Transcript Pre-school - Kindergarten

Misunderstood Minds
 http://www.pbs.org/wgbh/misunderstoodminds/
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Basics of Mathematics
 Mathematics is often thought of as a subject that a
student either understands or doesn't, with little in
between …
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Wide Variety Skills and Concepts
 Mathematics encompasses a wide variety of skills and
concepts.
 These skills and concepts are related and often build
on one another…
 It is possible to master some and still struggle with
others.
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Success in Different Areas
A child may have difficulty with basic multiplication
facts but may be successful in another area, such as
geometry…
A student may have some areas of relative strength and
others of real vulnerability…
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Brain Research
 Researchers have examined aspects of the brain that
are involved when children think with numbers. ..
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Neurodevelopmental Functions
 Memory,
 Language,
 Attention,
 Temporal-sequential ordering,
 Higher-order cognition, and
 Spatial ordering
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Process Ongoing
 These components become part of an ongoing process
in which children constantly integrate new concepts
and procedural skills as they solve more advanced
math problems.
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Brain Functions Need to Work
Together
 Memory to recall rules and formulas and recognize
patterns
 Language to understand vocabulary, instructions, and
explain their thinking
 Sequential ordering to solve multi-step problems and
use procedures…
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Brain Functions Need to Work
Together
 Spatial ordering is important to recognize symbols and
deal with geometric forms…
 Higher-order cognition helps children to review
alternative strategies while solving problems,
 to monitor their thinking,
 to assess the reasonableness of their answers,
 and to transfer and apply learned skills to new problems.
 These brain functions often need to operate
simultaneously.
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Try This Problem
 Multistep problem from Misunderstood Minds
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Big Ideas
 Math is cumulative
 Competence in math draws on more than just the
ability to calculate answers correctly
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Math Encompasses
 Problem Solving
 Communicating About Mathematical Concepts
 Reasoning and Establishing Proof
 Representing Information in Different Forms
 Making Connections in the Classroom, and Later in
the Workplace
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Developmental Variation and
Learning Disorders
 Dr. Levine outlines many of these milestones for four
age groups, pre-school through grade 12 in his book.
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Pre-school - Kindergarten
• During this stage, children should begin to: count aloud
• compute the number of objects in a group
• understand that a particular number of objects has a fixed
value despite the size or nature of those objects
• understand relative size and be able to sort objects by size
and shape
• follow a sequence of two- and three-step commands
• be able to perform simple addition and subtraction
computations
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Grades One to Three
• During this stage, children should: begin to perform simple
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addition and subtraction computations efficiently
Master basic math facts (such as, 3 + 2 = 5)
Recognize and respond accurately to mathematical signs
Begin to grasp the concept of multiplication (grade three)
Understand the notion of measurement and be able to
apply this understanding
Improve their concepts of time and money
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Grades Four to Seven
• During this stage, children should: recall basic
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mathematical facts, including multiplication tables, with
ease
Become competent with fractions, decimals, and
percentages
Begin to understand the relationships among fractions,
decimals, and percentages
Develop facility with word problems
Be adept at estimating quantities and rounding off
numbers
Develop basic computer skills
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Grades Eight to Twelve
• During this stage, children should be able to: employ an
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increasingly high level of abstract, symbolic thinking
Perceive relationships and make translations among
decimals, fractions, and percentages
Deal easily with a wide array of equations, formulae, and
proofs
Explain and illustrate mathematical concepts, rather than
simply apply them
Plan and self-monitor during multi-step problem solving
use calculators and computers with facility
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Principles and Standards for
School Mathematics
 http://standards.nctm.org/
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NCTM Standards Compared to Connecticut
Scope and Sequence
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Connecticut Scope and Sequence
Number Sense
Operations
Estimation
Ratio, Proportion and Percent
Measurement
Spatial Relations and Geometry
Probability and Statistics
Patterns
Algebra and Functions
Discrete Mathematics
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NCTM Content Standards
Numbers and Operations
Algebra
Data Analysis and Probability
Geometry
Measurement
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NCTM Process Standards
Problem Solving
Reasoning and Proof
Connections
Communication
Representation
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NCTM and CT Scope and Sequence
 http://www.nctm.org
 http://www.sde.ct.gov/s
de/cwp/view.asp?a=2618
&q=320872
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