The Common Core Wisconsin Standards

1
The Common Core Wisconsin Standards
Opportunities for Students Mathematics
Learning

• Hank Kepner
• National Council of Teachers of Mathematics,
  Past-President
• University of Wisconsin-Milwaukee
• Milwaukee Public Schools
• kepner_at_uwm.edu

2
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 PointsPK-8 NCLB
• 2009 Focus in High School Mathematics
  Reasoning Sense Making

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..

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 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.

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 only
• Source PARCC

6
Common Core State Standards

• Standards for Mathematical Practice (3 pages)
• K8 Grade level standards
• Domains
• Clusters
• Standards
• High School standards
• conceptual categories

7
These are student behaviors!!
8
NCTM Process Standards and the CCSS Mathematical
Practices
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.
9
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 ones own efficacy.

10
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.

11
How Many Border Tiles for a Square Pool?
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 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.

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 making
• Students demographics too often predict those
  opportunities
• Expectations, 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
  analyzethe 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)

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 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!

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!

20
hkepner_at_nctm.org