Test Information Guide

Overview and Test Objectives
Field 09: Mathematics

Test Overview

Table outlining the test format, number of questions, time, and passing score.
Format Computer-based test (CBT); 100 multiple-choice questions, 2 open-response items
Number of Questions
  • Subarea I: 14–16 multiple-choice questions
  • Subarea II: 27–29 multiple-choice questions
  • Subarea III: 23–25 multiple-choice questions
  • Subarea IV: 12–14 multiple-choice questions
  • Subarea V: 19–21 multiple-choice questions
  • Subarea VI: 2 open-response items
Time 4 hours (does not include 15-minute CBT tutorial)
Passing Score 240

The Massachusetts Tests for Educator Licensure (MTEL) are designed to measure a candidate's knowledge of the subject matter contained in the test objectives for each field. The MTEL are aligned with the Massachusetts educator licensure regulations and, as applicable, with the standards in the Massachusetts curriculum frameworks.

The test objectives specify the content to be covered on the test and are organized by major content subareas. The chart below shows the approximate percentage of the total test score derived from each of the subareas.

The test assesses a candidate's proficiency and depth of understanding of the subject at the level required for a baccalaureate major according to Massachusetts standards. Candidates are typically nearing completion of or have completed their undergraduate work when they take the test.

Pie chart of approximate test weighting.

Sub area I 12%, Sub area II 23%, Sub area III 19%, Sub area IV 10%, Sub area V 16%, and Sub area VI 20%.

Test Objectives

Table outlining test content and subject weighting by sub area and objective.
Subareas Range of Objectives Approximate Test Weighting
Multiple-Choice
I Number Sense and Operations 01–03 12%
II Patterns, Relations, and Algebra 04–10 23%
III Geometry and Measurement 11–15 19%
IV Data Analysis, Statistics, and Probability 16–18 10%
V Trigonometry, Calculus, and Discrete Mathematics 19–23 16%
80%
Open-Response*
VI Integration of Knowledge and Understanding 24 20%

*The open-response items may relate to topics covered in any of the subareas.

Subarea I–Number Sense and Operations

Objective 0001: Understand the structure of numeration systems and solve problems using integers, fractions, decimals, percents, ratios, and proportions.
Objective 0002: Understand the properties of real and complex numbers and the real and complex number systems.
Objective 0003: Understand the principles of number theory.

Subarea II–Patterns, Relations, and Algebra

Objective 0004: Understand and use patterns to model and solve problems.
Objective 0005: Understand the properties of functions and relations.
Objective 0006: Understand the properties and applications of linear relations and functions.
Objective 0007: Understand the properties and applications of linear and abstract algebra.
Objective 0008: Understand the properties and applications of quadratic relations and functions.
Objective 0009: Understand the properties and applications of polynomial, radical, rational, and absolute value functions and relations.
Objective 0010: Understand the properties and applications of exponential and logarithmic functions and relations.

Subarea III–Geometry and Measurement

Objective 0011: Understand the principles, concepts, and procedures related to measurement.
Objective 0012: Understand the axiomatic structure of Euclidean geometry.
Objective 0013: Prove theorems within the axiomatic structure of Euclidean geometry.
Objective 0014: Apply Euclidean geometry to solve problems involving two- and three-dimensional objects.
Objective 0015: Understand the principles and properties of coordinate and transformational geometry and characteristics of non-Euclidean geometries.

Subarea IV–Data Analysis, Statistics, and Probability

Objective 0016: Understand the principles and concepts of descriptive statistics and their application to the problem-solving process.
Objective 0017: Understand the methods used in collecting and analyzing data.
Objective 0018: Understand the fundamental principles of probability.

Subarea V–Trigonometry, Calculus, and Discrete Mathematics

Objective 0019: Understand the properties of trigonometric functions and identities.
Objective 0020: Understand the concepts of limit, continuity, and rate of change.
Objective 0021: Understand differential calculus.
Objective 0022: Understand integral calculus.
Objective 0023: Understand the principles of discrete/finite mathematics.

Subarea VI–Integration of Knowledge and Understanding

Objective 0024: Prepare an organized, developed analysis emphasizing problem solving, communicating, reasoning, making connections, and/or using representations on topics related to one or more of the following: number sense and operations; patterns, relations, and algebra; geometry and measurement; data analysis, statistics, and probability; trigonometry, calculus, and discrete mathematics.