1 / 40

Mathematics Content Specifications, Item Specifications, and Depth of Knowledge Training Module

Mathematics Content Specifications, Item Specifications, and Depth of Knowledge Training Module. Purpose of Training Module. Introduce primary source materials Common Core State Standards for Mathematics Smarter Balanced Mathematics Content Specifications

milo
Télécharger la présentation

Mathematics Content Specifications, Item Specifications, and Depth of Knowledge Training Module

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Mathematics Content Specifications, Item Specifications, and Depth of Knowledge Training Module

  2. Purpose of Training Module • Introduce primary source materials • Common Core State Standards for Mathematics • Smarter Balanced Mathematics Content Specifications • Smarter Balanced Mathematics Item Specifications • Describe how these documents will be used for item writing • Define Depth of Knowledge

  3. Foundation for Item and Task Development Items and Performance Tasks Smarter Balanced Item and Task Specifications Smarter Balanced Content Specifications Common Core State Standards

  4. Structure of the Common Core State Standards for Mathematics • Research-based learning progressions • Internationally benchmarked • Focused and coherent • Standards for Mathematical Practice • Identify important processes and proficiencies • Standards for Mathematical Content • Grade specific expectations

  5. Structure of theCommon Core State Standards for Mathematics DOMAIN STANDARD CLUSTER Number and Operations in Base Ten 3.NBT Use place value understanding and properties of operations to perform multi-digit arithmetic. Use place value understanding to round whole numbers to the nearest 10 or 100. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies on place and properties of operations..

  6. Structure of the Smarter Balanced Assessment Consortium Mathematics Content Specifications • General Considerations • Claims and Assessment Targets • Rationale and Evidence for Each Claim • Cognitive Rigor Matrix / Depth of Knowledge • Introduction and Background

  7. Cognitive Rigor and Depth of Knowledge • The level of complexity of the cognitive demand. • Level 1: Recall and Reproduction • Requires eliciting information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. • Level 2: Basic Skills and Concepts • Requires the engagement of some mental processing beyond a recall of information. • Level 3: Strategic Thinking and Reasoning • Requires reasoning, planning, using evidence, and explanations of thinking. • Level 4: Extended Thinking • Requires complex reasoning, planning, developing, and thinking most likely over an extended period of time.

  8. Level 1 ExampleGrade 8 Select all of the expressions that have a value between 0 and 1. 87∙ 8–12 74 7–3 ∙ 1 3 2 1 3 9 (–5)6 (–5)10

  9. Level 2 ExampleGrade 8 A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills this tank with water at a rate of 8 cubic feet per minute. How many minutes will it take Jane to completely fill the tank without overflowing at this rate? Round your answer to the nearest minute.

  10. Level 3 ExampleGrade 8 • The total cost for an order of shirts from a company consists of the cost for each shirt plus a one-time design fee. The cost for each shirt is the same no matter how many shirts are ordered. • The company provides the following examples to customers to help them estimate the total cost for an order of shirts. • 50 shirts cost $349.50 • 500 shirts cost $2370 • Part A: Using the examples provided, what is the cost for each shirt, notincluding the one-time design fee? Explain how you found your answer. • Part B: What is the cost of the one-time design fee? Explain how you found your answer.

  11. Level 4 ExampleGrade 8 During the task, the student assumes the role of an architect who is responsible for designing the best plan for a park with area and financial restraints. The student completes tasks in which he/she compares the costs of different bids, determines what facilities should be given priority in the park, and then develops a scale drawing of the best design for the park and an explanation of the choices made. This investigation is done in class using a calculator, an applet to construct the scale drawing, and a spreadsheet.

  12. Cognitive Rigor Matrix This matrix from the Smarter Balanced Content Specifications for Mathematics draws from both Bloom’s (revised) Taxonomy of Educational Objectives and Webb’s Depth-of-Knowledge Levels below.

  13. Smarter Balanced Assessment Consortium Mathematics Content Specifications

  14. Mathematics Assessment Claims • Claim 1: Concepts and Procedures • Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency • Claim 2: Problem Solving • Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies • Claim 3: Communicating Reasoning • Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others • Claim 4: Modeling and Data Analysis • Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems

  15. Claim 1Concepts and Procedures Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.

  16. Claim 1 Concepts and Procedures Target A [m]: Use the four operations with whole numbers to solve problems. (DOK 1, 2) Tasks for this target will require students to use the four operations to solve straightforward, one-step contextual word problems in situations involving equal groups, arrays, and finding an unknown number, including problems where the remainder must be interpreted. Some of these tasks will draw on contexts in 4.MD Target I using measurement quantities such as time, liquid volume, and masses/weights of objects, and money (with decimal representations limited to those described in standards 4.NF.6 and 4.NF.7). Grade 4 Operations and Algebraic Thinking

  17. Claim 1 Assessment TargetsGrade 3 Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. Understand properties of multiplication and the relationship between multiplication and division. Multiply and divide within 100. Solve problems involving the four operations, and identify and explain patterns in arithmetic. Number and Operations – Base 10 Use place value understanding and properties of arithmetic to perform multi-digit arithmetic.

  18. Claim 1 Assessment TargetsGrade 3 Numbers and Operations – Fractions Develop understanding of fractions as numbers. Measurement and Data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Represent and interpret data. Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Geometry Reason with shapes and their attributes.

  19. Claim 1 Assessment TargetsGrade 4 Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Gain familiarity with factors and multiples. Generate and analyze patterns. Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations – Fractions Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand decimal notation for fractions, and comparedecimal fractions.

  20. Claim 1 Assessment TargetsGrade 4 Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Represent and interpret data. Geometric measurement: understand concepts of angle and measure angles. Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

  21. Claim 1 Assessment TargetsGrade 5 Operations and Algebraic Thinking Write and interpret numerical expressions. Analyze patterns and relationships. Number and Operations – Base 10 Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. Number and Operations – Fractions Use equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

  22. Claim 1 Assessment TargetsGrade 5 Measurement and Data Convert like measurement units within a given measurement system. Represent and interpret data. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Classify two-dimensional figures into categories based on their properties.

  23. Claim 1 Assessment TargetsGrade 6 Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Compute fluently with multi-digit numbers and find common factors and multiples. Apply and extend previous understandings of numbers to the system of rational numbers.

  24. Claim 1 Assessment TargetsGrade 6 Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one-variable equations and inequalities. Represent and analyze quantitative relationships between dependent and independent variables. Geometry Solve real-world and mathematical problems involving area, surface area, and volume. Statistics and Probability Develop understanding of statistical variability. Summarize and describe distributions.

  25. Claim 1 Assessment TargetsGrade 7 Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical problems. The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Expressions and Equations Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

  26. Claim 1 Assessment TargetsGrade 7 Geometry Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Statistics and Probability Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. Investigate chance processes and develop, use, and evaluate probability models.

  27. Claim 1 Assessment TargetsGrade 8 The Number System Know that there are numbers that are not rational, and approximate them by rational numbers. Expressions and Equations Work with radicals and integer exponents. Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Functions Define, evaluate, and compare functions. Use functions to model relationships between quantities.

  28. Claim 1 Assessment TargetsGrade 8 Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. Understand and apply the Pythagorean theorem. Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Statistics and Probability Investigate patterns of association in bivariate data.

  29. Claim 1 Assessment TargetsGrade 11 Number and Quantity Extend the properties of exponents to rational exponents. Use properties of rational and irrational numbers. Reason quantitatively and use units to solve problems. Algebra Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. Perform arithmetic operations on polynomials. Create equations that describe numbers or relationships. Understand solving equations as a process of reasoning andexplain the reasoning. Solve equations and inequalities in one variable. Represent and solve equations and inequalitiesgraphically.

  30. Claim 1 Assessment TargetsGrade 11 Functions Understand the concept of a function and use function notation. Interpret functions that arise in applications in terms of a context. Analyze functions using different representations. Build a function that models a relationship between two quantities. Geometry Prove geometric theorems. Statistics and Probability Summarize, represent and interpret data on a single count or measurement variable.

  31. Claims 2, 3, and 4 Assessment Targets for Claims 2, 3, and 4 are not divided into a grade-by-grade description. A general set of assessment targets applicable across grade levels.

  32. Assessment TargetsClaim 2 – Problem Solving Claim 2: Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies. • Apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace • Select and use tools strategically • Interpret results in the context of the situation • Identify important quantities in a practical situation and map their relationships.

  33. Assessment TargetsClaim 3 – Communicating Reason Claim 3: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. • Test propositions or conjectures with specific examples. • Construct, autonomously, chains of reasoning that justify or refute propositions or conjectures. • State logical assumptions being used. • Use the technique of breaking an argument into cases. • Distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in the argument—explain what it is. • Base arguments on concrete referents such as objects, drawings, diagrams, and actions. • Determine conditions under which an argument does and does not apply.

  34. Assessment TargetsClaim 4 – Modeling and Data Analysis Claim 4: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. • Apply mathematics to solve problems arising in everyday life, society, and the workplace. • Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem. • State logical assumptions being used. • Interpret results in the context of a situation. • Analyze the adequacy of and make improvement to an existing model or develop a mathematical model of a real phenomenon. • Identify important quantities in a practical situation and map their relationships. • Identify, analyze, and synthesize relevant external resources to pose or solve problems.

  35. Structure of the Smarter Balanced Assessment Consortium Mathematics Item and Task Specifications • Evidence Statements • Task Models • Sample Items • Mathematics Glossary

  36. Structure of Item Specification Table

  37. Grade 5 Evidence Statement Assessment Target C: Understand the place value system. (DOK 1, 2) Evidence Statement: The student explains patterns in the number of zeros of the product/quotient when multiplying/dividing a number by powers of 10.

  38. Grade 5 Task Model Evidence Statement: The student explains patterns in the number of zeros of the product/quotient when multiplying/dividing a number by powers of 10. Task Model 2. CR (DOK 1, 2) Prompt Features 1: The student is prompted to explain patterns in the number of zeros of a product when multiplying a number by powers of 10. Stimuli: The student is presented with a multiplication problem involving powers of 10. Prompt Features 2: The student is prompted to explain patterns in the number of zeros of a quotient when dividing a number by powers of 10. Stimuli: The student is presented with a division problem involving powers of 10.

  39. Alignment to Claims and Assessment Targets

  40. Module Summary • Common Core State Standards: foundation for claims and assessment targets • Smarter Balanced Content Specifications: define claims and assessment targets • Depth of Knowledge: Level of cognitive processes applied by students • Smarter Balanced Item and Task Specifications: define evidence required and describe task models

More Related