1. I am working with *Tony* one on one while the rest of the class is performing the "Big 4" problem set which includes fraction simplification, 4 digit subtraction and addition with borrowing, word problems and "less than greater than" problems. We sit in the back of the classroom and work on problems such as these to improve Tony's skills by practicing and repetition. Tony is an English Language Learner and gets pulled out of the classroom multiple times a day for extra help in literacy. So, Tony is working on his subtraction skills with borrowing so he can take timed tests with the rest of the class.
2. This learning tasks matches up with the Common Core Standard: 4.NBT.4: use place value understandings and properties of operations to perform multi-digit arithmetic. The whole class has been working on timed tests starting with addition and subtraction and moving up at an individual pace through different stages of multiplication and division. Tony is not advancing at the appropriate pace as the other students so this math task was given to him in order to allow him to practice his subtraction skills so when he does perform timed tests he will be more prepared. This math task is moderated for Tony because he is allowed to finish it at his own pace and a teacher to help him with corrections.
3. a. one possible way to approach the given problem is to allow Tony to finish all the questions and once he is finished, if there is incorrect answer(s), I could ask Tony if he would like to correct or look over any of his problems to allow for self-correction.
b. another effective way is to start working with Tony on the first couple questions by walking him through the steps in how to find the answer and then as the questions go on, direct less and less until he is able to work through the problem by himself.
4.
-I will anticipate that Tony will use "counting" (on his fingers) to find the answers
-I will anticipate that Tony will borrow from the tens place when he does not have to and get an incorrect answer
-I will anticipate that Tony will use self correction to fix errors in his problems
-I will anticipate that Tony will perform mistakes because of his technique of "counting"
5. The first step is to look at the ones place and look at the subtraction problem. If the top number is larger there is no need to borrow from the tens place and he can perform the "ones place" problem. Then he will move onto the tens place subtraction and subtract the top number from the bottom number to get the tens place. If the one's place top number is smaller than the bottom number, he will move over to the tens place and borrow a "tens." he will cross off the tens place and take away one "tens" value and add it to the ones place. The ones place will have ten added to it in order to have a correct subtraction problem. He will take the previously stated steps in order to find the correct answer probably using the technique of counting or from memorization.
6. Tony's current mathematics understanding shows that he is capable of performing subtraction problems with guidance and consistent practice
Tony's current mathematics understanding demonstrates that he is still making simple mistakes with the borrowing rule in 2-3 digit subtraction
7. With the results of his student work, I would advance Tony's student thinking by
a. continuing practice with two digit but with more 3 digit subtraction problems
b. start timing his work and take note of how many problems he can perform in a specific amount of time
c. use flashcards to help memorize and increase sight problems of basic subtraction problems.
d. introduce new techniques of how to solve subtraction problems besides counting on fingers
Your analysis is thorough, though I am somewhat confused by your use of future tense...is this how you anticipated the student would solve the problem? If so, what did he actually do as you watched him, and what does this tell you? In the future, try to differentiate between these two steps in the analysis (e.g., what you anticipate and what you actually see). Also, as you think about ways of advancing the student's thinking, also think about different representations that he can use to conceptualize subtraction, that is, as opposed to simply giving him more practice. You do hint towards this (e.g., "introduce new techniques"), but try to be specific about how you might increase the cognitive demand of this practice, or introduce a new way of conceptualizing the process of subtraction (e.g., using manipulatives, direct modeling, number facts, etc.)
ReplyDelete