CMM Math Review

Study the following to Review for the Final

May 6, 10:30 Room 204

Learning TheoriesConstructivist

Direct Instruction / ObjectivistBloom’s Taxonomy

5E Lesson

ConstructivistO Understand the characteristics of

Constructivism and know examples of the application in the classroom.

BehavioristO Understand the characteristics of

Behaviorism and know examples of the application in the classroom.

Bloom’s TaxonomyO Understand the 6 levels of Bloom’s

Taxonomy and how they apply to lesson planning and questioning

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Bloom’s Learning Domains

O CognitiveO AffectiveO Psychomotor

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Define and apply the following terms:

5E Lesson ModelO Know the 5E’s and examples of each.O EngageO ExploreO ExplainO ElaborateO Evaluate

Constructivist Theory provides the best directions for teachers of special students.

Pay careful attention to the child & how she learns.

Design instruction, not content, that maximizes the strengths of the child

while minimizing the impact of weaknesses.

Multicultural & social equity

Research repeatedly shows that African American, Hispanic, and Native American children &

children from homes with low socioeconomic status do poorly in mathematics.

Students in at-risk populations are not getting the same access to quality teachers, resources,

technology, & curriculum.

Learning Disabilities

O Students with learning disabilities have very specific problems with perceptual or cognitive processing.

These problems may affect memory or the ability to:

1. Speak or express ideas in writing, 2. Perceive auditory or written

information,3. Integrate abstract ideas.

Intellectual Disabilities

O Intellectual disabilities are generally identified as IQ scores between 50-70.

O This limits the kind and degree of mathematical reasoning such children can perform.

O Severely disabled children are generally best served in a special classroom, but are also likely to be present in the regular classroom.

Adaptations for perceptual deficits

Some perceptual problems are visual & others auditory. All involve confusion of input in one way or another.

O Give the child preferential seatingO When using visuals, show only one main idea or problem

at a timeO Maintain a classroom environment where only one person

talks at a timeO Design worksheet pages for the childO Provide templates to block out all but one problem at a

timeO Use centimeter graph paper – write one digit per squareO Use headphones to explain materialO Assign a buddy to repeat directions

Adaptations for integrative deficits

Children with integrative deficits have difficulty with abstract ideas & conceptualization.

O Use familiar physical models as long as neededO Have students use written & oral expression to tell

what they doO Require explanations so that students can make a

connection to new ideasO Repetition!O Restate word problems in their own wordsO Peer teachingO Use multiple representations such as words, symbols,

drawings, etc.

Adaptations for attention deficits

ADD or ADHD students have chronic difficulties with attention span, impulse control, & sometimes

hyperactivity.

O Establish clear routinesO Make expectations and consequences clearO Avoid lengthy periods of silent seat workO Independent practice should be done in an environment

free of distractionsO Highlight key ideas in textO Keep assignments short. Plan smaller subtasks within

projectsO Assign a buddy for a separate group of two – avoid

cooperative groups of 3 or more

Touch MathO Be able to give steps of using Touch

MathO Be able to identify learning

disabilities that can benefit from using Touch Math

Treatments for Math Anxiety

O Know ideas for responding to math anxiety in the short term – researched ideas, not just your own

O http://www.math.com/students/advice/anxiety.html

O http://magazine.good.is/articles/a-fix-for-math-anxiety-might-be-in-your-head

O Know ideas for planning long term strategies for alleviating math anxiety (building math confidence) – again find the ideas that have a research basis

O http://littlescholarsllc.wordpress.com/2011/07/08/5-strategies-to-build-math-confidence/

Problem Solving Strategies

O use or draw a pictureO look for a patternO write a number sentenceO use actions (operations) such as add,

subtract, multiply, divideO make or use a tableO make or use a listO work a simpler problemO work backwards to solve a problemO act out the situation

Strategies for the Basic Facts

O Facts with Zero

O Count-Ons (Addend of 1, 2, or 3) - Also called One-More-Than & Two-More-Than

O Doubles

O Doubles +1 – Also called Near-Doubles

Strategies for the Basic Facts(continued)

O Make Ten (3+7, 4+6, etc.)

O Make Ten, Add Extra (7+5, 8+4, etc.)

O Magic Nines

Avoid Premature Drill

As long as a strategy is completely mental & does not rely on a model,

picture, or tedious counting, repeated use of the strategy will

almost certainly render it automatic.

The Hundreds ChartO The hundreds chart is an important

tool in the development of place-value concept.

O K-2 classrooms should have a hundreds chart prominently displayed.

Review your hundreds chart and know the vocabulary used on it

Relational Understanding

Base-Ten ConceptsStandard & Equivalent Groupings

To Physically RepresentQuantities

Oral NamesStandard: thirty-two

Base-Ten: Three tens and two

Written Names

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Counting• By Ones

• By Groups & Singles• By Tens & Ones

VocabularyNumerals – 1, 2, 3, 4, 5, 6, 7, 8, 9, 10Cardinal Words – one, two, three, four, five,

etc.Ordinal Words – first, second, third, etc.

1st, 2nd, 3rd, etc.Sequential – in a particular orderSpatial – a sense referring to the ability of an

individual to interact in a spacious environment 

Consecutive – in a row