Effective Instruction in the Secondary Mathematics Classroom

1. Effective Instruction in the Secondary Mathematics Classroom ACT/ESL Summer Institute Michael Bolling Instructional Specialist for Mathematics June 18, 2009

2. Get to know your kids! • Find out where your students are from. • Visit their native region using Google Earth. • Let them share information with the class about the region. • Develop a mathematics problem in their native region.

3. Learning Problems that Impact Students in Mathematics • Not just students with disabilities • Know their underlying issues, not just their symptoms and accomodations • Check their IEP • Talk to them

4. 37 30 40 Conceptual vs. Procedural Round 37 to the nearest ten. Conceptual What tens number is 37 close to? Procedural If this digit is 5 or more make the underlined digit one more. If this digit is less than 5 keep the underlined digit the same. 37 Rounding

5. Conceptual vs. Procedural Procedural Conceptual 3 4 A= l x w P = 2(l + w) Area and Perimeter

6. It takes 6 sixths to make a whole, so it’s 1 whole with 1 sixth left over… 1 1/6 Conceptual vs. Procedural Change 7/6 to a mixed number. Fractions Conceptual: • Procedural: • Divide the numerator by the denominator. • Write the quotient as the whole number. Write the remainder as the numerator. Use the same denominator. • 7  6 = 1 R1 … 1 1/6

7. x x x x Algebra 2 packages of cookies and 6 extras 2x + 6 Concept Procedure 2(x + 3)

8. Concept Relationships Big Ideas Understanding Metacognitive strategies Procedure Skills Step by step algorithms Conventions (agreed upon rules or definitions) Rote learning Concept or Procedure?

9. Vocabulary Development • Clarity and precision • Modified Fraher Model • Vocabulary cards • Interactive notebooks • Cognates • Beware of key words • Connect to prior knowledge

10. Clarity and Precision Be aware of your spoken and written words • “goes into” or “divided by” • “3 over 4” or “three fourths” • “cancel” or “simplify” • “3 point 4” or “3 and 4 tenths”

11. Definition Vocabulary Word Modified Frayer Model My Definition Characteristics Formal Definition Examples Non - Examples

12. Vocabulary Cards • Words • Pictures • Examples • Highlighting • Grouping by big ideas

13. Interactive Notebooks • Left side is the teacher side • Notes • Definitions • Examples • Right side is the student side • Reflections • Pictures • Examples • Solutions

14. Cognates • Cognates are words that are very similar to words in another language • Translations available at www.appliedlanguage.com

15. Watch out for “key words” Is doesn’t always mean “equal”. More doesn’t always mean “add”.

16. Connecting to Prior Knowledge • Informal observation/assessment • Background information • Notation/alternative algorithms

17. Informal Assessment/Error Analysis • Be a watcher/observer • Watch for error patterns in student work • Notice alternate algorithms

18. Communication – Oral and Written • Journaling/Diaries • Graphic organizers • Think-pair-share • Justification