Welcome!Welcome!Welcome!Welcome!
MAE 4326 Teaching Children MAE 4326 Teaching Children MathematicsMathematics
IntroductionsIntroductionsIntroductionsIntroductions
TP TP
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