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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
[email protected]
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 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

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
o
In Math Dept of
College of Science & Math
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?
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
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
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 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
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

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
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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


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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 5
10
2
10x10=
100
2x10=
20
10x10=
100
2x10=
20
10x5=
50
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
–x
2
3x
2
–x · x² –x · 3x –x · 2
= –x³ = –3x² = –2x
2 · x²
= 2x²
2 · 3x
= 6x
2·2
=4
Add Across and then Down
(– x + 2)(x² + 3x + 2)
–x
2
x²
3x
2
–x³
–3x²
–2x
– x³ – 3x² –2x
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
2 l • 3m
Factor
0
0
2 0 • 30
1
0
1
2 0 • 31
3
1
0
2 1 • 30
2
1
1
21 • 31
6
2
0
2 2 • 30
4
2
1
2 2 • 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]