Mathematics Gap Analysis Phase I

Transcription

1 Mathematics Gap Analysis Phase I Organizing Structure: The Standards Compared to the Common Core College and Career Readiness Standards The Mathematics College and Career Readiness Standards (CCRS) are designed to help students understand the specific content knowledge and academic skills necessary for college readiness. The CCRS are broad in nature, equipping students for general education college mathematics courses, but are not intended to encompass all skills necessary for students entering majors that require specific mathematical knowledge. SAW System: S = Strong Alignment A = Adequate Alignment W = Weak Alignment For example: S9, A1 = Nine of the ten vertical team members rated the item as having strong alignment and one as average. Common Core State The Common Core State Standards Initiative is a joint effort by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO) in partnership with Achieve, ACT and the College Board.The College and Career Readiness Standards for Mathematics consist of three interconnected parts: a Standard for Mathematical Practice, ten Standards for Mathematical Content, and a set of Example Tasks. I. Numeric Reasoning A. Number representation "Number" s.1, c.a,b,c,d 1. Compare real numbers. 2. Define and give examples of complex numbers. W4, A1 Mentioned in "Equations" paragraph 4; c.d B. Number operations 1. Perform computations with real and complex numbers. Real numbers: S3, A2 Complex numbers: W5 Real numbers are covered in "Number" s.2, 3, 4 Computations with Complex numbers are not mentioned. C. Number sense and number concepts Page 1

2 1. Use estimation to check for errors and reasonableness of solutions. Common Core State cp.6; "Number" s.5; "Number" paragraph 3 II. Algebraic Reasoning A. Expressions and equations 1. Explain and differentiate between expressions and equations using words such as solve, evaluate, and simplify. S3, A2 The difference between expressions and equations is made clear in "Expressions" c.a, B, C, and D, and "Equations" c.a, B. However, the differentiation is weak in delineating the "solve," "evaluate," and "simplify" processes. B. Manipulating expressions 1. Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational expressions). C. Solving equations, inequalities, and systems of equations 1. Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to solve equations, inequalities, and systems of linear equations. 2. Explain the difference between the solution set of an equation and the solution set of an inequality. "Expressions" c.c, D; s.1, 2 S4, A1 "Equations" paragraph 1; s.2, 3, 4, 5, 6 TxCCRS does not mention identities or c.d A4, W1 "Equations" s.4, 5, 6 and paragraph 6 discuss the similarities and imply the differences. D. Representations 1. Interpret multiple representations of equations and relationships. (assumes that the CCSSO interprets "equations and relationships" to mean "equations and functions") cp.3; "Functions" paragraph 5, s.2; "Modeling" paragraph 5, s.1; "Quantity" s.3 Page 2

3 2. Translate among multiple representations of equations and relationships. (assumes that the CCSS interprets "equations and relationships" to mean "equations and functions") Common Core State cp.3; "Functions" paragraph 5, c.a,b; "Modeling" paragraph 4, 5, s.1, 2, 3, 4, 5; "Quantity" s.3 III. Geometric Reasoning A. Figures and their properties 1. Identify and represent the features of plane and space figures. 2. Make, test, and use conjectures about one-, two-, and three-dimensional figures and their properties. 3. Recognize and apply right triangle relationships including basic trigonometry. "Shape" c.a; s.3 "Modeling" s.2 S1, A4 "Coordinates" s.3 "Shape" s.2 cp.2 Assuming that the core practices apply to all strands TX CCRS does not mention "proof," whereas the CCSS mentions "prove theorems" in "Shape" s.2 "Shape" c.d; s.6 B. Transformations and symmetry 1. Identify and apply transformations to figures. 2. Identify the symmetries of a plane figure. 3. Use congruence transformations and dilations to investigate congruence, similarity, and symmetries of plane figures. C. Connections between geometry and other mathematical content strands 1. Make connections between geometry and algebra. S2, A3 "Shape" paragraph 3; c.b; s.5 "Coordinates" paragraph 5 S1, A4 "Shape" c.b; s. 2, 5; paragraph 3; "Coordinates" paragraph 3 "Shape" paragraph 3; c.b; s.2, 5 "Coordinates" c.a, B, C; s.1, 2, 3; paragraph 2 Page 3

4 2. Make connections between geometry, statistics, and probability. 3. Make connections between geometry and measurement. Common Core State W5 Implied in "Probability" c.b, "Shape" c.a, and in "Statistics" s.3 "Shape" c.a; s.4, 5, 6; paragraph 2 "Coordinates" s.3 "Quantity" c.b, paragraph 3 D. Logic and reasoning in geometry 1. Make and validate geometric conjectures. 2. Understand that Euclidean geometry is an axiomatic system. A5 "Shape" s.2; cp.2, assuming that the core practices apply to all strands TX CCRS does not mention "proof," whereas the CCSS mentions "prove theorems" in "Shape" s.2 A5 "Shape" c.a; s.2; paragraph 1 "Coordinates" paragraph 1 How do students understand an axiomatic system without involving proof? TX CCRS does not mention "proof" IV. Measurement Reasoning A. Measurement involving physical and natural attributes 1. Select or use the appropriate type of unit for the attribute being measured. "Quantity" c.a, B, C; s. 2, 3, 4 B. Systems of measurement 1. Convert from one measurement system to another. 2. Convert within a single measurement system. W5 A3, S2 "Quantity" paragraphs 4, 5; c.b, C; s.1, 4 CCSS does not specifically mention conversion from one measurement system to another, and is possibly implied in "Quantity" paragraph 2 C. Measurement involving geometry and algebra Page 4

5 1. Find the perimeter and area of twodimensional figures. 2. Determine the surface area and volume of three-dimensional figures. 3. Determine indirect measurements of figures using scale drawings, similar figures, Pythagorean Theorem, and basic trigonometry. Common Core State "Shape" c.4, 5; "Coordinates" s.3; "Quantity" c.b "Shape" c.4, 5; "Coordinates" s.3; "Quantity" c.b "Shape" c.b, C, D; paragraph 3, 4; s.5, 6 D. Measurement involving statistics and probability 1. Compute and use measures of center and spread to describe data. 2. Apply probabilistic measures to practical situations to make an informed decision. "Statistics" paragraph 2; s.2, 3; c.b "Statistics" paragraph 1; c.a, D; s.4; "Probability" c.d; s.5, 6 V. Probabilistic Reasoning A. Counting principles 1. Determine the nature and the number of elements in a finite sample space. B. Computation and interpretation of probabilities 1. Compute and interpret the probability of an event and its complement. 2. Compute and interpret the probability of conditional and compound events. S4, A1 "Probability" c.a; s.1, 3; paragraph 2 A5 "Probability" c.b,c,d; s.1 CCSS does not mention "complement" "Probability" c.c; paragraph 3 and 4; s. 2, 3, 4, 6; Note that CCSS uses "combined events" in c.c, but the explanations in paragraph 3 and in s.2 and 3 are consistent with the TX CCRS. Page 5

6 Common Core State VI. Statistical Reasoning A. Data collection "Statistics" s.1; c. A, D; paragraph 4 1. Plan a study. B. Describe data A5 "Statistics" s.3--must determine the type of data in order to use it appropriately CCSS emphasizes quantitative over qualitative data 1. Determine types of data. 2. Select and apply appropriate visual representations of data. 3. Compute and describe summary statistics of data. 4. Describe patterns and departure from patterns in a set of data. C. Read, analyze, interpret, and draw conclusions from data 1. Make predictions and draw inferences using summary statistics. 2. Analyze data sets using graphs and summary statistics. 3. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software. "Statistics" c.b, s.2, 3; paragraph 2 "Modeling" paragraph 4, s.5 "Statistics" c.b, s.2, 3; paragraphs 2, 5 "Modeling" s.5 "Statistics" s. 3, 4, 5; paragraph 2; c.c, D "Statistics" c.c, D; s.3, 4, 5; paragraph 2 "Modeling" s.5, 6 "Statistics" c. B; s. 2, 3, 4; paragraphs 2, 5 "Statistics" s.2; paragraph 5; cp. 6; "Modeling" s.5 Page 6

7 Common Core State S3, A2 "Statistics" paragraph 3, 4, 5; s. 5 TX CCRS uses "reliability" to imply "validity" 4. Recognize reliability of statistical results. VII. Functions A. Recognition and representation of functions 1. Recognize whether a relation is a function. 2. Recognize and distinguish between different types of functions. W5 This is not expressed explicitly in the CCSS; however it is implied in "Functions" s.1 and 3. In addition, "relations" are not mentioned in the CCSS. A5 "Functions" c.d; paragraph 4; s.1, 2, 4 CCSS emphasizes linear and exponential; other functions are deemphasized. B. Analysis of functions 1. Understand and analyze features of a function. 2. Algebraically construct and analyze new functions. C. Model real world situations with functions "Functions" s. 1, 2, 3, 4, 5 TX CCRS does not mention rate of change W5 Implicit in "Functions" s.3 "Modeling" s. 4; "Functions" c.c; s.4 1. Apply known function models. 2. Develop a function to model a situation. "Modeling" c.a, B; s. 1,3,4,5,6; paragraphs 4, 5; cp.3; "Functions" c.3; "Modeling" paragraphs 3, 4; c. A, B; s.1 Page 7

8 Common Core State VIII. Problem Solving and Reasoning A. Mathematical problem solving 1. Analyze given information. 2. Formulate a plan or strategy. cp.1, 3, 6; "Expressions" paragraph 2; "Functions" s. 3 S4, A1 cp.1, 3,4, 6; "Number" s.3; paragraphs 1 and 2; "Equations" paragraph 3; s.1; "Statistics" c.a, D; s.1, 4; paragraph 3 cp.3, 4, 5, 6; "Number" s.3, 4, 5; "Quantity" s. 4; "Equations" s. 2, 4, 5, 6; "Modeling" paragraphs 1-4; s.1; "Probability" paragraph 4; "Statistics" c.a, D; s.4 3. Determine a solution. 4. Justify the solution. S1, A4 cp.2,3,5,6; "Number" s.5; "Quantity" s.4; "Equations" c.b; "Modeling" paragraph 4 A5 "Modeling" paragraph 3, s.6; "Equations" c.d; "Statistics" paragraph 3, s.5 5. Evaluate the problem-solving process. B. Logical reasoning 1. Develop and evaluate convincing arguments. cp.2; "Shape" c.a; s.2; "Statistics" paragraph 4; s.5; "Modeling" paragraph 3; "Equations" c.c' paragraph 3 A5 cp.2, 3, 4, 5, 6; "Equations" c.c; "Coordinates" paragraph 5" 2. Use various types of reasoning. C. Real world problem solving 1. Formulate a solution to a real world situation based on the solution to a mathematical problem. cp.2; "Modeling" paragraph 1, 3, 5; c.a,b; "Shape" paragraph 5; s.6; "Probability" paragraph 4; c.d; s.3, 5, 6; "Statistics" paragraph 1, 2; s.3; "Quantity" c.a; paragraph 6; "Shape" c.c; "Coordinates" paragraph 4; "Expressions" s.3, 4;"Function" paragraph 3 Page 8

9 2. Use a function to model a real world situation. Common Core State "Function" paragraph 1, 2, 3, 4, 5; c.c; s.1, 4; "Modeling" c.a; paragraph 1, 3, 4; s.3; A5 "Modeling" paragraph 3, s.6; "Statistics" paragraph 3, 4; s.5 3. Evaluate the problem-solving process. IX. Communication and Representation A. Language, terms, and symbols of mathematics 1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem. 2. Use mathematical language to represent and communicate the mathematical concepts in a problem. 3. Use mathematics as a language for reasoning, problem solving, making connections, and generalizing. cp. 1, 4, 5; "Expressions" c.a, B, C, D; paragraphs 1-5; s.1, 2, 3; "Quantity" c.a; s.4; "Number" s. 1; "Equation" c.b; s.1, 2; "Modeling" s.1, 3, 4; "Functions" c.a, B, C; paragraphs 2, 3, 4, 5; s.1, 2, 3, 4 cp. 1, 3 ;"Equation" s.3; "Functions" c.c; "Expressions", "Equations", "Functions", and "Modeling" cp.2, 3, 4, 5, 6; "Equations" c.c; paragraph 3; "Coordinates" paragraph 5"; "Statistics" paragraph 4; s.5; "Modeling" paragraph 3; "Shape" c.a; "Functions" paragraph 4; s.4 B. Interpretation of mathematical work 1. Model and interpret mathematical ideas and concepts using multiple representations. 2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context. C. Presentation and representation of mathematical work 1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, graphs, and words. S4, A1 cp. 3; "Expressions" s.4; "Functions" paragraph 5, s.2, 5; c.a,b; "Quantity" s.3; "Modeling" paragraph 4, 5, s.1, 2, 3, 4, 5; "Equations" s.4, 5, 6 S4, A1 cp.1, 3, 5; "Number" s.4, 5; "Quantity" s. 4; "Expressions" s.4; "Functions" s. 2, 3, 4, 5: "Statistics" paragraph 2, 4; c.b; s.2, 3, 4, 5 S4, A1 cp. 1, 2, 3, 6; "Expressions" s.3, 4; "Functions"; "Modeling" s. 1-6; paragraphs 4, 5; "Shape" c.c, D; paragraphs 1, 5; s.2, 4; "Coordinates" c.b, paragraphs 1-5; s.2; "Statistics" c. B, D; paragraphs 2, 3; s. 2, 3; "Equations" c.c Page 9

10 2. Create and use representations to organize, record, and communicate mathematical ideas. 3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications. Common Core State S4, A1 cp. 1, 2, 3, 5, 6; "Expressions" s.3, 4; "Equations" paragraph 5; s.6; "Statistics" c.b, D; s.1, 2, 3, 4; paragraph 2; "Modeling" paragraph 4, s.5; "Shape" c.c,d; paragraphs 1, 5; s.4, 5 A5 cp. 1, 2, 3, 5; implied in "Modeling," "Shape," and "Statistics" X. Connections A. Connections among the strands of mathematics cp3; Last paragraph of each standard lists connections 1. Connect and use multiple strands of mathematics in situations and problems. 2. Connect mathematics to the study of other disciplines. B. Connections of mathematics to nature, real world situations, and everyday life 1. Use multiple representations to demonstrate links between mathematical and real-world situations. 2. Understand and use appropriate mathematical models in the natural, physical, and social sciences. 3. Know and understand the use of mathematics in a variety of careers and professions. W5 Implied in a few examples, but not specified in any standard cp.3; "Functions" paragraph 4, 5, s.2; "Modeling" paragraph 5, s.1, 2, 3, 4, 5; "Quantity" s.3 W5 W5 Implied in a few examples, but not specified in any standard Not specified in any standard Page 10