Bill and anyone interested.
One of the "side" activities I engage involves a middle school afterschool
homework/tutorial club. Here is an example of part of a fieldnote from the
site. It seems remarkable to me for its convincing detail. What do you think?
mike
--Ms. Penney announced that we were going to do homework problems CP 1-47 for the first hour, and then hands-on activity for the next hour. Everyone got just right into doing homework. Some kids had already done most of the homework, and others had just started. The first boy I helped (I don't know his name) had already done his homework, so he wanted me to check it. He had the wrong answer for CP-5. It read, "One number is five more than a second number. The product of the numbers is 3300. What are the numbers?" He didn't understand what the product meant. So I told him that the product was multiplication. He had already had two numbers, X and X+5, so I let him set up the equation. But he wasn't quite getting it, so I said, "X times X+5 equals 3300, right?" Then he wrote X(X+5)=3300. He was actually supposed to use the guess and check table, but I didn't read that part in the textbook (I noticed that now), so I told him to solve for X. I don't think these kids have already learned how to factor, but I showed him how to do it. I said, "first, you have to use the distributive property, so X squared + 5X=3300. Then you're going to bring 3300 to the left side. So, it's going to be X squared +5X-3300=0. Then you're going to factor." I asked him if he knew how to factor, and he said "yes," so I asked him what times what makes 3300, and what plus what makes 5. He wasn't getting it, and I knew the answers, which were 55 and 60. I did this problem at home and when I did it, I used the guess and check table. So, I was trying to show him how to factor, but I couldn't get the answers. I've been trying to solve this problem using the equation, but X is always going to be 60 and 55 or 55 and 60. I guess we're not supposed to solve this by using the equation. When I was helping him, another girl asked me for help, so I went to help her (I don't know her name). She was doing CP-4. It read, "My new Saturn cost $14,000. Each month, it depreciates $100. In how many months will it be worth only $10,000?" So, I asked her what she was going to let X. I read the problem again, and she said "month." I knew the answers and how to do this problem, but it was hard to explain. I did this at home, and I did it like "14,000-10,000=4000. 4000 divided by 100=40. The answer is 40 months." But I didn't know how to explain it to her. So I said, "how much money decreased? What's 14,000-10,000?" Then she calculated it on the calculator. Right then, another kid asked me for help, so I went. He (I don't know his name) was doing CP-7. It read, "Chris is three years older than David. David is twice as old as Rick. The sum of Rick's age and David's age is 81. How old is Rick?" He let X=David's age. Then he had 3+X=Chris, and 2X=Rick, which were wrong. He had to let X=Rick's age. So I read the problem out loud, and asked him what he was going to let X. He wasn't really getting it, so I had to help him by saying that Rick's age=X. Then I said, "OK, David is twice as old as Rick. Which one is older?" He said, "David" and put 2X=David. Then he could figure it out the rest.
At about that time, Ms. Penney showed us one example on the board. The problem read "3+3X=9+2X." Some kids knew how to do this and were saying it out loud, but it seemed that others didn't really know. I noticed the difference between the kids. Those who knew how to do it had more confidence and their personalities were more cheerful and outgoing. Those who didn't know had less confidence and were shy.
After Ms. Penney showed us how to solve that problem, I was walking around to see if anyone was stuck. One boy was asking for help, so I went. He was doing CP-45. It read, "Right triangle ABC has an area of 45. Find the coordinates of B and C. Show all subproblems." A=(3,4), B=(8,w), and C=(x,y). He had no idea what to do. So, first I asked him if he knew the formula for a triangle's area. He didn't know. So I said that it was = times base times height. I let him write out the equation, but he didn't know, and I had to walk him through. I said, " = times base, which is AB, times height AC equals 45." He wrote down " = x AB x AC=45." Then I said, "what is the length of AB?" He didn't know. So, I had to tell him that 8-3=5, that is, AB. He wasn't really paying attention, so I just had to tell him the equation. So, I said, "it's going to be 1/2 times 5 times AC=45. What's the length of AC? So, you have to subtract, right? It's going to be AC=y-4. So, it's going to be 1/2 X 5 X (y-4)=45. Then what do you do?" Then he said, "it's going to be 5/2 X (y-4)=45." Then I asked him, "What's the opposite of 5/2?" He said, "2/5." Then I said, "so you have to multiply it to the both sides. Then you can cancel out, and it's y-4=18." There were many kids who needed to help, so I had to go. Some kids are really easy to work with, but others are hard. They don't know what I'm talking about, so they lose focus. It's hard to work with "hard" ones because I have to walk them through each step, which takes a long time, and therefore I can't help other kids.
I noticed that Olga (sp?) was copying her friend's notes. But I had to help other kids, so I couldn't say anything. I heard from Catherine that Olga needed a lot of help, so I wanted to help her, but there was Richard with that group, so I thought that I would go help other kids. Most of the kids need one-on-one help, and six or seven tutors aren't enough. I wish I could help them more.
Mario was separated from the group because he was just talking or something, and was sitting in the corner. William was helping him because he was done with his homework. William asked me to help them, so I went. In the beginning, William was just telling Mario the answers, so I interrupted. William also had some questions, so as I helped William, Mario listened to us talking and wrote it down. William is pretty smart and easy to work with. He had a question on CP-8. It read, "find three consecutive numbers whose sum is 57." He knew the answers, which were 19, 20, and 21 because he looked at the answer keys. He had also set up the equation, X+(X+1)+(X+2)=57. He just didn't know how to solve it. So, I said, "what's X+X+X?" He answered, "3X. Now what?" I said, "what's 1+2?" He said, "3. So, 3X+3=57, and then subtract 3 from both sides. . ." Then he got the answers. William was helping Mario on CP-9, which read "Margaret is twice as old as Jenny, and Sarah is twice as old as Margaret. Their combined ages total 133 years. How old is each person?" William said to Mario, "let X=Jenny, 2X=Margaret, and 2(2X)=Sarah." It was correct, but I had to ask William why he let X=Jenny just to make sure if he understood. I said, "why did you let X=Jenny?" William said, "because we don't know about Jenny, so we let X=Jenny." I said "good" to him. Then William had the equation X+2X+2(2X)=133, but he didn't know what to do after that. I said, "what's 2 times 2X?" Then he said, "4X, and X+2X+4X=7X=133, and then divide by 7. X=19." Then I told both William and Mario to write the answers in a sentence. They were like "no. It's ok." But they knew that they had to. So, I asked them, "how old is Jenny?" Then they wrote "Jenny=19" although I told them to write in a sentence! Then William said, "Margaret is 2 times 19=38, and Sarah is 2 times 38=76. Wow! These people are old!" He calculated by using the calculator. William was done with his homework. Mario had one more left, and William was going to just tell him the answer, but I said "no." I sat next to Mario. The problem was "On a 520-mile trip, Thu and Cleo shared the driving. Cleo drove 80 miles more than Thu drove. How far did each person drive?" I asked Mario what he was going to let X. He said "Thu." I said, "and Cleo?" He said, "X+80." Then I said, "then the total is 520, so?" He said, "X+(X+80)=520." He said, "2X+80=520. Then subtract 80. 2X=440. X=220." William was shouting the answer the whole time, so I had to say, "William, shhhh!" Then I asked Mario, "So, how far did each person drive?" Mario wrote down "Thu drove 220 miles, and Cleo drove . . ." He was calculating 220+80 in his head. He
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