Standards, Equity,and the

Math Wars

Alan H. Schoenfeld

University of California, Berkeley

Outline:

• Equity-Related Goals• How the Stars Should Align• Existence Proofs and Evidence• A Motivating Example• Some Challenges• Some Tools• The Truth About the Math Wars

Equity-Related Goals

• Experiential: Meaningful engagement with powerful mathematics for all children.

• Content & Process: The real stuff!

• Outcomes: Performance for any demographic group looks like performance for the whole population

How the Stars Should Align

REAL progress is possible when the following are all in place:

1. Mathematically rich content and process standards;

2. Curricula aligned with those standards;

3. Assessments aligned with those standards;

4. Meaningful PD aligned with those standards;

5. Stability that allows for professional growth & change, and learning from experience.

Evidence, 1: Pittsburgh

• 40,000 students

• 97 schools

(59 el, 19 middle, 11 high, 8 other)

• 56.4% African American

• 43.6% White/Other

• 62.2% Free or reduced price lunch

Pittsburgh, Continued

A subset of Pittsburgh schools got everything lined up - the new standards-based curricula were consistent with a decade of PD in the district, etc.

A matched subset was “low compliance”: new materials on the shelves, traditional texts in use.

White students in “weak implementation” schools

African American students in “weak implementation” schools

White students in demographically similar “strong implementation” schools

African American students in demographically similar “strong implementation”schools

Percentage of 4th grade students in demographically matched“weak implementation” and “strong implementation” schools

who achieved the skills, problem solving, and concepts standard in 1998

0

10

20

30

40

50

60

70

80

SKILLS

PROBLEM SOLVING

CONCEPTS

Legend

Percentage of Students who Met or Exceeded the Standard

0

10

20

30

40

50

60

70

Year

19961997

199820001999

Skills

Concepts

Problem Solving

Grade 4 Mathematics Exam

Percentage of Students who Scored Well Below the

Standard

0

10

20

30

40

50

60

70

80

90

Year

19961997 1998 20001999

Skills

Concepts

Problem Solving

Grade 4 Mathematics Exam

Evidence, 2: The 90/90/90 Schools

The 90/90/90 Schools have the following characteristics:• More than 90 percent of the students are eligible for free and reduced lunch…• More than 90 percent of the students are from ethnic minorities.• More than 90 percent of the students met or achieved high academic standards, according to independently conducted tests of academic achievement.

Common Characteristics of the 90/90/90 Schools:

Five characteristics that were common to all 90/90/90 Schools were:• A focus on academic achievement• Clear curriculum choices• Frequent assessment of student progress

and multiple opportunities for improvement• Written responses in performance

assessments• Collaborative scoring of student work

Evidence, 3: The ARC Center Tri-State (Illinois, Massachusetts, & Washington)

Student Achievement Study

This study examined achievement test data from three states for a near census of students in schools using NSF-funded comprehensive elementary mathematics curricula… The principal finding of the study is that the students in the NSF-funded reform curricula consistently outperformed the comparison students: All significant differences favored the reform students; no significant difference favored the comparison students. This result held across all tests, all grade levels, and all strands, regardless of SES and racial/ethnic identity. The data from this study show that these curricula improve student performance in all areas of elementary mathematics, including both basic skills and higher-level processes.

Evidence, 4: Senk & Thompson on the NSF Curricula

“Students in these new curricula generally perform as well as other students on traditional measures of mathematical achievement, including computational skill, and generally do better on formal and informal assessments of conceptual understanding and ability to use mathematics to solve problems”“The curricula can indeed push students beyond the ‘basics’ to more in-depth problem-oriented mathematical thinking without jeopardizing their thinking in either area”

Broad Test

(Balanced Assessment)

Skills Test

(SAT-9)

Pass Fail

Pass 32% 28%

Fail 2% 38%

Evidence, 5: Tests Matter!

If you only test skills, you don’t find out what kids understand. Test scores misrepresent what kids

know and can do.

E.g., two tests of more than 5000 7th graders:

A Motivating Example

Recall the experiential goal:

Meaningful engagement

with

powerful mathematics

for

all children.

Imagine an algebra class..

• Students at groups in tables

• Teacher hands out problems

• At this table, one high-flying Anglo, three ESL speakers.

• Here’s the problem:

x

1

1

1

Algebra Tiles

The Task: What is the perimeter of this figure?

The teacher approaches the table.

T: What’s the perimeter?

S: 10x + 10

T: Where’d the 10 come from?

S: ACK!

T: I’ll be back.

The teacher leaves.

HS: Tell her you get 10 because when you add everything up some of the (x-1)’s cancel with the 1’s and only 10 1’s are left.

S: I don’t get it… and, you know that’s not gonna work. She’s gonna ask me more questions, and if I don’t understand I won’t be able to explain. Your job is to make sure I understand.

It works. But why?

• An interesting, accessible, and rich mathematical task

• High standards (no excuses, no letting anyone off)

• Students are accountable to:- the teacher- the mathematics- each other.

Some Challenges

• Teacher mythse.g., “Motivation is the key”

• Wrong Standards/Wrong Assessments

“I have to teach to the tests”• Lack of curricular coherence or

data at the school or district level

Motivation is not enough!

A teacher had her students do an extended project drawing up plans for their fantasy gardens…

but when all was said and done, it was indeed fair to ask,“Where’s the math”?

Drilling on Skills can give the illusion of competence.

Take a simple problem like 87 - 24

and test kids on it.

Now, what happens when you ask:

subtract 24 from 87”?

In a “high stakes” testing district, test scores plummeted from 83% to 66%.

In a “low stakes” testing district, test scored dropped from 77% to 73%.

And there are so many more challenges!

(Like, the system is incoherent, or…)

What to do, What to do?

You might want to check out

http://www.toolkitforchange.org/

(The 1st half-page of a 7-page PDF…)

The Truth About the Math Wars

(From Wikipedia): Weatherman may refer to…

• A weather presenter.

• Weatherman (organization), a leftist organization.

• The Weather Man, a 2005 film.

• J. Walter Weatherman, in Arrested Development.

• The Weathermen, a Belgium electropop band.

• The Weathermen, an Australian avant-rock duo.

• The Weathermen, American hip-hop supergroup.

• The Weatherman LP, by Dilated Peoples’ Evidence.

• Weathermen, a group of Marvel Comics characters.

• Henry Bendix, a fictional character from Wildstorm.

• The Mascot of Skyview High School, Vancouver, WA.

• A terrorist in the Seattle Math Wars.

She whizzes through the standard algorithm (SA) to compute

26 x 31 = 806,

while showing you how hard it is to use the alternative methods in reform texts. She says…

You’ve seen M. J. McDermott on YouTube…

Now, the standard algorithm seems easy once you understand place value. But some other stars show what happens if you don’t…

“Partial products work every time, but personally I get confused about which bit adds to which bit, and I’ve made mistakes in here on the addition part…”

A pause for technology at this point. See

http://www.youtube.com/watch?v=Bfq5kju627c

And what about Cliff Mass’s YouTube Video,

“Math Education:

A University View” ?

Mass says:

• “The National Research Council – the Leading provider of objective scientific information in the U.S. – established a committee to evaluate NSF-sponsored NCTM curricula.”

• “Their report On evaluating curricular effectiveness: Judging the quality of K-122 Mathematics Evaluations” was damning.”

• The committee’s finding was that There was no evidence of effectiveness of NCTM curricula.”

Here’s his slide:

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

He cites ONE study:

“But there are other objective studies that have shown the poor results of reform NCTM math.”

“A recent study published by William Hook and colleagues [Wayne Bishop and John Hook] in the peer reviewed journal Educational Studies in Mathematics demonstrated that that in California the switch from a reform math program to one reflecting the curricula of leading math nations resulted in a stunning increase in student performance.”

Here’s what the NRC report says:

The committee emphasizes that it was not charged with and therefore did not: • Evaluate the curriculum materials directly; or • Rate or rank specific curricular programs.In addressing its charge, the committee held fast to a single commitment: that our greatest contribution would be to clarify the proper elements of an array of evaluation studies designed to judge the effectiveness of mathematics curricula and clarify what standards of evidence would need to be met to draw conclusions on effectiveness. (P. 2)

The report goes on to say that a proper evaluation of a curriculum requires a wide range of studies including content analyses, comparative studies, and case studies.No single study comes close.

So, in his talk, Professor Mass:• Completely mis-states the purpose of the

NRC study, which was NOT to evaluate the “reform” curricula, but to provide a careful analytic framework for the thorough evaluation of curricula;

• Implies that one published study shows the superiority of a non-reform curriculum, when the NRC volume clearly says that single analytic studies are inadequate for such analytic purposes.

And you should remember what the overwhelming majority of studies, cited above, really says:

This raises some questions.

When instruction offers a balance of skills, concepts, and problem solving, students will do as well on tests of skills as students whose instruction focused on skills only, and they will do much better on tests of conceptual understanding and problem solving.

REAL progress is possible when the following are all in place:

1. Mathematically rich content and process standards;

2. Curricula aligned with those standards;3. Assessments aligned with those

standards;4. Meaningful PD aligned with those

standards;5. Stability that allows for professional

growth & change, and learning from experience.

In Sum:There is a reachable goal state:

systemic alignment with high qualitystandards.

There is evidence things can be done right.

There are tools for doing the job.

And most important…

There’s you, who can get it done.

Selected ReferencesARC Center. (2003). Tri-State Student Achievement Study. Lexington, MA: Arc

Center. See also <http://www.comap.com/elementary/projects/arc/index.htm>.

Reeves, D. (Ed.) (2000) Accountability in action: A blueprint for learning organizations. Denver, CO: Advanced Learning Press.

Schoenfeld, A. H. (2002, January/February). Making mathematics work for all children: Issues of standards, testing, and equity. Educational Researcher, 31(1), 13-25.

Schoenfeld, A. H. (2004). The math wars. Educational Policy, 18(1), 253-286. Schoenfeld, A. H. (2008) Problem Solving in The United States, 1970-2007:

Research and Theory, Practice and Politics. In: G. Törner, A. H. Schoenfeld, & K. Reiss (Eds.). Problem Solving Around the World – Summing up the State of the Art. Special issue of the Zentralblatt für Didaktik der Mathematik.

Senk, S., & Thompson, D. (Eds.). (2003). Standards-oriented school mathematics curricula: What does the research say about student outcomes? Mahwah, NJ: Erlbaum.