Presentation on theme: "The Common Core Wisconsin Standards – Opportunities for Students’ Mathematics Learning Hank Kepner National Council of Teachers of Mathematics, Past-President."— Presentation transcript:
1 The Common Core Wisconsin Standards – Opportunities for Students’ Mathematics Learning Hank KepnerNational Council of Teachers of Mathematics, Past-PresidentUniversity of Wisconsin-MilwaukeeMilwaukee Public Schools
2 NCTM History Informing My Remarks 1980 An Agenda for Action – problem solving1989 Curriculum and Evaluation Standards for School Mathematics1991 Professional Teaching Standards2000 Principles and Standards for School Mathematics2006 Curriculum Focal Points–PK-8 NCLB2009 Focus in High School Mathematics: Reasoning & Sense MakingTo put my own remarks in context for those of you who do not know me, let me indicated the lens I bring to this work.
3 The NCTM 1989 Standards Initiated the Standards Movements An internally established set of beliefs about what is important for students to learn and to do – built primarily within the mathematics education community.Promoted two decades of research & development focusing on elaboration, clarification, curriculum development, and instructional implementation..To put my own remarks in context for those of you who do not know me, let me indicated the lens I bring to this work.
4 The Political Common Core State Standards Initiative Following over 2 decades of math standards development and refinement initiated by National Council of Teachers of Mathematics:Spring National Governors Association (NGA) & the Council of Chief State School Officers (CCSSO) agreed to develop a common core of state standards, starting in Mathematics and English/Language Arts.Fall College- and Career Readiness Math Standards,June 2, Common Core State Standards in Mathematics and English/Language Arts released. Wisconsin adopted.
5 NGA and CCSSO Common Core State Standards Released June, 2, 2010 Adopted by 44 States, DC Maine and Washington have adopted the CCSS provisionally ** Minnesota adopted the CCSS in ELA onlySource: PARCC
6 Common Core State Standards Standards for Mathematical Practice (3 pages)K–8 Grade level standardsDomainsClustersStandardsHigh School standards –“conceptual categories”
8 NCTM Process Standards and the CCSS Mathematical Practices Problem SolvingMake sense of problems and persevere in solving them.Use appropriate tools strategicallyReasoning and ProofReason abstractly and quantitatively.Critique the reasoning of others.Look for and express regularity in repeated reasoningCommunicationConstruct viable argumentsConnectionsAttend to precision.Look for and make use of structureRepresentationsModel with mathematics.
9 Mathematical Proficiency Adding It Up (NRC, 2001)Conceptual understanding – Comprehension of mathematical concepts, operations, and relationsProcedural fluency – Skill in carrying out procedures flexibly, accurately, efficiently, and appropriatelyStrategic competence – Ability to formulate, represent, and solve mathematical problemsAdaptive reasoning – Capacity for logical thought, reflection, explanation, and justificationProductive disposition – Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.
10 #3 Construct viable Arguments & Critique the reasoning of others understand & use stated assumptions, definitions, and previously established results in constructing argumentsmake conjectures and build a logical progression of statements to explore the truth of their conjecturesjustify their conclusions; communicate them to otherslisten to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
12 How many border tiles for a square pool of side s feet?
13 Sample Student Solutions for a Square Pool of side s s + s + s + s + 4 4(s + 1) 2s + 2(s + 1) 4(s + 2) – 4 (s + 2)2 - s 2
14 Construct viable Arguments & Critique the reasoning of others understand & use stated assumptions, definitions, and previously established results in constructing argumentsmake conjectures and build a logical progression of statements to explore the truth of their conjecturesjustify their conclusions; communicate them to otherslisten to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
15 Equity: Mathematical reasoning and sense making must be evident in the mathematical experiences of all students.Courses students take have an impact on the opportunities that they have for reasoning and sense makingStudents’ demographics too often predict those opportunitiesExpectations, beliefs, and biases have an impact on the mathematical learning opportunities provided for students
16 Next Steps for the Common Core Standards The standards will make sense only when we have instructional and assessment exemplars to use and analyze—the operational definitions!Most standards do not describe depth of cognitive demand to be assessed. Caution about trivial levelMonitor the assessment developments to ensure sound assessment – more than multiple choice:Department of Education: Funded Assessment Consortia to develop assessment systems for use byPartnership for the Assessment of Readiness for College and Careers (PARCC includes Illinois, Achieve)SMARTER Balanced Assessment Consortium (includes Wisconsin, California)
17 Developing advanced systems for professional development The Standards of Mathematical Practice are STANDARDS that the participating states have signed on to implement.CAUTION: Too many implementation and assessment projects are already starting to ignore or avoid the Standards for Mathematical Practice.Placing attention and focus only on content standards is insufficient!
18 Key RecommendationsWork on instructional strategies and tasks to refine your mathematical engagement of students in the Standards of Mathematical Practice.With colleagues, study content in a domain, cluster chunks -- across grades: attending to connections & sequencing- not as isolated standards!
19 Major Concerns NOT Addressed The CCSS for Mathematics a lock-step content sequence “all students” K- 8.For high performing students, how will this be addressed in typical school implementation and accountability assessments?For struggling students – not likely to master at grade level stated; RtI? Concepts grow more slowly!