Work of the TNE Mathematics Group at Michigan State University

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Work of the TNEMathematics Group at Michigan
State University
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TNE Mathematics Group

• Faculty Mike Battista, Sharon Senk, Sandra
  Crespo, Dick Hill, Gail Burrill, Anna Sfard, Mary
  Winter, Dennis Gilliland, Vince Melfi, Jeanne
  Wald, Joan Ferrini-Mundy, Helen Featherstone,
  Sandy Wilcox, Karen King, Mike Frazier
• Faculty Doing Work Connected to TNE
  MathematicsRaven McCrory, Natasha Speer
• Graduate Students
• Aaron Brakoniecki, Dong-Joon Kim, Aaron Mosier,
  Ji-Won Son

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Units Involved in TNE Mathematics Collaborations

• Teacher Education
• Mathematics
• Statistics
• Division of Science and Mathematics Education
  (DSME)

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Major TNE Mathematics Activities

• Standards Development
• Course Development
• Self Studies

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Standards to Guide Faculty and Programs
(www.tne.msu.edu/)

• STANDARD 1Mathematical Knowledge for Teaching
• STANDARD 2Knowing and Investigating How Students
  Learn Mathematics
• STANDARD 3Knowledge of Teaching Mathematics

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Course Development

• Statistics course for future elementary (K-8)
  teachers
• Capstone course for secondary (7-12) math majors
• Complex instruction in elementary mathematics
  education course
• Mathematics minor for future elementary teachers
  (Math. Dept. initiative)

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Self Studies

• University study of MTH 201/202
• Secondary mathematics capstone course (in
  progress)

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Investigating Preservice Elementary Teachers
Understanding of Mathematics and Students
Mathematical Thinking
Research Team Michael Battista, Teacher
Education Aaron Brakoniecki, DSME Sandra
Crespo, Teacher Education Michael Frazier,
Mathematics, (now at University of
Tennessee) Dong-Joong Kim, Mathematics Aaron
Mosier, DSME Sharon Senk, Mathematics
DSME Ji-Won Son, Teacher Education
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Research Question

• What do prospective elementary teachers learn
  about mathematics and students mathematical
  thinking in their mathematics and mathematics
  education courses at MSU?
• Two content domains
• Numbers and operations (preliminary report today)
• Geometry and measurement (data not yet analyzed)

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Opportunities to Learn Mathematics for Teaching
at MSU
Prerequisite College Algebra
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Design of Study

• Cross-sectional Data Collection

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Instruments Used

• Extended written tasks Whole numbers and
  fractions
• Completed in-class
• MATH post-test tasks embedded in final exam
• In all other cases, tasks did not count as part
  of course grade
• In both high-stakes and low-stakes situations,
  instructor observation suggests all tests were
  taken seriously

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Coding and Scoring

• Scoring rubrics developed iteratively by an
  interdisciplinary research team consisting of
  faculty and graduate students from the
  Departments of Mathematics and Teacher Education.
• Maximum number of points varied per task

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Detailed Look at Two Problems

• Whole Numbers
• There are 4
• We discuss Item W1
• Fractions
• There are 5
• We discuss Item F4

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Whole Number Problem W1

• Imagine that one of your students shows you the
  following strategy for subtracting whole numbers
• 37
• - 19
• - 2
• 20
• 18
• W1a. Do you think that this strategy will work
  for any two whole numbers?
• Yes No I don't know
• W1b. How do you think the student would use this
  strategy on the problem below?
• 423
• 167
• Adapted from Ball Hill (2002). Cultivating
  knowledge for teaching mathematics Early fall
  survey. Cultivating Teachers Knowledge for
  Teaching Mathematics Study. Ann Arbor, University
  of Michigan

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Types of Responses for W1b
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Types of Responses for W1b
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• To compare performance across problems a
  standardized measure was computed
• Difficulty Index mean / (max. no. of points)
• Index ranges from 0 to 1.
• 0 means nobody got the problem correct
• 1 means everybody got the problem correct.

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Numeric Score Summary for W1
W1a. Do you think that this strategy will work
for any two whole numbers?
W1b. How do you think the student would use this
strategy on the problem below? 423 167
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Fraction Problem - F4

• Suppose that one serving of rice is two-thirds of
  a cup.
• How many servings are in 4 cups of rice?
• (a) Show how to solve this problem by drawing a
  diagram.
• (b) Show how to solve this problem by calculating
  the value of a numerical expression.
• Adapted from Beckmann, S. (2002 ).
  Mathematics for Elementary Teachers Volume I
  Numbers and Operations Preliminary Edition (with
  Activities Manual). Addison Wesley.

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Rubric for Problem F4a
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Example Student Representations
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Rubric for Problem F4b
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Numeric Scores for F4
F4. Suppose that one serving of rice is
two-thirds of a cup. How many servings are in 4
cups of rice? (a) Show how to solve this problem
by drawing a diagram. (b) Show how to solve this
problem by calculating the value of a numerical
expression.
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Summary of Overall Results
expressed as a
Table of
Note Percentages are based on 3 whole number and
2 fraction items that have been analyzed, so far.
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Conclusions

• Performance of MATH students improved
  dramatically during the semester. Levels of
  performance on fraction tasks, in particular, are
  considerably higher than that of elementary
  teachers involved in other studies, e.g. Ma
  (1999).
• On the pretests, MATH-ED-S students outperformed
  the MATH students, suggesting that preservice
  teachers retain some knowledge gained in MATH
  courses.
• On the posttests, MATH students outperformed
  MATH-ED-S students, suggesting that preservice
  teachers do not retain all the knowledge and
  understanding gained in previous courses and
  tested by these tasks.

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Next Steps

• Complete analyses of remaining problems about
  number
• Analyze data on geometry measurement collected
  in Math 2
• Follow up with longitudinal study of original
  MATH 1 samples.
• Share results with instructors in MATH and
  MATH-ED courses.
• Coordinate curricula of MATH and MATH-ED courses.
• Design new instructional activities, as needed,
  for MATH and MATH-ED courses.
• Share results with professional colleagues.
• Collect data from practicing teachers. (Perhaps
  this is another study.)