Presentation on theme: "The Common Core State Standards for Mathematics"— Presentation transcript:
1 The Common Core State Standards for Mathematics High School
2 Common Core Development Initially 48 states and three territories signed onFinal Standards released June 2, 2010, and can be downloaded atAs of November 29, 2010, 42 states had officially adoptedAdoption required for Race to the Top funds
3 Common Core Development Each state adopting the Common Core either directly or by fully aligning its state standards may do so in accordance with current state timelines for standards adoption, not to exceed three (3) years.States that choose to align their standards with the Common Core Standards accept 100% of the core in English language arts and mathematics. States may add additional standards.
5 Benefits for States and Districts Allows collaborative professional development to be based on best practicesAllows the development of common assessments and other toolsEnables comparison of policies and achievement across states and districtsCreates potential for collaborative groups to get more mileage from:Curriculum development, assessment, and professional development
6 CharacteristicsFewer and more rigorous. The goal was increased clarity.Aligned with college and career expectations – prepare all students for success on graduating from high school.Internationally benchmarked, so that all students are prepared for succeeding in our global economy and society.Includes rigorous content and application of higher-order skills.Builds on strengths and lessons of current state standards.Research based.
7 Intent of the Common Core The same goals for all studentsCoherenceFocusClarity and specificity
8 CoherenceArticulated progressions of topics and performances that are developmental and connected to other progressionsConceptual understanding and procedural skills stressed equallyNCTM states coherence also means that instruction, assessment, and curriculum are aligned.
9 Focus Key ideas, understandings, and skills are identified Deep learning of concepts is emphasizedThat is, adequate time is devoted to a topic and learning it well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.
10 Clarity and Specificity Skills and concepts are clearly defined.An ability to apply concepts and skills to new situations is expected.
11 CCSS Mathematical Practices The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics.
12 CCSS Mathematical Practices Make sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.
13 Common Core Format High School K-8 Conceptual Category Grade Domain ClusterStandardsK-8GradeDomainClusterStandards(No pre-K Common Core Standards)
14 Format of High School Domain Cluster Standard Note no grade level, different way of labeling domain in the gray box.
15 Format of High School Standards Regular StandardModelingSTEM
16 High School Conceptual Categories The big ideas that connect mathematics across high schoolA progression of increasing complexityDescription of the mathematical content to be learned, elaborated through domains, clusters, and standards
17 Common Core - DomainOverarching “big ideas” that connect topics across the gradesDescriptions of the mathematical content to be learned, elaborated through clusters and standards
18 Common Core - ClustersMay appear in multiple grade levels with increasing developmental standards as the grade levels progressIndicate WHAT students should know and be able to do at each grade levelReflect both mathematical understandings and skills, which are equally important
19 Common Core - Standards Content statementsProgressions of increasing complexity from grade to gradeIn high school, this may occur over the course of one year or through several years
20 High School PathwaysThe CCSS Model Pathways are NOT required. The two sequences are examples, not mandatesTwo models that organize the CCSS into coherent, rigorous coursesFour years of mathematics:One course in each of the first two yearsFollowed by two options for year 3 and a variety of relevant courses for year 4Course descriptionsDefine what is covered in a courseAre not prescriptions for the curriculum or pedagogy
21 High School PathwaysPathway A: Consists of two algebra courses and a geometry course, with some data, probability, and statistics infused throughout each (traditional)Pathway B: Typically seen internationally, consisting of a sequence of 3 courses, each of which treats aspects of algebra; geometry; and data, probability, and statistics.
22 Conceptual Categories Number and QuantityAlgebraFunctionsModelingGeometryStatistics and Probability
23 Numbers and QuantityExtend the Real Numbers to include work with rational exponents and study of the properties of rational and irrational numbersUse quantities and quantitative reasoning to solve problems.
24 Numbers and Quantity Required for higher math and/or STEM Compute with and use the Complex Numbers, use the Complex Number plane to represent numbers and operationsRepresent and use vectorsCompute with matricesUse vector and matrices in modeling
25 Algebra and Functions Two separate conceptual categories Algebra category contains most of the typical “symbol manipulation” standardsFunctions category is more conceptualThe two categories are interrelated
26 Algebra Creating, reading, and manipulating expressions Understanding the structure of expressionsIncludes operating with polynomials and simplifying rational expressionsSolving equations and inequalitiesSymbolically and graphically
27 Algebra Required for higher math and/or STEM Expand a binomial using the Binomial TheoremRepresent a system of linear equations as a matrix equationFind the inverse if it exists and use it to solve a system of equations
28 Functions Understanding, interpreting, and building functions Includes multiple representationsEmphasis is on linear and exponential modelsExtends trigonometric functions to functions defined in the unit circle and modeling periodic phenomena
29 Functions Required for higher math and/or STEM Graph rational functions and identify zeros and asymptotesCompose functionsProve the addition and subtraction formulas for trigonometric functions and use them to solve problems
30 Functions Required for higher math and/or STEM Inverse functions Verify functions are inverses by compositionFind inverse values from a graph or tableCreate an invertible function by restricting the domainUse the inverse relationship between exponents and logarithms and in trigonometric functionsFinding the inverse of a function Is a part of the Common Core for all students (i.e., not STEM) but the ideas listed here are expected of STEM students
31 ModelingModeling has no specific domains, clusters or standards. Modeling is included in the other conceptual categories and marked with a asterisk.
32 ModelingModeling links classroom mathematics and statistics to everyday life, work, and decision-making. Technology is valuable in modeling. A model can be very simple, such as writing total cost as a product of unit price and number bought, or using a geometric shape to describe a physical object.
33 ModelingPlanning a table tennis tournament for 7 players at a club with 4 tables, where each player plays against each other player.Analyzing stopping distance for a car.Modeling savings account balance, bacterial colony growth, or investment growth.
34 Geometry Understanding congruence Using similarity, right triangles, and trigonometry to solve problemsCongruence, similarity, and symmetry are approached through geometric transformationsCongruence includes proving theorems and geometric constructions.
35 Geometry Circles Expressing geometric properties with equations Includes proving theorems and describing conic sections algebraicallyGeometric measurement and dimensionModeling with geometry
36 Geometry Required for higher math and/or STEM Non-right triangle trigonometryDerive equations of hyperbolas and ellipses given foci and directricesGive an informal argument using Cavalieri’s Principal for the formulas for the volume of solid figuresNote deriving equations of circles and parabolas is a part of the Common Core for all studentsNote using Cavalieri’s Principal to find volume is a part of the Common Core for all students
37 Statistics and Probability Analyze single a two variable dataUnderstand the role of randomization in experimentsMake decisions, use inference and justify conclusions from statistical studiesUse the rules of probability
38 Interrelationships Algebra and Functions Algebra and Geometry Expressions can define functionsDetermining the output of a function can involve evaluating an expressionAlgebra and GeometryAlgebraically describing geometric shapesProving geometric theorems algebraically
39 Additional Information For the secondary level, please see NCTM’s Focus in High School Mathematics: Reasoning and Sense MakingFor grades preK-8, a model of implementation can be found in NCTM’s Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics
40 AcknowledgmentsThanks to the Ohio Department of Education and Eric Milou of Rowan University for providing content and assistance for this presentation