Download Evidence-Based Practices to Improve Achievement in Computation

Evidence-Based Practices to Improve
Computation With Regrouping and
Problem-Solving Skills
2014 AASE National Conference
Bradley J. Kaffar, Ph.D.
St. Cloud State University, USA
Advance Organizer
 Evidence-Based Practices
 Explicit Instruction
 Cognitive Strategies
 Graduated Sequence of Lessons
 Addition With Regrouping and Word Problems
 Subtraction With Regrouping and Word Problems
 Field Test Results
Introduction
Mathematics is one of the most challenging aspects of the school
curriculum for many students, and a concern is the lack of
achievement in multi-digit computation with regrouping and word
problems. Specifically, out of 29 mathematics difficulties, special
education teachers ranked word problems as the most problematic,
multi-step problems as second most problematic, and regrouping as
the seventh most problematic area for students with learning
disabilities (LD) (Bryant & Bryant, 2008).
Explicit Instruction
 Advance Organizer
 Describe and Model
 Guided Practice
 Independent Practice
 Problem-Solving Practice
The “RENAME” Strategy for Addition
With Regrouping
Read the problem.
Examine the ones column: 10 or more, go next door.
Note the ones in the ones column.
Address the tens column: 10 or more, go next door.
Mark tens in the tens column.
Examine and note hundreds; exit with a quick check.
“10 or More” Sentences
Adding the Ones:
If adding the numbers in the ones column results in 10 or more,
regroup to form a ten (10 or more, go next door).
Adding the Tens:
If adding the numbers in the tens column results in 10 or more,
regroup to form a hundred (10 or more, go next door).
Read the problem.
3 5 7
+ 2 8 4
Examine the ones column: 10 or
more, go next door.
1
3 5 7
+ 2 8 4
If adding the numbers in the ones column results
in 10 or more, regroup to form a ten
(10 or more, go next door).
Note ones in the ones column.
1
3 5 7
+ 2 8 4
1
Address the tens column: 10 or
more, go next door.
1
1
3 5 7
+ 2 8 4
1
If adding the numbers in the tens column results in
10 or more, regroup to form a hundred
(10 or more, go next door).
Mark tens in the tens column.
1
1
3 5 7
+ 2 8 4
4 1
Examine and note hundreds; exit
with a quick check.
1
1
3 5 7
+ 2 8 4
6 4 1
The “RENAME” Strategy for
Subtraction With Regrouping
Read the problem.
Examine the ones column: use the BBB Sentence for ones.
Note the ones in the ones column.
Address the tens column: use the BBB Sentence for tens.
Mark tens in the tens column.
Examine and note hundreds; exit with a quick check.
“BBB” Sentences
BBB Sentence for Ones:
Bigger number on Bottom means Break down a ten and trade.
BBB Sentence for Tens:
Bigger number on Bottom means Break down a hundred and trade.
Read the problem.
4 5 7
- 2 6 8
Examine the ones column: use the
BBB Sentence for ones.
4 17
4 5 7
- 2 6 8
Bigger number on Bottom means Break
down a ten and trade.
Note ones in the ones column.
4 17
4 5 7
- 2 6 8
9
Address the tens column: use the
BBB Sentence for tens.
14
3
4 17
4 5 7
- 2 6 8
9
Bigger number on Bottom means Break
down a hundred and trade.
Mark tens in the tens column.
14
3
4 17
4 5 7
- 2 6 8
8 9
Examine and note hundreds; exit
with a quick check.
14
3
4 17
4 5 7
- 2 6 8
1 8 9
1
1
1 8 9
+ 2 6 8
4 5 7
The “FAST RENAME” Strategy for
Word Problems With Regrouping
Step 1: Find what you’re solving for.
Step 2: Ask yourself, “What are the parts of the
problem?”
Step 3: Set up the numbers.
Step 4: Tie down the sign.
Use the “RENAME” Strategy for computation.
Problem-Solving Practice
words
books
Concrete-Representational-Abstract
(CRA) Teaching Sequence
 Concrete Phase
 Base-ten blocks
 Place-value mat
 Representational Phase
 Squares represent hundreds
 Vertical lines represent tens
 Horizontal tallies represent ones
 Abstract Phase
 Mnemonic devices
Field Test Results:
Addition With Regrouping
Computation
Mean Pretest
Mean Posttest
Treatment Group
Comparison Group
49%
66%
90%
72%
Treatment Group
Comparison Group
Word Problems
Mean Pretest
41%
51%
Mean Posttest
89%
69%
Field Test Results:
Subtraction With Regrouping
Computation
Mean Pretest
Treatment Group
Comparison Group
60%
76%
Mean Posttest
86%
78%
Treatment Group
Comparison Group
Word Problems
Mean Pretest
45%
62%
Mean Posttest
77%
57%
Post Organizer
 Evidence-Based Practices
 Explicit Instruction
 Cognitive Strategies
 Graduated Sequence of Lessons
 Addition With Regrouping and Word Problems
 Subtraction With Regrouping and Word Problems
 Field Test Results
Thank You!