DMI Ch.4

After completing this week’s readings, I found Ch. 4 of our DMI textbook to be very insightful. Throughout the two separate case studies, Lynn has her students experiment with a variety of problem solving strategies when completing diverse addition problems. Each student appears to have his or her own way of completing these problems and becomes slightly confused when the standard borrow/carry or regrouping algorithm comes into play. Many of the children solved the addition problems beginning with the tens column. On page 64, we can see a chart that Lynn comprised for her class along with responses from the children saying, “I did it that that way! Or “I solved it the green way”. For example, one of these strategies utilized when adding 38 and 25 was 30+20=50, 8+5=13, 50+13=63. In this strategy, the student begins by adding the tens column then adds the ones column. The final step is adding the two answers together to receive the total. Another strategy used was 38+2=40, 40+20=60, 60+3=63. In this particular problem the student rounded 38 up to 40 by adding two. They then added the tens columns together 40+20 to get 60. Rather than adding the remaining five in the ones column, the student remembered they had to first subtract the 2 that was initially added and thus, add only 3 to retrieve 63. Though many of the students were familiar with adding the tens column first and disliked the standard way of doing things (adding the ones column first) Lynn states, “What amazed me was that they could all make some sense of the pink way” (66). Given all of this information, we can identify the various ways and multiple strategies utilized by these students in order to obtain the correct answer to the given addition problem. In Case 2, students also used a variety of methods to obtain the correct answer to two-digit subtraction problems. For example, when Paul was asked to solve 39-17 he decided to take the 17 apart in 3 steps. He first computed 39-10 to get 29. He then took 29-4 to receive 25 and then 25-3 to get 22. Essentially, he broke 17 up in 10, 4, and 3, and subtracted each portion from 39 individually. Nathan on the other hand, approached this problem quite differently and used addition to solve this subtraction problem. He first added 17 and 3 to get 20 and then added that 20 to ten to get 30. Nathan then added 30 to 9 to get 39. In essence, Nathan begins with the lower number and continues to add a variety of numbers to it until he gets to the higher number. He then takes each number he added to the originally number (17) and adds those together to retrieve the answer. These are two very different and unique strategies utilized by two distinct students.

In the second case, Fiona is trying to complete the subtraction problem 37-19 and in the process, loses track of the numbers she is supposed to be subtracted. She begins by subtracting 10 from 30 to get 20. (She rounds 30 down from 37 in order to make the number more manageable.) She then takes the 20 and subtracts 9, the remaining portion of 19 left after the 10 had already been subtracted. Fiona then gets confused because she is unsure if she should add or subtract the initial 7 that she dropped from 30 in order to make the number more manageable. With the teachers prompt, “Did those 7 pigeons leave or stay” she realizes the 7 needs to be added in order to obtain 18. This is a strategy that children implement and often results in the inability to correctly track numbers throughout their thought process.

Figuring out how each of these children solved the given equations and implemented reason and logic in a way that makes sense to them truly allowed me to view math through the eyes of a child. Many of these strategies are ones that I would not think of on my own, yet they are astonishingly accurate and sensible. By walking through the process each child took, I was able to understand the wide array of strategies present and will be able to keep these in mind when teaching in the future.