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

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.

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

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. Rounding What tens number is 37 close to? Round 37 to the nearest ten. Conceptual Procedural Conceptual vs. Procedural

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

Fractions Procedural: 1.Divide the numerator by the denominator. 2.Write the quotient as the whole number. Write the remainder as the numerator. Use the same denominator. 7  6 = 1 R1 … 1 1/6 Conceptual: Change 7/6 to a mixed number. It takes 6 sixths to make a whole, so it’s 1 whole with 1 sixth left over… 1 1/6 Conceptual vs. Procedural

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

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

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

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”

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

Vocabulary Cards Words Pictures Examples Highlighting Grouping by big ideas

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

Cognates Cognates are words that are very similar to words in another language Translations available at

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

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

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

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