Mathematics Courses for Overview of Current...

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1 1/22/08 ME.ET Project 1 Mathematics Courses for Elementary Teachers: An Overview of Current Research Projects AMTE Annual Conference Tulsa, OK • January 24, 2008 1/22/08 ME.ET Project 2 1/22/08 ME.ET Project 3 Participants What we are measuring: Yaa Cole, LMT Project, University of Michigan Projects using LMT measures: Lou Ann Lovin, James Madison Unversity Meg Moss, Pellissippi State Technical Community College Stephanie Smith, Georgia State University Beth Costner & Frank Pullano, Winthrop University Raven McCrory, Michigan State University DIscussion: Sybilla Beckmann, University of Georgia 1/22/08 ME.ET Project 4 Overview What have we learned about what these students (future elementary teachers) are learning in their undergraduate mathematics classes? What matters? What works? What do we wish we knew? AMTE2008 -- Session January 24, 2008 Mathematics Courses for Elementary Teachers: An Overview of Current Research Projects 1

Transcript of Mathematics Courses for Overview of Current...

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1/22/08 ME.ET Project 1

Mathematics Courses forElementary Teachers: An

Overview of Current ResearchProjects

AMTE Annual ConferenceTulsa, OK • January 24, 2008

1/22/08 ME.ET Project 2

1/22/08 ME.ET Project 3

Participants

• What we are measuring: Yaa Cole, LMT Project,University of Michigan

• Projects using LMT measures:– Lou Ann Lovin, James Madison Unversity– Meg Moss, Pellissippi State Technical Community College– Stephanie Smith, Georgia State University– Beth Costner & Frank Pullano, Winthrop University– Raven McCrory, Michigan State University

• DIscussion: Sybilla Beckmann, University of Georgia1/22/08 ME.ET Project 4

Overview

• What have we learned about whatthese students (future elementaryteachers) are learning in theirundergraduate mathematics classes?

• What matters? What works?• What do we wish we knew?

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The Learning Mathematics forTeaching (LMT) Instruments

Heather HillHarvard University

Yaa Cole, Hyman Bass, Laurie Sleep,Deborah Loewenberg Ball

University of Michigan

AMTE Annual ConferenceTulsa, OK • January 24, 2008

35x25

Knowing multiplication:

Multiply:

Student A Student B Student C

x

3

2

5

5 x

3

2

5

5 x

3

2

5

5

+

1

7

2

5

5

+

1

7

7

0

5

0 1

2

5

5

0

875

+

1

6

0

0

0

0

875

875

Which of these students is using a method thatcould be used to multiply any two whole numbers?

Knowing multiplication for teaching Learning Mathematics for Teaching(LMT) Instruments

Multiple-choice math tests for teachers inspecific content domains (number/operations,algebra, geometry)

But not typical mathematics tests• Composed of items meant to represent

problems that occur in teaching

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Representing operations

Which model cannot beused to show that1 1/2 x 2/3 = 1?

Constructs represented

Content knowledge• Common• Specialized

Knowledge ofcontent and students

Number/operations Patterns, functions

and algebra Geometry Probability/statistics

Validation efforts

Practicing teacher MKT scores linked to studentgains• Better performance = higher student gains

Practicing teacher MKT scores linked to themathematical quality of their classroom instruction(r=.77)

Responses on items match teacher thinking aboutitems in cognitive interviews

Content matching to NCTM standards within strand

Uses• Evaluating professional development• Evaluating pre-service teacher preparation

programs

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Mathematical Knowledge for Teaching ofProspective Elementary Teachers:

James Madison University

LouAnn [email protected]

James Madison University

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Brief Program DescriptionIDLS MajorCandidates choose between 2 concentrations:

Mathematics/Science Humanities/Social Science

Emphasis is(supposed to be)unpackingschoolmathematics

Required Mathematics Courses•MATH 107

Number, Number Systems, Operations , Algebra

•MATH 108Number con’t , Geometry

•MATH 207Probability, Statistics

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Additional mathematics courses formathematics/science concentration: Algebra, Analysis, Geometry, Statistics Courses not taken by mathematics majors

Mathematics Methods Courses•ELED 433 and ELED 533 (PreK-6)

• Two mathematics methods course• 433: Number and Operations, Algebra, Geometry• 533: Geometry (con’t), Probability, Statistics

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Overview of Study

Using the LMT measures we are examiningelementary teachers’ performance at our institutionby Examining assessment data at different points in the

program; Comparing the math/science elementary teacher

candidates’ performance with that of the humanities/socialscience elementary teacher candidates.

Comparing the elementary teacher candidates’performance with that of beginning mathematics majors.

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DevelopingMathematical Knowledge for Teaching:

Two Camps

Camp A Teachers need to know

mathematics of the schoolcurriculum in depth;

Courses that treat advancedmathematics are useless toteaching.

Camp B Teachers need to know

more than they areresponsible for teaching;

Advanced mathematicsstudy is important to beingable to have perspectiveand make good judgments.

Ball, D. (2002). What do we believe about teacher learning? Proceedings of the Twenty-Fourth Annual Meeting of the Psychology of Mathematics Education-North AmericanChapter, Vol. 1, (pp. 3-19). Athens, GA.

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Points of Assessment

For elementary candidates At beginning of first mathematics course, MATH 107 At end of last required mathematics course, MATH 207 At end of mathematics methods course, ELED 433

(PreK-6)For mathematics majors At beginning of MATH 235 (Calculus I)

MATH 107

MATH 235

MATH 108 MATH 207 ELED 433

Freshman Sophomore Senior

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Elementary Teacher Candidates andMathematics Majors – Fall 2006

Methods and235 > 107

Methods>207235>207

Methods = 235

All Others >107Methods>207

235>207Methods = 235

All Others > 107Methods>207

235>207Methods = 235

All Others > 107Methods>207

235>207Methods = 235

Post HocResults

p<0.000p<0.000p<0.000p<0.000sig

59.84%69.23%62.50%63.83%Math 235

57.03%70.94%66.89%65.43%Methods

48.75%60.52%53.70%54.43%Math 207

48.26%54.53%50.95%52.19%Math 107

Patterns,Functions, &

AlgebraGeometryNumbers &Operations

Total Score(Correct %)

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Differences betweenMathematics/Science vs. Humanities/Social Science

Math 107 (N = 465, Fall 2004-Fall 2006)

Math 207 (N = 270 Fall 2005-Fall 2006)

p< 0.001p< 0.016p< 0.001p< 0.000sig

44.31%52.90%48.50%49.55%Hum

50.15%55.96%53.88%54.40%M/S

Patterns,Functions, &

AlgebraGeometryNumbers &Operations

Total Score(% Correct)

p< 0.002p< 0.005p< 0.001p< 0.000sig

48.06%63.01%56.01%55.98%Hum

54.29%68.04%62.32%61.87%M/S

Patterns,Functions, &

AlgebraGeometryNumbers &Operations

Total Score(% Correct)

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Discussion Significant growth from MATH 107 to MATH 207 across all

subscores for all candidates.

Less growth in Patterns, Functions, and Algebra.

Math/Science concentrations start and end by performing significantlybetter than Humanities concentrations.

Beginning math majors performed significantly better than combinedmath/sci, humanities MATH 107 and MATH 207.

It appears that the mathematics methods course matters! Significant growth from MATH 207 to ELED 433 across all subscores for

all candidates. After the methods course, the elementary candidates are performing

about the same as beginning math majors.10

The growth (or lack of growth) is more apparentin particular kinds of items.

Performance on items evaluating students’alternative methods does not improve overall,although on some items there is some evidencethat they begin to move away from evaluating thework as incorrect if the student did not use astandard algorithm.

Little emphases on analyzing student work inELED 433 this particular semester.

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Sample Response Analysis(Difficult Items – Evaluating Student Work)

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

A B C D E

Response

Percent Math 107

Math 207

Methods

Math 235

a. Method was wrong, even though answer is right.b. Answer is wrongc. Method is right, but would be messyd. Method only works sometimese. Not sure

c

CorrectResponse

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Sample Response Analysis(Difficult Items – Evaluating Student Work)

a. Made a mistake and then tried to compensateb. Used an easy number and then dealt with other numbersc. Made a mistake with the standard procedured. Added ten to both numbers, then subtracted (Describes what student did)e. Not sure

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

A B C D E

Response

Percent Math 107

Math 207

Methods

Math 235

CorrectResponse

d

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Implications Develop openness to alternative methods

Increase focus on analysis of student work in content and methods Fall 2007: 3 sections of ELED 433 on a continuum Concurrent mathematics education seminar with the mathematics courses

Increased emphasis on Patterns, Function, and Algebra Supplement with Navigations

Any mathematics course for prospective elementary teachers? Data at end of mathematics major, end of secondary math methods course in

graduate year. Because teachers need to have fluency with MKT, especially SKC, is there a

difference in response time on particular items between the elementarycandidates and math majors?

Data at end of 2nd elementary math methods course in graduate year.

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Specialized Understanding of

Mathematics: A Study of

Prospective ElementaryProspective Elementary

Teachers

Meg MossMeg Moss

Research QuestionsResearch Questions

1) What are the areas of strength and areas of weakness i th t t k l d f t hi th ti fin the content knowledge for teaching mathematics ofprospective elementary teachers as they enter their mathematics methods course?

2) Does a relationship exist between quantity or type of content courses and the CKTM of prospective elementary teachers?elementary teachers?

3) Does the CKTM change as prospective elementary t h t k th i th d ?teachers take their methods course?

Description of SampleDescription of Sample

• Four universities seven sitesFour universities, seven sites

• n=244 pretest, n=221 posttest

St d t ll d i l t• Students enrolled in elementary

mathematics teaching methods course

Measures and VariablesMeasures and Variables

• Content Knowledge for Teaching Mathematics –Content Knowledge for Teaching Mathematics

measures developed by Learning Math for

Teaching/ Study for Instructional Improvement

P j t th h Th U i it f Mi hiProject through The University of Michigan

• Number and Operation Content Knowledge (NOCK)

C C t t K l d– Common Content Knowledge

– Specialized Content Knowledge – representing

mathematical ideas providing explanationsmathematical ideas, providing explanations,

analyzing alternate algorithms

• Geometry Content Knowledgey g

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MethodologyMethodology

• Question 1: What are the areas ofQuestion 1: What are the areas of

strength and what are the areas of

weakness in the CKTM as prospectiveweakness in the CKTM as prospective

elementary teachers enter their methods

course?course?

– Pretest item analysis

MethodologyMethodology

Question 2: Does a relationship existQuestion 2: Does a relationship exist

between quantity or type of content

courses and the CKTM of prospectivecourses and the CKTM of prospective

elementary teachers?

Analysis of relationship between content– Analysis of relationship between content

courses and content understanding

MethodologyMethodology

Question 3: Growth during MethodsQuestion 3: Growth during Methods

Course?

Pretest during first two weeks of semester– Pretest during first two weeks of semester,

posttest during last two weeks of semester

– Paired Samples t-testPaired Samples t test

– Item analysis of items that saw growth

Data Analysis and FindingsData Analysis and Findings

• Question 1: What are the areas ofQuestion 1: What are the areas ofstrength and what are the areas of weakness in CKTM as prospectivep pelementary teachers enter their methods course?

Conducted an item analysis on 11 items with highest number of correct answers

d 11 it ith l t b fand 11 items with lowest number ofcorrect answers

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Areas of StrengthAreas of Strength

• Six items from NOCKSix items from NOCK

– Five of these common content knowledge

One was specialized content knowledge– One was specialized content knowledge –

representing fraction subtraction

• Five items from Geometry• Five items from Geometry

– Analyze characteristics of two and three

dimensional shapesdimensional shapes

– Interpreting definitions of three dimensional

shapesshapes

Areas of WeaknessAreas of Weakness

• NOCK – 9 itemsNOCK 9 items

– One was common content knowledge –xy

– Eight were specialized content knowledgeEight were specialized content knowledge• Providing mathematical explanations (3)

• Representing mathematical ideas (2)

• Interpreting non-standard algorithms (3)

• Geometry – 2 items

– Relationship between area and pi

– Effects of changing one dimension on the area volume and surface areaarea, volume and surface area

Question 2: Relationship between

i t t d CKTMprevious content courses and CKTM• Previous content courses

• Do students who take math for teachers I

and II score differently than those who do y

not? Yes p=.008, effect size .40

Group Statistics

186 .0940932 .97198252 .07126922

58 -.3017472 1.03697867 .13616197

yesnoelemmath

1.00

.00

Zscore(scorepre) score1

N Mean Std. Deviation Std. Error Mean

Independent Samples Test

F Si

Levene's Test for Equality

of Variances

df Si (2 il d)

Mean

Diff

Std. Error

Diff L U

95% Confidence Interval

of the Difference

t-test for Equality of Means

.102 .750 2.665 242 .008 .39584039 .14853857 .10324686 .68843391

2.576 90.419 .012 .39584039 .15368599 .09053562 .70114515

Equal variances assumed

Equal variances not assumed

Zscore(scorepre) score1

F Sig. t df Sig. (2-tailed) Difference Difference Lower Upper

NOCK IndicatorsNOCK Indicators

• Do students who take Math for Teachers IDo students who take Math for Teachers I

score differently on the NOCK items?

No p= 182No p=.182Group Statistics

197 0418017 96957948 06907968

mathteachI

1Zscore(scoreNOCK)

N Mean Std. Deviation Std. Error Mean

197 .0418017 .96957948 .06907968

47 -.1752112 1.11273633 .16230927

1

0

Zscore(scoreNOCK)

Independent Samples Test

.629 .429 1.339 242 .182 .21701288 .16207106 -.10223715 .53626290Equal variances assumedZscore(scoreNOCK)

F Sig.

Levene's Test for Equality

of Variances

t df Sig. (2-tailed)

Mean

Difference

Std. Error

Difference Lower Upper

95% Confidence Interval

of the Difference

t-test for Equality of Means

1.230 63.684 .223 .21701288 .17639814 -.13541661 .56944237Equal variances not assumed

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Geometry IndicatorsGeometry Indicators

• Do students who take Math for Teachers IIDo students who take Math for Teachers II

score differently on Geometry items?

Yes p= 017 effect size 38Yes, p=.017, effect size .38Group Statistics

mathteachII N Mean Std. Deviation Std. Error Mean

196 .0751715 .98262659 .07018761

48 -.3069501 1.02195829 .14750697

mathteachII

1

0

Zscore(scoregeo)

N Mean Std. Deviation Std. Error Mean

Independent Samples Test

Levene's Test for Equality

of Variances

Mean Std. Error

95% Confidence Interval

of the Difference

t-test for Equality of Means

.160 .690 2.396 242 .017 .38212159 .15949661 .06794275 .69630043

2.339 69.829 .022 .38212159 .16335424 .05630781 .70793538

Equal variances assumed

Equal variances not assumed

Zscore(scoregeo)

F Sig. t df Sig. (2-tailed) Difference Difference Lower Upper

Quantity or TypeQuantity or Type

• Do students who take a higher number ofDo students who take a higher number of

content courses score differently? No, p=.138Descriptive Statistics

Between-Subjects Factors

<= 2 99

3 - 3 87

1

2

totalmath

(Banded)

Value Label N

Dependent Variable: Zscore(scorepre) score1

-.0909223 1.03805914 99

-.0468434 .91190588 87

.2254600 1.04231224 58

totalmath (Banded)

<= 2

3 - 3

4+

Mean Std. Deviation N

4+ 583.2254600 1.04231224 58

.0000000 1.00000000 244

4+

Total

Tests of Between-Subjects Effects

Dependent Variable: Zscore(scorepre) score1

3.958a 2 1.979 1.995 .138

.198 1 .198 .200 .655

3.958 2 1.979 1.995 .138

Source

Corrected Model

Intercept

bandtotmath

Type III Sum

of Squares df Mean Square F Sig.

239.042 241 .992

243.000 244

243.000 243

Error

Total

Corrected Total

R Squared = .016 (Adjusted R Squared = .008)a.

Question 2: Growth during Methods

C ?Course?

• Statistically significant growth was foundStatistically significant growth was found

• Growth equivalent to about one item out of

48 p = 015 effect size = 12348, p = .015, effect size = .123

Paired Samples TestPaired Samples Test

95% Confidence Interval

of the Difference

Paired Differences

.12610642 .76641272 .05155450 .22771032 .02450253 -2.446 220 .015Zscore: score1 - standzpPair 1

Mean Std. DeviationStd. Error Mean Lower Upper t df Sig. (2-tailed)

Items with largest growthItems with largest growth

• Four of the items that showed the mostFour of the items that showed the mostimprovement were from the geometry content area

• Four were from the number and operation content area

• Of the four number and operation items that showed the most improvement, three pof those were from the specialized content knowledge domain.

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Special ThanksSpecial Thanks

• Dr P Mark Taylor Committee ChairDr. P. Mark Taylor, Committee Chair

• The Appalachian Math and Science

Partnership an NSF funded projectPartnership, an NSF funded project

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The Impact of a DevelopmentalTeacher Preparation Program onElementary Preservice Teachers’

Mathematics Beliefs and Knowledge

Stephanie Smithwith acknowlegment to

Susan SwarsMarvin Smith (Kennesaw State)

Lynn Hart

Background of Study

• Mathematics Endorsement ResearchProject (MERP) is the outcome of arecently mandated four-coursemathematics sequence

• Longitudinal, comparative studies thatexamine the mathematics beliefs andknowledge of elementary preserviceteachers

Three Study Phases• Baseline study of 2-semester math methods

sequence, with a 3-course math contentrequirement (2 journal articles)

• Comparative study of exchanging 2nd semesterof math methods for a reorganized 4-coursecontent requirement (in progress)

• Extension study of 1 cohort in 4 experimentalmath content courses—focused onunderstanding content, children’s thinking, andelementary curriculum in number, geometry,algebra, and data analysis (in progress)

Theoretical Perspectives

• Research has established a robustrelationship between beliefs and teachingpractices (Romberg & Carpenter, 1986;Thompson, 1992; Wilson & Cooney, 2002)

• Focus on impact of methods course(s) isprimarily on change in beliefs

• Focus on impact of content courses is onchange in knowledge for teaching andchange in beliefs

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Theoretical Perspectives

Teacher efficacy is considered by manyresearchers to be a two-dimensionalconstruct Personal teaching efficacy Teaching outcome expectancy

Theoretical Perspectives

• Teacher change model: Generate interest in change Problematize current practices and propose

possible solutions Experiment with possible solutions Reflect on the outcomes for students and

teachers(Smith, Smith, & Williams, 2005)

• To propose and experiment with possiblesolutions involves beliefs and PCK

Theoretical Perspectives

• Increasing literature on the importance ofelementary teachers having highly developed,specialized content knowledge for teachingmathematics (Ball, 1991; Ma, 1999)

• Components of this specialized contentknowledge include generating representations,interpreting student work, and analyzing studentmistakes (Hill, Schilling, & Ball, 2004)

Phase 1 Research Questions

• What are the changes in elementary preserviceteachers’ mathematics beliefs during adevelopmental teacher preparation program thatincludes a two-semester mathematics methodssequence?

• What is the relationship between elementarypreservice teachers’ mathematics beliefs andtheir specialized content knowledge for teachingmathematics at the end of a developmentalteacher preparation program?

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Phase 1 Setting and Participants

• 24 elementary preservice teachers• Enrolled in a Bachelor of Science program

at a large urban university• Teacher preparation program has a

developmental model for field placements• Completed a two-semester sequence of

mathematics methods courses– First semester focus PK-2– Second semester focus 3-5

Phase 1 Mixed Methods Data• Mathematics Teaching Efficacy Beliefs

(PMTE+MTOE), administered four times (seeEnochs, Smith, & Huinker, 2000)

• Mathematics Beliefs Instrument (MBI),administered four times (derived from Peterson,Fennema, Carpenter, & Loef, 1989)

• Learning Mathematics for Teaching Instrument(LMT), administered one time at end of program(see Hill, Schilling, & Ball, 2004)

• Interview Protocol, one time at end of 2nd mathmethods course)

Quantitative Results

• Significant increases in mathematicsteaching efficacy beliefs and significantshifts in pedagogical beliefs towardcognitive perspective during the program

• Cognitively-oriented pedagogical beliefs(MBI) increased significantly after the firstmethods course; slight decrease after thesecond methods course was notsignificant; decrease after studentteaching was small but significant

Quantitative Results

• Teaching efficacy (PMTE) scores largelychanged after the second methodscourse; mean remained constant afterstudent teaching

• Outcome expectancy (MTOE) scoresincreased after first and second methodscourses; mean decreased slightly afterstudent teaching

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Additional Quantitative Results

• MARS (Mathematics Anxiety RatingScale), see Richardson & Suinn, 1972– 98-item instrument (Initial, Post1, Post 2)– Anxiety scores changed inversely to PMTE– Discontinued this measure for methods

courses; reinstated for Phase 3 (experimentalcontent courses)

Quantitative Results

1

2

3

4

5

Initial Post 1 Post 2 Final

PMTE

MTOE

MBI

MARS

Score Correlations

• No relationship between teaching efficacy,outcome expectancy, and pedagogicalbeliefs at the beginning of the firstmethods course

• Significant relationships between all threeat the end of the second course andbetween teaching efficacy andpedagogical beliefs at the end of studentteaching

LMT Results

• Significant correlation between teachingefficacy, cognitively-oriented pedagogicalbeliefs, and LMT scores at the end of theteacher preparation program

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Qualitative Results ExplainConverging Teaching Efficacy

Profile 3

Profile 1

Profile 2

Teaching Efficacy B

eliefs

Start of Math Methods Courses End of Program

Phase 1: Conclusions

• Two-methods-course developmentalprogram produced more cognitivelyoriented beliefs and increased confidence.

• As these preservice teachers studied,experimented with, and reflected on waysto implement standards-based pedagogy,most became more confident in theirabilities to teach mathematics effectively.

Phase 1: Conclusions

• At the end of the program, the correlationbetween knowledge of mathematics forteaching (LMT), personal teaching efficacybeliefs (PMTE), and cognitively-orientedpedagogical beliefs (MBI) shows thecomplexity and interrelatedness of thesevarious aspects of teachers’ beliefs andknowledge.

Phase 1: Conclusions

• As students developed theirunderstanding of the mathematical contentknowledge needed to teach in theelementary grades they became betterable to understand and embrace morecognitively-oriented pedagogy and moreconfident in their skills and abilities toteach mathematics effectively. Thissupports content courses focused onunderstanding mathematics needed forteaching.

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Phase 1: Conclusions

• The timing of these effects varied acrossthe semesters of the program– Focus of methods course semesters– Focus of developmental field placements– Effects of traditional student teaching

• Value of longitudinal study: observe timingand persistence of changes

• Value of interviews: disclose diverseprofiles of change hidden withinquantitative means

Phase 1: Conclusions

• LMT provides a useful measure of contentknowledge for teaching and a connectionbetween changes in beliefs and changesin content knowledge for our continuingMERP studies

Phase 3: Course Content

• Typical emphasis on elementary/middle contentin number, geometry/spatial sense,probability/statistics, and algebraic concepts

• Experimental cohort emphasizes understandingcontent in the context of worthwhile tasks in theelementary curriculum as well as children’sthinking during those tasks– Children’s Mathematics: CGI– Thinking Mathematically: Integrating Arithmetic &

Algebra in Elementary School– Developing Mathematical Ideas

Contact & References

[email protected]• Swars, Smith, Smith, & Hart. (in

review). JMTE.• Swars, Hart, Smith, Smith, &

Tolar. (2007). SSM.

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The Winthrop Story

Beth Greene CostnerFrank Pullano

General Program Information

• Early Childhood (PK to 3)• Elementary (2 to 6)• Middle Level Math & Language Arts (5 to 8)• Special Education (PK to 12)• Family and Consumer Sciences

Courses

• CTQR 150: CriticalThinking & QuantitativeReasoning• General Education

Requirement• Sets (w/counting)• Logic• Probability• Statistics

• MATH 291: Basic NumberConcepts for Teachers

• Problem Solving(w/patterns)

• Basic Number &Computation

• Number Theory(primes, factors, etc.)

Courses

• MATH 292: Number,Measurement, & GeometryConcepts for Teachers

• Basic Geometry• Rational Numbers• Measurement

• MATH 393: Algebra, DataAnalysis, and GeometryConcepts for Teachers

• Required for ELEM andML only

• Proportional Reasoning• Geometry &

Measurement• Algebraic Thinking

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Common Elements inMATH Courses

• Lab Kits• Activity Supplement• Article Responses• Problem Solving• Projects• Skills Check

• Use of Standards• Course Coordinator• Billstein, Libeskind, & Lott• Coordination w/ Methods

Faculty (esp in ELEM)• Grade Requirements

Skills Check Requirements

• Given three times per semester in MATH 291, 292, & 393• Equivalent to one midterm exam grade• 30 questions• 80% correct to earn points• Mix of question types• Some common questions across courses• Review opportunities

Skills Check Topics

• Simplifying fractions• Careless mistakes• Computation

• Whole numbers• Integers• Rational numbers

• Order of operations• Percentages• Basic word problems• Using variables• Solving equations• Simplifying radicals• Measures of center

• Place value• Set operations• Subsets and elements• Interpreting graphs• LCM & GCF• Prime factorization• Basic measurement skills• Geometric terminology• Triangle theorems• Area and perimeter of

irregular figures• Decimal, fraction, and

percent relationships

MATH 291 Grades vs. MajorsMATH 291 Grades by Major

21 22 3

29

47

5

25

10

2

11

1

0%

20%

40%

60%

80%

100%

ECED ELEM SPED

Major

Per

cen

t

F

D

C

B

A

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MATH 292 Grades vs. MajorsMATH 292 Grades by Major

25 263

23

36

5

22

132

3 13

23

0%

20%

40%

60%

80%

100%

ECED ELEM SPED

Major

Per

cen

t

N

F

D

C

B

A

Grade Comparison

21816201520Increased

76442534357Unchanged

21822281824Decrease

n%n%n%

SPEDELEMECED

Course Grades vs. Skills Check

291

Grade Score

Times

to Pass

# Not

Passing

292

Grade Score

Times

to Pass

# Not

Passing

A 27.5 1.6 0 A 27.3 1.8 0

B 25.8 2.2 0 B 26.5 2.4 0

C 24.1 2.6 7 C 24.9 2.5 5

D 21.0 1.0 1 D 17.5 2.0 3

F 22.0 1 F 18.5 4

N 18.0 1.0 2

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1/22/08 ME.ET Project 5

The ME.ET Project

Mathematical Education ofElementary Teachers

Raven McCroryMichigan State University

http://meet.educ.msu.edu

This work is supported by the national Science Foundation, Grant # 0447611,Michigan State University’s College of Education, & the Center for Proficiency inTeaching Mathematics (CPTM) at the University of Michigan.

1/22/08 ME.ET Project 6

ME.ET Data

• 70 mathematics departments in 3 states• 63 instructors from 33 institutions

– 32% of instructors who received the surveyfrom 47% of institutions in the study (33 of70)

• Student data: pretest 822, posttest 783,matched pre and post (matched) 615from 36 sections of 25 instructors

1/22/08 ME.ET Project 7

Instructors

4Doctoral student1Other title5Lecturer

10Instructor15Assistant professor13Associate professor13Professor2N/A no formal rank

1/22/08 ME.ET Project 8

Instructor Knowledge

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1/22/08 ME.ET Project 9

Textbooks

• Primary resource for the class:– Billstein et al 12– Other textbook 11– Musser et al 8– Other materials (non-textbook) 8– Long 3– Wheeler 3– Bennett 2– Parker 2– Sonnabend 2– Bassarear 1

1/22/08 ME.ET Project 10

Textbook Use

1/22/08 ME.ET Project 11

Student Learning

• Objective: model student achievement• Multilevel model: student:instructor• Student level variables: demographics,

attitudes, prior knowledge (pretest andSAT)

• Instructor level variables: textbook,instructor demographics, OTLmeasures

1/22/08 ME.ET Project 12

Achievement Model

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1/22/08 ME.ET Project 13

Results

• Gain of 0.14 SD• Problems with design: Students may

not be taking the test seriously in somesections

• Predictors (controlling for pretest): SAT,“I like math.” “I am good at math.”

1/22/08 ME.ET Project 14

Test Scores

Pre/post scores by School

1/22/08 ME.ET Project 15

An idea

• Create a database of preserviceteacher responses to LMT items

• Analyze for reliability, factors• Recalculate item parameters• Include beliefs items if possible, and

look at correlations

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Mathematics Courses for Elementary TeachersComments and Discussion

Sybilla Beckmann

Department of MathematicsUniversity of Georgia

AMTE January 2008

Sybilla Beckmann (University of Georgia) Courses for Teachers 1 / 9

Which problems/activities are most important?in courses for elementary teachers

What is the importance to actual elementary school teaching ofvarious kinds of problems and activities we give in courses forelementary teachers?

Sybilla Beckmann (University of Georgia) Courses for Teachers 2 / 9

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Make-a-Ten Strategy

The make-a-ten strategy relies on breaking numbers apart andimplicitly uses the associative property of addition:

8 + 6

Sybilla Beckmann (University of Georgia) Courses for Teachers 3 / 9

Make-a-Ten Strategy

The make-a-ten strategy relies on breaking numbers apart andimplicitly uses the associative property of addition:

8 + 6

2 4

Sybilla Beckmann (University of Georgia) Courses for Teachers 4 / 9

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Make-a-Ten Strategy

The make-a-ten strategy relies on breaking numbers apart andimplicitly uses the associative property of addition:

8 + 6 = 8 + (2 + 4)

2 4

Sybilla Beckmann (University of Georgia) Courses for Teachers 5 / 9

Make-a-Ten Strategy

The make-a-ten strategy relies on breaking numbers apart andimplicitly uses the associative property of addition:

8 + 6 = 8 + (2 + 4) = (8 + 2) + 4 = 14

Sybilla Beckmann (University of Georgia) Courses for Teachers 6 / 9

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Understanding why the multiplication algorithm workswith the distributive property as well as with pictures

3×10

10×10 10×4

3×4

14×13 12 30 40 100 182

10 + 4

10

+ 3

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Decimal notation

To write a googolplex in decimal notation you would need to write a 1followed by a googol zeros.Explain why nobody could actually write a googolplex in decimalnotation.

Sybilla Beckmann (University of Georgia) Courses for Teachers 8 / 9

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Using a definition

The diagram below is a map of Mr. McGregor’s garden. Each plot inMr. McGregor’s garden has been divided into 3 pieces of equal area.The shaded parts show where lettuce has been planted. What fractionof Mr. McGregor’s garden is planted with lettuce? Using our definitionof fraction, explain clearly why your answer is correct.

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