Test Information Guide

Overview and Test Objectives
Field 47: Mathematics (Middle School)

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: 18–20 multiple-choice questions
  • Subarea II: 30–32 multiple-choice questions
  • Subarea III: 21–23 multiple-choice questions
  • Subarea IV: 14–16 multiple-choice questions
  • Subarea V: 12–14 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 15%, Sub area II 25%, Sub area III 18%, Sub area IV 12%, Sub area V 10%, 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
I Number Sense and Operations 01–04 15%
II Patterns, Relations, and Algebra 05–10 25%
III Geometry and Measurement 11–15 18%
IV Data Analysis, Statistics, and Probability 16–17 12%
V Trigonometry, Calculus, and Discrete Mathematics 18–20 10%
VI Integration of Knowledge and Understanding 21 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 multiple representations of numbers.
Objective 0002: Understand principles and operations related to integers, fractions, decimals, percents, ratios, and proportions.
Objective 0003: Understand and solve problems involving integers, fractions, decimals, percents, ratios, and proportions.
Objective 0004: Understand the properties of real numbers and the real number system.

Subarea II–Patterns, Relations, and Algebra

Objective 0005: Understand and use patterns to model and solve problems.
Objective 0006: Understand how to manipulate and simplify algebraic expressions and translate problems into algebraic notation.
Objective 0007: Understand properties of functions and relations.
Objective 0008: Understand properties and applications of linear relations and functions.
Objective 0009: Understand properties and applications of quadratic relations and functions.
Objective 0010: Understand properties and applications of exponential, polynomial, rational, and absolute value functions and relations.

Subarea III–Geometry and Measurement

Objective 0011: Understand principles, concepts, and procedures related to measurement.
Objective 0012: Understand the principles of Euclidean geometry and use them to prove theorems.
Objective 0013: Apply Euclidean geometry to analyze the properties of two-dimensional figures and to solve problems.
Objective 0014: Solve problems involving three-dimensional shapes.
Objective 0015: Understand the principles and properties of coordinate and transformational geometry.

Subarea IV–Data Analysis, Statistics, and Probability

Objective 0016: Understand descriptive statistics and the methods used in collecting, organizing, reporting, and analyzing data.
Objective 0017: Understand the fundamental principles of probability.

Subarea V–Trigonometry, Calculus, and Discrete Mathematics

Objective 0018: Understand the properties of trigonometric functions and identities.
Objective 0019: Understand the conceptual basis of calculus.
Objective 0020: Understand the principles of discrete/finite mathematics.

Subarea VI–Integration of Knowledge and Understanding

Objective 0021: Prepare an organized, developed analysis on a topic related to one or more of the following: number sense and operations; patterns, relations, and algebra; geometry and measurement; data analysis, statistics, and probability; and trigonometry, calculus, and discrete mathematics.