Cognitively-Guided Instruction Anticipatory Framework

Cognitively Guided Instruction - Anticipatory Framework
School: Dunwoody
Springs
Problem
Type
JRU
Problem
Teacher: Kimberly Wood
JRU
SRU
PPW-WU
CDU
M
JCU
SCU
CQU
MD
JSU
SSU
PPW-PU
CRU
PD
I have 3 red pencils and 4
blue pencils. Simon has 5
red pencils and 2 blue
pencils. We have the
same amount of pencils.”
Show me how this
statement is true or not
true.
Grade: 1st
Date:
Rationale/Goals (Why are you asking this problem type with
these particular numbers?):
Students have been working on math fluency. They have solved
basic addition and subtraction problems, word problems, and
problems with missing numbers. The next step is for students to
understand the meaning of the equal sign and prove if a number
sentence is true or false based on their knowledge of what the
equal sign means.
Direct Modeling
Strategies
No Base-Ten Evidence
lll (3)
llll(4) =
Base-Ten Evidence
lllll(5)
ll (2)
1. Student counts all from start.
2. Student counts on from 3 and on from 5
3. Student counts on from larger numbers (4
and 5).
Flexible/Base-Ten Strategies
(Invented Algorithms)
Counting Strategies
7=
7
Student thinks 4 in his/her head and counts up 3
times. (4,5,6,7)
Student counts by ones
4,5,6,7
Student things 5 in his/her head and counts up 2
times (5,6,7)
Student counts by ones
5,6,7
Combining Tens and Ones
Invented Algorithm
Tens 0+0=0
Ones 4+3=7
5+2=7
Compensating
Invented Algorithm
4+4=8
8-1=7
5+5=10
10-3=7
7=7
Incrementing
Invented Algorithm
4+1=5
5+1=6
6+1=7
5+1=6
6+1=7
7=7
7=7
© 2008-2012 Stephanie Z. Smith and Marvin E. Smith
Recalled or
Derived-Fact
Strategies
4+3=7
5+2=7
7=7
© 2008-2012 Stephanie Z. Smith and Marvin E. Smith
Cognitively Guided Instruction - Observation Framework
No Base-Ten Evidence
Direct Modeling Strategies
1.
Counting Strategies
Counts all
Jonathan drew a picture for 3+4 and a picture for 5+2. He
then counted all of the circles to realize the equations were
true.
1. One ten as a unit
4. Collects tens and ones
2. More than one ten as a unit
5. Counts tens as ones
3. Direct Place Value Explanation
6. Increments by tens
Alaiya drew a picture for each side of the equation and
counted all of the circles. She made a mistake in counting
her circles and did not complete the problem correctly
because of this.
Diajonae also drew a picture for both sides of the equation
and counted all the circles correctly.
2.
Counts from first
3. Counts from larger
1.
Counts on from first
7a. Counts on from first
Xavier started counting from the first number. For 3+4, he started at
three and counted up four times using his fingers to keep track. For
5+2, he started at five and counted up two times using his fingers to
keep track.
2. Counts on from larger
8. Combining Tens and Ones
Invented Algorithm
7b. Counts on from larger
11. Compensating
Invented Algorithm
Incrementing
Invented Algorithm
9. Combines tens then increments
10. Increments
Recalled or
Derived-Fact
Strategies
Flexible/Base-Ten Strategies
(Invented Algorithms)
Base-Ten Evidence *
© 2008-2012 Stephanie Z. Smith and Marvin E. Smith
Reflection
(What did I learn as a result of this lesson? What did I observe that corresponded with my anticipatory framework? What
did I not anticipate? What are my next steps? How will this guide my instruction?)
I learned that the students that participated in this problem depended highly on direct modeling. The students could have
used counting or derived facts strategies to solve these problems more quickly. I did observe that the students were able to
understand the meaning of the equal sign. All students solved both sides instead of recording the answer to the left side on
the right side of the equation. Direct modeling was the strategy that I observed the most that corresponded with my
anticipatory framework. One student did use a counting by one strategy to solve the problem that I had anticipated prior to
the lesson. On the anticipatory framework, I recorded base ten strategies, invented algorithms, and derived facts strategies,
but I did not see my students use these. My next steps would be to use large numbers. I would be curious to see if the
students used other strategies than direct modeling. I will use this knowledge to guide my instruction on solving problems in
different ways. Students are currently working on math fluency, so I want to be sure that they are applying this knowledge to
when they are solving problems.
* Indicates use of combinations in 10 to make a model for ones from a stick of ten (e.g., breaks off 3 from 10 to make 7)
© 2008-2012 Stephanie Z. Smith and Marvin E. Smith

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