Department of Mathematics

General Curriculum MTEL (03), Mathematics Subtest

Study Guide Framework

Elementary Mathematics Education, Westfield State College

MTEL Review MTEL Math Objectives
MTEL Review Session Dates/Times
Official MTEL Practice Test
Test Registration
MTEL Review, Questions
MTEL Review, Answers
Contact: Marcus Jaiclin, Anna Rokicki, Volker Ecke


Candidates should not only know

Content Areas:

Study Suggestions

Undergraduate students take mathematics coursework as part of their program at Westfield State College. The four mathematics content courses Math 150, 251, 252, 253 are aligned with the areas of the Massachusetts Curriculum Frameworks. These courses are designed to cover the various content areas tested on the mathematics subtest of the General Curriculum test. This, combined with what the student already knows from their high school experience, will help students to effectively demonstrate their knowledge of content areas.

As you start preparing for the mathematics subtest of the General Curriculum MTEL (03), here are a few points to keep in mind.

  1. Take as many of the "Foundations of Mathematics" courses as you can fit into your schedule (Math 150, 251, 252, 253). If possible, take Math 253 Foundations of Number Systems.
  2. If you are anxious about taking the mathematics test (or testing in general), seek support for working with testing anxiety. Make a pact with yourself not to abandon the test half-way. When you notice anxiety, put down your pen and give yourself a few minutes to check in with your body and to calm yourself.

Suggestions for Self-Guided Preparation:

  1. Create a study guide for yourself. The General Curriculum test objectives are available online. These objectives give you a great framework to build your study guide around. We encourage you to purchase a binder and divider tabs. Each divider tab should represent one objective. The contents within each section should answer to the terms outlined in an objective area. Setting up a binder like this may take some time, but with advanced planning will be well worth it!
  2. Collect and organize your resources: e.g. your class portfolio, text books, handouts, the Van de Walle book, high school textbooks, online resources etc.
  3. ALEKS or some other foundational mathematics course of study (e.g. Mary DeSouza's book). While not aligned with the MTEL, you will have a chance to gain practice and confidence with basic arithmetic and computational techniques.
  4. Practice Exams. One of the best ways to prepare for the General Curriculum test is to work with the practice exam, or at similar practice exams for other states.
  5. Almost all of the problems on the Practice Exam are multi-step problems. A single reading is not enough to unravel what you need to do. There is no obvious formula to solve any of these problems. You will need to grapple with the material to make sense of it, and you will need to give yourself the time and focus to do that. That's normal and expected.
  6. Read carefully: it may help to underline or mark the important concepts listed in the problem. Write down whatever you know about that concept. As you prepare for the exam, write down the resources you have to fill in details about this concept.
  7. The commented solutions below are intended to show you a framework how to approach using MTEL-like problems in order (a) to identify mathematical concepts that you understand, (b) to identify mathematical concepts that you do not understand, (c) to assemble information about your resources, and (d) to observe a step-by-step process that might help you in problem-solving more generally.
  8. Below are sites that offer practice exams which may prove to be helpful study tools:
  9. Additional Resources. Please note that some of these suggestions are based on student recommendations and are not designed to ensure passage on this test, but to help provide you with supplemental information.
    1. Massachusetts Comprehensive Assessment System (MCAS). Previous test items are available online at
    2. What Your Fourth Grader Should Know by E.D. Hirsch.
    3. What Your Sixth Grader Should Know by E.D. Hirsch.


Van de Walle, Elementary and Middle School Mathematics-Teaching Developmentally is the text book required for all Mathematics Foundations courses at Westfield State College. The references given here are for the seventh edition. If you have a different edition, use the Index of your book with your key words in order to guide your search.

Note: The "Activities" listed throughout the Van de Walle book are all considered "good types" of problems to work on in your elementary school class. They are also excellent activities or contexts to use in creating the Math MTEL problems. Compare, for instance, MTEL problem (4.) about Neptune with Activity 23.3 in Chapter 23, on p. 478.

Resources on Problem-Solving: Improving Performance of High-Stakes Tests, Test-taking Strategies (p.89 ff).

Resources on Math Anxiety: Metacognition, Disposition, Attitudinal Goals (p.46 ff).

Resources on Number Systems: Chapters 8-13, 15-17, 23.

Resources on Patterns, Algebra, Functions: Chapter 14.

Resources on Geometry and Measurement: Chapters 19-20.

Resources on Data Analysis and Probability: Chapters 21-22.

Tips and Suggestions for Taking this Test

Have a game plan for how you are going to approach the test.
The great thing about the MTEL is that you are not required to take the test in chronological order-how you take it is entirely up to you. We encourage you to look at the open response items first, set-up an outline about how you are going to approach answering these questions, and then go back to get started on multiple choice items. Approaching the test this way may help to alleviate some test anxiety and set a good pace for yourself with the rest of the test.
Be clear and consistent with your responses.
One of the goals of the MTEL is to determine whether or not you will be able to communicate clearly with students and parents alike. This being the case, it is essential that your handwriting on open response items is legible, your spelling and grammar are exceptional, and your answers are well thought out.
Get focused!
To calm your nerves once the test begins, it is best to give yourself a few minutes to relax and look over the test in its entirety before getting started. Given that you have a full four hours to take the test, take advantage of a restroom break. Getting up from the test for a few minutes and throwing some cold water on your face will work wonders.

Step-by-step process

Please note that there are many different ways to solve these problems! Memorizing any particular methods or answers will not help you in the actual exam. Use the process of working on the problems to identify areas of mathematics content or reasoning that you need to refresh or review. Your understanding is solid if you are able to explain precisely why certain steps are taken in solving a problem. No calculator was used and none is allowed for taking the MTEL.

The following list outlines steps you can take in approaching a problem.

Identify important information in the problem:

Identify the related mathematics concepts:

Draw a picture or a diagram to capture the relevant pieces of information and how they relate:

What do I know about these mathematics concepts?

What are my Resources?

Test-taking strategy:

Look at the answers to see whether anything stands out. For example, is the problem looking for precise answers, or just an estimate.

What could you do as a First step?