The Common Core Wisconsin Standards –

Opportunities for Students’ Mathematics

Learning

Hank KepnerNational Council of Teachers of Mathematics,

Past-PresidentUniversity of Wisconsin-Milwaukee

Milwaukee Public Schoolskepner@uwm.edu

NCTM History Informing My Remarks

• 1980 An Agenda for Action – problem solving

• 1989 Curriculum and Evaluation Standards for School Mathematics

• 1991 Professional Teaching Standards

• 2000 Principles and Standards for School Mathematics

• 2006 Curriculum Focal Points–PK-8 NCLB

• 2009 Focus in High School Mathematics: Reasoning & Sense Making

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..

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 2009. 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 2009. College- and Career Readiness Math Standards,

•June 2, 2010. Common Core State Standards in Mathematics and English/Language Arts

released. Wisconsin adopted.

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 only

Source: PARCC

Common Core State Standards

• Standards for Mathematical Practice (3 pages)

• K–8 Grade level standards– Domains

• Clusters

– Standards

• High School standards –

“conceptual categories”

These are student behaviors!!

NCTM Process Standards CCSS Mathematical Practices

Problem Solving Make sense of problems and persevere in solving them.Use appropriate tools strategically

Reasoning and Proof Reason abstractly and quantitatively.Critique the reasoning of others.Look for and express regularity in repeated reasoning

Communication Construct viable arguments

Connections Attend to precision.Look for and make use of structure

Representations Model with mathematics.

NCTM Process Standards and the CCSS Mathematical Practices

Mathematical Proficiency Adding It Up (NRC, 2001)

• Conceptual understanding – Comprehension of mathematical concepts, operations, and relations

• Procedural fluency – Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

• Strategic competence – Ability to formulate, represent, and solve mathematical problems

• Adaptive reasoning – Capacity for logical thought, reflection, explanation, and justification

• Productive disposition – Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.

#3 Construct viable Arguments &Critique the reasoning of others

• understand & use stated assumptions, definitions, and previously established results in constructing arguments

• make conjectures and build a logical progression of statements to explore the truth of their conjectures

• justify their conclusions; communicate them to others

• listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

How Many Border Tiles for a Square Pool?

How many border tiles for a square pool of side s feet?

Sample Student Solutions for a Square Pool of side s

s + s + s + s + 44(s + 1)2s + 2(s + 1)4(s + 2) – 4(s + 2)2 - s 2

Construct viable Arguments &Critique the reasoning of others

• understand & use stated assumptions, definitions, and previously established results in constructing arguments

• make conjectures and build a logical progression of statements to explore the truth of their conjectures

• justify their conclusions; communicate them to others

• listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

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 making

• Students’ demographics too often predict those opportunities

• Expectations, beliefs, and biases have an impact on the mathematical learning opportunities provided for students

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 level

• Monitor the assessment developments to ensure sound assessment – more than multiple choice:

• Department of Education: Funded Assessment Consortia to develop assessment systems for use by 2014-2015

• Partnership for the Assessment of Readiness for College and Careers (PARCC includes Illinois, Achieve)

• SMARTER Balanced Assessment Consortium (includes Wisconsin, California)

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!

Key Recommendations

• Work 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!

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!

hkepner@nctm.org