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MAE 4326 Teaching Children MAE 4326 Teaching Children MathematicsMathematics

IntroductionsIntroductionsIntroductionsIntroductions

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How do you feel How do you feel about math?about math?

How do you feel How do you feel about math?about math?

Human LineHuman Line

The Professional Standards for Teaching

Mathematics

1. Knowledge of Mathematics and General Pedagogy

2. Knowledge of Student Mathematical Learning

3. Worthwhile Mathematical Tasks4. Learning Environment5. Discourse6. Reflection on Student Learning7. Reflection on Teaching Practice

Copyright © 2010 by Pearson Education, Inc. All rights reserved.

As you become a teacher of

mathematics you will need:

• Knowledge of mathematics• Persistence• Positive attitude• Readiness for change• Reflective disposition

Copyright © 2010 by Pearson Education, Inc. All rights reserved.

Verbs of Math• Think about what you experienced

during your elementary school math education. Make a list of verbs to describe. Try to be specific!

Traditional Views of School Mathematics

• Teacher represents the source of all that is known

• Review material from previous day• Move on to explanation of new material• Practice exercises• Lesson’s focus is primarily on getting the

answers.• Students rely on teacher to determine

whether or not their answers are correct

The Verbs of Mathematics

• Traditional– Work– Getting the Answer– Plussing– Doing Times– Listen– Copy– Memorize– Drill

• Reform – Explore– Investigate– Solve– Verify– Discover– Describe– Predict– Explain

What Does It Mean to DO MATHEMATICS?

• Engaging in the science of pattern and order

• Mastering mathematical concepts by doing NOT drilling

• Drill should NEVER come before understanding and will NEVER result in understanding

Applying Procedures

Schifter and Fosnoton the Role of

Teachers"No matter how lucidly and patiently

teachers explain to their students, they cannot understand for their students."

From D. Schifter and C. T. Fosnot, Reconstructing Mathematics Education:Stories of Teachers Meeting the Challenge of Reform (New York: Teachers College Press, 1993), p. 9.

What does this quote mean to you related to teaching mathematics?

An Environment of Doing Mathematics

• The teacher’s role is to create a spirit of inquiry, trust, and expectation where students feel comfortable taking risks

• Students are invited to do mathematics • The focus is on students actively figuring

things out, testing ideas, and making conjectures, developing reasons and offering explanation

• Students work in pairs, groups, or individually

What the Researchers said about Our Mathematics Standards

“A Mile Wide, An Inch Deep”

– For Florida’s Grades 1-7, the average number of mathematics grade level expectations (GLEs) = 83.3

– Singapore, the highest performing nation as measured by Trends in International Math and Science Study (TIMSS), has 15 GLEs per grade level

Top Achieving TIMSS Countries’ Mathematics Curriculum

s I ntended by 4 out of the 6

top- achieving countries

l I ntended by all but one of the

top- achieving countries (5 out of 6).

n I ntended by all of the top- achieving countries.

Grade

Topic 1 2 3 4 5 6 7 8 9 10 11 12

Whole Number: Meaning n n n l lWhole Number: Operations n n n n lMeasurement Units s n n n n n lCommon Fractions s n n lEquations & Formulas s l l l n n n n n nData Representation & Analysis s s l l s s s s s2-D Geometry: Basics s l l l n n l2-D Geometry: Polygons & Circles s l l n n n lMeasurement: Perimeter, Area & Volume l l l l s sRounding & Significant Figures l lEstimating Computations l l lWhole Numbers: Properties of Operations l lEstimating Quantity & Size s sDecimal Fractions l n lRelation of Common & Decimal Fractions s n lProperties of Common & Decimal Fractions l lPercentages l lProportionality Concepts l l l sProportionality Problems l l n n s s2-D Geometry: Coordinate Geometry s s l l n l lGeometry: Transformations l l l s s sNegative Numbers, I ntegers, & Their Properties s lNumber Theory l s sExponents, Roots & Radicals l l n lExponents & Orders of Magnitude s s sMeasurement: Estimation & Errors sConstructions Using Straightedge & Compass n s3-D Geometry l n n l n sGeometry: Congruence & Similarity n lRational Numbers & Their Properties s sPatterns, Relations & Functions s n n n nProportionality: Slope & Trigonometry s l lReal Numbers, Their Subsets & Properties lValidation & J ustification l n l lStructuring & Abstracting sUncertainty & Probability s n lComplex Numbers & Their Properties s sI nfinite Processes n nChange n nVectors n sSystematic Counting s s

© Center for Research in Math and Science Education, Michigan State University

Mathematics Topics Intended at Each Grade by 1989 NCTM StandardsGrade

Topic 1 2 3 4 5 6 7 8

Whole Number Meaning

Whole Number Operations

Measurement Units

Common Fractions

Equations & Formulas

Data Representation & Analysis

2-D Geometry: Basics

Polygons & Circles

Perimeter, Area & Volume

Rounding & Significant Figures

Estimating Computations

Properties of Whole Number Operations

Estimating Quantity & Size

Decimal Fractions

Relationship of Common & Decimal Fractions

Properties of Common & Decimal Fractions Percentages Proportionality Concepts Proportionality Problems 2-D Coordinate Geometry

Geometry: Transformations

Negative Numbers, Integers & Their Properties Number Theory

Exponents, Roots & Radicals Exponents & Orders of Magnitude

Measurement Estimation & Errors

Constructions w/ Straightedge & Compass

3-D Geometry

Congruence & Similarity

Rational Numbers & Their Properties Patterns, Relations & Functions

Slope & Trigonometry Number of additional topics intended by the standards

to complete the curriculum at each grade level.70 0 1 1 2 3 5

A+ Profile

Intended Topic

© Center for Research in Math and Science Education, Michigan State University

Describing the Standards

• Old Standards had an average of 83.3 Grade Level Expectations (GLEs) per grade.

• The new Standards have an average of 19 benchmarks per grade.

Describing the Standards

Grade Level Number of Old GLE’s

Number of New Benchmarks

K 67

1st 78

2nd 84

3rd 88

4th 89

5th 77

6th 78

7th 89

8th 93

Describing the Standards

Grade Level Number of Old GLE’s

Number of New Benchmarks

K 67 11

1st 78 14

2nd 84 21

3rd 88 17

4th 89 21

5th 77 23

6th 78 19

7th 89 22

8th 93 19

Mathematics Proficiency

The five process standards (NCTM, 2000):

• Problem Solving

• Reasoning and Proof

• Communication

• Connections

• Representations

The five “strands” of mathematics proficiency (NRC, 2001):

• Conceptual Understanding – comprehension of mathematical concepts, operations, and relations

• Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

• Strategic Competence – ability to formulate, represent, and solve mathematical problems

• Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification

• Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

Syllabus• Review Syllabus• Discuss Specifics• Expectations