impacting change: the leader's role in student-centered mathematics instruction copyright ©...
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Copyright © 2015 American Institutes for Research. All rights reserved.
Impacting Change: The Leader's Role in Student-Centered Mathematics Instruction
Illinois Center for School Improvement Research ForumFebruary 19, 2015
Kirk Walters, Principal Researcher, AIR
1. Why bother studying this topic?
2. Are we making any progress?– A look at one study
3. Where should we go next?– A look at one promising improvement model
Goals
Why bother studying student centered math teaching?
Some people say this is the main reason: – https://vimeo.com/117345678?from=outro-embed
The 21st century economy rewards people who can solve complex problems creatively and collaboratively.
Why bother?
This message has been shared widely by others:
Making It in America In the past decade, the flow of goods emerging from U.S. factories has risen by about a third. Factory employment has fallen by roughly the same fraction…
Why bother?
Including education reformers:
“I cannot teach anybody anything. I can only make them think.”
Socrates
Why bother?
“Any fact, whether of arithmetic, or geography, or grammar, which is not led up to and into out of something which has previously occupied a significant position in the child's life for its own sake, is forced into this position.”
John Dewey
Why bother?
“Students should become confident in their ability to do mathematics, become mathematical problem solvers, and learn to communicate and reason mathematically.”
NCTM (1989)
Why bother?
“Students should become confident in their ability to do mathematics, become mathematical problem solvers, and learn to communicate and reason mathematically.”
NRC (2001)
Why bother?
“Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution...”
CCSS (2010)
Why bother?
Ok, now we’re a little more serious.
Why bother?
Now that we’re serious…Would you say the glass is half full or half empty?
More challenging standards, but limited resources.
Half empty?
Some reforms fail because they are too ambitious, ignoring real classroom constraints.
A good read
Inside Teaching , Mary Kennedy
Half empty?
We’re still not sure what types of instructional practices are most effective in achieving better outcomes for students on more rigorous assessments.
Half empty?
Public and political backlash.
Over 1,000,000 YouTube views
Half empty?
From your experience, what are the key barriers to successfully implementing reforms that involve complex forms of instruction?
Half empty?
High-quality instructional resources:
Or is it half full?
Improved information sharing technologies:
Half full?
Emerging research on benefits of “deeper learning.” Two AIR studies:
Hewlett Foundation: http://www.air.org/project/study-deeper-learning-opportunities-and-outcomes
Nellie Mae Foundation: http://www.air.org/resource/close-look-student-centered-math-teaching
Half full?
A new study about student-centered math teaching
Student-centered instruction is…
a broad construct
considered promising
not well understood
perhaps less pervasive at h.s. level
Why this study?
Focus on highly-regarded teachers, to create a fair contrast of instructional styles.
Include qualitative and quantitative data, from teachers and students.
Attend to cognitive and non-cognitive outcomes.
Design
Strong reputations of helping students succeed.
Maintained supportive learning environments.
Had different types of math teaching approaches.
Confirmed by referrals, interviews, observations
Highly-Regarded Teachers
1. What are different ways in which highly regarded high school mathematics teachers implement student-centered instructional practices?– Role of teaching philosophy and instructional
environment. – Student perceptions of different types of approaches.
Research Questions
2. Are there differences in student engagement and problem-solving skills that are associated with the degree to which student-centered instructional practices are implemented?
Research Questions
Mixed methods design: 22 highly-regarded teachers in New England and New York.
Case study (7 teachers) RQ1.
Quantitative study (7 case study teachers + 15 non-case study teachers) RQ2.
Design
Among study’s 22 teachers, 11 were initially identified as more traditional and 11 as more student-centered.
Sample MORE MORE TRADITIONAL STUD-CENTERED
CASE NON- STUDY CASE STUDY
Most of these teachers had11+ years of experience (70%) and were female (75%).
About ½ taught in rural schools, ¼ urban and ¼ suburban schools.
Sample
Any burning questions about the study design?
Questions
Think of a memorable high school math class or teacher…
What stands out?
Can you describe any features of the learning environment?
Do you remember how you felt about learning the material?
Turn back the clock
When I asked her to describe what makes a good math teacher…
(She said she didn’t like math as a student but thought it was more her fault than her teachers)
Here’s what my Uber driver said yesterday…
Cab ride 2-18-15.m4a
Focus on features of student-centered instruction in mathematics.
General student-centered classroom environment features held constant.
Study framework
Classroom EnvironmentSupportive Learning Environment• Respectful• Strong relationships• Focus on the individual –
scaffolding, differentiation and choice
Mathematics InstructionMeaningful Engagement with Mathematics• Use mathematical reasoning to
understand the “why” as well as the “how”
• Communicate mathematical thinking and critique the reasoning of others
• Make connections between and among mathematical concepts and real-world contexts
• Engage and persevere in solving mathematical problems that extend beyond rote application of procedures
Use mathematical reasoning to understand the “why” as well as the “how.”
Meaningful engagement with mathematics
Communicate mathematical thinking and critique the reasoning of others.
Meaningful engagement with mathematics
Make connections between and among mathematical concepts and real-world contexts.
Meaningful engagement with mathematics
Engage and persevere in solving mathematical problems that extend beyond rote application of procedures.
Meaningful engagement with mathematics
RQ 1: Case study data sourcesSource Nature of DataInstructional logs
Instructional practices implemented throughout a week of instruction
Classroom videos
Instructional practices implemented in lessons where a new mathematics concept is introduced
Teacher interview
Perceptions of teaching context, philosophy mathematics teaching and learning, instructional practices, and challenges
Student focus groups
Perceptions of their experiences in math class and factors contributing to success in math
Development of new mathematics: time is spent fully developing a new mathematics concept, relationship, rule or procedure.
Reinforcement of mathematics learning: opportunity for students to strengthen understanding or skill.
Two common approaches to math instruction
Teacher-guided with some student contribution.
Teacher-guided with strong student contribution.
Active student exploration.
Development of new mathematics
Teacher guides the development by focusing on the conceptual underpinnings, making connections to students lives, and posing low-level questions.
Teacher-guided with some student contribution
Teacher guides the development by presenting student with a series of mini-explorations and provides opportunities for students to share their thinking.
Teacher-guided with strong student contribution
Teacher engages students in a carefully designed exploration where students work together to reason about and develop the new mathematical ideas.
Exploration, with strong student contribution
Observed differences in mathematics problems offered to students and mathematical communication around those problems.
Reinforcement of mathematics
Solve by substitution:
Rote application problem
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Problem that involves critical thinking and communication
Faced with the system of equations shown here, two students, Lincoln and Claire, both decided to use the substitution method to find the solution(s).
There are errors in the work of both Lincoln and Clare, but one of them was “lucky” and got the correct solution.
a. What are the errors in each case?b. Which student got the correct solution?
How do you know?
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Teacher: What multiplies to 8? 1 times 8 and 2 times 4, right? So, if I go with 2 times 4, which one of those is the square?
Student: Four.
Teacher: So that’s the one I can square root. When I square root that four, what does it become?
Student: Two.
Teacher: Good…and then what’s left inside still.
Highly scaffolded communication
Teacher: OK, interesting! Joan, did you add your variables?
Student: I don’t know what to put for x.
Teacher: Well, apparently there is not agreement. What you think is best, and we’ll have a discussion about that. So, I’m seeing a lot that look alike, but Jonas and Mike, yours looks different. What do you guys want to say about that?
Student: (We put the) hip angle on the x-axis and the height on the y.
Teacher: What was your reasoning behind that?
Student: The height doesn’t depend on the hip angle. The hip angle depends on the height.
Allowing students to reason and persevere
Student-centered instructional tasks…Focus on the “why” as well as the “how.”
Allow for multiple entry points and solution methods.
Challenge students to look for patterns, make conjectures, examine connections among concepts, and justify solutions.
Make explicit the connections between mathematics and real-life experiences.
Encourage use of tools, including technology, to explore mathematics and solve problems.
Communication in student-centered classrooms…Focus on the “why” as well as the “how.”
Encourage students to justify and explain their solution strategies and critique the reasoning of others.
Support students in advancing their thinking as they engage in productive struggle with mathematics.
Elicit and make connections between different mathematical ideas/approaches to same problem.
Encourage use of tools, including technology, to explore mathematics and solve problems.
Teachers who were more strongly student centered…
Believed in the importance of these approaches for supporting success in mathematics
Worked in schools that prepare students for a variety of life pathways
Had flexibility in lesson design
Had access to instructional resources that emphasize these approaches
Philosophy & context
Students appreciate teachers who …Are organized
Go out of their way to support student success
Help them to develop confidence in mathematics
Students in more student-centered classrooms…
Find the content meaningful and interesting
Begin to like mathematics
Student Perspectives
RQ 2: Quantitative data sourcesSource Nature of Data
Challenging assignments
Examples of most challenging assignment offered to target class over a specified period of time
Teacher survey Frequency of instructional practices implemented with target class
Student survey Perceptions of their school and their experiences in the target math class
Math problem-solving test
Publicly released items from PISA, an international assessment given to 15- and 16-year-old students
Created independent measure of student-centered instruction.
Composite: teacher survey items + challenging assignments
Analytic approach
Created dependent measures of math problem solving skills and student engagement.
Math problem solving skills: 9 public-release items from 2009 PISA; reliability = 0.76
Student engagement: student survey items
Analytic approach
Sample problem solving itemEXCHANGE RATE
Mei-Ling found out that the exchange rate between Singapore dollars (SGD) and South African rand (ZAR) was 1 SGD = 4.2 ZAR. Mei-Ling changed 3,000 Singapore dollars into South African rand at this exchange rate.
HOW MUCH MONEY IN SOUTH AFRICAN RAND DID MEI-LING GET?
On returning to Singapore after three months, Mei-Ling had 3,900 ZAR left. She changed this back to Singapore dollars, noting that the exchange rate had changed to 1 SGD = 4.0 ZAR. How much money in Singapore dollars did Mei-Ling get?
During these three months, the exchange rate had changed from 4.2 to 4.0 ZAR per SGD. Was it in Mei-Ling’s favor that the exchange rate now was 4.0 ZAR instead of 4.2 ZAR, when she changed her South African rand back to Singapore dollars? Give an explanation to support your answer.
Students in more student-centered math classrooms reported higher levels of engagement, compared to students in less student-centered math classrooms.
Results
Our measure of engagement included two constructs:
Students’ self-assessment of learning (e.g., “this math class really makes me think”)
Students’ interest/motivation (e.g., “in this math class, sometimes I get so interested in my work I don’t want to stop”)
Results
Students in all study classrooms performed well above the U.S. average on each item in study’s problem solving assessment.
Results
Students in more student-centered math classrooms showed higher growth in problem-solving skills, compared to students in less student-centered classrooms.
Statistically significant difference in a value-added model
Study not designed to measure magnitude of difference
Results
ImplicationsMultiple-entry points for teachers who want to become more student-centered, but may not know where to start.
More research needed to understand why and how teachers implement student-centered approaches in different contexts.
ImplicationsStudy measures of student centered learning need to be validated with other groups of teachers and students.
ImplicationsDo any of these findings have implications for your work?
If so, what are they?
What next?Continuous improvement research methods promising way to understand contextual factors in real classrooms.
New project seeks to build on study findings to learn from network of practitioners.
Network improvement community (NIC)Practitioners & researchers working side by side, solving common problems of practice.
Common, practical measures needed to assess progress in real-world classroom settings.Bryk, A. S., Yeager, D., Muhich, J., Hausman, H., & Morales, L. (2013). Practical measurement. Stanford, CA: Carnegie Foundation for the Advancement of Teaching.
A continuous R&D approach for a NIC
PDSA guiding questionsHow do we understand the problem?
What are we trying to accomplish?
What changes can be introduced towards these ends?
How will we know if these changes are an improvement? Bryk, A.S., Gomez, L., & Grunow, A. (2011). Getting ideas into action: Building networked improvement communities in education. Stanford, CA: Carnegie Foundation for the Advancement of Teaching.
Long-term effects of PDSA cyclesOver time, challenging problems of practice are solved incrementally and collaboratively.
Challenges are realSpecifying common problems to solve.
Availability of good, practical measures for assessing progress.
Incentives and supports for participation—it can’t be a significant “add on.”
Opportunities are great
Challenges
West Virginia
Chicago
Maine
Connections to your workHow do you incorporate continuous improvement principles into your work?
What are the barriers and enablers to doing this work well?
