Test Information Guide
Overview and Test Objectives
Field 03: General Curriculum
Test Overview
Format 
Computerbased test (CBT) MultiSubject Subtest
Mathematics Subtest


Number of Questions 
MultiSubject Subtest
Mathematics Subtest

Time  4 hours for one or both subtests (does not include 15minute CBT tutorial) 
Passing Score  240 on each subtest 
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 General Curriculum test comprises separately administered and scored multisubject and mathematics subtests and is designed to assess the candidate's knowledge of the elementary subject matter required for a Massachusetts Elementary educator license and other licenses as defined in the educator licensure regulations.
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 openresponse items on the multisubject subtest will relate to topics covered in the History and Social Science or Science and Technology/Engineering subareas as described by the associated objectives. The openresponse items on the mathematics subtest will involve the application of mathematical knowledge and reasoning to communicate multiple solutions in detail to a problem involving two or more of the following subareas: Numbers and Operations, Functions and Algebra, Geometry and Measurement, and/or Statistics and Probability.
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.
Test Objectives
MultiSubject Subtest
Subareas  Range of Objectives  Approximate Test Weighting 

MultipleChoice  
Language Arts  01–05  30% 
History and Social Science  06–09  30% 
Science and Technology/Engineering  10–14  30% 
90%  
OpenResponse  
Integration of Knowledge and Understanding  15  10% 
Subarea–Language Arts^{1}
Objective 0001: Understand the history and structure of the English language.
For example:
 Identify major developments in the history of the English language (e.g., invention of the printing press, standardization of written language, development of dictionaries).
 Recognize major linguistic origins of the English language (e.g., AngloSaxon roots, Celtic influences, Greek and Roman elements).
 Recognize examples of derivatives and borrowings.
 Analyze differences in written English (e.g., level of formality, how dialects are used).
 Recognize fundamental language structures (i.e., morphology, semantics, syntax, and phonology).
 Identify parts of speech (e.g., noun, verb, adjective, preposition).
 Recognize sentence types (e.g., simple, compound, complex) and sentence purposes (e.g., declarative, interrogative).
 Apply knowledge of the rules of English grammar and conventions of edited American English.
Objective 0002: Understand American literature and selected literature from classical and contemporary periods.
For example:
 Recognize historically or culturally significant works, authors, and themes of U.S. literature.
 Demonstrate knowledge of selected literature from classical and contemporary periods.
 Recognize literature of other cultures.
 Recognize elements of literary analysis (e.g., analyzing story elements, interpreting figurative language).
 Demonstrate knowledge of varied focuses of literary criticism (e.g., the author, the context of the work, the response of the reader).
Objective 0003: Understand literary genres, elements, and techniques.
For example:
 Demonstrate knowledge of basic literary terminology (e.g., flashback, foreshadowing).
 Recognize characteristics of different genres and types of literature (e.g., folktales, nonfiction, drama, poetry).
 Recognize types of nonfiction (e.g., biography, informational text, documents) and common organizational features of nonfiction (e.g., chronological order, comparison and contrast, illustrations, captions, keys).
 Apply knowledge of elements of fiction (e.g., plot, character, setting, theme, voice).
 Identify types of poetry (e.g., lyric, narrative, haiku).
 Recognize characteristics of poetry and poetic techniques (e.g., meter, rhyme, alliteration, figurative language).
 Recognize types of drama (e.g., comedy, tragedy) and common dramatic devices (e.g., suspense, soliloquy).
Objective 0004: Understand literature for children, including genres, literary elements, and literary techniques.
For example:
 Recognize major works and authors of children's literature.
 Recognize genres of children's literature and their characteristics.
 Identify major themes associated with children's literature.
 Analyze rhetorical and literary devices (e.g., analogies, similes, metaphors, symbolism) in children's literature.
 Compare different styles and communicative purposes in children's literature.
 Identify criteria for evaluating children's literature (e.g., reading level, literary quality, richness of vocabulary, student interests, illustrations, gender and cultural bias).
 Analyze excerpts of children's literature in relation to style, theme, or voice.
 Identify uses of children's literature (e.g., enhancing other areas of the curriculum, fostering crosscultural understanding).
Objective 0005: Understand the writing process and formal elements of writing and composition.
For example:
 Demonstrate knowledge of prewriting strategies, including techniques for generating topics and developing ideas (e.g., brainstorming, semantic mapping, outlining, using graphic organizers).
 Identify formal elements of writing (e.g., paragraphing, topic sentences, cohesive transitions).
 Identify revisions of written texts that improve unity, coherence, and logical organization.
 Edit written work to ensure conformity to conventions of edited American English (e.g., grammar, punctuation, spelling, usage).
 Identify techniques and styles for writing for various purposes (e.g., to respond, inform, analyze, persuade, entertain), including factors related to the selection of topic and mode of written expression.
 Recognize intended audience.
 Recognize various techniques to convey meaning (e.g., precise vocabulary, figurative language).
1. Knowledge of the following content will be measured on a separate Foundations of Reading test for all prospective early childhood, elementary, and special education teachers: 1) reading theory, research, and practice; 2) development of an oral and reading vocabulary; 3) theories on the relationship between beginning writing and reading; 4) approaches and practices for developing skills in using writing tools; and 5) theories of first and secondlanguage acquisition and development.
Subarea–History and Social Science
Objective 0006: Understand major developments in the history of the United States and the Commonwealth of Massachusetts from precolonial times to the present.
For example:
 Demonstrate knowledge of indigenous peoples before the arrival of Europeans.
 Describe European exploration and the settlement of North America.
 Analyze the causes and effects of the Revolutionary War (e.g., the Stamp Act, the Boston Massacre).
 Recognize key developments in the formation of the national government.
 Examine the origins and events of the Civil War.
 Analyze issues associated with Reconstruction.
 Demonstrate knowledge of the settlement of the West.
 Analyze the transformation of the United States from an agrarian to an industrial economy.
 Compare the Progressive Era and the New Deal.
 Examine the emergence of the United States as a world power (e.g., the era of U.S. overseas expansion, World War I, World War II, the Cold War).
 Demonstrate knowledge of the civil rights and women's movements.
 Analyze U.S. leadership in world affairs from the collapse of the Soviet Union to the present.
Objective 0007: Understand the founding documents and governmental systems of the United States and the Commonwealth of Massachusetts; the principles, ideals, rights, and responsibilities of U.S. citizenship; and the fundamental principles and concepts of economics.
For example:
 Identify the purposes of government.
 Demonstrate knowledge of the functions of federal, state, and local governments in the United States.
 Identify the three branches of the U.S. government and analyze their roles and functions.
 Describe various forms of local selfgovernment in Massachusetts and the United States.
 Demonstrate knowledge of how laws are enacted and enforced.
 Analyze the political process in the United States.
 Demonstrate knowledge of the democratic principles and values contained in the Declaration of Independence, the U.S. Constitution, and the Constitution of the Commonwealth of Massachusetts (e.g., the rule of law, due process, majority rule).
 Recognize the responsibilities of U.S. citizens (e.g., paying taxes, jury duty, voting).
 Apply basic economic terms (e.g., scarcity, opportunity cost) to analyze contemporary economic issues.
 Examine the fundamental concepts and principles of capitalism (e.g., private property, profit, supply and demand).
Objective 0008: Understand major developments and figures in world history.
For example:
 Identify the characteristics of early human civilizations.
 Demonstrate knowledge of major figures (e.g., Saladin, Julius Caesar, Isaac Newton, Mohandas Gandhi, Elizabeth I), eras, developments, and turning points in world history with stress on Western civilization (e.g., ancient Israel, the emergence of Greek civilization, the rise and fall of the Roman Empire, the Middle Ages, the Renaissance and Reformation, the Age of Exploration, the Scientific Revolution, the Enlightenment, the Age of Revolutionary Change, World Wars I and II).
 Analyze the impact of industrialization, nationalism, immigration, and globalization on modern world history.
Objective 0009: Understand basic geographic concepts, phenomena, and processes, and demonstrate knowledge of the major geographic features and regions of the world, the United States, and the Commonwealth of Massachusetts.
For example:
 Demonstrate knowledge of the basic concepts of geography (e.g., location, place, movement).
 Use globes, maps, and other resources to access geographic information.
 Identify global features (e.g., continents, hemispheres, latitude and longitude, poles).
 Recognize the major physical features and regions of Massachusetts, the United States, and world areas.
 Analyze the relationship between geographic factors (e.g., climate, topography) and historical and contemporary developments (e.g., human migrations, patterns of settlement, economic growth and decline).
Subarea–Science and Technology/Engineering
Objective 0010: Understand and apply basic concepts and principles of life science to interpret and analyze phenomena.
For example:
 Identify the basic characteristics and needs of living things (e.g., growth, reproduction, life cycles of common organisms).
 Demonstrate knowledge of the basic concepts and processes related to energy flow in ecosystems and how organisms use energy.
 Demonstrate knowledge of plant structures, functions, and processes (e.g., photosynthesis).
 Demonstrate knowledge of the systems of the human body.
 Recognize the basic principles of genetics and heredity.
 Recognize how species adapt and evolve over time by the process of natural selection.
 Analyze how organisms interact with one another and their environments.
Objective 0011: Understand and apply basic concepts and principles of the physical sciences to interpret and analyze phenomena.
For example:
 Demonstrate knowledge of the composition and structure of matter (e.g., atoms, molecules).
 Demonstrate knowledge of the properties and states of matter.
 Recognize forms of energy (e.g., heat, electrical, magnetic, sound, light).
 Analyze how heat energy is transferred (e.g., convection, conduction, radiation).
 Demonstrate knowledge of basic concepts related to the motion of objects (e.g., inertia, momentum).
 Apply the principles of the conservation of matter and energy.
 Recognize the use of simple machines in everyday life.
 Understand how engineering uses the laws of physical science and the properties of matter to solve practical problems.
Objective 0012: Understand and apply basic concepts and principles of the earth and space sciences to interpret and analyze phenomena.
For example:
 Analyze the forces that shape the earth's surface (e.g., erosion, weathering, volcanism, plate tectonics).
 Demonstrate knowledge of the rock cycle and soil formation.
 Recognize the structure of the earth and atmosphere.
 Demonstrate knowledge of factors that affect weather and climate.
 Identify the physical characteristics of oceans (e.g., currents, waves).
 Analyze the components and processes of the hydrologic cycle.
 Demonstrate knowledge of the structure of the solar system.
 Recognize the relationships among objects in the solar system (e.g., the moon's effect on the earth, the change of seasons).
Objective 0013: Understand the foundations of scientific thought; the historical development of major scientific ideas and technological discoveries; and the relationships among scientific discoveries, technological developments, and society.
For example:
 Demonstrate knowledge of the development of scientific thinking (e.g., during ancient times, during the Scientific Revolution of the seventeenth century).
 Recognize the importance of observation and evidence in the development of scientific knowledge.
 Recognize major scientific and technological discoveries and inventions.
 Analyze cultural and historical factors that have promoted or discouraged scientific discovery and technological innovation.
Objective 0014: Understand the principles and procedures of scientific inquiry and experimentation; the relationships among science, technology, and engineering; and the principles of engineering design.
For example:
 Demonstrate knowledge of the basic concepts and processes of scientific experimentation (e.g., hypothesis, control, variable, replication of results, collection and communication of scientific information).
 Demonstrate knowledge of health and safety measures related to scientific inquiry and experimentation.
 Recognize the relationships among science, technology, and engineering.
 Demonstrate knowledge of the processes of engineering design (e.g., research, design and development, testing, evaluation and redesign).
Subarea–Integration of Knowledge and Understanding
Objective 0015: Prepare an organized, developed analysis on a topic related to History and Social Science or to Science and Technology/Engineering.
 (Refer to objectives 0006 through 0014 and associated descriptive statements.)
Mathematics Subtest
Subareas  Range of Objectives  Approximate Test Weighting 

MultipleChoice  
Numbers and Operations  16–19  41% 
Functions and Algebra  20–22  22% 
Geometry and Measurement  23–24  18% 
Statistics and Probability  25–26  9% 
90%  
OpenResponse*  
Integration of Knowledge and Understanding  27  10% 
*The openresponse items may relate to topics covered in any of the subareas.
Candidates should not only know how to do elementary mathematics, but should understand and be able to explain to students, in multiple ways, why the mathematics makes sense.
Subarea–Numbers and Operations
Objective 0016: Understand the number system and the concept of place value.
For example:
 Analyze the structures and properties of the base10 and other numeral systems (e.g., expanded form of a number, visual representations of place value, numeration systems of ancient cultures).
 Recognize decimal expansions.
 Use scientific notation in the real world.
 Analyze procedures (e.g., rounding, regrouping) for estimation.
 Determine the reasonableness of estimates.
 Identify subsets of the real numbers (e.g., integer, rational, irrational) and their characteristics.
Objective 0017: Understand integers, fractions, decimals, percents, and mixed numbers.
For example:
 Understand the meanings and models of integers, fractions, decimals, percents, and mixed numbers and apply them to the solution of word problems.
 Analyze and convert among various representations of numbers (e.g., graphic, numeric, symbolic, verbal).
 Use number lines.
 Compare, sort, order, and round numbers.
 Recognize equivalent representations of numbers (e.g., fractions, decimals, percents).
Objective 0018: Understand and apply principles of number theory.
For example:
 Identify prime and composite numbers and their characteristics.
 Find the prime factorization of a number and recognize its uses.
 Demonstrate knowledge of the divisibility rules and why they work.
 Find the least common multiple (LCM) and greatest common factor (GCF) of a set of numbers.
 Apply the LCM and GCF in realworld situations.
Objective 0019: Understand operations on numbers.
For example:
 Understand the meaning and models of operations on numbers (e.g., integers, fractions, decimals).
 Analyze and justify standard and nonstandard computational algorithms and mental math techniques (e.g., by application of the arithmetic properties, such as commutative, associative, distributive).
 Evaluate the validity of nonstandard or unfamiliar computational strategies.
 Recognize and analyze various representations (e.g., graphic, pictorial, verbal) of number operations.
 Recognize relationships among operations (e.g., addition and subtraction, addition and multiplication, multiplication and exponentiation).
 Identify and apply the arithmetic properties and the transitive properties of equality and inequality.
 Apply the order of operations.
 Apply the laws of exponents.
 Demonstrate fluency in arithmetic computation, including operations on fractions.
 Interpret the concept of absolute value.
 Apply appropriate strategies (e.g., proportional thinking, ratios) to estimate quantities in realworld situations.
 Solve problems using arithmetic operations with various representations of numbers.
Subarea–Functions and Algebra
Objective 0020: Understand algebra as generalized arithmetic.
For example:
 Recognize and apply the concepts of variable, function, equality, and equation to express relationships algebraically.
 Manipulate simple algebraic expressions and solve linear equations and inequalities.
 Justify algebraic manipulations by application of the properties of equality, the order of operations, the number properties, and the order properties.
 Use algebra to solve word problems involving fractions, ratios, proportions, and percents.
 Identify variables and derive algebraic expressions that represent realworld situations.
Objective 0021: Understand the concept of function.
For example:
 Understand the definition of function and various representations of functions (e.g., input/output machines, tables, graphs, mapping diagrams, formulas).
 Recognize and extend patterns using a variety of representations (e.g., verbal, numeric, pictorial, algebraic).
 Identify and analyze direct and inverse relationships in tables, graphs, algebraic expressions and realworld situations.
 Use qualitative graphs to represent functional relationships in the real world.
 Translate among different representations (e.g., tables, graphs, algebraic expressions, verbal descriptions) of functional relationships.
Objective 0022: Understand linear functions and linear equations.
For example:
 Recognize the formula and graph of a linear function.
 Distinguish between linear and nonlinear functions.
 Find a linear equation that represents a graph.
 Analyze the relationships among proportions, constant rates, and linear functions.
 Interpret the meaning of the slope and the intercepts of a linear equation that models a realworld situation.
 Select the linear equation that best models a realworld situation.
Subarea–Geometry and Measurement
Objective 0023: Understand and apply concepts of measurement.
For example:
 Estimate and calculate measurements using customary, metric, and nonstandard units of measurement.
 Use unit conversions and dimensional analysis to solve measurement problems.
 Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures.
 Determine how the characteristics (e.g., area, volume) of geometric figures and shapes are affected by changes in their dimensions.
 Solve a variety of measurement problems (e.g., time, temperature, rates, average rates of change) in realworld situations.
Objective 0024: Understand and apply concepts of geometry.
For example:
 Classify and analyze polygons using attributes of sides and angles, including realworld applications.
 Classify and analyze threedimensional figures using attributes of faces, edges, and vertices.
 Analyze and apply geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to concepts of symmetry, similarity, and congruence; and use these concepts to solve problems.
 Match threedimensional figures and their twodimensional representations (e.g., nets, projections, perspective drawings).
 Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem).
Subarea–Statistics and Probability
Objective 0025: Understand descriptive statistics.
For example:
 Use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret realworld data.
 Select appropriate ways to present data and communicate statistical information (e.g., tables, graphs, line plots, Venn diagrams).
 Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles).
 Compare different data sets.
Objective 0026: Understand and apply basic concepts of probability.
For example:
 Calculate the probabilities of simple and compound events and of independent and dependent events.
 Recognize and apply the concept of conditional probability.
 Recognize the difference between experimentally and theoretically determined probabilities in realworld situations.
 Apply knowledge of combinations and permutations to the computation of probabilities.
Subarea–Integration of Knowledge and Understanding
Objective 0027: Apply mathematical knowledge and reasoning to communicate multiple solutions in detail to a problem involving two or more of the following subareas: Numbers and Operations, Functions and Algebra, Geometry and Measurement, and Statistics and Probability.
 (Refer to objectives 0016 through 0026 and associated descriptive statements.)
This is the end of section 3: Overview and Test Objectives. Proceed to section 4: MultiSubject Subtest Sample MultipleChoice Questions.