This course is a resource to help you prepare exceptionally well for your state's high-school mathematics teachers' licensure exam.

Each state requires its new teachers to demonstrate the necessary content knowledge and practice skills to be an effective secondary mathmematics educator. The content required varies to some degree from state to state, but all demand a proficiency at least at the level provided by beginning mathematics baccalaureate courses. Many states use the Praxis Mathematics: Content Knowledge Test (test code 0061, Mathematics CK) developed by the Educational Testing Service (www.ets.org/praxis). The remaining states administer their own version of this test.

**Visit your state government's Department of Education website to determine which test your state administers.** (Searching under "[state name], secondary mathematics licensure" usually does the trick.

This course covers the entire content knowledge required by all fifty states and the District of Columbia.

**MATH 1500: Praxis Math Test Prep: State Math Licensure Exam** is divided into eight broud categories, outlined below. A ninth “various topics” section contains questions that integrate the separate themes.

Your state’s Department of Education website should outline a similar breakdown of mathematical topics.

Material from the **history of mathematics** appears throughout the content sections of this course. Some state Departments of Education list the history of mathematics as a separate category.

**MATH 1500: Praxis Math Test Prep: State Math Licensure Exams** contains over six hundred short-answer/multiple-choice questions covering the entire content outlined.

All state exams have a significant multiple-choice component, and some, including Praxis Mathematics: Content Knowledge Test (0061), are purely multiple choice in their structure. However, a number of states do include one or two “open response” or essay questions to be completed as part of their exam. (See your state’s department of education website for details and examples of what might be required.) We will briefly discuss open response questions later in this section. A full and complete understanding of the content covered in this course will help prepare you well for any essay question.

Each question is presented as either a multiple-choice question or a short-answer question. The choice to not present all questions in the multiple-choice format is deliberate: having a selection of answers to review offers the crutch of being able to eliminate incorrect answers. As a result, many of the questions in this course are a tad harder than what shall appear on your exam.

Each page of the course consists of 2–4 questions from one particular theme. **Have pencil and paper in hand and work through each question on your own.** After you have attempted each question, click to the next page. Not only are the answers revealed, but full explanations of the mathematics behind the topics at hand appear as well. **In your notebook, write a summary of the mathematics.** If you find you need deeper explanation than offered in this course, **search the internet or look at your mathematics textbook** for further discussion. We have assumed that the user already has at least at basic introduction to all the topics discussed but, of course, one might have areas that need more thorough review.

Ideally you should start work on this course several months before the date of the exam. A good practice is to **work through the material of 10–15 questions each day**.

Most states allow the use of a calculator when taking the exam. (Check this on your state’s Department of Education website.) However, **try to do as much as you can on each question without a calculator**. Working to exercise your mental faculties now will serve you well on the test.

The styles of the questions in this course mimic the questions that appear in all secondary mathematics licensure exams. However, each state’s exam has its own feel and it is important to understand the feel of the exam you will be taking. **Download the practice materials from your state’s licensure exam website (or the ETS Praxis website) and work through them too.** After doing this course, you will find the topics, content, and style familiar. It is nonetheless important to focus on the particular style of exam you will face.

- Set aside, as best you can, a regular time each day to study. Work through 10–15 questions per day, taking notes along the way.
- Reserve a regular study place with few distractions. Turn off your cell phone during your study time.
- Write summary sheets of your notes. The act of rewriting material forces you to examine content slowly and with purpose and focus. The physical act of writing aids in memory. (You may well find a moment in the exam of remembering on which part of the page you wrote a particular idea, and that will aid the recall of the idea itself.)
- Periodically review the material you have covered. Take a few moments at different parts of the day to read over one of your summary sheets.
- Consider organizing a study group if you have colleagues also taking the exam.