Planning for the New Regulation versus Implementation

1. Planning for the New Regulation versus Implementation Presented at Framingham State College The FORUM, McCarthy College Center April 3, 2008 by Stan Dick UMass Boston ssdick@comcast.net

2. Teacher Ed Programs and Math Requirements @ UMass Boston – Before the Regulation Numbers of Candidates About 15 Undergraduate Candidates per year About 50 Graduate Candidates per year Math Requirements Before: Undergraduates: 1 Content/Methods Course Graduates: ½ Content/Methods Course + Additional Course available as Elective

3. Early Planning for the New Regulation • I Attended Several Meetings @ Worcester State College to Understand and Plan for New Regulations • Decided Students Need Three Math Courses to Pass new MTEL • Existing course could be 1st Course

4. Where Should We House the Courses, GCE or Math Dept? • Currently we have a Strong Math Person in Grad College of Ed, and • Person in Math Dept who Understands Elementary Math Education . . . But that may not be true in the future

5. So, Both! We Planned to Cross List the Courses Put Courses Through Governance Simultaneously: • In Math Dept of College of Science & Math • In Curriculum & Instruction Dept of Grad College of Ed

6. So We Developed a To Do List • Develop New Rubric in the Math Department (MTT Math for Teachers) • Cross List Courses in Math & GCE • For Undergrad Program: Get Quantitative Reasoning Distribution for One of Courses • Make Room for One Course in Undergrad and 2-3 in Grad Program • Develop Two New Courses

7. Sohowzthetodolistgoin? • New Rubric in the Math Department  • Cross Listing in Math Dept. & GCE  • Get Quantitative Reasoning Distribution for one Undergrad Course (working on it) • Make Room for the Extra Courses (not so fast) • Develop Two New Courses (oops! just developing one)

8. What went wrong? • You see I am fairly new in the GCE (for an old guy) • And, evidently, this is not the first demand that DOE has made of GCE • Evidently they want something called Literacy as well! • Yes, I said, OK! OK! . . . But what about the MTEL?

9. Prospects for Success • At the moment we have only two courses • Second course will be taught in Spring of 2009 . . after the first MTEL • So I have serious concerns about the preparation of our elementary school teachers

10. But we have commissioned an online Programmed Instruction Course • More about this later . . .

11. Nature of Needed Courses • Very Specialized Courses are Needed, . . . and very special teachers

12. Elementary Math is not Elementary Three Kinds of Math Knowledge are Needed by Elementary School Teachers – 1. Content Knowledge, 2. Specialized Content Knowledge, and 3. Pedagogical Content Knowledge

13. Calculating 3¼ ÷ ½ • Content Knowledge: 3¼ ÷ ½ = ? • Specialized Content Knowledge: There are two fundamental models of division – quotative (including repeated subtraction where 6 ÷ 3 yields two piles of 3) partitive (one for me, one for Mary, one for Joe, one for me, . . where 6 ÷ 3 yields three piles of 2) • Pedagogical Content Knowledge: 3¼ ÷ ½ can be based on Repeated Subtraction

14. Specialized Content is Only One reason specialized courses are needed . . . the other is that elementary school teachers have little confidence in their ability in mathematics, and may not fare well if put in courses with undergrad students.

15. Outline of Two Courses Math for Elementary Teachers I: Natural Numbers thru Real Numbers + Number Theory (taught since 2004) 1. Introduction a) Difficulty of Elementary Math b) Discussion of Liping Ma Study c) Discussion of Procedural vs. Constructivist Curricula d) Discussion of Communication, Connections & Representations

16. 2. Whole Numbers and Integers Plus & Minus Cards 3. The Rational and Real Number Systems Operations with Rationals, Reals as Distances or Infinite Decimals, Fact that Rationals repeat, Irrationals don’t, Conversion of repeaters to fractions 4. Number Theory: LCM, GCD, Division Algorithm, Prime Factorization & applications to number of factors, finding LCM, GCD, Euclidean Algorithm, Venn Diagram

17. 5. Standard Arithmetic Algorithms and Intermediate Algorithms, and mathematical underpinnings (an example to follow) 6. Percents

18. Math for Elementary Teachers II: Algebra, Geometry, TI-83 Calculator 1. Linear relationships, linear models and linear problem solving; 2. basic geometric concepts: congruence, similarity and the effect of various transformations; 3. perimeter, area and volume of basic geometric figures; 4. Circle Properties and the number Pi 5. Basic Algebra including variables and unknown quantities

19. 6. Probability and Statistics (if time allows)

20. Course Format • In Math I course, students, in alternating groups, present the homework as soon as they come into class • Presenting Group must answer questions from class members and instructor • Surprisingly students find this much less intimidating than a written exam • This practice puts the students in charge from the beginning and sets a good tone for the class • May have to be modified for 2nd Course

21. Innovation in Format • Assistant in Each Class - goes around helping students during the period • $50 Laboratory Fee per student pays for the Assistant • Pioneered in the Quantitative Reasoning Course in Math Department

22. Including Special Ed and TVI’s • Basic Principle: If Teachers Truly understand the math and the techniques, they will be able to teach it to their special constituents • Concentrate on Key Concepts and Make them Accessible • Example: Multi-Digit Multiplication 12 x 25

23. Open Products: 12 x 25

24. Add Across and then Down

25. Open Products Can Be Used in Algebra as Well Calculate: (2 – x)(3x + X2)

26. (– x + 2)(x² + 3x + 2)

27. Add Across and then Down(– x + 2)(x² + 3x + 2)

28. For Teachers of the Visually Impaired • The blank table can be formed using Wikki Stix on the Math Window Magnetic Board

29. Math Window

30. And Filled in using the Math Window Tiles

31. For Special Education • Open Products Form their own Advance Organizer (depending on the no. of digits) • Open Products are scalable with respect to difficulty, i.e. scaffoldable • Open Products are also scalable with respect to Level of Innovation Required by Student (instead of 10 + 2 for 12, 5 + 5 + 2 can be used if student is comfortable with 5 times table

32. Similar Advantages to Finding All Factors of say 12 = 22 • 3, using prime factorization (but much harder)

33. Stan Using GeomeSticks

35. Online Programmed Instruction

36. Programmed Instruction Goals • Prepare students for MTEL exam – based on new Guidelines for the Mathematical Preparation of Elementary Teachers released by MA Dept of Education • Online tool for students to learn content, practice problems, take assessments, and complete sample tests, all at their own pace • Easy tracking system for administrators to monitor student progress • Designed for students to develop a strong mathematics foundation, both skills and a comprehensive in-depth understanding of the underlying structure of math mary@omegateaching.com Math for MTEL & Beyond

37. 50 categories divided into 8 modules to cover all areas that students must master for MTEL 1000 questions, each with detailed explanations, so student can practice as much as they need to Students can absorb material at their own pace, monitor their own progress, and continually review before their certification exam until mastery is achieved For each module: assessment, lessons, rules, questions, explanations, vocabulary, tips, tricks, and strategies on approaching problems Features mary@omegateaching.com Math for MTEL & Beyond

38. 8 Modules

39. Categories within Modules

40. 50 Lessons

41. 1000 Practice Questions

42. Detailed Explanations & Feedback

43. Educational Software Solutions • Developed by Mary DeSouza • Founder of Omega Teaching • MIT BS and MS in Computer Science & Electrical Engineering • Over 10 years of teaching experience, including TAing at MIT, developing curriculum and teaching computer science, planning all materials and teaching Advanced Algebra and Geometry classes, private tutoring and teaching Kaplan LSAT courses, and teaching middle school and elementary school reading, computers, math, and science. • 650-281-3681 • mary@omegateaching.com • www.omegateaching.com mary@omegateaching.com Math for MTEL & Beyond

44. I need help in my negotiations with my colleagues • Better Understanding of New Regulation • Will Regulation Test Specialized Content knowledge, Pedagogical Content Knowledge? • A Sample MTEL or a Proxy (Math Placement Exam?) to gauge Student capability.

45. That’s All Folks! by Stan Dick • Center of Science & Math in Context (COSMIC Center) • UMass Boston • ssdick@comcast.net