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Case Study on Student Thinking
Transcript
Case Study on Student Thinking
Reflection
The Intervention and Activity
Examples of Difficulties
Combining Like Terms Dice Activity:
- Rolling dice to build an algebraic expression.
- Using combining like terms to simplify the expression
Key Points:
- Student used an interactive notebook to keep track of her practices and notes.
- Having the student 'think aloud' increased her ability to catch her own mistakes.
- When I could see a mistake happening I would try to ask her questions to get her to find her mistake if she did not find it first.
- Questions usually pertained to procedures.
Difficulties:
- She continued to make the same negative number related mistakes.
- Example 1: multiplying 2 negatives make a positive not a negative.
- Example 2: when adding a 2 negatives forgetting the negative number.
PEMDAS
Ex 1:
16 / 2 + 3 x 4
8 + 2 x 4
10 x 4
Ex 2:
21 / 3 x 4 - 6
21/12 - 6
??
C.L.T
Ex 1:
2x + 4 + 3x +5
5x^2 + 9
Ex 2:
2(s - 1) + 4 + 5s
2s - 1 + 4 + 5s
7s^2 + 3
(DP issue here
as well.)
Negatives
Ex 1:
8 - ( - 6) - 4
8 + (- 6 ) - 4
2 - 4
-2
Ex 2:
-2(4x - 7)
8x + 14
I wish I had more time because I learned more about my student in week 2 than in week one.
I am super impressed with how quickly she took to the activity and seemed to enjoy it as well as to the I.N. and Cover Copy Compare.
If I could change one thing I would set it up differently to begin with. I would have made it more interactive and less like practice.
Activity: There was really little need for probing questions so the set up could have been different for the activity. The probing questions I did ask were often too shallow so wish I included some kind of question that would require her to fully consider the purpose behind the activity.
Probing Questions/Process
1. After reading the directions I asked her to explain to me what we were doing.
a. Added: How many times do you roll the dice?
2. Asked her how she would solve the first line after she had finished rolling her dice before moving on.
a. By thinking aloud her steps she answered my question, though I wish I had asked her say it before actually doing it.
3. Asked her about one of her steps because I wanted to hear her say the step. This usually helps her catch her own mistakes. I do this multiple times.
4. I ask her "Positive or negative?" often while she is working out a step and then I have her explain why its negative instead of positive.
5. I do ask her often if she is done after she had completed a problem. Sometimes she would find her mistakes sometimes not.
Session Analysis
Ideas of Design
By asking certain questions she would think aloud thus working her way through a problem in a verbal context not just written.
Some of the probing questions were shallow and didn't require much thought but still had her stop and question her own work. By having her question herself she was able to self edit.
Sometimes it was just a matter of reminding her of a basic process and she was fine. Overall she really enjoyed the activity and found it challenging.
Overall the activity went well and was pretty successful.
Objectives:
- Student will be able to simplify numerical expressions using PEMDAS
- Student will be able to combining like terms with both single variable and multi-variable expressions.
- Internally within the 2 other objectives I wanted my student to better understand multiplying, adding, and subtracting negative numbers.
Grade Level Knowledge:
- CCSSM 7ee part 1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
CCSSM Standards:
- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP5: Use appropriate tools strategically
- MP6: Attend to precision
- MP7: Look for and Make use of structure.
Case Study Info
Test Analysis
First 3 probes scores were in order 4 6 5.
- She did not handle negatives properly.
- Ignored parenthesis
- Combining like terms an issue
- Ignored all comparing measurement questions
The next 3 probes were in order 8 7 8.
- After working with her she went stagnant with her work. She would do what we practiced well but miss things she had previously done correctly.
Last 2 probes were in order 12 15 (Roughly a 18% to 68% increase)
- After going over testing strategies she did much better. Worked less problems but got more correct.
- Was using the procedural strategies we had covered to help with problems.