These Are the Facts

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These Are the Facts

• Intellication SeminarDiocese of Toledo -
  Catholic Youth School Services
• June 9, 2009

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Number Activity

• Count up the number of letters in your first
  name.
• Think of your favorite number.
• Add, Subtract, Multiply, or Divide the two
  numbers together.
• Introduce yourself to someone sitting next to
  you.
• Share and formulate a way to combine your unique
  number together with your partner.

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What are the Facts?
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Moores Law
(môrz lâ) (n.) The observation made in 1965 by
Gordon Moore, co-founder of Intel, that the
number of transistors per square inch on
integrated circuits had doubled every year since
the integrated circuit was invented. Moore
predicted that this trend would continue for the
foreseeable future. In subsequent years, the pace
slowed down a bit, but data density has doubled
approximately every 18 months, and this is the
current definition of Moore's Law, which Moore
himself has blessed. Most experts, including
Moore himself, expect Moore's Law to hold for at
least another two decades.
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4x Work Problem
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Elementary, My Dear
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Math Course of Study
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• K - Use place value concepts to represent whole
  numbers.
• 1st - Use 100s chart to show understanding of
  place value.
• 2nd - Understand numbers, ways of representing
  numbers, relationships among numbers from
  100-1000.

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• 3rd - Develop fluency with multiplication and
  division facts.
• 4th - Demonstrate fluency in adding, subtracting,
  multiplying, and dividing.
• 5th - Use order of operations, including
  parentheses to simplify problems.

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• 6th - Decompose and recompose whole numbers using
  factors and exponents
• 7th - Solve linear equations and inequalities
  symbolically, graphically, and numerically
• 8th - Understand numbers, ways of representing
  numbers, relationships among numbers and number
  systems

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National Math Panel
1. Fluency with Whole Numbers. By the end of
Grade 5 or 6, children should have a robust
sense of number. This sense of number must
include an understanding of place value and the
ability to compose and decompose whole numbers.
It must clearly include a grasp of the meaning of
the basic operations of addition, subtraction,
multiplication, and division. It must also
include use of the commutative, associative, and
distributive properties computational facility
and the knowledge of how to apply the operations
to problem solving. Computational facility
requires the automatic recall of addition and
related subtraction facts, and of multiplication
and related division facts. It also requires
fluency with the standard algorithms for
addition, subtraction, multiplication, and
division. Fluent use of the algorithms not only
depends on the automatic recall of number facts
but also reinforces it. A strong sense of number
also includes the ability to estimate the results
of computations and thereby to estimate orders of
magnitude, e.g., how many people fit into a
stadium or how many gallons of water are needed
to fill a pool.
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Tech Recommendation
Recommendation The Panel recommends that
high-quality computer-assisted instruction (CAI)
drill and practice, implemented with fidelity, be
considered as a useful tool in developing
students automaticity (i.e., fast, accurate, and
effortless performance on computation), freeing
working memory so that attention can be directed
to the more complicated aspects of complex tasks.
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Balanced Math
To prepare students for Algebra, the curriculum
must simultaneously develop conceptual
understanding, computational fluency, and
problem- solving skills. Debates regarding the
relative importance of these aspects of
mathematical knowledge are misguided. These
capabilities are mutually supportive, each
facilitating learning of the others. Teachers
should emphasize these interrelations taken
together, conceptual understanding of
mathematical operations, fluent execution of
procedures, and fast access to number
combinations jointly support effective and
efficient problem solving.
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Teaching Computation

• A teacher from the Key Academy in Washington D.C.
  describes how she provides entering fifth-grade
  students who represent a wide range of
  preparation, the foundational number sense and
  computational skills needed to perform at the
  fifth grade level.

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Developing Fluency
Developing Conceptual Understanding, Fluency, and
Problem Solving is critical in establishing the
value of simultaneously teaching concepts,
procedures, and problem solving. The
presentation will also focus on the importance of
practice distributed over time in developing
automaticity and improving fluency, including the
use of technology-based tools and the
relationship between student beliefs about
learning and mathematics performance.
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Simultaneous Teaching
Dr. Ferrini-Mundy discusses the interrelations
between conceptual understanding, computational
fluency, and problem-solving skills suggests
ways to plan lessons and units addresses the
role of teacher wisdom and judgment and
recommends ways that schools and districts can
support teachers. She also talks about the impact
of student beliefs about effort on mathematics
achievement.
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NCTM Focal Points

• Important mathematical topics for each grade
  level, Pre K-8.
• Organizes curriculum design and instruction.
• Conveys knowledge and essential skills.
• Provides foundation for further mathematical
  thinking.

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Grade 2 - Number and Operations and Algebra
Developing quick recall of addition facts and
related subtraction facts and fluency with
multi-digit addition and subtraction Children
use their understanding of addition to develop
quick recall of basic addition facts and related
subtraction facts. They solve arithmetic problems
by applying their understanding of models of
addition and subtraction (such as combining or
separating sets or using number lines),
relationships and properties of number (such as
place value), and properties of addition
(commutativity and associativity). Children
develop, discuss, and use efficient, accurate,
and generalizable methods to add and subtract
multi-digit whole numbers. They select and apply
appropriate methods to estimate sums and
differences or calculate them mentally,
depending on the context and numbers involved.
They develop ?uency with efficient procedures,
including standard algorithms, for adding and
subtracting whole numbers, understand why the
procedures work (on the basis of place value and
properties of operations), and use them to solve
problems. multiplicative situations, developing
initial understandings of multiplication as
repeated addition.
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Ohio Department of Ed

• Fluency is just not timed tests, but a
  combination of many strategies and approaches.
  Currently the ODE is working with the state
  legislature to revise standards. NCTMs Focal
  Points will be a guide for big ideas, but were
  not throwing away the current program. The goal
  is to provide clarity to teachers and for
  standards to serve as a guide for instruction,
  with an emphasis on non-repetitive objectives
  (ex.Whole Number Operations). At this time they
  are also in the process of Investigating
  International Benchmarks too. Anita Jones,
  2009

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2007 TIMSS Results

• Comparisons of the mathematics achievement of
  fourth-graders in 2007 are made among the 36
  participating countries and for eighth-graders in
  2007, comparisons are made among the 48
  participating countries
• U.S. fourth-graders scored 529, on average, in
  mathematics, which was higher than the TIMSS
  scale average of 500
• The average mathematics score of U.S.
  fourth-graders was higher than those in 23 of the
  35 other countries, lower than in 8 countries
  (all 8 were in Asia or Europe), and not
  measurably different from the average scores of
  students in the remaining 4 countries
• U.S. eighth-graders scored 508, on average, in
  mathematics, which was higher than the TIMSS
  scale average of 500
• The average mathematics score of U.S.
  eighth-graders was higher than those in 37 of the
  47 other countries, lower than in 5 countries
  (all of them in Asia), and not measurably
  different from the average scores of students in
  the remaining 5 countries

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2007 TIMMS Scores
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2007 NAEP Results

• At both grades 4 and 8, the percentages of
  students performing at or above Basic and
  Proficient were higher in 2007 than in all
  previous assessment years
• Scores were higher in 2007 than in all previous
  assessment years for White, Black, and Hispanic
  students at both grades 4 and 8, and for
  Asian/Pacific Islander students at grade 4
• Average scores were higher in 2007 than in 2005
  for 23 jurisdictions at grade 4 and for 26
  jurisdictions at grade 8

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NAEP Questions
4th Grade
8th Grade
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Before its Too Late

• Are your student's mathematics and science
  achievement levels on state and classroom
  assessments at an acceptably high level?
• Are you actively seeking to deepen your content
  knowledge?
• Are you actively seeking to learn new teaching
  methods for diverse student learners?

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Before its Too Late

• Actively seek new knowledge about teaching in
  your discipline,work with your peers on a
  continuing basis to improve your skills,and take
  full advantage of the professional development
  opportunities offered by your district and state.
• Actively work to improve your knowledge and
  skills to incorporate educational technology into
  your learning and teaching.
• Communicate to parents the specific standards
  that students are to meet at each grade level and
  update parents on their child's progress in
  meeting these standards.
• Regularly work with colleagues to compare the
  achievement level of your students against the
  standards in your district and state,identify
  areas for improvement,set goals,and make plans
  for achieving these goals.
• Actively share your knowledge and experience
  with new teachers.

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U.S. Education Agenda

• Make Math Science a National Priority through
  the 5 billion Race to the Top fund.
• Encourage states to improve the quality and
  supply of Math Science teachers, including
  alternative routes into teaching and proposals to
  upgrade teacher training and promote and reward
  effective teachers. 
• States can also use Recovery Act funds to
  modernize and renovate new science labs.

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Three is a Magic Number
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What is Fluency?

• Fluency is the building block of expertise in all
  things that we do well.Bloom, 1986

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Fluency Defined

• Fluency can be defined as the ability to perform
  skills and demonstrate knowledge both accurately
  and quickly, without hesitation.

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Information Processing
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Importance of Fluency

• When students lack fluency in the foundational
  skills, performance requiring application of
  those skill is likely to be painfully slow,
  difficult, and full of errors.

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Human Processing
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Power of Fluency

• Fluency frees up working memory for higher order
  applications rather than creating cognitive
  overload with the mechanics of performance.

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Computational Fluency

• Students must develop computational fluency if
  they are expected to solve complex and
  interesting problems.Curriculum Focal Points
  for Prekindergarten through Grade 8
  MathematicsNational Council of Teachers of
  Mathematics, 2006

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Memorizing

• Memorizing the basic number facts, frees up
  working memory to master the arithmetic
  algorithms and tackle math applications. Students
  who do not memorize the basic number facts will
  flounder as more complex operations are required,
  and their progress will likely grind to a halt by
  the end of elementary school. There is no real
  mathematical fluency without memorization of the
  most basic facts. The many states that do not
  require such memorization of their students do
  them a disservice.The State of State Math
  StandardsDavid Klein, 2005

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Fact Fluency Assessment

• Fluency standards accepted by most schools range
  from 40 to 60 correct digits per minute.
• When these standards are met it is generally
  considered that the student has reached fluency.

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Assessment Concerns

• First, students develop such rapid counting
  strategies that they can still meet the criteria
  for fluency and not have developed declarative
  knowledge of the facts.
• Second, rate fails to identify those facts that
  are part of the declarative knowledge network and
  those that are answered using counting
  strategies.
• Third, more than half of the facts in all
  operations have a 0, 1, or 2 as part of the fact
  set.
• The use of rate (number of correct digits per
  minute) to measure mathematical fluency creates a
  false positive when trying to assess fact
  fluency in students.

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Chronometric Analysis

• An alternative to rate per minute as a measure of
  fluency is the use of chronometric analysis.
• Chronometric analysis requires that a response
  latency be measured for each fact.
• The response latencies can then be used to
  determine which facts fall above the criterion
  for fluency.
• The best way to measure response latency is
  through a computer.
• Most importantly, response latency data can be
  used to identify individual facts for fluency
  intervention, as simple rate per minute data do
  not provide this information.

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Developing Fluency

• Before fluency can be developed, information must
  be moved from working memory to long term memory.
• Experts do this through deliberate practice.
• Fluency requires that information stored in long
  term memory be retrieved accurately and quickly
  without hesitation (e.g. math facts, sight words,
  spelling words, etc.).

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Working Memory
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Memory Capacity
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Memory Test 1
Get Ready!
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2571325
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What was the number?
2571325
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Memory Test 2
Get Ready!
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6157246398
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What was the number?
6157246398
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Memory Conclusions

• Because of the limitations of working memory we
  must help students to systematically move
  information from working memory to long-term
  memory.

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Power of Technology

• Although fact fluency can be achieved without the
  use of technology, we have found is that
  technology offers many advantages for developing
  of fluency in a variety of skills.

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FASTT Model
Fluency and Automaticity through Systematic
Teaching with Technology
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FASTT Instruction

• Controlled response time
• Builds on existing fluent facts
• Small instruction set
• Requires recall from memory
• Feedback critical
• Space presentation of new material

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Expanding Recall
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Quantifying Fluency
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FASTT Practice

• Practice only learned facts
• Provide many opportunities to respond
• Variable time constraint
• Feedback on progress

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Fluency is Robust

• Once fluency reaches a particular level of
  accuracy and precision, it can be maintained at
  that level over long periods of time with only a
  small amount of practice from time to
  time.Book, W.F. (1908). The psychology of
  skill. Montana Studies in Psychology.

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Fluency _at_ School

• The school, especially at the elementary level,
  has some responsibility for developing fluency in
  the basic skills and processes that students need
  for more complex learning at later
  levels.Bloom, 1986

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QA
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My Hero, Zero
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It Takes a Village

• Intellication SeminarDiocese of Toledo -
  Catholic Youth School Services
• June 9, 2009

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How do we define a school community?
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Who are the stakeholders?
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What are the strategic goals of a school learning
community?
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Compact Activity

• Divide into four equal teams.
• Nominate one person to be the recorder.
• Strategize as a team on how your groups role
  would help build and foster community
  involvement.
• Devise five strategies which should be specific
  and attainable.
• Prepare to share your findings.

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