Math Remediation , Course Sequence, and the Senior Year

Mark Wilpolt, M.S. Math Ed. mwilpolt@csuchico.edu

Early Assessment Program CSU Chico

Research Question

With regards to satisfying the CSU Entry Level Math requirement,

Is there a significant difference between Chico State freshmen that stopped at Algebra 2 in high

school and those that took up to Advanced Math?(Answer: “yes”)

Some Secondary Questions• What percentage of our applicants take a senior year

math class, and does it make a difference in preparation?

• Are students doing better in math (meeting the ELM requirement) because they are moving onward from Algebra 2, or are students moving past Algebra 2 because they are doing better in math?

• Is “Statistics” as good as “Advanced math”?• Are other variables like gender, ethnicity, GPA,

geographic origin, factors in college readiness?• Is there a course sequence that’s “the best” for college

preparation in math?

Some Notes On Coursetaking

• 33% of U.S. students taking Precalculus or Calculus -up from 10.7% in 1982 (Planty 2007)

• Only 77% of U.S. students in 11th grade math in 2006 – (EdSource 2007)

• Only 10 states require 4 years of math (2012) • California among lowest requirements nationwide: “at

least two years…must meet or exceed to rigor of the content standards for Algebra I”(CDE 2010)

• Poorer students “attend high schools that are much less likely to offer any math above Algebra 2 than schools serving students in the upper quintiles “ (Adelman 2005)

Algebra 2in senior year 10%

Alg.II then no grade12 math

13% Algebra 2 then AP Stats3%

Algebra 2 then Stats5%

Algebra 2 then other 1%

Advanced math in senior year28%

Advanced then no grade12 math

13%

Advanced then AP Stats8%

Advanced then Sta-tistics

2%

Advanced then Other

0%Calculus

16%

What Are Our Students Taking? - nine major course sequences(CSU Chico Fall 2010 freshmen n=1755)

23% did not go past Algebra 2

“Advanced Math”: Trig, Analytic Geometry, Algebra 3, PreCalculus, Trig/PreCalc, Analysis…

27% did not take math in

grade 12

FTF 2010 Summary (All freshmen combined):

total Math Ready

Remedial % Remedial

Avg. ELM score

% Exempt

Alg. 2 in senior year 181 61 120 66.3% 40.4 12.7%

Alg.2 then no grade12 math 232 109 123 53.0% 42.5 26.7%

Alg.2 then AP Stats 44 28 16 36.4% 44 47.7%

Alg.2 then Stats 84 54 30 35.7% 45.5 41.7%

Advanced math in senior year 493 359 134 27.2% 47.8 45.8%

Advanced then no grade12 math 234 174 60 25.6% 45 55.6%

Advanced then Statistics 43 34 9 20.9% 47.4 51.2%

Advanced then AP Stats 143 130 13 9.8% 51.3 79.0%

Calculus 277 261 16 5.8% 53.4 83.8%

Alg. 2 then some other class 17 11 6 35.3% 49.1 35.3%

Advanced then Some Other Class 7 7 0 0.0% 74 85.7%

1755 1230 527 30.0% 45.2 49.9%

Nine major course sequences:

Alg. 2 in senior year

Alg.2 then no grade12 m

ath

Alg.2 then Stats

Alg.2 then A

P Stats

Adv.M

ath in senior year

Adv.M

ath then no grade12 ...

Adv.M

ath then Stats

Adv. M

ath then AP Stats

Calculus

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

33.7%47.0%

64.3% 63.6%72.8% 74.4% 79.1%

90.9% 94.2%

High School Course Sequence and Math Placement Success CSU Chico fall 2010 freshmen (n = 1755)

2 semesters remediation needed

1 semester remediation needed

Math Ready

Here’s a powerful

picture that counselors,

parents, administrators

can use

Alg. 2 in senior year

Alg.2 then no grade12 m

ath

Alg.2 then Stats

Alg.2 then A

P Stats

Adv.M

ath in senior year

Adv.M

ath then no grade12 math

Adv.M

ath then Stats

Adv. M

ath then AP Stats

Calculus

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

16.6%

17.7%

11.9% 11.4%

8.9% 8.5%9.3%

4.2%2.9%

49.7%

35.3%23.8% 25.0%

18.3% 17.1%11.6%

4.9% 2.9%

High School Course Sequence and Math Placement Success CSU Chico freshmen Fall 2010 (n = 1755)

2 semesters remedia-tion needed

1 semester remedia-tion needed

Passed ELM Test

Exempt EAP

Exempt SAT II

Exempt SAT

Exempt ACT

Exempt AP test

A more detailed picture including

“how” they fulfilled the ELM

requirement

Main Question

• The students whose highest class was Advanced Math placed remedial at less than half the rate of those that stopped at Algebra2.

FTF 2010 Summary (All freshmen):

Total Remedial % Remedial

95% CI for difference from highest math =Alg.2

Highest math = Alg. 2 413 243 58.8% Algebra 2 then Stats or Other 145 52 35.9% 0.1360, 0.3187 (p<0.0001)

Highest math = Advanced Math 727 194 26.7% 0.2631, 0.3778(p<0.0001)

Advanced then Stats or Other 193 22 11.4% 0.4066, 0.5373 (p< 0.0001)

Calculus 277 16 5.8% 0.4733, 0.5831 (p<0.0001)

1755 527 30.0%

Gender• Females (32.5%) significantly more remedial than males

(26.8%). Even wider gap statewide (42.7% vs. 25.4%). • More females stopping at Algebra 2. ..More males moving on

to Advanced math

FTF 2010 Summary (Male vs. Female):

Male Female % Remedial (Male)

% Remedial (Female)

p-value

Highest math = Alg. 2 158 (20.8%)

255 (25.7%)

58.2% 60.0% 0.7216

Algebra 2 then Stats or Other 56 (7.4%)

89 (9.0%)

40.4% 32.6% 0.3391

Highest math = Advanced Math 330 (43.4%)

397 (39.9%)

23.0% 29.7% 0.0422

Advanced then Stats or Other 95 (12.5%)

98 (10.6%)

9.2% 14.3% 0.2671

Calculus 122 (16.0%)

155 (15.6%)

3.3% 9.0% 0.0538

761 994 26.8% 32.5% 0.01

…yet stopping at Algebra 2 seems to

be an “equal opportunity”

condition

Where % remedial is more than twice

as much as “Advanced math”

Ethnicity• Hispanic: 31.3% remedial not significantly different from overall

(30%) or from White (27.3%). Interestingly, almost the same percentages are taking Advanced math

Big difference statewide, though. (49.4% remedial vs. 35.5% overall )

White % remedial

Hispanic % remedial

Total Freshmen F2010 984 27.3% 412 31.3%

Highest math= Alg.2 23.2% 57.9% 26.7% 55%

Highest math=Advanced 67.8% 23% 65.3% 24.5%

Again, Alg. 2 remedial is more than twice as much as “Advanced math”

Is the senior year significant?

• Students in senior year math have around 12.5% lower probability of remediation than those taking the senior year off.

• But this is not as significant as “going past Algebra2”

Took any math in senior year Total # remedial % remedial 95% CI for difference

Highest class not beyond algebra 2 181 120 66.3%

Completed a class beyond Algebra 2 1108 226 20.4% 0.3862, 0.5318

(p <0.0001)

1289 346 26.8%

No senior year mathematics

Highest Class not beyond algebra 2 232 123 53.0%

Completed Advanced math 234 60 25.6% 0.1886, 0.3589 (p< 0.0001)

TOTALS 466 183 39.3% 0.0738, 0.1749 (p < 0.0001)

The “Algebra 2 about twice as likely to be remedial as Advanced math” is happening

Regardless of Gender, Ethnicity or “whether it’s senior year”

Consistent with previous research:

Berry, 2003 North Arkansas CollegeHoyt & Sorensen 2001, Utah Valley State College

Fong 2008, Nevada State CollegesAmerican College Testing Inc (ACT), 1993-2004 (n=81,574)

Ford 2007 (CSU Chico)

Are the students moving past Algebra 2 “already” better at math?

• Sophomores – No, not significantly better (except *)

SOPHOMORES IN ALGEBRA 2: Algebra 2 GPA

s Total remedial

% Remedial

t-test for difference

Will take no more math after Alg.2 2.558 0.63273 26 16 61.50%

Will take just Advanced math in grade 11 or 12

2.746 0.67601 216 61 28.20% P = 0.1788

Will take Advanced + more 2.780 0.71386 226 17 7.50% p = 0.1303

Will take Advanced + Calculus 2.983 0.72252 153 6 3.90% P = 0.0054 *

Will take just Stats 2.477 0.61024 24 8 33.30% P= 0.6476

Will repeat Alg. 2 then Advanced 1.599 0.93721 28 9 32.10%

Will repeat Alg. 2 then stats 1.731 0.76762 8 4 50.00%

Will repeat Algebra 2 then no math 1.664 0.71594 28 7 25.00%

TOTAL 702

Here are 88 students with a lower average grade, yet still moved on and were less remedial

We need to encourage

lower performing students to keep going

These 26 students stopped math in Grade

10?? We could discourage this

Are the students moving past Algebra 2 “already” better at math?

• Grade 11 : Yes, the students that move on from Algebra 2 do have a significantly higher grade average than those that do not move on.

JUNIORS IN ALGEBRA 2:

Will take no more math after Alg.2 2.512 0.44531 159 88 55.35%

Will take Advanced in Grade 12 2.865 0.49077 343 98 28.57% P < 0.0001*

Will take Stats in Grade 12 2.672 0.39837 102 38 37.25% P = 0.0035*

Will repeat Alg. 2 in grade 12 1.546 0.73272 65 41 63.08%

TOTAL 669

SOPHOMORES IN ALGEBRA 2: Algebra 2 GPA

s Total remedial

% Remedial

t-test for difference

Are the students moving past Algebra 2 “already” better at math?• From Grade 10, the ones moving past Algebra 2 are not

significantly “smarter” on average.• In fact, many lower performing 10th graders that did move

on ended up better prepared• From Grade 11, the ones moving on past Algebra 2 are

already higher performing on average.• But what would happen if those lower performing juniors

were still encouraged to move on?Of 60 seniors that earned below C average in 12th grade Advanced math, only 38.3% placed remedial.

Those that didn’t move on from Algebra 2: 53% remedial Advanced math was hard, but it helped

FTF 2010 Summary (All freshmen combined): total % Remedial

95% CI for difference from highest math =Alg.2

p-value

Highest Class = Algebra 2 413 243(58.8%)

Alg.2 then AP Stats 44 16 (36.4%)7.24% - 37.24% 0.0047

Alg.2 then Stats 84 30 (35.7%)12.01% - 34.57% 0.0001

Advanced Math in senior year 493 134 (27.2%)25.26% - 37.58% <0.0001

Advanced then no grade12 math 234 60 (25.6%)25.7% - 40.3% <0.0001

Advanced then Statistics 43 9 (20.9%)23.11% - 50.19% <0.0001

Advanced then AP Stats 143 13 (9.8%)43.77% - 56.77% <0.0001

Calculus 277 16 (5.8%)47.31% - 58.33% <0.0001

Is “Statistics” as good as “Advanced math”?

• Coming from Algebra 2, math readiness significantly improved (though not as much as Advanced math).

• Stats and AP Stats show about the same result (≈23% improvement from taking nothing after Algebra 2)

Advanced + AP Stats is a potent course sequence (thanks to ELM exemption granted by AP Exam)

Repeating Algebra 2

• Good, if it’s in Grade 11 only 26.7% ended up remedial, even when taking no math in

grade 12 They did significantly better than classmates taking Alg2 for first

time and then no grade 12 math (55.4% remedial)

• But 62.8% of those repeating Algebra 2 in grade 12 still ended up remedial.

• Not significantly better than classmates taking Alg2 for first time in grade 12 (69.6% remedial)

Results Summary

1. For students stopping at Algebra 2, remediation is twice as likely as for those taking Advanced math - regardless of gender, ethnicity, geographic origin. Remediation likelihood decreases for each additional math class past Alg. 2

2. Females need remediation more than males, especially the ones from our local area.

3. Ethnicity seems to make a difference. Hispanics small difference, Hmong big difference

4. A Senior year math class is associated with a 12.5% decrease in remediation; but that is not as powerful an indicator as “going past Algebra 2”.

5. Statistics and AP Statistics have about the same association: both associated with reduction in remediation, but not as well as Advanced math

6. The juniors that move onward past Algebra 2 are higher performing students; for sophomores, the evidence is not as strong

What Can We Take Away From This?Students that are “on schedule” with their college prep mathematics classes (students that are taking Algebra 2 by their junior year) are not “done” preparing for college with that Algebra 2 class. They need to continue on in their senior year.

CSU or UC preparedness requires successful completion of Algebra 1 in 9th grade (Alg 2 in 12th grade = not prepared)

• It’s not about “taking senior year math” – It’s about “how far have we progressed by the senior year”

Counselors Can Help with• Take math past Algebra 2: remediation is

twice as likely as those who don’t go beyond Algebra 2.

• Senior math ALWAYS better than no senior math• Even students who do poorly in Advanced math

improve their chances greatly (36% vs. 59%)• 12 graders in Algebra2: study hard, get tutoring,

test prep, ALEKS,…• Scared of Calculus? Stats/AP Stats a great option• 3-year requirement fulfilled in grade 10? Please

don’t stop there! (61% remedial for those that did)

• Keep up the good work increasing Awareness that “getting into college” is not the same as “Getting ready for college”.

• Keep up the good work increasing Awareness of college placement tests : only 40% of 11th graders knew CSU has placement tests (Conley 2005)

• Encourage, not discourage challenging courses, especially girls: Students are “discouraged” from taking challenging courses because of low expectations by teachers (Bamburg 1994, Russell 2008, Ali & Jenkins 2002)

• Please tell our high school students:

Advanced Math is not “what the smart kids do”. It’s “what you do to prepare for college”

Counselors Can Help with

4 year math requirement? - 18 states will have it in 2013

• California state standards say math “expected” up to Algebra 2, but only Algebra 1 required to graduate

• (and CSU only requires Algebra 2 for admission)• Students will respond to raised standards: 8th grade Alg.1

enrollment has increased by 41% in last 9 years (but BoE has just relaxed the 8th grade math policy ..)

• San Jose 3 year requirement: “did not lead to more dropouts but greater achievement”: A-G enrollment from 30% to 47% in ten years . 2008 EAP college ready 23% (8% above avg.)

• Students want it: 80% say “would have worked harder” had their school demanded it (Hart 2005)

• Requiring 4 years would not “force” Advanced math but “nudge toward”

The Good News: Momentum

• Math coursetaking is improving: • Algebra 2 or above enrollment (Ca.): 44% of juniors (2007)

to 51% (2011) • 33% of U.S. students taking Precalc or Calculus (up from

10.7% in 1982) – 20 states require going to at least Algebra 2

• CSU Statewide remedial: 35% (2010) 33% (2011) 30% (2012) http://www.asd.calstate.edu/performance/proficiency.shtml

• But It’s the 30% remedial we are worried about. And most of them did not take Advanced math.