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: jlee@capstoneinstitute.org

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

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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