TEACHING-It’s exciting!-It’s electric!But… It’s not a walk in the park!

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

Suggested personal goal for the week

• Voice a frustration…leave with a plan.• Recall your personal story… understand the impact of your

experiences.• Recall your students… use the Models to understand them and

plan an approach.• 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 Part 1

Resources for Beliefs• Meichenbaum, D. (1977) Cognitive-Behavior

Modification Chapters 4-8.• McEntire/ Kitchens (1984) A new focus for

educational improvement based in cognitive and structuring of Subconscious Personal Axioms. (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)

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-- Part 2 Approach to Thinking• Intuitive vs Logical

Right-Brained vs Left-Brained(Kitchens Mathematics: Yes You Can p.59-80)

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

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. Leron/Huzzan p.116

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)

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.

Model 1 The Failure Syndrome (Beliefs involving the past)

Experiences Beliefs Behaviors

Model 2

Study Skills (Ch.2)

Beliefs (Ch.4)

Learning Styles (Ch. 3)

Model 3

About frustrations, upsets, difficulties

Important Not important

Out of your control

In your control

Your Personal Positive Plan

Teaching is not a walk in the park.Goal:• Voice your frustration• Determine a plan based in the model(s).

Discussion Questions

• How do you use Cognitive Psychology in teaching?• What specifically do you do to make students aware…?• When do you teach the failure syndrome to students? • How do you use the power of the subconscious mind?

• Dissonance (not comfort) is more a part of successful teaching… agree/disagree• How do these three relate?• Purposeful Intent,• Affective Domain • Cognitive Domain

C O G N I T I V E

AFFECTIVE

Purposeful Intent

Why are the following important?• Do not let students convince you that they cannot do, or

that they do not care.• Communicate with each other.• Catch yourself (each other) in human nature.• Dissonance /Self –Talk.

• How do you use these to help you teach?

• Have a “modeled” way to interpret negative behavior.

Exciting Lunch Discussions (great for digestion) • Enabling: (Tuesday)• Teacher Enabling. Lynch/Hurford/Cole (given)

• Parental Enabling. Landfried (given)

• What is it?• What you do about it?• Where is it in the MODELS

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

Math Education (given)

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

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 Model(s))?

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

• What will your response to a negative classroom behavior be? (within the Model?)

Let’s start talking• What is Enabling? • What is Locus of Control?

• See you at lunch

• Thank you for your thoughts and participation.