Clip 4/11: Lesson - Part 2
During the processing of the first problem, Sarah notes that the second answer is incorrect. This puzzles other students. Together we take a critical look at the words in a word problem and see how those words connect to the symbols used in the number sentences provided.
I intended for students to not only look at how their peers decomposed numbers to come up with answers, but also look at how they documented it. Did they use a complete number sentence and words to clearly explain their thinking? If not, my goal here was for students to link the words in the problem to the symbols that would complete the number sentence. This resulted in the lesson taking a bit of a turn. I needed to know what my students were thinking in regards to this new dilemma presented by Sarah and supported by a few others (Aaryn and Nia). In this segment of the lesson Sarah is very quick to point out the error made by another student in how they understood the problem. She expresses very clearly where the mathematician went wrong in their understanding and how the answer they provided just does not make sense. She states her observations and conclusions very quickly.
During math lessons early in the year we spent a lot of time decomposing numbers to help answer questions and learn regrouping. While some students agree with Sarah's position, others continue to be puzzled by how she knew to subtract. Aaryn points out that the words in the word problem "how many more" are a clue to subtract.
The key idea I wanted my students to gain was "DOES THIS MAKE SENSE, GIVEN WHAT YOU KNOW AND HAVE BEEN TAUGHT." Iyanna who is a very strong reader, struggles in math and often shuts down. The process of re-engaging a task allows students like Iyanna time and space to make sense of a problem and get clarification.
After Sarah shares her thinking I am very careful about the statements and questions I use. "...but, you are thinking this should be a subtraction problem? Does anybody else think that? What are you thinking? I'm not sure. What do you think?" I am intentionally opening the door for students to also say exactly where they are in their process with this problem. There is no pressure. In fact Iyanna boldly states where she is in her thinking. It is the place where she is stuck. Keeping in mind that my goal here is to get struggling students to ask more questions and secure students in math to share their thinking. Through this process we can all learn more. As students speak up, and mumble on the carpet, I have a window into how they approached the problem. Now we can begin to attack misconception and break this poor habit of looking for number and just adding them together.
On way to break this habit is the use of thinking of certain phrases as code words. Nia speaks up and says, "How many more is the code!" D'wone, another struggling mathematician understand that it is a code for the number sentence. However, he is not 100% clear on what exactly it is supposed to tell him.
It is very tempting to jump in and make this a lesson about the words, "How many more" in a word problem. This group of students have found it useful to equate this phrase to subtraction, however I could have really taught this as a "comparison" or strategies for finding the difference by adding. I choose to maintain my course and allow student space and time to explore and discover errors, knowing that they will get to do this with their own work soon.
2nd Grade Math - ¿Como Se Suma? How Do We Add?
In this Number Talk, Katy Arrillaga engages her 2nd grade Spanish bilingual students in a discussion about strategies...