MSP Regional ConferenceMSP Regional ConferenceLearning ProcessesLearning Processes
National Math Panel and BeyondNational Math Panel and Beyond
A. Wade Boykin, Ph.D.Howard UniversityJanuary 6, 2009
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Learning ProcessesScientific Knowledge on Learning and Cognition Needs to be Applied to the Classroom to Improve Student Achievement:
• Most children develop considerable knowledge of mathematics before they begin kindergarten.
• Children from families with low incomes, low levels of parental education, and single parents often have less mathematical knowledge when they begin school than do children from more advantaged backgrounds. This can hinder their learning for years to come.
• There are promising interventions to improve the mathematical knowledge of these young children before they enter kindergarten.
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• To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, factual knowledge and problem solving skills.
• Limitations in the ability to keep many things in mind (working-memory) can hinder mathematics performance.
- Practice can offset this through automatic recall, which results in less information to keep in mind and frees attention for new aspects of material at hand.
- Learning is most effective when practice is combined with instruction on related concepts.
- Conceptual understanding promotes transfer of learning to new problems and better long-term retention.
Learning Processes
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Learning Processes
Children’s goals and beliefs about learning are related to their mathematics performance.
• Children’s beliefs about the relative importance of effort and ability can be changed.
• Experiential studies have demonstrated that changing children’s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes.
• Engagement and sense of efficacy for Black and Hispanic students can be increased in mathematical learning contexts.
• Teachers and other educational leaders should consistently help students and parents understand that an increased emphasis on the importance of effort is related to improved mathematics grades.
Learning Processes
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8th Grade Mathematics 2005
2005 average main NAEP mathematics scores for eighth graders by race and parents’ highest level of education
RaceParent Education Level
Did not finish H.S.
Graduated H.S. Some Ed. After H.S.
Graduated College
White 266 276 288 297Black 243 247 262 260Hispanic 257 259 271 272White-Black 23 29 26 37White-Hispanic 9 17 17 25
© 2008 Capstone Institute @ Howard University
12th Grade Mathematics 2005
2005 average main NAEP mathematics scores for twelfth graders by race and parents’ highest level of education
RaceParent Education Level
Did not finish H.S.
Graduated H.S. Some Ed. After H.S.
Graduated College
White 280 292 305 316Black 263 266 275 281Hispanic 277 280 291 291White-Black 17 26 30 35White-Hispanic * 12 14 25
© 2008 Capstone Institute @ Howard University
The Achievement Gap is Multi-faceted
Minority Group vs. Majority Group
American Students vs. “The World”
20th Century Preparation vs. 21st Century Preparation
Transactional vs. Technocratic
Solutions
K & S Accumulation
Long Term Retention
Retrieval Mechanisms
First Order Learning Outcomes
Knowledge Transfer
Knowledge Production & Application
Knowledge Reflection &
Judgment
Knowledge Communication
Higher Order Learning Outcomes
21st Century Outcomes
3D Gap Closing
Outcomes
EngagementGuiding Functions
TransactionalStrategies
Professional
Development
General Scheme
Engagement as a Precursor to Achievement
Behavioral
Affective
Cognitive
Guiding Functions
Self-Efficacy(Confidence that one can do what it takes
to accomplish the desired outcome)
Self-Regulated Learning(Planning, monitoring & assessing ones own
learning)
Belief Change(From Smartness as Fixed to Smartness as
Incremental)
Borman & Overman (2004)
Resilient Students are higher thannon-Resilient students in terms of:
More positive attitudes toward school Engagement (Teacher Rating) Efficacy
Strategy Types that Impact Guiding Functions, Engagement, and Math
Achievement
Information Processing Quality Classroom Interpersonal Relationship
Quality Enabling Learning Goals Classroom Collaboration Meaningful Learning (Individual,
Social, Cultural)
Information Processing Quality
Cognitive Load Reduction
Elaboration
Schema Based Instruction
Multiple Representations
1/3+1/3= 2/3
1/3 + 1/3
One third plus one third equals two thirds
Multiple Representations
.33
+ .33
.66
TSRQ Elements
Caring (Genuine) Empathy Affective Support Instructional Support Encouraging the Best Holding Optimistic view of
student(s) Non-Patronizing
Ways That Teachers Convey Differential Achievement Expectations to Students
Teacher calls on low expectation (LE) students less often than
high expectation students (HE)
Teacher likely to give less praise and more criticism for failure to
LE students
Teacher shows less acceptance and use of ideas put forth by LE
students
Teacher provides briefer and less informative feedback to
questions raised by LE students
Teacher gives LE students less benefit of the doubt
Wait time before teacher provides an answer is less for low
expectation (LE) students
Teacher more likely to give low expectation (LE) students the
answers, while more likely to give high expectation (HE) students
clues or to rephrase a given question
Adapted from Good (1987) & Ferguson
(1998)
Kaplan & Maehr (1999)
Goals Goals
Emotional Tone -.35
Peer Relationships -.31
Perceived Academic Efficacy .49
Disruptive Behavior -.41
Significant Regression Coefficients
Mastery Performance
Enabling Learning Goals
Collaboration and collaborative learning
Student accountability, ownership and
responsibility
Student voice and choice
Inclusiveness
Classroom Collaboration
Collaborative ActivitiesNumbered Heads Together
Students with mixed abilities are place in groups of four and randomly assigned numbers. While in groups students are given problems or questions to solve or answer. They are given time to “put their heads together” to reach a correct response. By randomly calling out numbers each group member is prompted to insure that all members are knowledgeable of the appropriate response. When certain numbered group members respond correctly, the whole group receives positive recognition.
Meaningful Learning
Relevance
Personal Connections
World Connections
Subject Matter Connections
Importance
Prior Knowledge, Competences and Understanding
PERSONALIZATION EXAMPLE
There are 3 objects. Each is cut in one-half. In all, how many pieces would there be? ABSTRACT
Billy had 3 candy bars. He cut each one of them in half. In all, how many pieces of candy bar did Billy have? CONCRETE
Joseph's teacher, Mrs, Williams, surprised him on December 15 when she presented Joseph with 3 Hershey Bars, Joseph cut each one of them in one-half so that he could share the birthday gift with his friends. In all, how many pieces of Hershey Bars did Joseph have for his friends? PERSONALIZED
Cultural Resources
Family, peer, community socialization
Traditions, rituals and practices
Fundamental core values
Culturally salient learning structures
Popular culture
Some Policy Implications
Top Down Support for Bottom Up Reform Focus More So On Transactional Solutions
(Immediate Context Matters) School Organization to Support
Achievement of Classroom Goals Invest in Human Capacity Building
Teachers as Adult Learners 3 Dimensional Leadership Parents/Community as Informed Advocates
Shift the Paradigm
Teacher Capacity Development
Ongoing Support (Coaching, Demonstrations, Constructive Feedback)
Learning Communities Practice Reflection Effective Use of Planning Time Asset-Based Focus Teacher Belief Change Content Focus
FOR MORE INFORMATION
ADDRESS: CAPSTONE InstituteHoward UniversityHoly Cross Hall, Room 4272900 Van Ness Street, N.W.Washington, D.C. 20008
PHONE: 202/806-8484 FAX: 202/806-8498 EMAIL: [email protected]
WEBSITE: www. capstoneinstitute.org
The Tricky Road from Research to Practice
Socially Complex Realities of the Classroom
Capacity Building Considerations
Filtering through Beliefs and Ideologies
ElaborationExhibit 7.2 Guides for Thought-Provoking
Questions
Generic Question Specific Thinking Skill Induced
What is another example of …? Application
What would happen if …? Prediction; hypothesizing
What are the strengths and weaknesses of …? Analysis; inference
What is the difference between … and …? Compare-contrast
Do you agree or disagree with …? Support your answer Evaluation and identifying evidence
Source: King, 1994, p.24. Reprinted by permission of Jossey-Bass, a Wiley company
Arithmetic Word Problem Structures
Change-Andy had five marbles. Then he gave three marbles to Nick. How many marbles does Andy have now?
Combine-Andy has two marbles. Nick has three marbles. How many marbles do they have altogether?
Compare-Nick has five marbles. Andy has two marbles. How many more marbles does Nick have than Andy?
Equalize-Nick has five marbles. Andy has two marbles. How many marbles does Andy have to buy to have as many marbles as Nick?
When You Work Really Hard In School, Which of the Following Reasons Are Most
Important To You
Percentages
Blk Wht Hisp Asn
My Teachers Encourage Me 47% 31% 41% 31%To Work Hard
The Teacher 15% 29% 19% 20% Demands It Ferguson (2003)
TSRQ
6.41
8.469.6310.19
76.72
0123456789
1011
C G I
African American European AmericanC= Communal study conditionG= Inter-Group Competition study conditionI = Interpersonal Competition study condition
Posttest Performance -Learning Condition by Ethnicity Interaction
SUPER SCHOOLS!!
Low Student and Staff Turnover
Multidimensional Leadership
Continuous Commitment to Improvement
Multiple Stakeholder Involvement
Education of the Whole Child
Shifting the Schooling Paradigm
Evidence Based Activities Optimizing Transactions Whole Child Continuous Improvement Multiple Success Pathways Asset Focus
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