CMM Math Review

1. CMM Math Review Study the following to Review for the Final May 6, 10:30 Room 204

2. Learning Theories Constructivist Direct Instruction / Objectivist Bloom’s Taxonomy 5E Lesson

3. Constructivist • Understand the characteristics of Constructivism and know examples of the application in the classroom. Behaviorist • Understand the characteristics of Behaviorism and know examples of the application in the classroom.

4. Bloom’s Taxonomy • Understand the 6 levels of Bloom’s Taxonomy and how they apply to lesson planning and questioning medicine.ukzn.ac.za

5. Bloom’s Learning Domains Define and apply the following terms: • Cognitive • Affective • Psychomotor http://www.icomproductions.ca/

6. 5E Lesson Model • Know the 5E’s and examples of each. • Engage • Explore • Explain • Elaborate • Evaluate

7. 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.

8. 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.

9. Learning Disabilities • Students with learning disabilities have very specific problems with perceptual or cognitive processing. These problems may affect memory or the ability to: • Speak or express ideas in writing, • Perceive auditory or written information, • Integrate abstract ideas.

10. Intellectual Disabilities • Intellectual disabilities are generally identified as IQ scores between 50-70. • This limits the kind and degree of mathematical reasoning such children can perform. • Severely disabled children are generally best served in a special classroom, but are also likely to be present in the regular classroom.

11. Adaptations for perceptual deficits Some perceptual problems are visual & others auditory. All involve confusion of input in one way or another. • Give the child preferential seating • When using visuals, show only one main idea or problem at a time • Maintain a classroom environment where only one person talks at a time • Design worksheet pages for the child • Provide templates to block out all but one problem at a time • Use centimeter graph paper – write one digit per square • Use headphones to explain material • Assign a buddy to repeat directions

12. Adaptations for integrative deficits Children with integrative deficits have difficulty with abstract ideas & conceptualization. • Use familiar physical models as long as needed • Have students use written & oral expression to tell what they do • Require explanations so that students can make a connection to new ideas • Repetition! • Restate word problems in their own words • Peer teaching • Use multiple representations such as words, symbols, drawings, etc.

13. Adaptations for attention deficits ADD or ADHD students have chronic difficulties with attention span, impulse control, & sometimes hyperactivity. • Establish clear routines • Make expectations and consequences clear • Avoid lengthy periods of silent seat work • Independent practice should be done in an environment free of distractions • Highlight key ideas in text • Keep assignments short. Plan smaller subtasks within projects • Assign a buddy for a separate group of two – avoid cooperative groups of 3 or more

14. Touch Math • Be able to give steps of using Touch Math • Be able to identify learning disabilities that can benefit from using Touch Math

15. Treatments for Math Anxiety • Know ideas for responding to math anxiety in the short term – researched ideas, not just your own • http://www.math.com/students/advice/anxiety.html • http://magazine.good.is/articles/a-fix-for-math-anxiety-might-be-in-your-head • Know ideas for planning long term strategies for alleviating math anxiety (building math confidence) – again find the ideas that have a research basis • http://littlescholarsllc.wordpress.com/2011/07/08/5-strategies-to-build-math-confidence/

16. Problem Solving Strategies • use or draw a picture • look for a pattern • write a number sentence • use actions (operations) such as add, subtract, multiply, divide • make or use a table • make or use a list • work a simpler problem • work backwards to solve a problem • act out the situation

17. Strategies for the Basic Facts • Facts with Zero • Count-Ons (Addend of 1, 2, or 3) - Also called One-More-Than & Two-More-Than • Doubles • Doubles +1 – Also called Near-Doubles

18. Strategies for the Basic Facts(continued) • Make Ten (3+7, 4+6, etc.) • Make Ten, Add Extra (7+5, 8+4, etc.) • Magic Nines

19. 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.

20. The Hundreds Chart • The hundreds chart is an important tool in the development of place-value concept. • K-2 classrooms should have a hundreds chart prominently displayed. Review your hundreds chart and know the vocabulary used on it

21. Relational Understanding Base-Ten Concepts Standard & Equivalent Groupings To Physically Represent Quantities • Counting • By Ones • By Groups & Singles • By Tens & Ones Oral Names Standard: thirty-two Base-Ten: Three tens and two Written Names 32

22. Vocabulary Numerals – 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Cardinal Words – one, two, three, four, five, etc. Ordinal Words – first, second, third, etc. 1st, 2nd, 3rd, etc. Sequential – in a particular order Spatial – a sense referring to the ability of an individual to interact in a spacious environment  Consecutive – in a row