Professional Development by Curriculum Differences on Student Achievement in Algebra and Number

1
Professional Development by Curriculum
Differences on Student Achievement in Algebra and
Number

• Mary Margaret Capraro
• Victor Willson
• Robert M. Capraro
• Gerald Kulm
• Texas A M University
• NCTM 06

2
Ineffective Mathematics PDs

• Short duration PD afforded little opportunity to
• Connect to student performance
• Learn pedagogy or content
• Network with others
• Spend time in leadership roles
• (Cohen Hill, 2000 Garat et al., 2001)

3
Effective Mathematics PDs

• Web-based PDs allowed for
• Consistent opportunities for reflection
• Shortened cycle for training (Schotsberger, 2001)
• Sustained Interaction PDs Effective
• Dual emphasis on content and pedagogy
• Support from school districts
• Interaction between Ts and PD provider(Ross,
  McDougall, Hogaboam, 2002)
• PDs provided by former teachers
• Actually taught the material
• Emphasis on certain materials/skip others
• (Cwikla, 2002 Langrell, Stafford,
  Scranyon, 2002)

4
PD that Supports School Mathematics Reform

• Be sustained and intensive
• Be informed about what we know about how people
  learn
• Center around teaching and learning not
  abstractions and generalities
• Foster collaboration
• Offer a rich set of diverse experiences
• (Borasi Fonzi, 2002)

5
Further findings from NSF Monograph on Effective
PD

• Engage Ts in mathematical experiences as learners
• Teachers analyze in-depth exemplars and/or
  student work
• Use cases as catalyst for reflection
• Support Ts as they engage in instructional
  innovation
• Empowering teachers to make sense of information
• (Borasi Fonzi, 2002)

6
Meta-Analysis of PD

• 1,027 mathematics and science teachers
• effective professional developments (PDs) focused
  on
• content knowledge
• provided time for active engagement
• fostered connections to state and district
  standards
• demonstrated coherence to other learning
  activities (Garat, Porter, Desimone, Birman,
  Yoon, 2001 2003).

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Meta Analysis cont.

• Professional development is likely to be of
  higher quality when it is both sustained and
  comprehensive.
• Teachers who participate in such PD have
  improved skills that translate to a more
  Positive influence on changing teacher practice
  
• (Garat, Porter, Desimone, Birman, and Yoon,
  2001, p. 934).

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Sample/Time Period

• Sample - Number
• 1350 students
• 25 teachers (TX/DE)
• Sample - Algebra
• 1200 student
• 26 teachers (TX/DE)
• Data Collected (Pre/Post)
• First wave 2002 -2003
• Second Wave 2003 - 2004

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Instrumentation

• Tests (Number Algebra)
• Theoretical structure was developed
• Number- fractions, decimals, and percents
• Algebra - change of one variable as another
  changes
• Curriculum
• Connected Mathematics (Dale Seymour)
• Mathematics Applications and Connections
  (Glencoe/McGraw Hill)
• Mathematics in Context (Encyclopedia Britannica)
• Middle Grades MathThematics (McDougal Littell)

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Teacher PD

• Length varied from 0 to 12 days -mainly summer
  but there was follow-up contact during fall
  spring
• Topics
• Effective instructional procedures
• Questioning techniques
• Representation of mathematical concepts
• Interpretation of student responses for
  misconceptions

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Special Features of PD

• Opportunities to view videotapes of their classes
• Focused on a specific criteria for improvements
• Viewed tapes individually and in dyads
• Second group became an experimental group with
  respect to time

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Research Methodology

• Multilevel GLM (Raudenbush Bryk, 2002
• First level - repeated factor for test for each
  student
• Inservice Hours and Curriculum effects at 2nd
  level (teachers) used to indicate change in slope
  and Post-test mean
• MPLUS 3.11 (Muthen Muthen, 2004)

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MULTILEVEL MODEL - ALGEBRA
POST
BETWEEN
CURRICULUM
INSERVICE HOURS
SLOPE
GRADE
WITHIN
POST
PRE
slope
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RESULTS - ALGEBRA
Average cluster size 42.667 Estimated
Intraclass Correlations for the Y Variables
Intraclass Intraclass
Intraclass Variable Correlation
Variable Correlation Variable Correlation
POST 0.084

• Number of clusters 21
• Size (s) Cluster ID with Size s
• 14 42
• 19 17 110
• 21 25
• 22 97
• 25 99
• 28 100
• 31 101
• 38 10
• 39 87
• 40 88
• 44 16
• 50 102 5
• 51 69
• 52 24
• 57 103

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RESULTS ALGEBRA

• MODEL RESULTS
• Estimates S.E.
  Est./S.E. PROBABILITY
• Within Level
• Residual Variances
• POST 19.407 1.421
  13.653 plt .001

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RESULTS ALGEBRA

• MODEL RESULTS
• Estimates S.E.
  Est./S.E. PROBABILITY NOTE
• Between Level
• S ON
• ISHRS 0.044 0.022
  1.989 Plt .025 IS PREDICTS GAINS
• CURR -0.046 0.110
  -0.422 ns
• POST ON
• ISHRS -0.573 0.148
  -3.869 plt .001
• CURR -0.529 0.811
  -0.652 ns
• Intercepts
• POST 10.829 1.629
  6.647 plt .001
• S 0.310 0.159
  1.943 plt .025
• Residual Variances
• POST 0.664 0.523
  1.270 ns
• S 0.022 0.018
  1.176 ns

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GAIN SCORE MODEL- ALGEBRA

• Evaluate gain scores as functions of in-service
  hours and curriculum
• Evaluates rate of gain as a function of
  in-service hours and curriculum

18
MULTILEVEL MODEL- ALGEBRA
GAIN
BETWEEN
CURRICULUM
INSERVICE HOURS
SLOPE
GRADE
WITHIN
GAIN
PRE
slope
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RESULTS OF GAIN SCORE ANALYSIS - ALGEBRA

• MODEL RESULTS
• Estimates S.E.
  Est./S.E. PROBABILITY
• Within Level
• Residual Variances
• GAIN 19.456 1.517
  12.826 p lt .001

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RESULTS OF GAIN SCORE ANALYSIS- ALGEBRA

• MODEL RESULTS
• Estimates S.E.
  Est./S.E. PROBABILITY
• Between Level
• S1 ON
• ISHRS 0.058 0.022
  2.696 p lt .01
• CURR -0.017 0.114
  -0.152 ns
• GAIN ON
• S1 -17.022 4.206
  -4.047 p lt .001
• Intercepts
• GAIN 1.686 1.767
  0.954 ns
• S1 -0.783 0.218
  -3.596 p lt .001
• Residual Variances
• GAIN 2.047 1.420
  1.442 ns
• S1 0.028 0.038
  0.745 ns

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RESULTS - ALGEBRA

• In-service hours predicted rate of gain
  independent of student knowledge.

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RESULTS ALGEBRA BY CURRICULUM
MIC and CMP classes started high, no significant
gains due to inservice, while MTh and Eclectic
classes started low, gained
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RESULTS ALGEBRA BY CURRICULUM
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Educational Significance

• Greater PD improved student performance equally
  across curricula for some teachers
• Greater PD increased the rate of gain of students
• Has not previously been considered systematically
  in the mathematics education literature.

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References

• Borasi, R., Fonzi, J. (2002). Professional
  development that supports school mathematics
  reform. Foundations (NSF Monograph), 3, 1-130.
• Cohen, D. K., Hill, H. C. (2000). Instructional
  policy and classroom performance The mathematics
  reform in California. Teachers College Record,
  102(2), 294-343.
• Cwikla, J. (2002). Mathematics teachers' report
  about the influence of various professional
  development activities. Professional Educator,
  24(2), 75-94.
• Desimone Laura, Garet, M. S., Birman, B. F.,
  Porter, A., Yoon, K. S. (2003). Improving
  teachers' in-service professional development in
  mathematics and science The role of
  postsecondary institutions. Educational Policy,
  17(5), 613-649.
• Garet, M. S., Porter, A. C., Desimone, L.,
  Birman, B. F., Yoon, K. S. (2001). What makes
  professional development effective? results from
  a national sample of teachers. American
  Educational Research Journal, 38(4), 915-945.

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• Graham, K. J., Fennell, F. (. (2001).
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• Smallwaters Corp. (2004). AMOS 5.0. Chicago
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