A Look Within (6 Questions)

1. When do I take time to reflect on my cultural perceptions and biases?


2. Do I consider equity issues when creating assessments or selecting curricula?

3. In my situation, do I have a safe environment in which to examine my attitudes, beliefs, and behaviors toward equity issues?

4. How do I contribute to such an environment for my colleagues?

5. How can my school's or district's equity policies guide my learning?

6. How can I help improve those policies?

Ideas That Work: Mathematics Professional Development (6 Questions)

1. What can I learn from the framework for designing and identifying professional development programs?

2. How can I use the framework diagram in creating my own learning plan?


3. Do I engage in any of the 15 strategies for professional development?

4. What are the enablers or barriers to engaging in the strategies?

5. How can my school's or district's improvement plan incorporate some of the 15 strategies?

Six Ways to Immediately Improve Professional Development (6 Questions)

1. In my school's professional development plans, do we consider long-term goals?


2. What are they?


3. If we do not, what process can we use for determining our long-term goals?


4. How do my school's goals influence my goals?


5. Does my school use any of the six strategies?


6. How might we use more of them?

Revisioning Professional Development (6 Questions)

1. How does my school or district embody the characteristics of learner-centered professional development?

2. How can we implement a more learner-centered professional development program?

3. What challenges have we overcome in establishing learner-centered professional development in my school or district?

4. What challenges might we face in becoming more learner-centered?

5. How can I structure my own professional development to ensure that it is learner-centered?

6. Where can I find opportunities for learner-centered professional development?

Dreaming All That We Might Realize (5 Questions)

1. What fundamental choices have I made that influenced my teaching practice?


2. What mental models do I have of teaching and student learning?


3. How do my choices or mental models impede or promote my professional learning?


4. Does my school district have a "deep change" or a "slow death" attitude towards change?

5. If we have a "slow death" attitude, how can I promote "deep change" in myself and my colleagues?

Parameters of TEXMAT and the MMT Program

I. Field Axioms - Exercises pp. 33-34 (Algebraic Structures)

This first section of the course focuses on the Real Number System and the Complex Number System. In our first several classes, we examine the general laws of behaviors or axioms for real numbers. The axioms are given in three sets; 1) the Field Axioms; 2) The Order Axioms; 3) The Completeness Axioms.

The first section focuses on the field axioms (6 in number) from which we can deduce all familiar properties of real numbers that depend ONLY upon addition and multiplication.


I. Field Axioms


Exercises

1. Prove that if a, b is an element of R and b not equal 0, then -a/b = a/-b = -(a/b).
2. Let a, b be nonzero real numbers. Show that (ab)-1 = a-1/b-1.
3. Let a, b elements of R and b not equal to zero. Prove: if x is a nonzero real number, then ax/bx = a/b.
4. Let a,b,c,d be an element of R where b is not equal to zero and d is not equal to zero.
Prove that a/b times c/d = ac/bd.
5. Verify that a/b = c/d if and only if ad = bc.
6. Assuming b is not equal to 0, verify the following:
a) a/b + c/b = (a+ c)/b b) a/b - c/b = (a-c)/b

I. Field Axioms - Exercises pp. 31-32 (Algebraic Structures)

This first section of the course focuses on the Real Number System and the Complex Number System. In our first several classes, we examine the general laws of behaviors or axioms for real numbers. The axioms are given in three sets; 1) the Field Axioms; 2) The Order Axioms; 3) The Completeness Axioms. The first section focuses on the field axioms (6 in number) from which we can deduce all familiar properties of real numbers that depend ONLY upon addition and multiplication.


Exercises

1. Use the technique of Theorem 12 to prove that (-a)(b = a(-b) = - (ab).
2. Prove that (-a)(-b) = ab. Hence deduce (-1)(-1) = 1.
3. Prove that -0 = 0.
4. Verify the following: i) -(a + b) = -a - b; ii) -(a-b) = -a + b; iii) -(-a+b) = a-b.

NCTM Assessment Principles

The NCTM Assessment Principle(s)

TEKS Discussion (MMT Journal)

Differentiated Instructional Strategies - One Size Doesn't Fit All

By Your Own Design CD--The First Five Star Structure

Read the following Articles and respond to the discussion/reflection questions in your MMT Journal.

1. Dreaming all that We Might Realize
2. Revisioning Professional Development: What Learner-Centered Professional Development Looks Like
3. Six Ways To Immediately Improve Professional Development
4. Ideas That Work: Mathematics Professional Development
5. A Look Within

HMC Calculus Tutorials

Visual Calculus

MacTutor History of Mathematics Archives