Elementary Math Education at CSUN--TNE

1. Elementary Math Education at CSUN--TNE Hillary Hertzog, Nancy O’Rode Elementary Ed Sister Rita Basta, Jerry Gold, Joel Zeitlin Mathematics

2. Math Content courses for K-6 • Math 210-Number & Operations texts: then: Billstein, Sowder, now: Parker & Baldridge, Beckmann • Math 310-Geometry, Probability & Statistics texts: Billstein, Sowder → Beckmann

3. Focus & Goals • PCK = Pedagogical Content Knowledge • MKT=Mathematical Knowledge for Teaching • CSUN focus: • Conceptual & procedural understanding • Engage candidates in explanation, discourse • Multiple representations + connections • Solve demanding problems

4. Measuring Success • Ball/Hill survey of MKT Advantages: • already developed • scaled (in-service teachers, z-scores) • reliable • valid • correlated with in-service teachers’ higher pupil gains Drawbacks: • Time & convenience (online?) • Not all sections participate

5. MKT Reporting Domains • Number & Operation CK = Content knowledge KSC = Knowledge of students & content PFA = Patterns, functions & algebra • Geometry CK = Content knowledge

6. Sample MKT Question –N & Ops CKhttp://sitemaker.umich.edu/lmt/files/LMT_sample_items.pdf • Mrs. Harris was working on divisibility rules. She told her class that a number is divisible by 4 if the last two digits are divisible by 4. One of her students asked her why the rule for 4 worked. She asked the other students if they could come up with a reason, and several possible reasons were proposed. Which of the following statements comes closest to explaining the reason for the divisibility rule for 4? (Mark ONE answer.) • Four is an even number, and odd numbers are not divisible by even numbers, • The number 100 is divisible by 4 (and also 1000, 10,000, etc.) • Every other even number is divisible by 4, for example, 24 and 28 but not 26 • It only works when the sum of the last two digits is an even number.

7. MKT Results for Geometry

8. MKT results for Numbers & Ops

9. Sample scatter plot F05 N & O CK

10. Boxplot of gains N & Ops F 05 CK

11. Statistical SignificanceF 05 N & Ops CK

12. Impacting how we teach Study Group • View videos of selected instructors using Ball Video Protocol http://sitemaker.umich.edu/lmt/faq_about_video_codes 2. Look at low score MKT items (”teaching to the test”?, markers vs. content?, items not publicly released.)

13. Long term considerations: • What is the effect of 1 or 2 content courses 2 or 3 years later? • “Do our graduates teach the way we think we are training them to?” • Institutionalizing practices • The Answer

14. The Answer Work with our colleagues in Elementary Ed so that we both are offering coherent, coordinated, well reinforced and cognitively demanding classes (and later experiences) for our teacher candidates.

15. Teacher Preparation Options • Undergraduate blended program • Freshman Option (for entering freshmen) • Junior Option (begin work in junior year) • Earn BA in Liberal Studies and preliminary credential • Fifth year program

16. Math Methods • Taken after math courses, before student teaching • Focus on “four essential components of mathematics”: Problem Solving Student Explanations Representations Connections

17. Student Teaching • First semester – 8 weeks Lang Arts/Math with seminar • Second semester – 9 weeks all subs with seminar • Placed in public school classrooms – some schools long-time partners • University supervision conducted mostly by part-timers – retired public school personnel • Minimum of five observations each semester

18. Needs Analysis Study • To what extent is subject matter content and “PCK” emphasized in the lesson planning/observation/reflection cycle in student teaching? • Analyzed 120 random sets of written observation notes by university supervisors • Found that feedback on “quality” of subject matter and PCK was extremely limited.

19. Development of Field Support Materials • Asked supervisors to identify preferred subject areas; volunteers worked with math methods faculty • Developed subject specific “field support materials” for student teachers and supervisors Lesson Planning Teaching Guide Reflection Sheet Observation Guidelines Observation Protocol

20. 05-07 Study of Undergraduates • Administered MKT survey at end of math methods in 05-06 • Tracked student teachers who had experienced Math 310 courses with “treatment” instructors • Placed those students in designated st. tchg. seminar sections and placed with identified supervisors in 06-07 . Those students used support materials; others did not. • Administered MKT survey at the end of student teaching to all student teachers

21. Table 1: Means (z-scores) of MKT Geometry Measures for Three Groups of Pre-Service Teachers

22. Table 2: Means (z-scores) of MKT Number and Operations Measures - Knowledge of Students and Content - for Three Groups of Pre-Service Teachers

23. 07-08 Research Studies • Math courses continuing to develop teaching and MKT surveys given in more sections • Longitudinal study continuing with second set of student teachers – will now have MKT scores from both math courses • Use of field support materials expanding to more supervisors • Follow-up study of nine first year graduates