# Faculty Debrief

## faculty debrief

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In this clip, Becca Sherman reflects on her lesson with observing faculty and coaches.

## faculty debrief

4th Grade Math - Number Operations: Multiplication & Division
Becca Sherman, Bayshore School District, Daly City, California

Previous:  Closure

LINDA FISHER: Most of the people I observed had the 24, 24, 24, and so, then Wayne also had 24. Um, and they did like, cookies, they did little squares, they did three Maria's with lots of hair, even though you told them not to do that, and the little Wayne picture. But somebody called Jarelle made three rolls of eight dots and then circled them, and he had it just like a text book solution, 24 divided by 3 is 8, Wayne is \$8, Maria is \$24. And then another little girl did eight 3's, so we know that it's...she did have the right answer, that Wayne had \$8 but it's really hard if Maria is 3 times as much as Wayne and he used the model this way instead of three groups of 8. How do you ever figure out what Wayne got? So, so it was just sort of a troubling picture because it doesn't show that mathematical relationship, it shows you just kind of a number sentence that equals 24.

BECCA SHERMAN: I asked her what...I don't remember the exact question I asked her but "What does this tell you?" And I said...oh, I think I may have said, "I noticed you said that Wayne has \$8, how does your picture tell you that?" And she said, "Well there are 8 boxes." So my...I agree with what you're saying. So she used the mathematics, understanding the mathematics to try to draw the diagram, then to represent it. And so, um, the 8 boxes doesn't make sense in the same way as having \$8.

LINDA FISHER: And then one little guy had 24 circles with 3 dots in each circle, which obviously isn't the relationship that you wanted, but he really got the idea of the pretense strategy. He goes, "Well, you know, I can make it cookies, I can make it pizza, it doesn't matter what group I choose for making my picture because the math will be the same," which, you know, that is a good mathematical concept that you can make it any friendly thing that you what to draw. So, I kind of like that but... And then the final thing that I just want to say is um, there was one table that pretty much all had the four 8's, and all four of them put 24 here too. And it wasn't until you then uncover the question, that one of the three changed their 24 to the 32. And all of them kind of wrote this sentence with the 32 in it but nobody, only one out of the four went back to change the number in this model. So they weren't really understanding kind of what this box out here was.

MEGAN MARTINS: One of the boys just was stuck in the 24 plus 24, plus 24. He actually, initially started with 24 times 3 and then got 62, and then got wrapped up in the whole multiplication of that but he insisted it was 62. And then he added different ways, tried to break numbers up and someone else in the group was like, "No, it's 72 and let me show you why." They were so wrapped up in that, in solving just that multiplication problem that the rest just...they couldn't follow the rest of the lesson. But one of the girls in the group, she drew out the bars and they were connected, but for Maria she had 24 in each box and for Wayne she had 8. When I asked her if she could explain how she knew Wayne had 8, she said, "Well, 8 times 3 is 24." And I said, "What does the 8 and 3 mean?" And she couldn't explain it. So there was a lot of misunderstanding at that table group.

LINDA FISHER: To, you know, not just teaching that process of multiplication but really trying to get kids to make that connection to equal groups, and then that's so critical for them in understanding what a unit is and to be able to do algebraic thinking. So you really want, you know, how do we get that connection when they first start making sense of multiplication, to really think about those equal groups so you don't have to force it out of them, or...you know, I think I had to even introduce the word "groups" to get them to say anything at all.

NORM FORBERT: It's really important that they build their algebraic and mathematical vocabulary. They just don't have it and it has to be repeated to them and they have to repeat it to feel comfortable with it. And I think that was the major part of what happened with reading the story problems, not cueing onto the wrong cues, and understanding the vocabulary and being able to use it.

I learned so much from teaching this lesson and even more from listening to my colleagues and by continuing to dissect the student responses myself. Admittedly, my first look at the student work was a bit devastating. However, I now see that we launched something much larger than a model (bar model) for division story problems. The students in the classroom are primed for active and thoughtful metacognition about their own math understanding. I truly believe that their continued experiences trouble-shooting math models, strategies, and connections will weave a strong foundation of vital math understandings which serve them well as they venture into more abstract mathematics such as formal algebra.