What Did You Notice About What the Teacher Did/Said?

CB February 6, 2006 Frameworks — The Horse Problem

What did you notice about what the teacher did/said? The teacher allowed for group participation, allowing the students to work as math team tables or with team member. She posed this problem as a famous math problem. At the end she explain that there are 4 different answers. She told them that the process was more important rather than the answer. She wanted to know the justification for their answers. What was the most critical detail within this practice? The most critical detail within this practice is group participation. This allows students to hear their strategies

What did you notice about student participation? Boys tended to answer more, and within group participation they still dominated conversation. The girl observed walked away as the boys tried to explain.

What did you notice about the mathematics? Some noticed that it this problem was about profit and not how much money the man began with. Some noticed it as negative numbers because he was losing money. Some explained their responses with algorithms; some gave the man starting money and worked from there.

What did you notice about issues of equity? Boys seemed to be given more of a chance to participate, though the teacher did encourage the girl to participate. She asked the boys if everyone had been given a chance to explain their answers. The teacher says if responses are better than others. The students explained that their responses are not necessarily better, but easier to understand.

What worked well in relation to this particular practice? What adjustments might support student learning and participation? The group participation really worked well. It allowed students to try out their strategies with each other. However, girls weren't give attention. The teacher sat down next to the boy, rather than trying to have the girl to answer. I liked the idea that the process to the mathematical answer is more important than the actually answers. Some students just to focus on getting the answer, rather than taking notice of how they reached that answer. Mathematics Teaching Practice Framework

Watch how the teacher teaches the horse problem.

What did you notice about what the teacher did/said?

-She tells them what they will be doing before they start anything. -They were too far away so she used another board to be closer to them. -She states the facts of the story and then afterwards, writes the facts on the board. -She speaks slowly so that the students can understand what she is saying and have time to write it down. -She tells the story in an expressive manner. -She explains what she wants them to do and tells them that they have to be able to explain their answer. -She explains to them the concept of team and review rules for it. She asks students to contribute. "What are some things we would expect to hear in a team if you guys solved this?" -She says, "The goal of this is to have everyone on your team to be able to explain how you solved the problem." She states the goal and then tells them she will draw sticks from team and whoever the person is, that will be the explainer and they can't just rely on one person to explain everything. -She states that the "team needs to agree on the solution" and stresses "team solution." -Had them work together in their groups. They had to explain their answers to each other, agree on the answer and then check to see if everyone explained it to each other and to see if they all agreed on each other's explanations on solutions.

-Another teacher explains that "We all have different ways of solving the problem so what's your final answer?" Asks children to explain all their answers because there are so many different ways of solving it. -Facilitates discussion by asking "Is there really a better way?" and saying "This is a good discussion here."

-When the class gets together as a group again, the teacher explains that this problem was done with grad students and "in one group, we had four different answers and people could explain thoroughly and completely how they got their answer." She explained it was all about how people could explain, not the particular answer that they came up with but how well they explained it. She said there were four different answers in one group and some people convinced other people that they were wrong, just by their explanation. "So I'm going to be very curious to see if my mind could get changed by some of the solutions." -When she called the first student up, she asked him, "Have you checked with every member of your team and do they agree with your solution?" -Asked student, "Could you indicate that for us so that it's very clea

Mathematics Teaching Practice Framework: Hurley/Fifth Grade/Horse Problem

Watch how the teacher __poses problems

"A man bought a horse for $50. He sold it for $60. He missed it so much that he bought it back '-70 Then, his neighbor loved the horse so much that she offered $80 for the horse so he sold it to her for $80. What do you think the final outcome was? Did he gain money, lose money or come out even? Explain your answer."

What did you notice about what the teacher did/said? •Students could work either with a partner or with their whole math table team. •She told the students to write the facts down first and modeled how for them. Guided them through the facts. •She asked if they had any questions about the facts. •The teacher went over what it would sound like working in groups, that they are looking for a team solution. •She made sure that each person in the group could explain their answers. •She mentioned that when she did this in grad school, her class got four different answers. 'She checked that everyone on the student's team agreed with the answer, although they said that they had different strategies. 'She pushes the student to be sure that he answers the question and tells him to indicate his answer so that it is clear to the rest of the class. 'She let the students be the teacher and call on people in the class as well as write their work on the board. 'When the Fifth graders came into the class, she asked one of the Fourth graders to explain the facts to them. 'She scaffolded them in what they wrote on the board and asked them to explain their thinking. 'When a student pointed out that he wasn't ready yet, she said that they had the same amount of time as everyone else. •She pointed out at the end that they had all gotten the same answer in different ways. Fonts ok- 0- '3 tzfrr.

What was the most critical detail within this practice? •It's not the answer; it's how you explain it. Also, students need to agree in their groups on the answer and all had to be able to explain it.

What did you notice about student participation? 'Students asked clarifying questions about the facts. •It sounded like most students participated in the groups, but that some students monopolized. 'When one student disagreed with the others, they others shut him down. 'Some of their answers were VERY confusing (especially Finn in the red hat)! 'Students asked each other about how they solved the problem. 'They were excited to have the opportunity to explain their answers and write them on the board in front of the class. 'One group got very creative and put on a play

What did you notice about the mathematics? •Students debated about whether it was more important to look at the dollar amounts or the profits. •Some students simply subtracted 70-50 and 80-60 (the most they paid and what they originally paid) and determined that they came out equally. Then they changed their mind and said that the man came out $20 ahead (I think!) 'They each had different ways to solve the problem, both the students who presented to the class and within each group. •All students came up with a $20 profit for the man.

What did you notice about issues of equity? •The students had to agree on their answer and it would be a random selection of who from the group would explain it, so they had to work together and make sure that everyone understood how to explain their answer.

What worked well in relation to this particular practice? What adjustments might support student learning and participation? •It was good that they had to explain their answers to each other in the groups to make sure that everyone understood. Random selection of who would explain the problem made sure that everyone could. 'Use of manipulatives (or at least access to them) might have helped, although by Fourth grade, perhaps they wouldn't want to use them. Mathematics Teaching Practice Framework Watch how the teacher______What did you notice about what the teacher did/said?

I explicitly told the students who immediately seemed to have the answer to, "Keep it in their brain," so their classmates could have a time to think about the problem. I told them to really think about what the problem is asking them to do. I tried to activate their prior knowledge of number facts, since this problem could be solved by either multiplication or division.

I also told them they could use any strategy they want to solve the problem and they could get manipulatives if they needed. time as I could.

What was the most critical detail within this practice?

I had students share their strategies, while doing this, I highlighted the different entry points of the students. I also tried to focus on connecting the different strategies together. I also never told the students if they were wrong or right (I wanted to try this out after watching Lilliam's video early in the quarter) and tried to ask open-ended questions. We have been studying the importance of "Wait Time," this quarter, so I really tried my best to give them as much. While it was slightly painful to just walk around and keep checking in with the students, I really wanted to allow every student ample time to think about the problem and attempt to come up with a strategy to solve it.

What did you notice about student participation?

What I found most interesting, is some of the students who do not typically share out during a language arts lesson (specifically two ELL students), were the first to raise their hands and volunteer to share their strategy for solving the problem. It was also cool how when we were discussing the problem, a few students just went up to the board and started solving it. Clearly it is easier for some to verbalize their strategy, while others actually have to write it out.

What did you notice about the mathematics?

I needed to clarify their knowledge of number facts. We did a few skip counting warm ups prior to the problem. Maybe it would make sense to do a word problem similar to what we worked on.

What did you notice about issues of equity? There was an opportunity for each child to participate. I had the students Think, Pair, Share for a few minutes before we discussed the problem as whole group.

What worked well in relation to this particular practice? What adjustments might support student learning and participation?

I really focused on trying to pose the problem really well. I definitely think I could do a better job. I also need to think more deeply about the problem before hand and think about the multiple entry points. I have experienced some difficulty solving math problems without using the standard algorithms. It takes me a really long time to think of alternative ways to solve problems. I really resisted the urge to show one student that particular strategy.

I was really pleased because the majority of the students were eager to participate and were helping the students around them encountered some difficulty with the task. The student participation is vastly different from other subjects such as ELD or Language arts. .ialk interesting to see that because I spent the majority of my time teaching Language arts in this 3`a grade class. They had math in the afternoon, which only gave me about 10 minutes each day and that was when I did a warm up of skip counting with them. Mathematics Teaching Practice Framework

Watch how the teacher___proposed three T/F number sentences

What did you notice about what the teacher did/said? The teacher placed the problems on the white board when students were putting their backpacks away. The students already knew to come to the carpet when they were ready so when they did come, they started looking at the problem and some even shouted out "That one's true!" or "That one's not true!". · The teacher did not validate anyone's answer at first. He asked the students why students believed what they believed and assured that an explanation was provided for different ideas before he actually circled the correct answer. For one question, the teacher had students take a vote to see who believed it was true and who believed it was false. Then he chose one person who believed it was true and another person who believed it was false to give their explanations.

What was the most critical detail within this practice? The most critical part of this practice was asking for students explanations. On multiple occasions, while one student was explaining his or her ideas, others would say things like, "Oh I get it!" or "No that does not make sense." On other occasions the student giving the explanation would question herself or himself in the middle of the explanation. This is a great way to monitors students thinking patterns as well and ask crucial questions that may guide them in the correct conceptual direction.

What did you notice about student participation? · As a class, students were excited to participate in this activity. They had seen it before and understood how to participate. On this note, however, it is important to note that not all students participate in this activity. The same vocal students tend to be excited and raise their hand to offer their ideas. The other students did participate when taking a vote but this does not mean that they were paying attention to the problems or to what their classmates were saying.

What did you notice about the mathematics? · All three T/F equations were True. The teacher should mix up the problems so that students do not begin to think that all of them are true. · Students at this level (first grade) do not seem to have a problem yet with having the equal sign in different places of the equation.

What did you notice about issues of equity? · The same students participated throughout the exercise. While this group of students include roughly an equal amount of girls and boys, perhaps the manner in which this exercise was administered may leave some students behind and make them believe that they are not good at mathematics. More opportunities need to be provided for individual and small group work.

What worked well in relation to this particular practice? What adjustments might support student learning and participation? · Through the explanation process, students were able to either confirm or reject an answer based on conceptual validity. Eventually, students began to see why each particular equation was true with little guidance/questioning from the teacher. · For this practice to be more inclusive, perhaps it should be done at the beginning of the math lesson instead of at the beginning of the day. This will give a little more time to the lesson. · Perhaps giving each student a little piece of paper and having them decide on one problem to write down, give an answer, and explain it might be a good way to have everyone participate as well. This would give the teacher concrete assessments to see to what degree each student is understanding the concepts on the board.