a. Start be describing the context of the learning. What School district and school? What subject(s)? What was the goal of this/these lesson(s)?
I currently substitute teach a Franklinville Central School District in Franklinville NY. I substitute at both the elementary school and the Junior/Senior High School. I do not have my own classroom, so I figured it would be beneficial to observe either a 5^{th} or 6^{th} grade teacher. I would consider Franklinville to be a more rural community. From the NYSED report card database, it says there are 630 in the district with 57% of students considered economically disadvantaged, and 94% of students are Caucasian (2018).
For this assignment I decided to observe a 6^{th} grade teacher in their elementary school (7^{th} grade is when student go to the Junior/Senior High School). This teacher has been teaching for 28 years, and even had my fiancée as a student when he went through the schools. The teacher had told me that this class was probably her most difficult one in all of her years teaching. The class consists of 6 girls and 9 boys, and only one of the boys are classified. During my observations over two days one boy was sent to the office on each day. One of these boys showed defiant behavior and refused to answer a teacher’s questions during class when given multiple prompts, and another was playing on the ipad when they weren’t supposed and then shoved the ipad in the teachers face when they were asked to hand it over. There were also incidents of bullying where one of the boys was calling another boy mean names. Overall, there are a few behavior problems that have to be handled at various times throughout the day.
During my observation over two days I decided to focus on the math lessons that this teacher taught. The goal for both of the lessons I observed was to find the value of a variable in one-step equations using inverse operations; using the operations of addition, subtraction, multiplication, or division. On the first day of the lesson they focused on using addition and subtraction, then on the second day they focused on division and multiplication. The Common Core Standard is: CCLS - Math: 6.EE.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
b. Next, describe (in as much detail as possible) the lesson(s) itself /themselves.
What did the teacher do? Why did he/she do it? What do you think their intentions were? How well orchestrated or cohesive was/were the lesson(s)?
The classroom is set up so that students are sitting at tables with a partner. There are also two tables put together in the front where 4 students sit together. The teacher had told me that the last principal got rid of all single desks and replaced them with tables; possibly to promote more collaboration between students. In Schmidt’s article he states, smaller groups offer many benefits to students, like friendship development, closer contact with other students and teachers, and it generates positive peer pressure to be diligent in work (2011). So, by having students sitting in partners or small groups can be more beneficial for students.
For both of the lessons she handed out a worksheet, which would be there notes (picture of sheet at the bottom of this post). She told me that she handed out these worksheets so that students can have organized notes that they can look back on, and it makes it easier to see if they have gotten everything written that they need to. Before the first lesson she played a Brain-Pop video to introduce solving equations with one step. I think she showed this video in order to get students ready for the lesson and activate prior knowledge. This video also showed the algebra in a real-life context. In the video they solved a problem of building a ladder and how far apart to place all of the rungs. Questions that are more relatable students find to be of higher quality and more interesting (Schmidt, 2011). Therefore, I think it was important to show this Brain pop video in order to show students one way Algebra can be used in real life.
Then she begins to review using inverse operations and keeping the equation balanced. She uses the metaphor of a see-saw to better illustrate how to keep an equation balanced and even shares a personal funny story of how she got hurt on a see-saw. Having a personal story was a good way to get students interested and ready to start the notes. Then she gave out the worksheet and a piece of loose-leaf paper, then had the worksheet on the Smartboard. She started the notes by calling on a student to read the directions and another to read the reminder. She then asked what an inverse operation was in order to get students to remember the process. Then the teacher completed the first problem as a model, completing the solve section and the check section. She explained her steps as she completed them and told students to copy exactly what she had on the board. This model was a good platform for student so they can go on to the next problem.
Then for the next problem she had students try it out on the loose-leaf first; this allowed them to try out the problem before putting it in their notes. Then once she checked over a few students work she stopped the class and asked what the students did. She would call on one student, then ask the other students if they agreed, then she showed the work on the board. Again, she wanted the students to copy what she had written on the board, especially for the students that didn’t do the problem correctly. Then she had students do the same thing for the third problem, having them do it on the loose-leaf first, then calling on some students.
After this she said that for the next four problems, she would work with students in the back that were struggling and needed more one-on-one attention. In Schmidt’s article he emphasizes; even just elaborating on and discussing topics can help the process of learning and it helps students to remember content for longer periods of time (2011). I think it is important for student to communicate more with each other and with the teacher when learning new concepts. I like that she took the time to work with this group more individually.
For the rest of the class they would work independently through the problems. Then she had me circulate around the room to monitor the students that were working independently and check their work when they were done. She also pointed out a couple of boys to me that she wanted me to monitor a little more and help them, since they didn’t go to the back table with her. I think she wanted to work with some of the boys in the back because she saw that they were struggling and not that engaged during the current lesson, and she needed to do something else.
I wasn’t able to see what she was doing with the table in the back because I was monitoring other students, but I think she was re-explaining the process of how to do the problems. The students that I was monitoring were working great independently and they were motivated to finish their work. I worked with a couple of students that she wanted me to keep an eye on that were struggling a bit. The students worked like this until math time was over.
During day two of this lesson we focused on one-step equations involving multiplication and division. There ended up being a lot of disciplinary problems over these past couple of days. During math time she had to have a “circle” with the class; this was a very interesting strategy to see. Everyone moved the tables out of the way and set up chairs in a circle facing each other. She had a tennis ball, and whoever had it was the only person that was talking. She started the circle by discussing why she was calling it, addressing students calling each other names, being rude to others and teachers, cursing in the class, and defiant behavior in the classroom. The ball was then passed around the circle a total of 4 times by the end of the session. She gave everyone multiple opportunities to talk that wanted to.
After the circle she had to have a meeting with the principle, so she gave me the opportunity to teach this lesson with the time I had left. She had a worksheet that was basically the same as yesterday’s lesson with 7 questions, but instead with multiplication and division problems. I think she wanted to keep the worksheet similar so that students could better see the connection between the two lessons. I didn’t have much time until the end of math, so we only got through a four of the problems together. I tried to keep the lesson similar to the other day, I had students read the directions and reminder, I modeled the first problem for students, then I had them try the other two problems on their own first, then discussed them as a class. I circulated around the room and monitored the students trying out the problems on their own. Then I called on students to tell me how they solved the problem and asked other students if they agree. I didn’t have much time to do this lesson, since it was the end of the day, so I let students continue on their own after that if they wanted to until they had to leave. Some students finished quickly and I checked their work, then for others I walked around the room and helped explain the problems in a different way.
c. Next, describe what the students were doing and how they did it. We're they engaged? All of them or just some of them? All of the time or just some of them?
What did the teacher do to manage their engagement? Were these actions effective? Why or why not?
During the first lesson when she showed the video, I saw that a decent number of students were paying attention to the video, but she did have to go around to a couple of students to remind them to continue to pay attention. They did not discuss the video after, so it is unclear what the students got out of the video. I think it might have been a good idea to ask a couple of the students to talk about some ideas after the video. Then a couple of students read the directions and the reminder. A few students did raise their hand to read each of them, so it seems like they like to participate. Then students copied down the notes as the teacher modeled the whole first problem.
Then after the first problem was done the students tried to do the next problem on their own on their loose-leaf paper. All of the girls were trying the next problem without any prompting, but some of the boys did need prompting in order to try out the second problem. Boys and girls raised their hands to say their answers once they completed the problems on their loose-leaf paper. There were a few boys that did need to be reminded to stay on task, complete the problems, and writing down the notes. A couple of boys were complaining that they didn’t understand how to do the problems. It seemed so far that her methods of engagement were more effective for the girls than for the boys. The girls were able to stay on task, but the boys needed reminders and encouragement. Hung points out in his article; if students can’t understand the purpose of learning something, then the learning is most likely not going to be meaningful to them (2008). I think that if there was more of a personal connection to the boys then they could have been more engaged in the lesson, and may have understood that material more easily.
To better manage the boys’ engagement, she decided to tell the class that for the back of the worksheet (problems 4-7) she would work with students in the back that still didn’t understand the problems. I think this was very effective, because she actually got to talk to the boys that seemed confused and really see where they were getting stuck. She got to work with this smaller group of struggling students and make a more individualized lesson. The other students that did not go with her to the back were all very independent and motivated to complete the work on their own or with their partner.
There were a couple of boys that should have probably gone to the back table but didn’t, but luckily, I was there to help them anyway. I’m not really sure if she would have done the same thing if I wasn’t there, or maybe should would have required those two boys to come to the back with her instead of giving them a choice. I’m glad she was using me in the classroom as an asset and let me help the other students so that everyone was able to get more individual attention that needed it. There was a boy that was sitting at the back table with the teacher, but she told me that he still needed to be worked with. This student understood how to get the answer to the problem, but did not know how to show the work algebraically, which is a common problem. She planned on working with this student more one-on-one, which I think is important for students that are really struggling. I ended up working with this student at the end of the day instead. I explained to him that showing your work algebraically is just another way to go about solving this problem, as opposed to how he was showing his work. The student seemed to get it and did the rest of the problems on his own, so this was a nice experience for me.
On the second day when they had the “circle” I think it was very effective. Everyone was facing each other in the circle so it was easy to see who was paying attention and who wasn’t. She did tell me this was pretty serious, and the students knew it, so they were all pretty attentive. There were some issues with giggling from a couple of the boys, but she reminded them that they weren’t talking about anything funny, and this was a serious situation. The ball was passed around the circle four times, so each student had four opportunities to talk if they wanted to. At first some students didn’t want to talk, but I think once more and more students did, everyone felt a little more comfortable to engage.
Then after the circle I was teaching as the teacher had the meeting with the principal. I was grateful that she was using me as she went and dealt with disciplinary actions. I tried to keep it similar to the lesson that she had taught the day before. I would say that most of the class was engaged, there was just a few of the boys that I had to remind to stay on task, try out the problems, and copy the notes. Solving equations is very new to them, and some of these boys are easily discouraged when faced with content they don’t understand. I tried to keep circulating so that I could help students that needed it. I would say that the circulating around the room helped with the engagement, but the students weren’t really motivated themselves to engage. In the future I may have tried having students complete the problems in groups and having the groups present to the class to make it a bit more interesting. Dron & Anderson emphasize; learning in itself seems to be enhanced when students are able to interact with one another; discus with each other, argue, interpret, and contextualize with each other (2014). I think that in this lesson the student could have benefited more from discussing the problem more with one another and trying to problem solve on their own before modeling of the problems was presented to them.
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Gerald ArditoMiranda,
You did an outstanding job with this Excursion. Your descriptions are detailed and insightful and your commentary is rich and smart.
I wanted to respond to some of the things that you said:
They did not discuss the video after, so it is unclear what the students got out of the video. I think it might have been a good idea to ask a couple of the students to talk about some ideas after the video.
In general, it seemed like the goal of this lesson, as it is so often with math, was procedural. How do I....? This focus was then supported by the video and then the individual practice. Now, you are talking about a very experienced teacher, and I respect her work. But I wonder if the behavior issues she described were related to math at all. It is commonly observed that when students are frustrated or struggling, there are often behavioral issues. It makes sense -- if I don't feel confident or competent, my anxiety level goes up and then I do things to alleviate my anxiety. These may not be things that further my understanding and/or ability in math. So, it's possible that the acting up then becomes a coping mechanism.
So, it looks like the two are separate when they are not.
i am wondering if it's possible that these students were not actually ready to do the work assigned. And this goes to the comment of yours that I quoted above. They could have been relieved to have watched a video (since they had nothing really to do except watch), but we don't really know if they learned anything.
I am not saying that I am right about this interpretation. I am eager to know what you think. Is this possible? If so, what actions might you follow to correct the situation?
And one last question - what would you do to bring these students into the topic that was NOT procedural in nature. How could you make the fundamental concepts of equality real to them?
I look forward to reading your responses.
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Miranda BarbaraHello Dr. Ardito!
I wasn’t really that clear in my post about the behavior. The behavior was occurring in her math class, as well as other classes that I followed them to, specifically in their science class with another teacher. The defiant behavior had occurred in the science class when the student was given multiple prompts to respond to a couple of questions and didn’t comply. In the math class I also observed that some of the students were not that engaged in the lesson; like not writing the notes or doing the problems. I do agree that I think these behaviors are most likely coping mechanisms for their lack of understanding with the content, in both math and science. I think that it could also be that the students are not that interested in the material they are learning. The math that they were learning was very procedural, which can be very boring for students. Even the behavior regarding the bullying and name calling could have been a way to steer the class off course so they didn’t have to complete their work. The main teacher that I observed, that taught the math class, told me that a lot of boys don’t have great home lives, and may be currently experiences things at home, so this could be a big factor as well.
Going forward, to deal with this behavior, I would try to give students pre-assessments for homework a couple of nights before new lessons, and group them up for the new lessons. I think it may be beneficial to group students by ability level and how they did on the pre-assessment of necessary skills. This may help to see as the teacher who the struggling students may be for this lesson and where the attention needs to be focused. I think that also trying to incorporate multi-sensory learning into the lessons could be beneficial to promote engagement. For example, showing the videos, incorporating manipulatives, or even listening to a podcast.
I think to make this lesson more real to the students I would have them instead work with manipulatives. One thing I could do is put students into group and set up stations with mini seesaws. At each station I could have a problem written and have weights in grams balanced on the seesaw to represent the written problem. For example, if the problem written was x+2=6, I would have six individual grams on the right side of the seesaw, then on the left side I would have two individual grams, and a block that has “x” written on it. In this case I would have to make sure that block “x” weighs 4 grams. The students would have to figure out how much block “x” weighs by adding or subtracting blocks, then show their work for the problem or write what they had to do to keep the seesaw balanced.
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Gerald ArditoMiranda,
I appreciate your thoughtful responses to the questions I raised. I also want to be clear that sometimes, as teachers, you just get a tough group. It's hard to say just what the X factor is, but I have seen it happen.
That being said, I think you have come up with some really interesting, and likely very productive strategies for helping motivate and empower students.