College of Education Chapters 6 (Ashlock, 2010)

 What’s the Difference? Chapters 7 (Ashlock, 2006)

3 Overview of D & C for Course T says: “Work on basic facts.” T says: “Work on a whole number operation (or algorithm).” T says: “Work on fractions, decimals, geometry, money, or time” Pre-test Basic Facts Card for that specified operation – test ALL facts for this operation. May’s test for that specified operationFind a worksheet or chapter test specifically on what you need to teach. Don’t forget to INTERVIEW CHILD! Use intro questions from homework to get to know child and try to build a trusting and caring relationship. Then… Use interview to give pre-test. Make 3 piles of cards: 1) know in time 2) Know after time 3) Does not know Use interview to see if your pre-diagnosis is correct by asking the student to solve problems out loud. ALSO, find out about problems you can’t figure out. Use interview to see if your pre- diagnosis is correct by asking student to solve problems out loud. ALSO, find out about problems you can’t figure out. Correction 1) Teach concept of the operation; 2) Teach and practice number strategies for EACH basic fact that was missed; and then 3) Work on automaticity. If final diagnosis shows that the error is basic facts only, follow correction steps for basic facts; both procedural and conceptual, begin with intermediate step and follow remaining correction steps;. basic facts and both procedural and conceptual, follow basic facts and work on intermediate, procedural, and independent practice. * Re-do correction steps if Independent Practice is not at least 85%! Make final diagnosis. Post-test Same post-test as the pre-test – for ALL facts. Same post-test as the pre-test.

Chapters 6 (Ashlock, 2010) Basic Facts (not known)  Procedural  Algorithm difficulties  Conceptual  Fraction/Decimal Concepts Part-Whole Relationship Equal Parts/Fair Shares Place Value  Equivalent Fractions/Decimals  Meaning of Operations in general  Meaning of Operations when fractions or decimals are involved  Properties Commutative Property Associative Property Zero Property Multiplicative Identity Property  Number Sense

 Work with a group of your peers to reach a consensus about… ◦ The procedural error(s)  Ask yourselves: What exactly is this student doing to get this problem wrong?  Basic Facts  Violations of Algorithm ◦ The conceptual error(s)  Ask yourselves: What mathematical misunderstandings might cause a student to make this procedural error?  Fraction Concepts  Part-Whole Relationship  Equal Parts/Fair Shares  Equivalent Fractions  Multiplicative Identity Property  Meaning of Operations in general  Meaning of Operations when Fractions are involved  Properties  Commutative Property  Associative Property  Zero Property  Multiplicative Identity Property  Number Sense

Conceptual Strategy? Intermediate Strategy? Procedural Strategy?

Conceptual Strategy? Intermediate Strategy? Procedural Strategy?

1. Conceptual Strategy? 1. Intermediate Strategy? 2. Procedural Strategy?

1. Conceptual Strategy? 1. Intermediate Strategy? 2. Procedural Strategy?

1. Conceptual Strategy? 1. Intermediate Strategy? 2. Procedural Strategy?

1. Conceptual Strategy? 1. Intermediate Strategy? 2. Procedural Strategy?

 Correctional Strategies for Fraction Operations  See Ashlock’s (2006) text,… Fraction Multiplication – pp Fraction Division – pp Decimal Multiplication – pp Decimal Division– pp. 183 – 184.

See you in next week!