Mathematics for Teachers II

INTRODUCTION
The central tenets of the Graduate School of Education conceptual framework "Education for
Transformation" are Excellence, Equity, Inquiry and Collaboration.
The mission of the University of Massachusetts Lowell is to meet the needs of the Commonwealth today and into
the future by supporting the development of sustainable techno logies and communities through its teaching,
research, scholarship and engagement. The Graduate School of Education (GSE) contributes to this mission
by educating new teachers and enhancing the professional development of those already in the field so that they
may assume leadership roles focused on transforming the lives of children and the vitality of the region.

The GSE's commitment to "Education for Transformation" produces graduates who:
• demonstrate excellent knowledge, judgment and skills in their professional fields;
• promote equity of educational opportunity for all learners;
• collaborate with other educators, parents and community representatives to support educational
excellence;
• use inquiry and research to address educational challenges.

Mathematical knowledge is crucial factor in successful teaching. Knowledge of school mathematics
involves the skills of communicating school mathematics to one that does not know or does not understand.

To teach mathematics effectively individuals must have knowledge of mathematics characterized by an
explicit conceptual understanding of the principles and meaning underlying mathematical procedures and by
connectedness of mathematical topics, rules and definitions. Without adequate content knowledge student teachers
would spend much of their planning time learning content, rather than planning how to present the content to
facilitate the student's understanding, and they are likely to lack confidence in their ability to teach well.

Current research and practice shows that teachers with strong content preparation are more likely
to be flexible in their teaching and responsive to student needs. They are able to provide conceptual explanation
instead of purely procedural ones. They also tend to place greater emphasis on the organization and connectedness
of knowledge within the discipline and less on the provision of specific information.

This course is designed to help mathematics pre-service and in-service teachers to become adequately
prepared to teach in a manner consistent with the conception of good teaching proposed by NCTM and the
Massachusetts Curriculum Frameworks.

All student teachers are expected to gain knowledge of how to assist their students to be able to think
deeply and flexibly about the relationships among facts, concepts, and procedures that constitute the
structure of knowledge of mathematics.

ASSIGNMENT AND EVALUATION

While there no particular text is required, each student must have at least one high school (or college) level Algebra
and one Geometry textbooks, and is encouraged to use a variety of textbooks (NOT a TEACHER ADDITION).
Readings from various sources will be provided for the purpose of classroom discussion.

Recommended texts

Sobel and Lerner. 1991. Algebra and Trigonometry. Prentice Hall

Algebra: Structure and Insight by Dolciani, Brown, & Cole
and/or

Algebra and Trigonometry by Dolciani, Brown, & Cole

Holt or other
Pre-Calculus (any authors, any edition)
Brown, R. (ANY YEAR). Advanced Mathematics. Houghton Mifflin

NOT RECOMMENDED: Clencoe, Prentice Hall, and Integrated Math
series

GRADING

The final grade will be de termined as follows :

Assignment	Rubrics	Grading
Homework Will be assigned and collected	The students MUST practice skills by doing assigned AND SELFASSIGNED homework to be adequately prepared for the midterm and final exams. Students are responsible to identify the concepts and the skills they need to exercise independently. It is strongly recommended practicing the concepts and skills discussed in class.	5 points
Midterm test		30 points
Take-home part In-class part	How to write an equation of a line knowing its slope and y-intercept. Relationship between parallel and perpendicular lines regarding their slopes. How to find the distance between a line and a point not on the line, or how to find the distance between two parallel lines. How to graph the function that contains absolute value . How to graph quadratic function in the form How to solve quadratic inequality How to solve quadratic equation that contains parameters. How to solve radical equations . About 1.5 hour test would include all of the concepts discussed in class and listed above.	40% of 30 points 60% of 30 points
Final test	In addition to the topics listed for the midterm: trigonometry, logarithms, geometry. Practice tests will be provided About 2-hour test will be given in the last class. Practice for the final test will be provided.	40 points
Project See assessment rubric	1. Select one math topic for in-depth study, search and organize the material that would reflect the following: a. the place and significance of the topic in the middle/high school math curriculum (when the topic is studied; what is the prerequisite knowledge; why it is important to study this topic/concept(s)? what skills students must demonstrate? (this section must not exceed 10% of the project) 3 points b. description/explanation of the real life circumstances/situations that prompted the creation/initiation of new math models/concepts/rules i.e. a brief historical overview that shows the origin and the development of the major idea/concept of the topic; (this section must not exceed 10% of the project) 3 points c. main ideas, basic notions (definitions, rules, formulas), and the concepts of the topic (this section must not be less than 60% of the project);: i) must be stated in correct and conventional terms; 5 points ii) must be described thoroughly and accompanied with pictures and diagrams, if necessary 5 points iii) must be supported (explained) by relevant examples 5 points d. some examples of problems (this section must not exceed 10 % of the project);    2 points e. some possible middle school students' misconceptions and confusion related to the topic (this section must not exceed 10% of the project). 2 points 2. The project (at least the text) must be typed. Pictures/diagrams can be drawn by hand and inserted. Indicate your name, course number, and the title of the project. Electronic submission is encouraged, but not required. No presentation is required. 3. Length: about 10-12 (double space 11-12 font size) pages including (small) pictures, diagrams and references. Large pictures must be submitted on separate pages. 4. APA style must be used for citations, references and headings. Points will be deducted for incorrectly applied or ignored APA style. • DO NOT SUBMIT LESSON PLANS • DO NOT FOCUS ON TEACHING STRATEGIES	25 points

COURSE OUTLINE
(Topics are subject to change)