.
Our potential for anything is deeply rooted in our beliefs. This is the effect of “Fixed Mindset” vs “Growth Mindset”.
Recent discoveries prove that the brain is much more malleable than we ever thought. Our brains can rewire, grow and change at any time in our lives.
Some of the world’s top mathematicians are slow thinkers because they think deeply about mathematics.

6. When do we accelerate?
At what grade is the decision made? What if we make the wrong decision? Accelerate when Inappropriate – Unprepared Discouraged Students Teacher is Blamed Must Repeat Slows Down the Class Don’t Accelerate when Appropriate Missed Opportunity for Student Difficult to Get Back on Track
When do we accelerate?

7. How long do they last?
Many districts may have the impression they retain most of their students on the accelerated track.
Over the past few years, many districts have reduced the number of students they accelerate.
Other districts accelerate ALL in the name of equity.
Trace the students that passed the AP Calculus exam back to grade 8. How many students in that cohort were accelerated into the 8th grade Algebra course?
For many districts, the numbers drop by as much as 50%, sometimes more, and minorities are underrepresented.
What is the impact on those students that were not accelerated, or were accelerated but were unsuccessful? What message does it send?

8. A Shift:
I found this graphic in a Utah State publication, but it applies to us as well. On the left, the pink represents the range and complexity of the 2005 standards. Notice the gap between 12th year and college. One interesting statistic in NY is that 65% of college incoming freshmen require remediation, and 75% of our students that would like to join the armed services can’t pass the entrance exam for mathematics. Common Core State Standard is addressing this gap as represented by the blue column. I think this is a nice visual to show the increased levels of complexity at every grade level. Notice that college coursework on the right is now after grade 11, and the increased complexity starts in Kindergarten.
I have done a lot of professional development at the elementary school level, and I can vouch for the shift that teachers and students are feeling at every grade level k-5. We must be sensitive to the transitional period here as kids shift from one lane to the other. In grade 5 common core, there is an assumption that students have hade rich common core experiences k-4.

9. 2005 Algebra 2/Trig Standards – Moved!
P and C, Trig
Rational and Irrational Expressions
Logarithms and e,
Trigonometry
Circles, Triangle Trig
Sequences, Functions, Quadratics
Expon/Rads, Statistics
De-Emphasized

10. Integrated Algebra – Where did it go?
Rational Expressions
Sets
Triangle Trig
Quadratics
Linear Algebra
Bivariate Stats
Expressions, Equations, Inequalities, Prob/Stats

11. Common Core Grade 8 – What is it?

12. ACT.org
Top 20 Topics Rated Most Important as Prerequisites by Instructors of Credit-Bearing First-Year College Mathematics Courses:

13. Ranked Most Important Pre-Requisite Topics for College Math
Where is it taught now?
1) Evaluate algebraic expressions
6, 7, 8…
2) Perform addition, subtraction, multiplication and division on signed rational numbers
Grade 7
3) Solve linear equations in one variable
Grades 6, 7, 8
4) Solve multi-step arithmetic problems
… 6, 7, 8
5) Locate points on a number line

14. Ranked Most Important Pre-Requisite Topics for College Math
Where is it taught now?
6) Perform operations (add, subtract, multiply) on linear expressions
Grades 7, 8, Algebra 1
7) Find the slope of a line
Grades 7, 8
8) Find equivalent fractions
…6, 7
9) Find and use multiples and factors
… 6, 7, 8 …
10) Perform operation (add, subtract, multiply) on polynomials
Algebra 1

15. Ranked Most Important Pre-Requisite Topics for College Math
Where is it taught now?
11) Locate points in the coordinate plane
Grade 6
12) Write expressions, equations, or inequalities to represent mathematical and real-world settings
… 6, 7, 8 …
13) Evaluate functions at a given value of x
Grade 8 and beyond
14) Graph linear equations in two variables
15) Order rational numbers

16. Ranked Most Important Pre-Requisite Topics for College Math
Where is it taught now?
16) Determine the absolute value of rational numbers
Grades 6, 7
17) Manipulate equations and inequalities to highlight a specific unknown
… 6, 7, 8 …
18) Manipulate expressions containing rational exponents
Algebra 2
19) Solve linear inequalities in one variable
Grade 6, 7…
20) Solve problems using ratios and proportions

17. The vast majority of math topics rated as the most important pre-requisites for college readiness are taught in middle school grades 6, 7, and 8.

18. What About Careers? Calculus in the workforce?
Physicists
Engineers
Statistics in the workforce?
All Sciences
Research and Development
Business
Marketing and Advertising
Wall Street
Education
Consumers and Citizens……

19. So Why Calculus?
Mathematical Association of America and the National Council of Teachers of Mathematics have taken the position that the goal of a K-12 mathematics curriculum shouldn't be to get students through calculus but to give students a strong foundation in mathematics that will prepare them for a range of college majors. 

20. Truth:
The Common Core Instructional Shifts for Mathematics are Focus, Coherence, and Rigor.
Rigor is defined as a balance between Deep Conceptual Understanding, Fluency, and Application.
The Standards for Mathematical Practices outline ways that students should exhibit perseverance, model and communicate mathematically, make deep connections between mathematical concepts and much more.
This type of mathematical instruction takes more time than traditional instruction.
The quality of mathematics instruction is more important that the speed in which we “cover” topics.

21. CCSSI: Appendix A “Compacted”
1. Compacted courses should include the same Common Core State Standards as the non-compacted courses.
2. Decisions to accelerate students into the Common Core State Standards for high school mathematics before ninth grade should not be rushed.
3. Decisions to accelerate students into high school mathematics before ninth grade should be based on solid evidence of student learning.
4. A menu of challenging options should be available for students after their third year of mathematics—and all students should be strongly encouraged to take mathematics in all years of high school.
The only guidance we have…… 6
7/8
8/A1 G A2 PC AP
Testing and the Grade 8 waiver create challenges in NYS.

22. Traditional acceleration:
A Brief History: Districts had increasingly offered Algebra in Grade 8. The Common Core Learning Standards have a tight progression of standards, without redundancy in grade 8.

23. Current practice in the field
Acceleration Model based on 2005 Standards
ACCELERATED TRACK 6 7 A1 G A2 PC AP
Grade 8 standards may not be adequately addressed

24. Was it working? Elaine Zseller, Ph.D Program Supervisor
Data Analysis and Curriculum Support
Nassau BOCES
When do we accelerate?

25. 2012 Integrated Algebra Success Rates
Was it working?
Level 2 Students were more successful in Integrated Algebra in a Traditional Program than in an Accelerated Program
2012 Integrated Algebra Success Rates
By Grade Seven Year
Grade 7 Level
7th in 2009
Extended Students
7th in 2010
Traditional Students
7th in 2011
Accelerated Students 1
28.1%
28.6% 2L
25.8%
55.5%
43.1% 2H
46.9%
80.4%
70.4% 3L
65.9%
91.6%
91.2% 3H
87.0%
97.2%
98.2% 4L
99.7%
99.6%
100% 4H
When do we accelerate?

26. 2013 Geometry Success Rates
Was it working?
Students Who Scored Level 1 or Level 2L in Grade 7 Did NOT Take Geometry as Accelerated Students
2013 Geometry Success Rates
By Grade Seven Year
Grade 7 Level
7th in 2009
Extended Students
7th in 2010
Traditional Students
7th in 2011
Accelerated Students 1 2L
47.4% 2H
65.4%
63.5% 3L
55.3%
85.8%
83.7% 3H
79.2%
93.3%
94.3% 4L
97.4%
98.1%
99.4% 4H
100%
When do we accelerate?

27. 2014 Algebra II / Trig Success Rates
Was it working?
Students in an Accelerated Program are not as Successful as Students in a Traditional Program in Algebra II/Trig
2014 Algebra II / Trig Success Rates
by Grade 7 Year
Grade 7 Level
2009
Extended Students
2010
Traditional Students
2011
Accelerated Students 1 2L
40.5% 2H
56.7%
37.3% 3L
68.6%
59.7% 3H
78.6%
77.9% 4L
88.2%
94.8% 4H
100%
When do we accelerate?

28. CC Algebra 1 Passing (3 or better)

29. CC Geometry Passing (3 or better)

30. ies Report: Who Repeats Algebra?
Students who attended a school that required Algebra I for All grade 8 students had a decline in course grades on average (–0.50) when they repeated the course, but students who did not attend such a school had an improvement of approximately half a grade (0.56) when repeating.

31. Common Core Learning Standards

32. Common Core Learning Standards

33. Best Pathways to AP Courses
GRADE 6 7 8 9 10 11 12
FOR ALL – COLLEGE AND CAREER 6 7 8 A1 G A2
PC or AP
HIGH ACHIEVER - ENRICHMENT 6H 7H 8H
A1H GH
A2H AP
CONCURRENTLY – A2/PC and STATS
STAT 6 7 8 A1 G
A2/PC AP
CONCURRENTLY – DOUBLE UP
AP Stats 6 7 8 A1 G
A2/PC AP

34. Best Compacted: High School
GRADE 6 7 8 9 10 11 12
3.5 Years in 3 : No Extra Time 6 7 8
A1+ G+
A2+ AP
2.5 Years in 2 : 1.5 Time in 11 or 12 6 7 8 A1 G+
A2+ AP
2 Years in 1 : Double Time in 12 PC 6 7 8 A1 G A2 AP
Concurrently : Double Up G 6 7 8 A1 A2 PC AP

35. Joining the Conversation:
Would we be the first?
Massachusetts Department of Education
San Francisco Bay Area Schools
New York School Districts
Sewanhaka
Bedford
North Salem
Ossining
Putnam Valley
South Huntington
Joining the Conversation:
Levittown
East Meadow
Jericho
Port Jefferson
East Williston
Hewlett-Woodmere

36. Why do we accelerate?
Pathway to Advanced Mathematics Parental Request ~ “Honors” Part of NYSED Regulations Increase Graduation Rate Appropriate for the Student

37. NYSED PART 100.4
d. Grade eight acceleration for diploma credit. 1. Public school students in grade eight shall have the opportunity to take high school courses in mathematics and in at least one of the following areas: English, social studies, languages other than English, art, music, career and technical education subjects or science courses. 3. Such opportunity shall be provided subject to the following conditions: The superintendent, or his or her designee, shall determine whether a student has demonstrated readiness in each subject in which he or she asks to begin high school courses in the eighth grade leading to a diploma.

38. NYSED PART 100.4
The Regulation calls for the opportunity to be accelerated in Math and at least one other subject, however the determination of readiness for acceleration is made by the superintendent.  If a student has mastered the intermediate (Gr 5-8) Math Standards, and a determination (using a consistently applied local policy) is made that a particular student would benefit from acceleration, AND the student asks to be accelerated, then the district must offer the opportunity. If the above does not happen, then it is conceivable that there may not be middle level students who demonstrate readiness for high school course work in a particular school or district.  There is no mandate to provide acceleration if the district concludes that this is the case.

39. Long Island Acceleration Consortium
Next Step?
Join the club!
Long Island Acceleration Consortium
ESBOCES

40. Mathematics Education Consultant, Long Island
Diana Kolhoff
Mathematics Education Consultant, Long Island