Pre-calculus Online for Teachers

A Teacher Quality Institute

Syllabus

The schedule: Pre-calculus consists of six modules of material. The modules as prescribed by the TEKS included the topics of functions and operations with them, models of real-life problems, with regression, sequences and series, parametric equations and conics, and vectors. It is planned over the year to cover in detail each of these modules as described at the website

http://distance-ed.math.tamu.edu/Precalculus_home/index.htm.

The production of these materials was funded as a part of the Teacher Quality Grant Type A funding, 2004. In addition, it is planned to present materials on technology, rubrics, pedagogy, assessment, and best teaching practices. Students will have opportunities at each step of the process to demonstrate their new skills. We plan to ask students to develop lesson plans based on various content levels, develop rubrics for assessment, analyze multiple-choice high stakes examinations for clues to their integrity, and to create assessments. Regular participant presentations will be required.

In more detail the class will meet during the regular semesters, fall 2004 and spring 2005, every Tuesday and Thursday for two hours 4:00-6:00pm. The hours are slightly longer than for a regular lecture class because a portion of this class will be laboratory based. The daily format will be one of four types.

Type 1 – Lecture style – break included

4:00-4:45 A regular lecture will be given on pre-calculus content

5:00-5:45 Guided discussion on the content, assigned tasks.

5:45- 6:00 Participants will maintain a session computer log of their activities. Specific issues of the day will be logged. As well, standard assessment methods such as the “one minute essay” and “the muddiest point” will be compiled online for feedback to the grant teaching staff. Special surveys will be given regularly.

Type 2 – Activity and technology – break included

4:00-4:45 Activites or technology will be covered by the presenter for about one hour.

5:00-5:45 Participants will develop new activities based on those discussed and/or develop activities based on using the technology.

5:45- 6:00 Participant log period.

Type 3 – Pedagogy and teaching related topics – break included

4:00-4:45 A regular one hour lecture will be given on aspects of pedagogy as described above.

5:00-5:45 Roundtable discussion, sometime participant led, will involve all students during the second hour.

5:45- 6:00 Participant log period.

Type 4 – Presentation day – break included

4:00-5:45 Participants will make monthly presentation on topics involving content, activities, technology, or pedagogy

5:45- 6:00 Participant log period.

Of course, it will be difficult to schedule precisely how this will proceed. However, in rough terms, the focus during the first term will be on the first two types of presentations, and the second term will emphasize the third type. The fourth type – presentations – will be a monthly feature of the year-long program.

Deliverables. In addition to the requirements above participants will provide written lesson plans, essays, papers and other instruments by which to evaluate their performance. Overall, numerous types of assessment and measure of teaching ability will be exacted to assure the best possible prepared teacher.

Weekly schedule: Academic Year 2004-2005

Date	Planned activity	Type	Activity
Sept 7*	Overview of the Type A online materials	I	Exploring the materials
Sept 9	Overview of the Type A online materials	I	Exploring the materials
Sept 14	Using functions. (TEKS module I)	I	Activities on functional form
Sept 16	Using functions. Operations with functions. (TEKS modules I and II.)	II	Teaching differences between function types.
Sept 21	Applications of functions to real situations. (TEKS modules I and II.)	I-II	Giving examples of functions as they fit in this work
Sept 23	Exponential and logarithm functions with applications. (TEKS modules I and II.)	I-II	Technology and activities
Sept 28	Piecewise functions, representation and applications	II	Technology and activities
Sept 30	Teaching shifts and using notation	III	Pedagogy
Oct 5	Presentations	IV	Content
Oct 7	Presentations	IV	Pedagogy and Technology
Oct 12	Highlights of regression. How it works. Why it works. (TEKS module III.)	I	Activities for regression.
Oct 14	Trig functions – the technical details and applications (TEKS module III.)	I-II	Developing winning activities
Oct 19	More applications of trig functions (TEKS module III.)	II	Using Internet resources to discover periodicity
Oct 21	Applications via technology. (TEKS module III.)	II	Technology and activities
Oct 26	Why teaching regression is difficult. (TEKS module III.)	III	Pedagogy and technology
Oct 28	Why teaching regression is difficult. (TEKS module III.)	III	Pedagogy and technology experiments
Nov 2	Presentations	IV	Technology
Nov 4	Presentations	IV	Pedagogy
Nov 9	Modeling with exponential and logarithmic functions. (TEKS module III.)	I	Activities
Nov 11	Calculus and transcendental functions – things to come. (TEKS module III.)	I	Activities from calculus. Rates of change.
Nov 16	Analyzing real problems using functions. (TEKS module III.)	II	Using technology and interesting activities
Nov 18	Teaching the exponential and logarithm	III	The actual practice of teaching complex functions
Nov 23	The basics of sequences and series – real world views (TEKS modules IV.)	I	Exploration of the ideas
Nov 30	Presentations	IV	Content
Dec 7	Presentations	IV	Technology
Dec 9	Presentations	IV	Pedagogy
End of Semester I – Beginning of Semester II
Jan 18	Making rubrics	IV	General theory and application
Jan 20	Sequences and series	I	Computations and formulas
Jan 25	Sequences and series	II	Using activities
Jan 27	Sequences and series	II	Using technology
Feb 1	Sequence and series	III	How to teach; how to convince students of the value.
Feb 3	Presentations	IV	Theory
Feb 8	Presentations	IN	Activities and pedagogy
Feb 10	Parametric equations - (TEKS modules IV.)	I	Theory
Feb 15	Parametric equations	I	Uses
Feb 17	Parametric equations	II	Applications
Feb 22	Parametric equations - applications	II	Using technology
Feb 24	Teaching parametric equations	III	The basics
Mar 1	Making lesson plans for teaching parametric equations	III	Key points for inclusions; traps to avoid
Mar 3	Presentations	IV	Theory
Mar 8	Presentations	IV	Applications
Mar 10	Presentations	IV	Activities and technology
Mar 14-18	Spring Break
Mar 22	Vectors (TEKS modules IV.)	I	Theory and representation
Mar 24	Vectors – world of applications	II	Theory
Mar 29	Vectors - applications	II	Activities and technology
Mar 31	Teaching vectors	III	Basics for consistent presentations
April 5	Forms of assessment	IV	Practices and theory
April 12	High stakes testing	IV	How problems
April 19	Distractor analysis	IV	Discriminating good questions from poor
April 26	Creating multiple choices test that are fair	IV	The art of multiple-choice answers
May 3	Presentations and evaluation	IV	Vectors – theory
May 5	Presentations and evaluation	IV	Vectors – technology and applications

* Dates will be adjusted to correspond to the regular school year.