Transcript Learning Processes National Mathematics Advisory Panel
MSP Regional Conference Learning Processes National Math Panel and Beyond
A. Wade Boykin, Ph.D.
Howard University January 6, 2009
Learning Processes
Scientific 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.
2
Learning Processes
• 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.
3 - 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
4
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.
5
Learning Processes
• 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.
8
th
Grade Mathematics 2005
2005 average main NAEP mathematics scores for eighth graders by race and parents’ highest level of education
White Black
Race
Hispanic White-Black White-Hispanic Did not finish H.S.
266 243 257 23 9
Parent Education Level
Graduated H.S.
Some Ed. After H.S.
276 288 247 259 29 17 262 271 26 17 © 2008 Capstone Institute @ Howard University Graduated College 297 260 272 37 25
12
th
Grade Mathematics 2005
2005 average main NAEP mathematics scores for twelfth graders by race and parents’ highest level of education
White Black
Race
Hispanic White-Black White-Hispanic Did not finish H.S.
280 263 277 17 *
Parent Education Level
Graduated H.S.
Some Ed. After H.S.
292 305 266 280 26 12 275 291 30 14 © 2008 Capstone Institute @ Howard University Graduated College 316 281 291 35 25
The Achievement Gap is Multi-faceted
Minority Group vs. Majority Group American Students vs. “The World” 20 th Century Preparation vs. 21 st Century Preparation
Transactional vs. Technocratic Solutions
21 st Century Outcomes First Order Learning Outcomes K & S Accumulation Long Term Retention Retrieval Mechanisms Higher Order Learning Outcomes Knowledge Transfer Knowledge Production & Application Knowledge Reflection & Judgment Knowledge Communication
D e v e l o p m e n t P r o f e s s l i o n a Transactional Strategies General Scheme Guiding Functions Engagement 3D Gap Closing Outcomes
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 than non-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
Multiple Representations
1/3+1/3= 2/3 1/3 + 1/3 One third plus one third equals two thirds .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)
Enabling Learning Goals
Mastery Performance Goals Goals Emotional Tone Peer Relationships Perceived Academic Efficacy .49
-.35
-.31
Disruptive Behavior -.41
Significant Regression Coefficients
Kaplan & Maehr (1999)
Classroom Collaboration
Collaboration and collaborative learning Student accountability, ownership and responsibility Student voice and choice Inclusiveness
Collaborative Activities
Numbered 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: PHONE: FAX: EMAIL: WEBSITE: CAPSTONE Institute Howard University Holy Cross Hall, Room 427 2900 Van Ness Street, N.W.
Washington, D.C. 20008 202/806-8484 202/806-8498
www. capstoneinstitute.org
The Tricky Road from Research to Practice
Socially Complex Realities of the Classroom Capacity Building Considerations Filtering through Beliefs and Ideologies
Elaboration Exhibit 7.2 Guides for Thought-Provoking Questions
Generic Question
What is another example of …?
What would happen if …?
What are the strengths and weaknesses of …?
Specific Thinking Skill Induced
Application Prediction; hypothesizing Analysis; inference What is the difference between … and …?
Do you agree or disagree with …? Support your answer evidence Compare-contrast Evaluation and identifying
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?
TSRQ When You Work Really Hard In School, Which of the Following Reasons Are Most Important To You My Teachers Encourage Me To Work Hard The Teacher Demands It Blk Percentages Wht Hisp Asn 47% 15% 31% 41% 31% 29% 19% 20% Ferguson (2003)
Posttest Performance -Learning Condition by Ethnicity Interaction 11 10 9 8 7 6 5 4 3 2 1 0 9.63
6.72
C African American
C=
C
ommunal study condition G= Inter-
G
roup Competition study condition I =
I
nterpersonal Competition study condition
8.46
G 7 6.41
I 10.19
European American
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