College of Education

Chapters 6 (Ashlock, 2010)

What’s the Difference?

Chapters 7 (Ashlock, 2006)

3

Overview of D & C for CourseT 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 operation Find 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. 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

Demonstrations

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 OperationsSee Ashlock’s (2006) text,…

Fraction Multiplication – pp. 178-180. Fraction Division – pp. 180-182. Decimal Multiplication – pp. 182-183. Decimal Division– pp. 183 – 184.

See you in next week!