I think the main mathematical goal of the lesson in the
video is trying to help students recognize and understand the difference
between area and perimeter. Based on the problem given, the students are forced
to choose the area based on two choices; one of the choices is correct while
the other one is a misconception and actually the perimeter of the square. By
giving students these two choices, this makes me believe that the teacher wants
students to identify that the incorrect answer is actually the perimeter while the
correct answer is the area. By having students use the picture to help them
determine whether or not they agree with Robbie, she is also pushing the
students to recognize what a square unit is and how it is used to find area.
Helping students develop this understanding of a square unit will help them
make a connection to what area means, furthering their understanding of the difference
between area and perimeter.
The debriefing is similar to our group lesson study because
the observers will also be looking out for ways in which students solve the task.
The goal of the observers was to write down how students interacted with the task
and student work. Our observers for lesson study are more focused on a specific
research question, which helps the observers focus their attention on specific conversations
that students will have while completing the task. Our research question involves
identifying what types of teaching from the teacher or methods the students use
that help them understand that rectangles can have the same set perimeter yet
their areas do not need to be the same. Observers will be listening for how the
students come to this understanding, rather than just how they complete the
task.
Since I will be teaching the lesson study this week, I paid
extra attention to some of the suggestions the Whitenack article suggested.
According to the author, instructional programs should enable students to develop
and evaluate math arguments and proofs of their work. By providing
opportunities for students to develop arguments that support or counter other
students’ thinking or my thinking, they will be able to better understand the
purpose of the lesson and work towards reaching the learning goal. I hope to
gives students instructional opportunity to discuss their ideas so that others
can benefit and develop their own math ideas or expand on peers’ ideas. Questioning
is a great way to do this because it will help students decide whether they
agree or disagree and evaluate on students’ responses to help them understand
mathematical concepts.
I think the most challenging part of the lesson study will
be to generate questions that the students may ask. This is always a fear before
any lesson plan that I’ve taught because it gives you the sense that you may
not be prepared to adequately respond to students. By thinking of various
answers, questions, or misconceptions that students have, it enables teacher to
be more prepared to answer or challenge questions that you may not be prepared
for. I am also afraid that I may not have a way to adequately explain my
understandings to help the students understand through questions. I know that
it is beneficial to challenge students’ thinking in order to develop their understanding,
but I am afraid that either me or the student will become so frustrated that I may
just begin providing reasoning for students instead of allowing them to complete
their discovery.
For me, the most beneficial aspect of this lesson study was
to discuss and collaborate with other teacher-education majors. This is
important to me because I recognized how well we worked on deriving a lesson
plan solely based on conversation. Having a casual discussion about mathematics
enabled us to create the task for the lesson plan, obtain ideas for great
classroom management ideas, and proved that group work can be extremely helpful
to completing any type of task. Our group work shows that all of our members
are able to work together to help students develop their mathematical learning.
This is extremely beneficial to put on a resume because I feel as though
schools look for teachers who can interact with one another to share ideas of
beneficial lesson ideas. Being able to get along with co-workers is another
aspect that many employers may find valuable. Overall, I have seen the benefit
in having a collaborative opportunity to create a lesson plan; our ideas were
all shared with one another to try and develop the most effective and motivational
way to help students understand that perimeter and area do not directly
correlate.
Thanks for posting Tracy! Now either I'm really lost or just can't navigate through ANGEL but I can't find the videos and don't see the articles, besides Whitenack & Yackel, to read so I'm just going to read that article and call it a day?
ReplyDeleteI think you did a fabulous job of combining the Whitenack article and your own experience with the lesson study group. After reading the article and going back to your post I really felt you captured the whole point of the article. Whitenack & Yackel's main focus seemed to be on the importance of allowing for instructional programs is that it is the most beneficial strategy for students from a teacher's lessons. Instructional programs, like Traci said, allow for students to "not only understanding the ideas better but also can help students develop NEW understandings." As I was reading this article I was reflecting on my observations in my MT's classroom. It saddens me because my MT really doesn't allow for student interaction when learning math and there is no room for students understand more thorough or discover new understandings. My MT strictly uses worksheets and discussions that are teacher directed when she is teaching math, or any subject for that matter. She has students filling out worksheets individually all the time and if a student is done ahead of time she hands them a worksheet that is more challenging than the one before.
My MT has several opportunities to incorporate instructional programs but she decides not to. Students could be asked to participate in an activity and then share with the class their findings and have others discuss and (dis)agree with their math research. In my groups lesson study we have an opportunity to allow for students to come together and reflect and interact with other students to develop an instructional program. Students divide into small groups and record their findings of different objects then they will come together to compare and contrast what each group discovered. My lesson study group is hoping this will spark conversation about the differences in measurements and this will allow for an instructional program moment to further understand these ideas based off other students. Our lesson study goal, from the teaching and observing stand point, is to help students utilize each others data to help them come to conclusions. As for observers, we want the observers to be looking to see if students are utilizing each others ideas and data collections to create a better understanding for themselves. Key things to look for are changes in conclusions or comments that are reflective of others thoughts. Like Tracy said, it is very daunting to try to make sure we, as teachers, are creating instructional program opportunities! I know I will need my groups help in creating questions and comments to allow for students to think more reflectively and utilize other students thoughts, seeing as my classroom is the one we picked to do the lesson in and my students aren't used to this program. Using the resource of our classmates, we can establish a broader sample of questions to ask students and come up with diverse ways to get students involved in other students understanding and thinking.
This comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
DeleteThe concepts of area and perimeter were always a challenge for me. I can remember memorizing equations and not understanding the ideas behind them, or how they get to the answer. The teacher did a good job of pushing students to discover the idea of square units. By giving the students choices, they are encouraged to try out each of the solutions, to find out which one best represents what the problem is looking for. The problem with this is that she is limiting their responses. If they were able to provide their own answers, she could see how they are thinking. I do, however, like that she is allowing the students to make connections on their own.
ReplyDeleteI like the way that they did their debriefing for the lesson. I agree with Tracy about how it relates to our lesson study project. I think that it is very similar, but that ours is focused more on finding out about our target research question. This is not to say that we will not be observing other aspects of the students’ performance and responses. I also think that our lesson study is more focused on the thinking and processing that occurs with students. Even though our debriefing may not go exactly like this one, I think that it was helpful to actually see an example of the debriefing process.
I thought the Whitenack article was very helpful. Although there were a few things I wish I had more clarification of, I thought that it was helpful to learn about ways we can get students to come up with valuable arguments. It just reinforced how important it is to ask the students advancing questions. In addition, it is important that we are asking the students questions that get them to think about their own thought process. It is one thing to do a task, but it is a completely different thing to think about HOW you completed the task.
I agree with Valand, i have always struggled with the difference between area and perimeter. I think that is because when i remember learning about both concepts they were taught separately instead together, which i think would have been easy for me to understand seeing that i always think one is the other. After reading the Whitenack article, i think that having instructional programs about mathematical poofs would have helped me understand the why behind each and that would have helped me with differentiation.I liked the way they went about the discussion in the article because it gain students a change to see what other think and different ways to solve one problem. I really liked this article because it allowed me to gain knowledge about different ways to engage students in a mathematical argument.
ReplyDeleteI also enjoyed the debriefing that was done in the video. It did closely relate to our lesson study project besides the fact that we focus on a specific research question. The observers were to focus on students work while in the lesson study our group focus on our research topic which is why students use certain objects to measure with. It focuses on a specific idea instead of how the task is completed like in this lesson.