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Transcript of Stimulating Discussion Around “What We Know” About Strengthening High School Mathematics...
Stimulating Discussion Around “What We Know” About Strengthening
High School Mathematics Programs and Outcomes
National High School Center’s Summer Institute
Breakout 5Thursday, June 19, 2008
Steven J. Leinwand
Principal Research Analyst, American Institutes for Research
Scary Perspective 1
As mathematics colonizes diverse fields, it develops dialects that diverge from the “King’s English” of functions, equations, definitions and theorems. These newly important dialects employ the language of search strategies, data structures, confidence intervals and decision trees.
- Steen
Scary Perspective 2
Evidence from a half-century of reform efforts shows that the mainstream tradition of focusing school mathematics on preparation for a calculus-based post-secondary curriculum is not capable of achieving urgent national goals and that no amount of tinkering is likely to change that in any substantial degree. - Steen
If Not Tinkering, Then Thinking Systemically:
A guiding vision of teaching and learning Adjust the curriculum – less IS more Focus on instruction Students need to grapple/struggle a little Focus on big ideas/conceptual understanding Ensure professional sharing and collegial
interaction High quality, common and aligned
assessments
From: Report on Key Practices and Policies of Consistently Higher Performing High Schools
Higher performing high schools tend to: set explicit academic goals – aligned with and often
exceeding state standards; support a culture of collaboration with focused
professional development activities; and provide teachers with the tools that will help them
meet those goals – for all students – and focus on broader learning objectives than just their own subject matter.
More Specifically: Extended class periods; Special catch-up courses; 9th grade academies; High-quality and well-defined curricula; In-service training on these curricula; Efforts to create professional learning
communities; Provide relevant data and accessible data systems; Provide targeted interventions to meet the needs of
struggling students; and Provide recognition of both teachers and students.
From Emerging Evidence on Improving High School Student Achievement and Graduation Rates
The larger lesson of this synthesis is that structural changes to promote personalization and instructional improvement are the twin pillars of high school reform.
Small learning communities and faculty advisory systems can increase students’ feelings of connectedness to their teachers.
From SREB: High Schools That Work
Key Practices: High expectations – setting and achieving
them Career/technical studies – applying the
math and science Academic studies – increasing access to
the college prep curriculum Work-based learning Teacher collaboration
SREB (continued):
Key Practices (continued): Actively engaged students; Guidance – so students don’t take the
easy way out; Extra help and time; and Keeping score for continuous
improvement and accountability.
Action Typical HS Railside HS
Lecture 21% 4%
Questioning 15% 9%
Individual Work Practicing
48%
Group Work 72%
Student Presentation 0.2% 9%
Typical High School Class: 2.5 minutes/problem 24 problems/class
Railside High School Class: 5.7 minutes/problem 16 problems/90 minute period
Jo Boaler’s Work: Multidimensional Classes
“In many classrooms there is one practice that is valued above all others – that of executing procedures (correctly and quickly). The narrowness by which success is judged means that some students rise to the top of classes, gaining good grades and teacher praise, while others sink to the bottom with most students knowing where they are in the hierarchy created. Such classrooms are unidimensional.”
Jo Boaler’s Work: Multidimensional Classes
“At Railside the teachers created multidimensional classes by valuing many dimensions of mathematical work. This was achieved, in part, by having more open problems that students could solve in different ways. The teachers valued different methods and solution paths and this enabled more students to contribute ideas and feel valued.”
When there are many ways to be successful, many more students are successful.
“When we interviewed the students and asked them “what does it take to be successful in mathematics class?” they offered many different practices such as: asking good questions, rephrasing problems, explaining well, being logical, justifying work, considering answers…
When we asked students in “traditional” classes what they needed to do in order to be successful they talked in much more narrow ways, usually saying that they needed to concentrate, and pay careful attention.”
Jo Boaler’s Work
Other characteristics at Railside: Teaching students to be responsible for
each other’s learning; High cognitive demand; Effort over ability; and Clear expectations and learning practices
In other words: instruction matters!
So, To Recapitulate, Thinking Systemically:
A guiding vision of teaching and learning Adjust the curriculum – less IS more Focus on instruction Students need to grapple/struggle a little Focus on big ideas/conceptual understanding Ensure professional sharing and collegial
interaction High quality, common and aligned
assessments
Resources
National High School Center
www.betterhighschools.org Report on Key Practices and Policies of
Consistently Higher Performing High Schools Emerging Evidence on Improving High
School Student Achievement and Graduation Rates: The Effects of Four Popular Improvement Programs
Resources
Southern Regional Education Boardwww.sreb.org
High Schools that Work project Partnership for 21st Century Skills
www.21stcenturyskills.org Results that Matter
Achieve, Inc. www.achieve.org
American Diploma Project
Resources
Jo Boaler’s Research http://www.stanford.edu/~joboaler/equitable.pdf
Horizon ResearchTitle: Status of High School Mathematics Teachinghttp://2000survey.horizon-research.com/reports/
high_math/high_math.pdf