Comprehensive Mathematics for

All Children

July 28, 20107:30 AM – 2:45 Board Room

3:00 Landmark Gym

Myth or RealityThere is a math gene that pre-determines if a child will be proficient in mathematics.

All children can make gains in mathematics if they try hard.

Computational fluency and conceptual understanding are a false dichotomy.

Instruction should simultaneously develop conceptual understanding, computational fluency, and problem solving.

Problem solving (applied mathematics) should always come last.

These are the kind of statements that led to the creation of the National Math Panel by President Bush. (2008)

CBMS Member Society TeamsAMATYC - American Mathematical Association of Two Year Colleges (T2)AMS – American Mathematical Society (T4)AMTE - Association of Mathematics Teacher Educators (T2)ASA - American Statistical Association (T4)ASL – Association for Symbolic Logic (T4)ASSM - Association of State Supervisors of Mathematics (T6)BBA - Benjamin Banneker Association (T8)MAA - Mathematical Association of America (T2)NAM - National Association of Mathematicians (L2)NCSM – National Council of Supervisor of Mathematics (T1)NCTM - National Council of Teachers of Mathematics A (T4)NCTM - National Council of Teachers of Mathematics B (R)NCTM - National Council of Teachers of Mathematics C (M)

National Professional Society TeamsAAAS - American Association for the Advancement of Science (L2)AFT - American Federation of Teachers (T2)

State School Systems or Coalition Teams AR - Arkansas Department of Education (L4)AZ - Peoria Unified School District (T7)AZ - Arizona Department of Education (T7)CA – California Algebra Forum Leadership Team (L1)CA - San Francisco Unified School District (T7)CO - Colorado Charter School Institute (T8)DC - Office of the State Superintendent of Education A (L3)DC – Office of the State Superintendent of Education B (T1)DC - Public Schools (L2)DODEA - Department of Defense Education Activity (L1)IA – Iowa Testing Programs (R)MA – Commonwealth of Massachusetts Team (T7)MA – Association of Teachers of Mathematics in Massachusetts (T6)MD – Calvert County Public Schools (L3)MD - Maryland State Team (T7)MD - Maryland Math Team (L3)NJ - New Jersey Department of Education (T7)NV – Nevada Department of Education (T7)OH – Cincinnati Public Schools Math Curriculum Council (L4)PA - Pennsylvania Department of Education (T4)SC – South Carolina Department of Education (L3)TX - Texas Education Agency (L4)VA - Virginia Mathematics and Science Coalition (T3)VA – Prince William County Public Schools (T3)VA – Virginia Beach Public Schools (T3)VA – Virginia STEM Teacher Education (T3)VA -- Mathematics for All: Students at Promise for Success (L2)WI – Wisconsin Group (M)

Academic Institution TeamsMichigan State University (T6)Texas A&M University (L4)Union College (T4)United States Military Academy (L2)University of Colorado Denver (T6)University of Maryland – Center for Mathematics Education (T6)University of Mississippi (L3)University of Vermont – Vermont Math Initiative (T1)University of Virginia (T3)

Non-Profit Educational Organization TeamsAchieve (L1)ACT Inc. (R)Center on Instruction - Math Strand (T8)College Board (L5)Cyberchase, Thirteen, WNET New York (L1)EduTron (T2)Mid Continent Comprehensive Center (T1)NCLD – National Center for Learning Disabilites (L1)NISL – National Institute for School Leadership (T1)Northwest Regional Educational Laboratory (T6)Reasoning Mind A (T8)Reasoning Mind B (L4)Teacher Ambassadors at the Department of Education (L5)WestEd (L5)

Publishers and Commercial Services TeamsBrown Publishing Network (M)Carnegie Learning A (R)Carnegie Learning B (T8)ETS – Educational Testing Service (T4)iLearn (R)Kendall Hunt (M)K12 Inc. (L5)McGraw Hill (M)Pearson Publishing A (M)Pearson Publishing B (R)Pearson Publishing C (T2)Scholastic (L5)Sylvan Learning (L1)Words and Numbers (M)

Joan Ferrini-Mundy, Ph.D.National Science Foundation and Michigan State University Ex-Officio Member, National Mathematics Advisory Panel and Co-Chair, Instructional Practices Task Group

Myth or RealityThere is a math gene that pre-determines if a child will be proficient in mathematics.

All children can make gains in mathematics if they try hard.

Computational fluency and conceptual understanding are a false dichotomy.

Instruction should simultaneously develop conceptual understanding, computational fluency, and problem solving.

Problem solving (applied mathematics) should always come last.

Imagine a classroom where all students expect mathematics to make sense, think strategically, and take an active stance in solving mathematical problems… this is our Glendale vision.

Glendale mathematics has been designed for our teachers with the knowledge that curriculum must be student, standard, and research driven. Math proficiency for our students will be our goal, the standard will be our framework, and the research will be our foundation.

What does the National Research Council say?

What does our State Standard say? Can we connect the terms from NMP, NRC, and AZ?

Imagine a classroom where all students expect mathematics to make sense, think strategically, and take an active stance in solving mathematical problems… this is our Glendale vision.

Let’s examine conceptual

understanding.

Represents mathematical situations in different ways and knows how different representations can be useful.

Connects mathematical ideas.

Clusters interrelated facts and principles which makes learning easier.

Uses reasoning to find solution. (even if formula is forgotten)

Evidence of Conceptual Understanding

Which character(s) had conceptual understanding? Justify your answer by actions you observed on the clip.

Which character(s) did NOT have conceptual understanding? Justify your answer by actions you observed on the clip.

What happens if there is NOT conceptual understanding?

Multiple representations develop conceptual understanding.

Represents mathematical situations in different ways and knows how different representations can be useful.

3 X 4

Representations allow us to accommodate our students’ needs by use of the instructional continuum.

Connecting mathematical ideas develops conceptual understanding.

Connects mathematical ideas.

Clustering interrelated facts and principles develops conceptual understanding.

Clusters interrelated facts and principles which makes learning easier.

If I know 4 X 3 = 12, then I know 3 X 4 = 12.

If I know 4 X 3 = 12, then I know 12 4 = 3.

If I understand 50%, then I understand ½ and .50.

Using logic and problem solving strategies rather than rules with no meaning will build conceptual understanding.

Uses reasoning to find solution. (even if formula is forgotten)

Your Turnconceptual

understanding

conceptual understanding

Let’s examine problem solving.

Evidence of Problem Solving

Utilizing representations, connections, reasoning/proof, and communication to INVENT a solution path and find a solution.

Using a systemic approach that makes problem solving easier.

Your Turnproblem solving

problem solving

conceptual understanding

Let’s examine fluency.

Evidence of Fluency (Computational/Procedural)

Accuracy

Efficiency

Flexibility

What does fluency look like in a classroom?

Does a “Number Talk” promote computational fluency?

31 + 59 =

Does a “Number Talk” promote computational fluency?

How does a “Number Talk” promote conceptual understanding and/or problem solving?

Your Turnfluency

fluency

problem solving

conceptual understanding

Let’s examine math attitude.

Myth or Reality

There is a math gene that pre-determines if a child will be proficient in mathematics. Myth

All children can make gains in mathematics if they try hard. Reality

Do you see math attitude in yourself? Do you see math attitude in your students?

Compare the math attitude instructional components to the climate descriptors.What do you notice?What will math attitude sound/look (evidence) like this year in your classroom in order to make it a reality?

Your Turnmath attitude

Imagine a classroom where all students expect mathematics to make sense, think strategically, and take an active stance in solving mathematical problems… this is our Glendale vision.

A few resources for support:

The Pacing Guide

The Lesson Planning Guide

GESD Resources

Number/Problem Solving Continuum (in the NEAR future)