Test Information Guide

Overview and Test Objectives
Field 51: Mathematics/Science (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: 9–11 multiple-choice questions
  • Subarea II: 14–16 multiple-choice questions
  • Subarea III: 10–12 multiple-choice questions
  • Subarea IV: 7–9 multiple-choice questions
  • Subarea V: 5–7 multiple-choice questions
  • Subarea VI: 9–11 multiple-choice questions
  • Subarea VII: 9–11 multiple-choice questions
  • Subarea VIII: 9–11 multiple-choice questions
  • Subarea IX: 9–11 multiple-choice questions
  • Subarea X: 9–11 multiple-choice questions
  • Subarea XI: 1 open-response item
  • Subarea XII: 1 open-response item
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 8%, Sub area II 12%, Sub area III 9%, Sub area IV 6%, Sub area V 5%, Sub area VI 8%, Sub area VII 8%, Sub area VIII 8%, Sub area IX 8%, Sub area X 8%, Sub area XI 10%, and Sub area XII 10%.

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 8%
II Patterns, Relations, and Algebra 05–10 12%
III Geometry and Measurement 11–15 9%
IV Data Analysis, Statistics, and Probability 16–17 6%
V Trigonometry, Calculus, and Discrete Mathematics 18–20 5%
VI History, Philosophy, and Methodology of Science 21–24 8%
VII Chemistry 25–28 8%
VIII Physics 29–32 8%
IX Biology 33–36 8%
X Earth and Space Science 37–40 8%
XI Integration of Knowledge and Understanding of Mathematics 41 10%
XII Integration of Knowledge and Understanding of Science 42 10%

*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–History, Philosophy, and Methodology of Science

Objective 0021: Understand the nature of scientific thought and inquiry and the historical development of major scientific ideas.
Objective 0022: Understand principles and procedures of research and experimental design.
Objective 0023: Understand procedures for gathering, organizing, interpreting, evaluating, and communicating scientific information.
Objective 0024: Understand the safe and proper use of tools, equipment, and materials (including chemicals and living organisms) related to classroom and other science investigations.


Subarea VII–Chemistry

Objective 0025: Understand the structure and nature of matter.
Objective 0026: Understand the nature of physical changes in matter.
Objective 0027: Understand the nature of chemical changes in matter.
Objective 0028: Understand the kinetic molecular model of matter.


Subarea VIII–Physics

Objective 0029: Understand the concepts of force, motion, work, and power.
Objective 0030: Understand the concept of energy and the forms that energy can take.
Objective 0031: Understand characteristics of waves and the behavior of sound and light waves.
Objective 0032: Understand principles of electricity, magnetism, and electromagnetism.


Subarea IX–Biology

Objective 0033: Understand the characteristics and life processes of living organisms.
Objective 0034: Understand principles related to the inheritance of characteristics.
Objective 0035: Understand principles and theories related to biological evolution.
Objective 0036: Understand characteristics of populations, communities, ecosystems, and biomes.


Subarea X–Earth and Space Science

Objective 0037: Understand geologic history and processes related to the changing earth.
Objective 0038: Understand characteristics and properties of the hydrosphere.
Objective 0039: Understand the earth's atmosphere, weather, and climate.
Objective 0040: Understand components of the solar system and universe and their interactions.


Subarea XI–Integration of Knowledge and Understanding of Mathematics

Objective 0041: 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.


Subarea XII–Integration of Knowledge and Understanding of Science

Objective 0042: Prepare an organized, developed analysis on a topic related to one or more of the following: history, philosophy, and methodology of science; chemistry; physics; biology; and earth and space science.