Student Work #1

Every day, my mentor teacher has the students do what she calls "Big 4 Math." Each student has a Big 4 Math notebook where they do the math each day. They all begin by splitting the paper into four sections, then my teacher projects the problems she would like them to solve in each of the sections. Each section has different types of problems in them, with the majority being review, and only one or two sections containing new material. This activity is not meant to take long, but it refreshes things they learned earlier in the year and also gives them extra practice on what they are learning that week. My mentor teacher then has the students go over the problems as a whole class, and she calls students to the projector one by one to show their work and provide the answer they got to the problems. My mentor teacher keeps track of their progress and the students never take the Big 4 Math folders home, so she can check their progress anytime. Also, my mentor teacher always uses the bottom right corner for a story problem of some sort because she knows this is where her students struggle most in math.

For the long division problems, there is really only one strategy for students to use, which is the method of solving long division that all of the students are taught. This is the same for adding 6-digit numbers. The students need to regroup when the answer is a number greater than 9, then add whatever was carried over into the next column. However, when looking at the problems in the top right corner, there are multiple ways that the students could approach finding the smallest fractions. The students could decide that since both numerator and denominator are even, they can begin by dividing by two, then repeat as needed until the fraction is in simplest form. The students could also attempt to divide the numerator into the denominator (which in more than one case works for the problems my mentor teacher provided). Finally, the students could think of the factors that make up both the numerator and denominator and find the greatest common factor to divide both by to obtain the simplest fraction. I expected the students to keep dividing by two because the majority of the problems of this type they had previously done required them to divide by two at least once. For the question that required the students to divide both numerator and denominator by 3, I expected the students to attempt to divide by two in the beginning, then realize that it does not work. I then expected them to move forward through trial and error counting up from two (i.e., does 3 work? 4? 5? etc.). There are also multiple ways to solve the time problem. The original word problem dealt with a plane taking off at 10:02 a.m. and the flight taking 3 hours and 17 minutes, and calculating what time the plane landed. The students could add the minutes right away, since there is no regrouping necessary, then move on to figure out the hour. I would expect students to know and remember that the numbering starts over once they reach 12:00 and the a.m. switches to p.m. Therefore, when counting the hours, I would expect the students to either subtract 10 from 12 to see how many hours it takes to get to noon, then add the remaining hours, or add 10 and 3 to get 13 and figuring out from there how to change it to 1:00 p.m.

The student I chose to look at is the student in my placement classroom who has been in the United States the shortest amount of time. I know that he struggles with reading and writing (although he has made great strides this school year and is catching up to the others rapidly), so I expected him to struggle with the word problem involving the plane. As you can see in the picture, I was surprised to learn that he did not struggle at all. He read the question a couple of times, wrote the numbers that he knew he needed, figured out what he was supposed to do to the numbers by reading the question again, then he preformed the addition task. After writing 13 initially, he looked back to the question to find that it took off at 10:02 a.m., erased the 13 and changed it to 1, while also adding the p.m. at the end of his answer. He did not ask questions about the language or get stuck with the second required step of the problem, instead he rather effectively used the information in front of him to figure out what he needed to do. Also surprisingly, this same student approached the simplest fraction problems by figuring out the greatest common factor. Unlike his peers who chose to divide by two as many times as necessary, he did the math in his head to figure out that the numerator and denominator could both be divided by 4, and did it this way instead.

Although this student has only been in the United States and speaking English for about four months, his language development does not in any way hinder his mathematical abilities. As seen in the picture, all of his answers are correct, and he even chose more abstract methods for solving the problems than his peers did. I did not expect that because he does not speak English well that he would not understand math either, but I did expect there to be some degree of communication error. It surprised me that he so easily understood what my mentor teacher had been teaching, without any additional explanation or help. I also noticed that he often helps his tablemates when they are stuck on a multiplication fact. I fully expected him to get tripped up on the word problem, simply for lack of language knowledge, but he did not show any amount of struggling with the problem other than taking a bit longer than the other students to read the actual question.

I think this student could be doing more advanced math than other students in the classroom. He seems to pick up the concepts very quickly and once he understands them, he is efficient at solving them. I think that it could be beneficial for he and a group of other students in the class who also are high-achieving math students to be given problems that challenge them a bit more once they have finished the work that takes the other students in the class more time. I think it is a great sign that he is already using more abstract representations for the problems given to him and it shows that he is a bright student, regardless of what he is able to communicate. The only thing I have noticed that may or may not be a future problem, is that when discussing with him why he did his problems the ways that he did, he struggles to communicate with me what he was thinking or understand what I am asking him to tell me. It is quite ironic that I expected the communication problem to be with understanding what to do, when in actuality, it is the communication of what he did, after understanding what to do to solve the problems.