MTEL Mathematics: Fields 53, 47 and 09

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About This Book and TESTware®

REA’s The Best Teachers’ Test Preparation for MTEL: Mathematics is a comprehensive guide designed to assist you in preparing for a mathematics educator license in Massachusetts. The practice exams in this book and software package are included in two formats: in printed format in this book, and in TESTware® format on the enclosed CD for Windows-based computers. We strongly recommend that you begin your preparation with the TESTware® practice exams. The software provides the added benefits of instant scoring and enforced time conditions.  To enhance your chances of success in this important step toward your career as a mathematics teacher, this test guide:

• Presents an accurate and complete overview of these three MTEL tests

• Identifies all of the important information and its representation on the test

• Provides a comprehensive review of every subarea on the test

• Provides three full-length practice tests (one for each test)

• Suggests tips and strategies for successfully completing standardized tests

• Replicates the format of the official tests, including levels of difficulty

• Supplies the correct answer and detailed explanations for each question on the practice tests, which enable you to identify correct answers and understand why they are correct and, just as important, why the other answers are incorrect.

This guide is the result of studying many resources. The editors considered the most recent test administrations and professional standards. They also researched information from the Massachusetts Department of Education, professional journals, textbooks, and educators. This guide includes the best test preparation materials based on the latest information available.

About the Tests

The MTEL mathematics tests are designed to assess the mathematical knowledge and competencies for a teacher of grades 5–8 and 8–12 (09), grades 5–8 (47), and grades 1–6 (53). The following chart is a clear representation of the subareas, approximate number

of questions, and the percentages of the total test that each subarea occupies. These subareas represent the combined expertise of Massachusetts educators, subject area specialists, and district-level educators who worked to develop and validate these tests. This book contains a thorough review of all these subareas, as well as the specific skills that demonstrate each area.

Who Administers the Test?

All the MTEL tests are administered by the Massachusetts Department of Education. See contact information below.

Can I Retake the Test?

The MTEL can be taken as many times as needed to achieve a passing score.

TESTS OVERVIEW CHARTS

MATHEMATICS (09)

Subareas                                              Approx # Questions    Approx. Test

Weighting of

                                                                         Subareas

Multiple-Choice:

I. Number Sense and Operations             14–16                         12%

II. Patterns, Relations, and Algebra             27–29                         23%

III. Geometry and Measurement             23–25                         19%

IV. Data Analysis, Statistics, and

Probability                                            12–14                         10%

V. Trigonometry, Calculus, and

Discrete Mathematics                             19–21                         16%

Open-Response:

VI. Integration of Knowledge and

Understanding                         2                                  20%

MIDDLE SCHOOL MATHEMATICS (47)

Subareas                                              Approx # Questions    Approx. Test

Weighting of

                                                                         Subareas

Multiple-Choice:

I. Number Sense and Operations             18–20                         15%

II. Patterns, Relations, and Algebra             30–32                         25%

III. Geometry and Measurement             21–23                         18%

IV. Data Analysis, Statistics, and

Probability                                            14–16                         12%

V. Trigonometry, Calculus, and

Discrete Mathematics                             12–14                         10%

Open Response:

VI. Integration of Knowledge and

Understanding                         2                                  20%

ELEMENTARY MATHEMATICS (53)

Subareas                                              Approx # Questions    Approx. Test

Weighting of

                                                                         Subareas

Multiple-Choice

I. Number Sense, Operations, and

Data Analysis                                       37–39                         30%

II. Patterns, Relations, and Algebra             30–32                         25%

III. Geometry and Measurement             30–32                         25%

Open Response:

IV. Integration of Knowledge and

Understanding                         2                                  20%

When Should the MTEL Be Taken?

Candidates are typically nearing completion of or have completed their undergraduate work when they take MTEL tests.

MTEL tests are administered five times a year at six locations around the state. To receive information on upcoming administrations of the MTEL, consult the MTEL

test date chart at the MTEL website. For all information, contact the Massachusetts Department of Education at:

Massachusetts Tests for Educator Licensure

National Evaluation Systems, Inc.

P.O. Box 660

Amherst, MA 01004-9013

Phone: (413) 256-2892

Fax: (413) 256-8221

Website: www.mtel.nesinc.com (refer to or download

the “Registration Bulletin”)

Is There a Registration Fee?

To take any MTEL test there is a fee. A complete summary of the registration fees is included in the MTEL Registration Bulletin at the website above.

Calculators

Examinees taking the MTEL Mathematics (09) will be provided a Texas Instruments TI 30X Solar Scientific calculator. You may not bring your own calculator to the test.

Examinees taking the MTEL Middle School Mathematics (47) and Elementary Mathematics (53) will not use calculators.

How to Use This Book

How Do I Begin Studying?

Identify which MTEL test you wish to prepare for, then review the organization of this test preparation guide.

1. To best utilize your study time, follow our MTEL Independent Study Schedule. The schedule is based on an six-week program, but can be condensed if necessary.

2. Take the practice test for the MTEL you wish to prepare for, score it according to directions, then review the explanations to your answers carefully. Then, study the areas that your scores indicate need further review.

3. Review the format of the MTEL.

4. Review the test-taking advice and suggestions presented later in this section.

5. Pay attention to the information about the objectives of the test.

6. Spend time reviewing topics that stand out as needing more study.

7. Take the practice test again and follow the same procedure as #2 above.

8. Follow the suggestions at the end of this section for the day before and the day of the test.

Note: Look above under “Calculators” to determine whether your test provides one. Or, see the MTEL website for details.

When Should I Start Studying?

It is never too early to start studying for the MTEL. The earlier you begin, the more time you will have to sharpen your skills. Do not procrastinate!

A six-week study schedule is provided in the book can assist you in preparing for the MTEL test you require.

Studying for the MTEL Mathematics Tests

It is very important for you to choose the time and place for studying that works best for you. Some students set aside a certain number of hours every morning to study, while some choose the night before going to sleep, and others study during the day, while waiting in line, or even while eating lunch. Choose a time when you can concentrate and your study will be most effective.

Be consistent and use your time wisely. Work out a study routine and stick to it. When you take the practice test, simulate the conditions of the actual test as closely as possible. Turn your television and radio off and sit down at a quiet table with your calculator, if you will be using one.

When you complete the practice test, score it and thoroughly review the explanations to the questions you answered incorrectly. Do not, however, review too much at any one time. Concentrate on one problem area at a time by examining the question and explanation, and by studying our review until you are confident that you have

mastered the material. Keep track of your scores to discover areas of general weaknesses and to gauge your progress. Give extra attention to the review sections that cover your areas of difficulty, as this will build your skills in those areas.

Format of the MTEL Mathematics Tests

The MTEL mathematics tests assess the candidate’s proficiency and depth of understanding of the subject at the level required for a baccalaureate major, according

to Massachusetts standards.

Referring to the previous chart, the MTEL Mathematics (09) and Middle School Mathematics (47) are composed of six subarea sections, five of which total

approximately 100 multiple-choice questions, and one of which involves two open-response questions. The MTEL Elementary Mathematics (53) has three multiple-

choice subarea sections and one subarea containing two open response questions. In all tests, the multiple-choice questions comprise 80% and the open-response questions comprise 20% of the total test.

About the Review Sections

The subject review in this book is designed to help you sharpen the basic skills needed to approach the MTEL test you are required to take, as well as provide strategies for attacking the questions.

Each subarea is examined separately, clearly delineating the tests to which it applies. The skills required for all subareas fulfill the objectives of the Massachusetts Department of Education and are extensively discussed to optimize your understanding of what your

specific MTEL test covers. Your schooling has taught you most of what you need to succeed on the test. Our review is designed to help you fit the information you have acquired into specific subareas. Reviewing your class notes and textbooks together with our reviews will give you an excellent springboard for passing the test.

Scoring the MTEL Mathematics Tests

Multiple-Choice Questions

A candidate’s performance on subareas with multiple-choice questions is based strictly on the number of test questions answered correctly. Candidates do not lose any points for wrong answers. Each multiple-choice question counts the same toward the total score.

These items are scored electronically and checked to verify accuracy.

Open-Response Questions

Open-response questions require a breadth of understanding of each test’s field of mathematics and the ability to relate concepts from different aspects of the field.

Open-response questions are scored holistically by two or more qualified educators. Scorers receive training in scoring procedures and are monitored for accuracy and consistency. Scorers are typically licensed teachers, administrators, arts and sciences faculty, teacher education faculty, and other content specialists.

Scorers judge the overall effectiveness of each response. That is, scorers are trained to provide an overall judgment, not to indicate specific errors. A score is assigned to each response based on a scale that describes various levels of performance from weak to strong or thorough. If a candidate’s response is blank, unrelated to the assignment, illegible, or in a language other than the target language, the candidate will receive no points for that question, and may or may not meet the qualifying score for the test, depending on performance on the other questions.

You are given four hours to complete the test, so be aware of the amount of time you are spending on each question. Using the practice test will help you prepare to pace your time evenly, efficiently, and productively.

Score Results

After you have taken the MTEL, you will receive a score report indicating whether you met the qualifying score, your total test score, and information about your performance on the subareas of the test. Score reports will be mailed to you, to the Massachusetts

Department of Education, and to those you designate to receive them according to the schedule published in the MTEL Registration Bulletin. Your score will not be released over telephone or fax. There is a fee for each additional score report requested.

Each MTEL test has its own qualifying score set by the Massachusetts Commissioner of Education. The scores for all test scores are reported on the same scale, in a range of 0 to 100, with a score of 70 representing the qualifying, or passing, score.

Test-Taking Tips

Although some of you may not be familiar with tests like the MTEL, this book will help acquaint you with this type of test and help alleviate your test-taking anxieties.

Tip 1. Become comfortable with the format of the MTEL. When you are practicing, stay calm and pace yourself. After simulating the test only once, you will boost your chances of doing well, and you will be able to sit down for the actual test with much more confidence.

Tip 2. Read all of the possible answers. Just because you think you have found the correct response, do not automatically assume that it is the best answer. Read through each choice to be sure that you are not making a mistake by jumping to conclusions.

Tip 3. Use the process of elimination. Go through each answer to a question and eliminate as many of the answer choices as possible. By eliminating two answer

choices, you have given yourself a better chance of getting the item correct since there will only be two choices left from which to make your guess. Answer all questions

you can; you are not penalized for wrong answers, but you are rewarded for correct ones.

Tip 4. Place a question mark in your answer booklet next to answers you guessed, then recheck them later if you have time.

Tip 5. Work quickly and steadily. Avoid focusing on any one problem too long. Taking the practice tests in this book for your MTEL test will help you learn to efficiently budget your time.

Tip 6. Learn the directions and format of the test. This will not only save time, but will also help you avoid anxiety (and the mistakes caused by getting anxious).

Tip 7. Be sure that the answer circle you are marking corresponds to the number of the question in the test booklet. Since the test is multiple-choice, it is graded by machine, and marking one answer in the wrong circle can throw off your answer key and your score. Be extremely careful.

The Day of the Test

Before the Test

On the day of the test, make sure to dress comfortably, so that you are not distracted by being too hot or too cold while taking the test. Plan to arrive at the test center early. This will allow you to collect your thoughts and relax before the test, and will also spare you the anguish that comes with being late.

You should check your MTEL Registration Bulletin and other registration information to find out what time to arrive at the testing center. Before you leave for the test center, make sure that you have your admission ticket and the following identification:

• one piece of current, government-issued identification, in the name in which you registered, bearing your photograph and signature • one clear and legible photocopy of your original government-issued identification for each test session in which you are testing (i.e., one copy for the morning and/or one copy for the afternoon session)

• one additional piece of identification (with or without a photograph)

Note: If you do not have the required identification, you will be required to complete additional paperwork and have your photograph taken. This additional step will result in a reduction of your available testing time. You must bring several sharpened No. 2 pencils with erasers, as none will be provided at the test center.

If you would like, you may wear a watch to the test center. However, you may not wear one that has a calculator, or one that makes noise. Dictionaries, textbooks, notebooks, briefcases, laptop computers, packages, and cell phones will not be permitted. Drinking,

smoking, and eating are prohibited.

During the Test

You are given four hours to complete the MTEL. Restroom breaks are allowed, but they count as testing time. Procedures will be followed to maintain test security. Once you enter the test center, follow all of the rules and instructions given by the test supervisor. If

you do not, you risk being dismissed from the test and having your scores cancelled.

When all of the materials have been distributed, the test instructor will give you directions for filling out your answer sheet. Fill out this sheet carefully since this

information will be printed on your score report. Once the test begins, mark only one answer per question, completely erase unwanted answers and marks, and fill in answers darkly and neatly.

After the Test

When you finish your test, hand in your materials and you will be dismissed. Then, go home and relax—you deserve it!