Bode--

            For week 2’s student sample work I brought in a transcript of a math conversation my mentor teacher had with the whole class while helping one student. The students were playing monster squeeze as a class. Someone will pick a number and the students have to guess what it is by asking, “is it bigger/smaller than [number]?” In this particular situation a student was having a hard time understanding that if he asked is it bigger than a certain number, why would either Ms. Hall or myself move? Wouldn’t just Ms. Hall move since she’s near the bigger number and he asked if it was bigger. This sample work shows the use of language in a math conversation and how visually showing students can aid their understanding when it comes to using a number line and understanding the concept of bigger/smaller than. In the sample work Ms. Hall allows another student to try and answer this confusion before she explains. The student was able to understand what the other student said and comprehend that the actual word bigger/smaller doesn’t mean the person near the bigger number moves when asked if its bigger and visa versa for the smaller number.

            This artifact reveals that the current mathematical understanding of this student may have been confused by the visual aid of using the number line on the wall. The concept of guessing if a number is bigger or smaller than the number being guessed has to do with being able to test students abilities understand which number value is greater or less than others. It may be safe to say that this student knows which number has a high value compared to others but that the visual use of the number line and yard sticks on the wall confused him because you had one teacher near the bigger numbers and another, myself, near the smaller numbers so he thought that that connected with the BIGGER and SMALLER question. Maybe this student is a auditory learner, some students need visuals while others it might throw them off from something they already understand. This shows to me that there may be a gap in this student’s ability to see a number line and still use it for concepts of bigger or smaller number values when guessing a number. When students learn greater or less than signs they have to be able to know which number value is greater or less than others, sometimes while looking at a number line. There may be a gap in this student’s ability to visualize these number values with a number line.

            One way I would aid this student is by utilizing a number line for some activities. One activity I would want the student to do is have a number line in front of them, ask the student to point to any number. When the student picks a number (lets say it’s 9), I will ask a series of questions like “is 6 greater or less than 9?”, and so on with different numbers. By doing this I want to get the student comfortable with using a number line and recognizing the value of a number associated with the number line. Another activity I would do with this student is then sit one on one with them and play the monster squeeze game with them except this time have the student be in charge of covering both ends of the number line. Having the student be in charge of moving the number line will help the student learn first hand how to move each side based on the questions he’s asking “if its bigger or smaller than ___?” I would ask questions like “how do you know that ___ is bigger than ___? Why did you move that side of the number line down and not the other side?” By asking the student along the way to explain themselves it will help him understand why he’s doing and also myself to understand maybe where the student is getting confused or what he is misunderstanding.

Student Math Sample Transcript

[Playing a game called monster squeeze where the teachers hold yard sticks over two numbers on a number line and the class tries to guess what number the teacher, or a student, is thinking of by asking questions like “is it bigger/smaller than…?”]

Ms. Hall: “The number is between 1 and 20, so Miss Bode and I are going to cover the 0 and 21. Who wants to guess what number were thinking of?”

Student: “Is it bigger than 14?”

Ms Hall: “No, so I move the stick to cover 14 while Miss Bode stays on 0 because the number is between 0 and 14.”

Student: “But why? Doesn’t Miss Bode have to move closer to the number 14 too?”

Ms. Hall: “Who can help ____ understand why I moved down from 20 to 14 and Miss Bode didn’t move from 0?”

Student: “Because ____ asked if the number was BIGGER than 14 and since Ms. Hall said no well then I think that the number is going to be smaller than 14 because its not bigger and it could be anywhere from 1 to 13 so Miss Bode don’t move.”

Ms. Hall: “Good. Miss Bode doesn’t move because the number is smaller than 14 meaning it could be any of the numbers between 1 and 13. Who wants to guess now?”

Student: “Is it bigger than 5?”

Ms. Hall: “Yes.” [Miss Bode moved the yard stick from 0 to cover 5]

Student: “Wait wait wait…now why did Miss Bode move? I thought only Ms. Hall was supposed to move if the question asked if it was BIGGER?”

Ms. Hall: “Ahh I see some confusion here. When a student asks if it’s bigger that doesn’t always mean that I am going to move…and if its smaller that Miss Bode will only move. What matters is if my number that I’m thinking of is bigger or smaller than the number your guessing. Let’s say I am thinking of the number 10…if you asked is it bigger than 14, id say no so then I move because 10 is less than 14. Now what if you ask is it bigger than 5, then I say yes. Miss Bode moves now because 5 is closer to 0 and she is on 0 still.”

Student: “So Miss Bode has to move since the number is gonna be between 5 and 13 now and you Ms. Hall stay there cus you have to cover 13 and Miss Bode is closer to 5 than you are.”

Ms. Hall: “You got it!”