Strategies to Increase Connectedness in Online Mathematics Courses
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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Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
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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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Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
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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.
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
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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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Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
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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
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
22
3
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
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
23
4
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
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
24
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
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
25
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
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
26
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
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
27
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
Sybilla Beckmann (University of Georgia) Courses for Teachers 7 / 9
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
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
28
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.
Sybilla Beckmann (University of Georgia) Courses for Teachers 9 / 9
AMTE2008 -- SessionJanuary 24, 2008
Mathematics Courses for Elementary Teachers:An Overview of Current Research Projects
29