Comprehensive Mathematics for
All Children
July 28, 2010
7:30 AM – 2:45 Board Room
3:00 Landmark Gym
Myth or Reality
There 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 Teams
AMATYC - 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 Teams
AAAS - 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 Teams
Michigan 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 Teams
Achieve (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 Teams
Brown 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 Reality
There 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.
Evidence of 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)
What happens if there is NOT 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.
Multiple representations develop conceptual understanding.
3X4
Represents mathematical situations in different ways and
knows how different representations can be useful.
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.
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.
Clusters interrelated facts and principles which
makes learning easier.
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 Turn
conceptual
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 Turn
problem
solving
conceptual
understanding
Let’s examine
fluency.
problem solving
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 Turn
fluency
conceptual
understanding
fluency
problem solving
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 Turn
math 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)