The lesson I chose to record was the five-step approach to addition and subtraction word problems in my fourth-grade class. This was the second day of the lesson, so students were introduced to the process the day before (i.e. given information, unknowns, number sentences, solve, and check). In the morning, we began by reviewing the homework. First, I read the questions to the students, such as “Joshua has $48, which is $16 less than what his sister, Lin, has. How much money does Lin have?” Next, I had the students read the material to themselves, and finally, I “pop-corned” on four students to read the remainder of questions.
Following the homework review, I reviewed one of the questions concerning given information from the PowerPoint, with no scaffolding, and asked: “what does that mean?” Students raised their hands immediately, and I waited about five seconds before I called a name. I noticed this wait time was typical for my questions, and I did not go over 12 seconds. The chosen student responded in about four seconds. He answered incorrectly by simply repeating the question as “Joshua has $48, Lin has $16 less.” Immediately, I asked the entire class who agreed with this answer. Our classroom procedure is a “thumbs up” or “thumbs down” in front of the chest so I can see. After scanning the room for about 5 seconds, I called on students with a thumb up and asked them why they agreed. I questioned these students’ incorrect thought processes to break the relationship they were creating between the incorrect answer and their analysis. I waited about three seconds before I asked, “who does not agree?” Immediately, hands went up and I chose to call on one of my top students because I knew he could articulate why the answer was wrong without confusing the class. I like to have the students explain as I think it is a friendlier approach and students react well when listening to their peers.
Once answers have been given, I tend to go back to the students who were answering them incorrectly at the beginning of the process, so they can see the connection towards the end. I use the class dojo about twelve times a lesson if I notice kids are not following along to reel them back in. I tend to ask students who I know are struggling specific questions because I feel like the ones who do not understand word problems are the same students who struggle in English. I will say things like “how do we read word sentences?” and the students will answer “left to right.” I then move into asking how to read a math problem. I try to make connections, such as illustrating the relationship between subtraction and a minuend or subtrahend, then provide definitions. Students in my school have more trouble reading than anything, so I try to bring a lot of interdisciplinary practice into my questions.
During step five—the check—I asked the students to give me a fact family. I called on a new student every time. This way, I could ensure I was not falling victim to the Fisheye problem and leaving out some students. One student could not find a fact family for the second subtraction (Gonzales, 2013). Using scaffolding, I asked, “is subtraction commutative?” The student replied “no,” so I suggested he switch the minuend and subtrahend and try again to make sure he knew his answer was correct.
Moving on, I used vocabulary to get them to make the connections and asked what patterns they noticed. I waited about 12 seconds before I called on anyone and then chose at random. The first answer given was that the addition of the two problems gave the same sum. Another student answered that the addend was the same. No one provided another answer, so I waited five seconds while looking at the problem and demonstrating that I was thinking. I probed the students to continue by saying, “I see two more.” The students began to analyze and were about to correctly respond using numbers, so I put the answer on the board and asked the class to respond using their vocabulary words while I pointed to the word wall and had them tell me how to create a fact family. The student I called on was not able to answer, so I waited about seven seconds, then turned to the board and asked a follow-up question to the same student: “This one is blank minus sixteen equals forty-eight. What are these minuends?” The student looked at the word wall and couldn’t answer, so I said, “in the alphabet, what letter comes first?” Immediately, the student realized it was the minuend.
I noticed that I will stay on a particular student and give about three scaffolding questions at which point I ask the student if they would like me to move on. Most of the time they say yes and pick a friend. I ensure all students are called on in class, and if a student was not able to give an answer, I always go back at the end to ensure they learned the lesson. I have fourth-grade double blocked every day in the morning, and I find I am more successful with this population because we have 100 straight minutes together. This allows time for a reteach, which takes about 20 minutes, and makes me able to still move on to the next concept. If students do not understand, no one moves on until everyone is learning. For example, we did addition and subtraction computation prior to the five-step approach, and I asked the students to think about where we learned these concepts before and what the relationship is between addition and subtraction.
Gonzalez, J. (2013). The fisheye syndrome: is every student really participating? Retrieved from https://www.cultofpedagogy.com/fisheye/