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.
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Alan H. Schoenfeld
University of California, Berkeley
How the Stars Should Align
Existence Proofs and Evidence
A Motivating Example
The Truth About the Math Wars
REAL progress is possible when the following are all in place:
• 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
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.
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.
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
• Collaborative scoring of student work
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.
“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”
Evidence, 5: Tests Matter! Massachusetts, & Washington) Student Achievement Study 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:
Recall the experiential goal:
T: What’s the perimeter?
S: 10x + 10
T: Where’d the 10 come from?
T: I’ll be back.
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.
- the teacher
- the mathematics
- each other.
e.g., “Motivation is the key”
“I have to teach to the tests”
Take a simple problem like 87- 24
and test kids on it.
Now, what happens when you ask: subtract 24 from 87”?
In a “low stakes” testing district, test scored dropped from 77% to 73%.
• A weather presenter.
• Weatherman (organization), a leftist organization.
• The Weather Man, a 2005 film.
• J. Walter Weatherman, inArrested 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 26x 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…
“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 University View” ?
Here’s his slide:
“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.”
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.
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.
There is a reachable goal state: systemic alignment with high quality standards.
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.