Planning for the New Regulation versus Implementation

Presented at Framingham State CollegeThe FORUM, McCarthy College Center

April 3, 2008

by Stan DickUMass Boston

ssdick@comcast.net

Teacher Ed Programs and Math Requirements @ UMass Boston – Before the Regulation

Numbers of CandidatesAbout 15 Undergraduate Candidates per yearAbout 50 Graduate Candidates per year

Math Requirements Before:Undergraduates: 1 Content/Methods Course

Graduates: ½ Content/Methods Course + Additional Course available as Elective

Early Planning for the New RegulationI 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

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

So, Both! We Planned to Cross List the Courses

Put Courses Through GovernanceSimultaneously:

o In Math Dept of College of Science & Math

o In Curriculum & Instruction Dept of Grad College of Ed

So We Developed a To Do ListDevelop 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

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)

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?

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

But we have commissioned an online Programmed Instruction Course

More about this later . . .

Nature of Needed Courses

Very Specialized Courses are Needed,

. . . and very special teachers

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

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

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.

Outline of Two CoursesMath for Elementary Teachers I: Natural Numbers thru Real Numbers + Number Theory (taught since 2004)

1. Introductiona) Difficulty of Elementary Mathb) Discussion of Liping Ma Studyc) Discussion of Procedural vs. Constructivist

Curriculad) Discussion of Communication, Connections & Representations

2. Whole Numbers and Integers

Plus & Minus Cards3. 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

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

6. Percents

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 Pi5. Basic Algebra including variables and

unknown quantities

6. Probability and Statistics (if time allows)

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

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

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

Open Products: 12 x 25

10 10 510 10x10=

10010x10=100

10x5= 50

2 2x10= 20

2x10= 20

2x5= 10

Add Across and then Down

10 10 510 100 100 50 250

2 20 20 10 50

250+50= 300

Open Products Can Be Used in Algebra as Well

Calculate: (2 – x)(3x + X2)

(– x + 2)(x² + 3x + 2)

x² 3x 2–x –x · x²

= –x³–x · 3x= –3x²

–x · 2 = –2x

2 2 · x²= 2x²

2 · 3x= 6x

2 · 2 = 4

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

x² 3x 2–x –x³ –3x² –2x – x³ – 3x² –2x

2 2x² 6x 4 2x² + 6x + 4

– x³ – x² + 4x +4

For Teachers of the Visually Impaired

The blank table can be formed using Wikki Stix on the Math Window Magnetic Board

Math Window

And Filled in using the Math Window Tiles

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

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

l m 2l • 3m Factor

0 0 20 • 30 1

0 1 20 • 31 3

1 0 21 • 30 2

1 1 21 • 31 6

2 0 22 • 30 4

2 1 22 • 31 12

Stan Using GeomeSticks

Online Programmed Instruction

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

Math for MTEL & Beyond mary@omegateaching.com

Features 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

Math for MTEL & Beyond mary@omegateaching.com

8 Modules

Categories within Modules

50 Lessons

1000 Practice Questions

Detailed Explanations & Feedback

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

Math for MTEL & Beyond mary@omegateaching.com

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.

That’s All Folks!

by Stan Dick Center of Science & Math in Context

(COSMIC Center) UMass Boston ssdick@comcast.net