TEACHING AND LEARNING.GOING BEYOND COGNITIVE CONTENT-THE AFFECTIVE DOMAIN

Dr. Anita Narvarte KitchensAppalachian State Universityanitankitchens@appstate.edu828-262-2368828-773-1536Math Education Leadership TrainingSummer 2015

Notable Failures- Larson, Milton E. (1973) “Humbling cases for career counselors,” Phi Delta Kappan, 54(6) p. 374.• Leo Tolstoy flunked out of college; Wernher von Braun flunked

ninth-grade algebra; Pasteur was rated mediocre in chemistry when he attended the Royal College; Isaac Newton did poorly in grade school, and Beethoven’s music teacher once said of him, “as a composer he is hopeless.” When Thomas Edison was a boy, his teachers told him he was too stupid to learn anything. Einstein was four years old before he could speak and seven before he could read. A newspaper editor once fired Walt Disney because “he had no good ideas.”

• Caruso’s music teacher told him, “You can’t sing. You have no voice at.

• Creative and imaginative people are often not recognized by their contemporaries. Even more often, they are not recognized in school by their teachers.

Model 2 -Solution

Study Skills (Ch.2)

Beliefs (Ch.4)

Approach to Thinking

(Ch. 3)

The Solution: Model 1 Breaking The Failure Syndrome. Discuss Beliefs-students’ teachers’ and parents’ beliefs.

Experiences Beliefs Behaviors

How do you know this works?

• Cognitive Behavior Modification. (Cognitive Restructuring)

• Recall your personal story… understand the impact of your experiences and your reaction to the experience.

• Evaluation at ASU is very strong.• Recall your students… use the Models to

understand them and plan an approach… A FIRST STEP.

• Can you change? • Can you be the catalyst in your students changing?

Activities

Today’s Agenda

• The Problem (from NCTM, from the classroom).

• The Solutions (from Psychology)• The Models – The framework for

change.

The Problem

From NCTMProfessional Standards for Teaching Mathematics (1991)

• (Among the) “ persistent obstacles to making significant changes in mathematics teaching and learning in schools (are) the beliefs and dispositions that both students and teachers bring to the mathematics classroom.”

NCTM --Societal Beliefs Principles and Standards for School Mathematics NCTM, 2000.

• “Some parents and other authority figures, as well as societal influences like the media, convey the message that not everyone is expected to be successful in mathematics …Such societal tolerance makes it less likely that all students will be motivated to sustain the effort to learn mathematics, which in turn makes the job of their teachers even more challenging.”

NCTM--Teachers – The Failure SyndromePrinciples and Standards for School Mathematics, NCTM, 2000.

•“Some teachers also believe that many students cannot learn mathematics, which supports those students in their beliefs that they cannot learn mathematics, which then leads to further disengagement. Thus, a vicious cycle takes hold.”

The Solution

• Beliefs • Approach to thinking.

• Left-Brained/Right-brained • Whole-Brained Thinking is desirable.• Too often we get “no-brained !”

Cognitive Psychology

Cognitive RestructuringRefers to “a variety of therapeutic

approaches whose major mode of action is modifying the patient’s thinking and the premises, assumptions, and attitudes underlying cognitions.” (Meichenbaum, 1977)

The Cognitive Therapist

The cognitive therapist helps the patient to identify specific misconceptions, distortions, and maladaptive attributions and to test their validity and reasonableness.

Cognitive Restructuring seeks to increase the patient’s awareness of negative self-statements and images, and thus to elicit a change in beliefs. (Meichenbaum, 1977)

The Solution–Beliefs Part 1

Resources for Beliefs• Meichenbaum, D. (1977) Cognitive-Behavior Modification.• McEntire/ Kitchens (1984) “A new focus for educational

improvement based in cognitive and other structuring of Subconscious Personal Axioms.” (given)

• Kitchens (1993) “Breaking the Failure Syndrome” (given).• Kitchens (2009). Math: Yes You Can. P. 81-116.• Kitchens/Hollar (2008) Merging Math Education with

Cognitive Restructuring.(given)• Hollar. “How’s it working for you?” (given)• Kitchens. One-sheet starter– what to give parents.

Model 2 -Solution

Study Skills (Ch.2)

Beliefs (Ch.4)

Approach to Thinking

(Ch. 3)

The Solution: Model 1 Breaking The Failure Syndrome. Discuss Beliefs-students’ teachers’ and parents’ beliefs.

Experiences Beliefs Behaviors

THE SOLUTION-- Part 2 Approach to Thinking—LB/RB.a) the teacherb) the student• Teacher Thinking– conceptual vs. procedural• Student Thinking-- Intuitive vs Logical

(Right-Brained vs Left-Brained)• Examples on the cards.

• (Kitchens Mathematics: Yes You Can p.59-80)

• S1 vs S2. Leron & Hazzan (Dual Process Theory (p.111) (given)

Examples from Algebra I

• 2324= ______• T F 2-3 = -8• Solve for x :• 2x +4 = 10• 2x + 4 = 7• -2x + 4 = -7

• Graph:• x + y = 10• 2x + 3y = 5• 2x + 3y = 7• Find 20% of 80• Find 8.3% of 9.2• (Kitchens. Yes You Can p.59)

More Examples

• A baseball bat and ball together costs one dollar and ten cents. The bat costs one dollar more than the ball. How much does the ball cost? Leron/Huzzan p.109

• Write an equation for the following: There are six times as many students as professors at this university.

Dual-Process TheoryLeron, U. and Hazzan, O., (2006) “The rationality debate: application of cognitive psychology to mathematics education”, Educational Studies in mathematics. 62: 105-126.

• P. 105..”affective and social factors are as much part of the student’s thinking and behavior as are cognitive factors.

• P.108” …mathematics education research is concerned with the relationship between the intuitive and analytical modes of thinking and behavior.

• p. 108-109.“..the quick and automatic responses of S1 and the frequent failure of the S2 to intervene in its role as critic of S1.”

• P. 113 …much effort is devoted to find cognitive interpretations for many types of behavior for which, perhaps, a different type of interpretation is more suitable….not every event in mathematics learning can be explained in cognitive terms..

• P.115 ..S1 hijacks the student’s attention too fast for S2 to act…..knowledge did not even have the chance to be expressed.

• P. 123 “…thus we suggest that the most important educational implication from our analysis is the need to train people to be aware of the way S1 and S2 operate, and to include this awareness in their problem-solving toolbox.

• P.124 If analyzing typical S1/S2 pitfalls became an inherent part of students’ problem solving sessions, they might become more successful problem solvers and decision makers.

Based in the MODELS, what specifically to do with:•Parents•Students•Self as teacher – ask … is your mindset fixed or growth

Establish your model- then interpret what you read in your model.

• Dr. Carol Dweck on Fixed vs. Growth Mindsets https://www.youtube.com/watch?v=MTsF2TaEaJA

Source: NCTM: Principles to Actions

• At the root of MINDSETS are BELIEFS– • Self-beliefs and Societal beliefs.• Direct and Indirect• First-order and Second-order Change

Your Personal Plan– take a minute to write this.• What is your “first step” in using Model 1.

Problems at school• – use MODEL 3 –How? Give examples

Model 3

About frustrations, upsets, difficulties

Important Not important

Out of your control

In your control

This week in the classroom.Memories from the past.

• Pushed beyond comfort zone—notice self-talk.• Ask or not-ask? That is the question.• Fixed Mindset? Find the belief.

• Recalling experiences from the past.• Self-memories – use techniques for change.• Student memories – red flags, think how to be

the catalyst for change. What is the first step?

More on Beliefs- How to use The Failure Syndrome• To change beliefs:

• First-Order Change/ Second -Order Change• World Beliefs / Personal Beliefs.• Teachers- hold your ground on expectations.• Understand dissonance as part of the solution.• Readiness-to-change. (student, parent and teacher)• Specifically what do you do for a student who “can’t

learn.” First Step?• Take notes as the student talks… “What’s wrong?”• Exercises into the subconscious.

C O G N I T I V E

AFFECTIVE

Summary Slide

Purposeful Intent

THE BIG UMBRELLA• Every Decision/ Every Reaction/Every Choice of

the teacher has PURPOSEFUL INTENT.• Give an example of something you do as a

teacher that has evolved accidentally, and over the years has become part of your plan.

• With every teacher reaction there is a MESSAGE SENT.• Give an example of something you have

done with students with an unintentional message sent.

Why are the following important?• Do not let students convince you that they

cannot do, or that they do not care.• Do not back down on expectations.• Communicate with each other – the whole

school unified translates to POWER.• Catch yourself (each other) in human nature.• Dissonance /Self –Talk. • Have a “modeled” approach for every behavior.

NCTM: Principles to ActionsNCTM –on beliefs.

The following slides are from: NCTM's Principles to Actionshttp://www.nctm.org/PtA/

Relate the following slides to the model.

Read “Principles to Actions” through the lens of BELIEFS.

Listen to the You-tube interview : Carol Dweck whose book is entitled MINDSET. Listen, also though the lens of BELIEFS.

(Sample slide from Principles to Action)

Quiz: (Is this) … Productive or Unproductive Belief3. Equity is the same as equality. All students need to receive the same learning

opportunities so that they can achieve the same academic outcomes.

Productive Belief or Unproductive Belief?

4. All students are capable of making sense of and persevering in solving challenging mathematics problems and should be expected to do so. Many more students, regardless of gender, ethnicity, and socioeconomic status, need to be given the support, confidence, and opportunities to reach much higher levels of mathematical success and interest.

Productive Belief or Unproductive Belief?

5. (side-stepping beliefs???)NCTM: Principles to Actions. This slide is taken from the PPT presentation “Access and Equity: Equitable

Pedagogy/” http://www.nctm.org/Conferences-and-Professional-Development/Principles-to-Actions-Toolkit/Equitable-Pedagogy/

Sample Slide

answer: Equity Is FairnessEquity does not mean that every student should receive identical instruction; instead, it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students.

Principles and Standards for School Mathematics, NCTM 2000, p. 12

Beliefs and Affect are side-stepped/ignored.

(sample) Bidirectional Relationships Support Equity

Equity is extended from a unidirectional exchange – as primarily benefitting growth of students and student groups that have historically been denied equal access, opportunity and outcomes in mathematics to a reciprocal approach.

What does this mean?

We contend that as a field we need to think of diversity as a resource for the learning of mathematics for all students. Civil, 2008

Great! But “beliefs” is the undertow… could make it impossible unless

addressed.Mention the movie Freedom Writers.

(sample) Access Supports Equity

The concept of equity includes “the equitable distribution of material and human resources, intellectually challenging curricula, educational experiences that build on students’ cultures, languages, home experiences, and identities; and pedagogies that prepare students to engage in critical thought and democratic participation in society”

Lipman, 2004, p. 3

Exciting Lunch Discussions. Keep the discussion going.• Enabling: (Tuesday)

• Teacher Enabling. Landfried (given)– examples from the group.

• Parental Enabling. Lynch/Hurford/Cole (given)

• Why does enabling make it impossible to change negative beliefs?

• How do you pre-empt enabling?• What will your school do to make parents a

part of the solution?

Lunch Discussion (Wednesday)• Beliefs• Kitchens/Hollar. (2008) Merging Cognitive

Restructuring with Math Education (given)• Give experiences from your personal schooling and discuss the impact.• Give experiences from your personal home and discuss the impact.

• Approach to Thinking • Lebron/Huzzan. Dual Process Theory (given)

Connect to student thinking, give examples from your students.

Lunch Discussion (Thursday) Can you think within the Models?• Hollar How’s it Working for you? (given)

• Kitchens Homework tips for parents (given)

• State a frustration from the classroom this week.

• State a frustration; write a plan. Demonstrate the use of the model(s) involved.

• Can you help your students (within the Models)?

• Can you help yourself? Give an example of a problem and a solution within the Model. (one thing you will try.)

• What will be your response to a negative classroom behavior?

Let’s continue talking• Take a card. Write a first step…

• See you during breaks. Call me anytime 828-773-1536.

• Thank you for your thoughts and participation.

Notable Failures- Larson, Milton E. (1973) “Humbling cases for career counselors,” Phi Delta Kappan, 54(6) p. 374.• Leo Tolstoy flunked out of college; Wernher von Braun flunked

ninth-grade algebra; Pasteur was rated mediocre in chemistry when he attended the Royal College; Isaac Newton did poorly in grade school, and Beethoven’s music teacher once said of him, “as a composer he is hopeless.” When Thomas Edison was a boy, his teachers told him he was too stupid to learn anything. Einstein was four years old before he could speak and seven before he could read. A newspaper editor once fired Walt Disney because “he had no good ideas.”

• Caruso’s music teacher told him, “You can’t sing. You have no voice at.

• Creative and imaginative people are often not recognized by their contemporaries. Even more often, they are not recognized in school by their teachers.