Markert-Student Work

For the past few weeks we have been working with coins in our class. During my unit we did work with pennies and nickels mainly and touched on dimes and quarters. This week we are starting to do more work with dimes and exchanging coins. On Monday we worked especially with coming up with ways to show a certain amount of cents using fewer coins. This was not the first time the students have worked with exchanging coins for fewer. I was teaching the dimes lesson and I wrote on the board N,N,N,P,P,P. I asked the students to think of a way I could show 18 cents with fewer coins. I gave the students time think about their answer before calling on one of the boys in my class. When I asked Sam to explain to me how I can create 18 cents with fewer coins he told me that I could exchange one of the “N” for five pennies. This was great because he recognized that the nickel is worth five cents and that pennies are each worth one. However, he exchanged the coins to create more rather than fewer. I decided to write his answer on the board so he could see what he had told me. I was hoping that by doing this he would recognize that in fact we are creating more coins. However, he still believed that I now have fewer. When I asked him to explain why this was fewer his response was “because a penny is worth less than a nickel.” I then explained to the student that he was right a penny is worth less than a nickel but we now have more coins rather than fewer like I had asked. He seemed to grasp what I was saying by nodding his head but I wasn’t positive.

            After this lesson I thought about this students response to the question. I realized that the word fewer to the student might have been the confusing part. To the student I believe he was taking the word “fewer” and comparing it to “less” then it seemed his immediately thought less value instead of less coins. I may have made this unclear during the lesson or this may be a misconception he may have in general. When I circulated the room during their independent practice time I noticed that he was having difficulty also computing a give amount of coins into a fewer amount as well. He seemed to become stuck once he figured out how much money was shown. This is what made me think because he knows his coins and how much they are worth but a misconception lies when translating and exchanging that amount to other coins. I also thought that coins could be very arbitrary for students at this age. They have difficulty seeing one coin and just simply knowing that it is worth a certain amount. One way I think we could expand their understanding and create a high-level task is having the students develop their own monetary system. This might help them see the reason we have coins of different amounts and why we need to know how to exchange them.  I also think that this particular student could benefit for spending more time dealing with the actual coins. We do some work using their own coins but it becomes very chaotic and hectic so it is difficult to do an entire lesson with their own set of coins. If he could spend more time holding coins and exchanging them he might realize what it means to have “fewer.” Overall I think it is interesting teaching money to students because it is something that they have all seen but it is somewhat difficult for them to grasp. I think coins is a topic that needs a lot of repetition and practice so it will be interesting to see when we get to quarters if there are any changes.