The video Number Operation- Multiplication & Division featured a mathematics lesson that took place in a 4th grade classroom with math coach/teacher Becca Sherman. No video of the teacher discussing pre-planning or the goals was included in this video series, and the clips began immediately with the teacher instructing the lesson. However, the teacher did have the phrase "A picture is worth 1,000 words" written on the board, which she explained to students was the focus of that day's math lesson. The lesson itself was divided into four major parts, which were titled "problems" in the video clips.
On the whiteboard, Ms. Sherman had the words "multiplication" and "division" written side by side. For Problem 1, students were asked to talk with their partners about what multiplication means. Students then gave their responses, which Ms. Sherman copied on the board. Some of the students explained that it's like (repeated) adding and groups are made. The teacher asked for students to provide examples, and the students dwelled on the 2's multiplication facts. Ms. Sherman then explained that they needed to try to create equal groups, and could use pictures to help them.
Once the list of things regarding multiplication was created, Ms. Sherman asked students to do the same thinking for division (Problem 2). Students talked with partners momentarily, and then shared responses. One of the students said it was like subtraction, but could not explain why. Other students said that division is like multiplication, and you can "switch them" around. Many were able to see the clear connection between multiplication and division. Ms. Sherman wrote the number 100 on the whiteboard and asked students how they could divide this into equal groups. One student said that they could do two equal groups of 50. She asked for other solutions, but the number seemed too big for students to grapple with. Then, she wrote the number 12 and asked students the different ways to divide this number into equal groups. Students provided several correct solutions.
Problem 3 occurred next, and this involved students doing mental math. Ms. Sherman had a multiplication problem written on butcher paper that read 26 x 4. She told students to think about it quietly and try to solve. Then, she asked for students to explain their methods and answers. Most of the students chose to use the more traditional multiplication method by setting up a vertical equation and "carrying". However, many who did this got incorrect answers (likely due to the mental aspect of this task). Ms. Sherman asked students if there was more than one correct answer, and surprisingly, some answered yes (which was not true). She asked for additional methods, and explained that creating a picture representing 4 groups of 26 would be a great way to solve this. One student had an alternate approach, which I found interesting in itself. He explained that he knew there were 2 tens and 6 ones. So, he counted off 20, 40, 60, 80 (20 four times). Then, he counted off 6, 12, 18, 24 (6 four times). Finally, he added 80 + 24 and got 104, the correct answer. Ultimately, this student used his knowledge of place value to find the correct solution, which I found very interesting.
The final problem for the lesson, Problem 4, had students working with word problems. Ms. Sherman posed a sentence on butcher paper about money. The sentence said, in short, that Maria had $24, which was three times the amount of money that Wayne had. At first, no questions were posed, but students picked up on the fact that they needed to find out how much money Wayne had. There was a surprising split in the answer. Almost half of the class immediately saw "times" and did the operation 24 x 3. Clearly, they did not understand that this was a division problem and 24 was actually the whole. Other students were able to find the correct answer of $8, but could not explain why they thought this was correct. Students were asked to draw pictures and have words that explained their answers. However, most of the student's pictures did not explain the word problem in any way. The majority of students who wrote that Wayne has $8 could not explain their reasoning whatsoever! Next, Ms. Sherman wrote a picture on the board that explained the problem. She asked students to look at the picture and see if they understood how it was setup. Then, she gave students another sheet with a sample problem on it. "Charlie" set up his problem using a bar model, and 24 was Maria's whole while an unknown amount was Wayne's whole. She instructed students to try and find the missing numbers. Again, many students jumped right to putting 24 in each of the part boxes on the bar model. Finally, she gave the students two questions regarding the problem. Ms. Sherman tried to explain why 72 was not the correct answer, but it was clear that students were still struggling. To conclude, she had students write a few sentences about what they learned from "Charlie's" model in relation to the problem. Students seemed to struggle with this.
At the faculty debriefing, Ms. Sherman noted that at the beginning of the lesson, it was hard for students to expand from their 2's multiplication facts. Additionally, she noted that the whole idea of creating equal groups was not there. Many students explained that addition was like multiplication and subtraction was like division, but could not back those statements up. She believed that this was because students had been told this at some time in their education, but did not know why this was. Ms. Sherman also said that she felt the drawings portion of the lesson kept students engaged, which made her happy. She was displeased that over half of the students continued to believe that Wayne had $72, even after her attempts at explanation. Some of the faculty members noted that some students had correct answers initially, but changed them once they saw that their group member's had a different answer. This made it evident that there was a copying problem in the classroom. Most of the students also had drawings, yet they could not make any sense of their drawings or explain what it had to do with the story problem. The biggest take away that the faculty members drew from the lesson was that these students really needed to work on making connections in multiplication and division and their actual meanings, instead of just reciting number facts.
A few things really struck me in this video that I would like to now comment on. First of all, I believe that Ms. Sherman is a decent teacher. However, while watching the video, I noticed quite a few things that I think she should have avoided doing. During Problem 1, she flip flopped back and forth quite a bit between various student examples of multiplication. This was not beneficial to students; it just confused them. In Problem 2, one student shared an example and she asked him to draw a picture on paper to explain his example. When the student said he was finished, she simply said that they would look at the picture another time. I did not think this was the right thing to do. She asked the child to take the time to draw the picture, which relates to the topic at hand. Why would she have him share it another time? Also in Problem 2, she asked students to break the number 100 into equal groups. This was much too big of a number to begin with. It was clear her students were struggling with the concept of equal groups, and she should have given them a much smaller number to work with. In Problem 4, she was again jumping around between different pictures and kept saying "we'll come back to that". This was not at all helpful, and really confused students. I liked this lesson, but I saw the students really losing focus toward the ladder part of it. I think Ms. Sherman had good intentions of getting a lot of material covered, but the reality was that students lost focus quickly. The last task was to write a few sentences about "Charlie's" method, and some of the students were so lost and gone by that point that there was just no sense in writing.
I took a lot of interest in watching this video, and I think that the lesson overall was a great concept. However, it was clear that this group of 4th graders needed quite a bit of work on understanding the meaning behind multiplication and division operations.
Very nice! Thanks Kaitlin:)
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