Work of the TNE Mathematics Group at Michigan State University

1. Work of the TNEMathematics Group at Michigan State University

2. 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

3. Units Involved in TNE Mathematics Collaborations • Teacher Education • Mathematics • Statistics • Division of Science and Mathematics Education (DSME)

4. Major TNE Mathematics Activities • Standards Development • Course Development • Self Studies

5. 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

6. 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)

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

8. 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

9. 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)

10. Opportunities to Learn Mathematics for Teaching at MSU *Prerequisite: College Algebra

11. Design of Study • Cross-sectional Data Collection

12. 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

13. 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

14. Detailed Look at Two Problems • Whole Numbers • There are 4 • We discuss Item W1 • Fractions • There are 5 • We discuss Item F4

15. Imagine that one of your students shows you the following strategy for subtracting wholenumbers: 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 ] Whole Number Problem W1*

16. Types of Responses for W1b

17. Types of Responses for W1b

18. 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.

19. Numeric Score Summary forW1 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

20. 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.] Fraction Problem- F4*

21. Rubric for ProblemF4a

22. Example Student Representations

23. Rubric for ProblemF4b

24. Numeric Scores forF4 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.

25. Points Earned Points Possible Summary of Overall Results Table of expressed as a % Note: Percentages are based on 3 whole number and 2 fraction items that have been analyzed, so far.

29. 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 outperformedMATH-ED-S students, suggesting that preservice teachers do not retain all the knowledge and understanding gained in previous courses and tested by these tasks.

30. 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.)