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Transcript of Planning for the New Regulation versus Implementation Presented at Framingham State College The...
Planning for the New Regulation versus Implementation
Presented at Framingham State CollegeThe FORUM, McCarthy College Center
April 3, 2008
by Stan DickUMass Boston
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
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 Governance
Simultaneously:
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 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
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. 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
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
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 Pi
5. 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 5
10 100 100 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 [email protected]
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 [email protected]
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• [email protected]• www.omegateaching.com
Math for MTEL & Beyond [email protected]
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 [email protected]