Study Guide
Field 182: Elementary Mathematics Specialist
Test Design and Framework
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The test design below describes general assessment information. The framework that follows is a detailed outline that explains the knowledge and skills that this test measures.
Test Design
*Does not include 15-minute C B T tutorial
Test Framework
| subareas | range of competencies |
approximate percentage of test |
|
|---|---|---|---|
| Selected-Response | |||
| roman numeral 1 | number concepts and operations | 0001to0002 | 18 percent |
| roman numeral 2 | algebra and functions | 0003to0004 | 16 percent |
| roman numeral 3 | geometry and measurement | 0005to0006 | 17 percent |
| roman numeral 4 | data analysis and probability | 0007to0008 | 16 percent |
| roman numeral 5 | professional knowledge and instructional leadership | 0009to0010 | 18 percent |
| this cell intentionally left blank. | 85 percent | ||
| subareas | range of competencies | approximate percentage of test | |
|---|---|---|---|
| constructed-response | |||
| roman numeral 6 | constructed-response assignment | 0011 | 15 percent |
subarea roman numeral 1–Number Concepts and Operations
Competency 0001–Apply knowledge of number sense, number systems, and the properties of the real number system.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Apply knowledge of prenumber concepts (e.g., one-to-one correspondence, cardinality, order operations), place value, and properties of operations to perform multi-digit arithmetic.
- Apply knowledge of how to represent, compare, and order numbers using a variety of models (e.g., number lines, base-ten blocks, diagrams).
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Identify different representations of equivalent rational numbers (e.g., fractions, decimals, percents) and how to convert between them in mathematical and real-world situations.
- Analyze the characteristics of numbers (e.g., odd and even, absolute value) and the sets of whole numbers, integers, rational numbers (e.g., fractions, decimals, percents, exponents), real numbers, and complex numbers.
- Recognize common student misconceptions and errors related to the structure of number systems and the properties of the real number system and identify appropriate interventions to develop student understanding.
Competency 0002–Analyze number operations and computational algorithms.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Apply knowledge of basic concepts of number theory (e.g., factors, prime numbers, least common multiple).
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Apply a variety of algorithms appropriately and demonstrate knowledge of their advantages, limitations, and relationships.
- Apply estimation techniques and mental math strategies to real-world problems involving integers, fractions, decimals, and percents.
- Analyze customary algorithms involving basic operations and their inverses with real and complex numbers and use number properties and the order of operations to justify procedures, solve problems, and evaluate basic algebraic expressions and equations.
- Analyze alternative algorithms and multiple representations (e.g., rectangular arrays, partitioning, decomposing) of basic operations with whole numbers, fractions, and decimals.
- Solve a variety of mathematical and real-world problems using whole numbers, integers, fractions, decimals, percents, roots, powers, rational exponents, and scientific notation.
- Recognize common student misconceptions and errors related to number operations and computational algorithms and identify appropriate interventions to develop student understanding.
subarea roman numeral 2–Algebra and Functions
Competency 0003–Apply knowledge of patterns, algebraic and proportional reasoning, expressions, and equations.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Identify and extend a variety of patterns (e.g., numbers, figures, expressions) and use a variety of number patterns to explore number properties.
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Analyze various representations of sequences (e.g., verbal, written, numeric, graphic, symbolic).
- Justify the manipulation of algebraic expressions, equations, and inequalities.
- Manipulate and simplify algebraic expressions (e.g., order of operations, factoring, distributive property, combining like terms) and solve equations and inequalities in both mathematical and real-world problems.
- Analyze mathematical and real-world problems and translate them into algebraic expressions and equations.
- Recognize common student misconceptions and errors related to patterns, algebraic expressions, and functions and identify appropriate interventions to develop student understanding.
Competency 0004–Apply knowledge and concepts of linear functions to model and solve problems.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Demonstrate knowledge of the attributes of functions and relations (e.g., domain, one-to-one, inverse) and multiple representations (e.g., graphic, verbal, algebraic) of them.
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Identify the relationships between linear functions, proportions, and direct variation.
- Analyze the relationships between a linear function, its average rate of change, and its graph.
- Analyze the effects of transformations on the graphs of linear functions.
- Analyze linear functions and inequalities using a variety of representations (e.g., tabular, graphic, verbal).
- Analyze and solve problems involving equations and inequalities using a variety of techniques (e.g., algebraic, graphic).
- Model and solve mathematical and real-world problems involving linear functions using a variety of representations (e.g., tabular, graphic, algebraic).
- Identify nonlinear functions (e.g., multistep, exponential) in various representations (e.g., numeric, algebraic, graphic).
- Recognize common student misconceptions and errors related to modeling and problem solving with linear functions and identify appropriate interventions to develop student understanding.
subarea roman numeral 3–Geometry and Measurement
Competency 0005–Apply knowledge and concepts of Euclidean, transformational, and coordinate geometry.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Demonstrate and apply knowledge of Euclidean geometry.
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Demonstrate and apply knowledge of geometric constructions and use logical reasoning to explain geometric relationships.
- Analyze and solve measurement problems involving composite geometric figures.
- Use concepts of geometry (e.g., congruence, symmetry, similarity, parallel and perpendicular lines) to solve mathematical and real-world problems involving one-, two-, and three-dimensional figures and shapes.
- Apply the Pythagorean theorem to solve problems.
- Analyze three-dimensional figures using two-dimensional representations (e.g., cross sections, perspective drawings).
- Recognize and model polygons and three-dimensional figures in real-life and mathematical situations.
- Analyze lines, geometric figures, and polygons in the coordinate plane in terms of distance, midpoint, slope, and parallel and perpendicular lines to solve problems.
- Analyze transformations and dilations of figures in terms of congruence and symmetry.
- Recognize common student misconceptions and errors related to concepts of Euclidean, transformational, and coordinate geometry and identify appropriate interventions to develop student understanding.
Competency 0006–Apply knowledge and concepts of measurement.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Demonstrate knowledge of how to use the customary (e.g., in, ft, yd) and metric (e.g., cm, m, km) systems appropriately and convert within them.
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Use dimensional analysis to represent and solve problems in a variety of situations.
- Analyze and solve a variety of measurement problems involving length, perimeter, circumference, degrees, area and surface area, volume, temperature, time, percentage, distance, speed, and acceleration.
- Analyze precision, error, and rounding in measurements and computed quantities.
- Represent and use proportional reasoning (e.g., ratios and proportions, percentages) to solve real-world measurement problems.
- Recognize common student misconceptions and errors related to concepts of measurement and identify appropriate interventions to develop student understanding.
subarea roman numeral 4–Data Analysis and Probability
Competency 0007–Analyze and interpret data.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Demonstrate knowledge of how to compare, organize, display, and analyze data in a variety of representations (e.g., frequency distribution, boxplot, circle graph).
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Apply concepts of central tendency (e.g., mean, median, mode) and dispersion (e.g., range, outliers, percentiles) to data sets and data distributions.
- Apply knowledge of how to describe and summarize data for the purpose of making decisions, predicting, and solving real-world problems.
- Analyze experimental designs, interpret results, and draw inferences from observations and experiments that investigate real-world problems.
- Demonstrate knowledge of how random sampling is used to draw inferences about a population.
- Analyze the effects of bias and sampling techniques and select the appropriate approach in real-world situations.
- Analyze the relationship between sample size and the level of confidence in conclusions.
- Recognize common student misconceptions and errors related to the analysis and interpretation of data and identify appropriate interventions to develop student understanding.
Competency 0008–Apply knowledge and concepts of probability.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Identify the appropriate sample space in problems involving probability.
- Demonstrate knowledge of how concepts of probability are used to solve problems involving simple and compound events.
- Calculate probabilities and solve problems involving the counting principle (e.g., counting techniques, combinations).
- Apply concepts of probability to identify simulations that model real-world and experimental situations and data collection scenarios.
- Apply appropriate probability distributions in given situations.
- Represent and solve problems using multiple representations (e.g., tree diagrams, Venn diagrams) of real-world situations.
- Recognize common student misconceptions and errors related to concepts of probability and identify appropriate interventions to develop student understanding.
subarea roman numeral 5–Professional Knowledge and Instructional Leadership
Competency 0009–Demonstrate knowledge of mathematics instruction and assessment.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Demonstrate knowledge of how tools (e.g., manipulatives, technology) can be used to enhance student understanding.
- Demonstrate knowledge of ways to promote equity for all students in mathematics instruction.
- Demonstrate knowledge of established research evidence on how students learn and use mathematics.
- Apply knowledge of levels of questioning to assess students' mathematical understanding and advance their mathematical learning.
- Apply knowledge of ways to support student learning with the use of academic language and vocabulary.
- Apply knowledge of sequences of instruction that develop students' content knowledge, reasoning skills, conceptual understanding, and computational fluency and precision.
- Apply knowledge of problem-solving tasks that develop students' content knowledge, reasoning skills, conceptual understanding, and computational fluency and precision.
- Analyze and use results from various types of assessments (e.g., diagnostic, formative, summative) to plan, inform, and adjust instruction.
- Integrate knowledge of the vertical alignment of mathematical topics and concepts across grade levels to plan instruction based on state standards.
Competency 0010–Demonstrate knowledge of instructional leadership in mathematics.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Identify and apply ways to establish a culture of collaboration regarding the use of data to plan, evaluate, and improve mathematics instruction and to promote positive changes in the school mathematics program.
- Identify and apply ways to promote and support a rigorous district instructional program based on research-supported best practices regarding mathematics curriculum, instruction, technology, and assessment.
- Identify and apply appropriate and effective methods for communicating professionally with educational stakeholders about students, curriculum, instruction, use of technology, and assessment.
- Demonstrate knowledge of ways for using professional resources (e.g., organizations, journals, discussion groups) to stay current regarding critical issues related to mathematical teaching and learning; enhancing one's own professional knowledge and skills; and engaging in reflective practices (e.g., evaluating and adjusting one's own performance in a variety of instructional contexts).
- Demonstrate knowledge of educational structures and policies that affect students' equitable access to quality mathematics instruction and encourage the use of practices with proven effectiveness in promoting academic success for students with diverse characteristics and needs.
- Analyze and apply knowledge of strategies for collaborating effectively with families/caregivers and community members to support students' mathematical development (e.g., partnering with families/caregivers and community members in promoting students' lifelong appreciation of mathematics; communicating findings of current research in mathematics development to various stakeholders, including families/caregivers, local libraries, businesses, and policy makers) and for supporting positive family/caregiver–student interactions related to mathematics.
- Analyze and apply knowledge of ways to collaborate effectively with colleagues to promote professional development and to meet the mathematics needs of all students (e.g., coaching, conducting professional study groups for teachers, providing constructive feedback on colleagues' practices related to mathematics instruction).
- Analyze and apply knowledge of components and procedures related to effective, evidence-based, and multi-tiered system of supports (M T S S) used in Oklahoma (e.g., Response to Intervention [R T I], Oklahoma Tiered Intervention System of Support [O T I S S]).
- Integrate knowledge of ways to use professional development (e.g., mentoring, coaching, peer-teaching, workshops) to facilitate appropriate research-supported, standards-based mathematics instruction and to promote the use of instructional methods supported by research.
subarea roman numeral 6–Constructed-Response Assignment
Competency 0011–Analyze student work and assessment data related to a student's development of mathematical knowledge and abilities and plan appropriate instructional strategies for the student.
start italics The following topics are examples of content that may be covered under this competency. end italics
- Analyze and interpret information from multiple assignments and assessments for a given student in order to identify and discuss significant needs that the student demonstrates in mathematics.
- Integrate expertise of mathematical knowledge and instruction to select and describe appropriate and effective evidence-based instructional strategies for the student featured in the assessment evidence.
- Integrate knowledge of development, assessment, and instruction in mathematics to explain and discuss the appropriateness and effectiveness of the selected instructional strategies.