In this lesson, we discussed money, what we use money for, and we talked about pennies and nickels--their values, ways in which they look different, but that they are both coins. Finally, the students discussed that coins are worth or represent certain amounts. Each coin is worth or represents its own amount. The students were asked to complete this worksheet and then we had a discussion of the various responses students had. The worksheet had a set of 6 pennies. The first question was "How many coins do you see?" This student answered "6." The next question was, "How many cents do these coins represent?" This student answered "1." The second set of coins was 1 nickel and 1 penny. When asked, "How many coins do you see?" The student answered "2." When asked, "How many cents do these coins represent?" The student answered, "1 5."
1. Did the wording of the question "How many cents do these coins represent?" confuse this child?
I'm wonder if this was confusing for this student because for the group of pennies she indicated that she knew a penny represented 1 cent. In the second question she also indicated that she knew the correct value of a nickel and a penny. She many have thought I was asking about the given coins, not the group of coins that was shown in the picture. Many if I had worded the question, "How many cents is this group of coins worth?" she would have understood to add the amount of each coin. Although, through the way in which she answered the question on the paper and explained the answer it is clear that she understands the value of each of these two coins, and that those values are independent of one another.
2. Going back to how she answered the question discussed above, this also makes me wonder, "Does the student understand that values of coins can be added together to make larger values? Or is she still at the phase of simply understanding that each coin has a value of its own?
In order to explore this I think I would have to do more money activities with this child. If it were my classroom I think I would set up a pretend store. I might make an item cost 12 cents. This way the students would realize through this game and exploration that you can put coins together to pay for things that don't have a coin to represent that specific amount.
3. I have a question about teaching money in general...Once all of the coins are introduced, it seems like it would be very difficult to differentiate, on a piece of paper, between a nickel, dime, and quarter--how do teachers do this?
My thinking is to of course discuss the different pictures on each coin, what they mean, and why they are important enough to be on our money. This way the students would look closely at each coin and truly understand the differences in the ways each one looks. I also think it would be a really good idea to make sure that all of the coins on a paper are "life size." This would be that if you put that coin on top of the picture of it on the paper it would fit exactly. I think this would be an important learning tool for kids because realistically, when I am searching through my wallet for a certain coin, I'm mainly focusing on the size and width, not the picture.
This is a great task and a great analysis...simple, but to the point, and it uncovers student thinking very well, as you analyze here. The question is a) what the next task might be in light of this and b) how are other students thinking about this problem...do other students have the same misunderstanding? What kind of mathematical discussion can students have about this concept based on their different interpretations of the problem?
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