If you do not know what the 5 practices for orchestrating math discussion are then begin here, otherwise skip this paragraph: There are five main practices for orchestrating math discussion and they are 1) anticipating student responses, 2) monitoring student work, 3) selecting which student work should be discussed among the entire class, 4) ordering which student work will be discussed first second and so on, and 5) connecting how the different student work fits together with the main lesson and with each other.
After reading about Japanese math lessons in The Teaching Gap I have found that the 5 practices for orchestrating math discussion are used in most lessons. Teachers everywhere monitor students work and often begin a class discussion. But in Japan they complete the most important parts of selecting specific students to present and order these presentations and discussion in a meaningful order. The part of class discussion that is the most difficult to do is the selecting ordering and connecting practices and according to TIMSS the Japanese teachers do this very well.
Perhaps the easiest way to describe the relationship between Japanese lessons and the 5 practices is through a Venn Diagram. Here is a poor looking Venn Diagram of there relationship.
As you can see, the 5 practices are a subset of Japanese Lessons because while the lessons do a lot more than just math discussions, when they do, they incorporate all five practices on a regular basis. In fact, the students seem to be so used to discussion done this way that it seems natural for the whole class.
So the past week (Feb. 10 – 14) I was officially in charge of leading the lesson for first period. On Monday I taught how to use area models, not particularly difficult but they had struggled with them on Friday. I taught allowing them to collaborate in pairs and then having a randomly selected student discuss what they had found or even come up to the front board and draw their area model. At the end of the lesson I felt pretty confident that the students knew how area models worked and could construct them on their own.
Tuesday’s lesson, however, proved me wrong. The lesson was going to use an area model and calculate the expected value for the situation. Expected value is the long term average and I didn’t think it was a big leap for the class. Unfortunately, the students had forgotten much about the area model and did not know certain concepts that I assumed they knew such as what percents are. This meant I was scaffolding their thinking on a foundation of knowledge that did not exist. Obviously, Tuesdays lesson was not good.
Tuesday night I prepared a lesson that did not use area models or percentages but rather only taught about expected value which was the main goal of the lesson. So Wednesday I was quite excited to see how it worked. As soon as I got into school that day, I heard they were having an assembly that day during first hour. So I was out of luck, I’d have to wait until another day and by then the students would’ve forgotten even more of what I had managed to teach. Unfortunately, on Thursdays the main teacher takes over since I don’t go in, and then on Friday he planned to have a quiz. So I really never got to implement my lesson plan that would address the expected value.
Looking at the quizzes on Friday, it seems the students have not successfully learned and internalized what expected value is or how to calculate it. This week, I have failed. Next week we continue working with probability but with binomial situations. I’ll let you know how it goes. Hopefully I have good news to report.
This past week I began taking a much more involved role in teaching the 1st period at my placement. Now starting on Monday I will be taking the full leadership role! This is a big step and a scary one but I am determined to either succeed at making learning occur. Or at least learn from some mistakes and be able to make learning occur the next time. I will be leading this 1st period for the next several weeks and will try to post here throughout the whole experience.
I have two goals for the next few weeks. One is to get all the students in the class involved in the lesson. This is particularly important since I have seen many students who have given up trying to learn math or have been discouraged by peers and teachers. If I can get these students to become engaged again, then I have made a difference. My second goal is to find what classroom procedures work for me. There are so many that can be used whether it is how to formatively assess, or how to manage the classroom. But I need to find which ones work with me and which will work with my students.
If you guys have any tips for my first week, please comment to this post and help me out!
Tomorrow morning a new phase of teach assisting begins. While my first two weeks were dedicated to review and mid year exams, tomorrow we start a new unit. This means I will get to really observe some teaching, lesson planning, and classroom management in these contexts. I am very excited to see first hand how my Cooperating Teacher (CT) works through these things.
To further prepare myself for this new phase, my GVSU Math Content Professor took my through a 20 minute process to cognitively coach me. This was not to prepare me to observe but rather to prepare my mind to transition and set goals for this semester. My primary goal is to get students to enjoy math rather than feeling like it is work or “just another subject”. This goal was set because of the current lack of engagement in the students that I observe. My end goal is for students to be self motivated to solve problems and honestly want to learn the new objective. Similarly the learners would be able to self teach through class discussion and hands on work and would feel a sense of ownership for the class and learning community. The teacher would be there to clear up any misconceptions that occur or disciplinary issues, the teacher may lead the discussion but would not be the center of attention for the most part.
Obviously this end goal picture that I have drawn is going to be tough to reach, and this picture is merely the optimal goal. It will be particularly difficult to succeed with this goal given that the students have already had half a year of doing things a different way whereas starting the year out in this pattern may have given a greater chance of success. Other challenges for this goal are the class discussions, allowing groups to work collaboratively allows for conversations to not be math related although there are many strategies out there to deal with these problems such as assigning roles to each individual in the group or challenging the students with an engaging task so that they actually want to work on the problem.
To help reach my goal I plan on working with my CT and partner Teacher Assistant (TA) to create lessons that are as engaging as possible and to have my partner TA takes notes on engagement levels during my lesson. This will allow me to figure out what works best with this group of students.
My only concern is that what works with these students may not translate with any other students I work with in the future. It is easy to argue that each learning community is different, just look at the different ethnicity, backgrounds and individual stories that come with each student. Thus we can conclude that what engages one learning community might completely fail to engage another. Thus I am concerned that finding an engaging task for this group may not engage any of my other groups and thus time and work is wasted. But perhaps the process of finding what works could be the most important lesson to learn about engaging my students. I will find out soon enough and will be sure to let you all know.
One of the many reasons for assessments in the classroom is to check for student understanding. Ideally, we are taught to teach conceptually and not so heavily on procedures.
While grading a recent exam I decided to tally up which problems students got wrong to see which problems seemed to stump most of the students. At the end I noticed a particular question had fooled nearly half the class. This was the question:
If an 8.2 oz bag of candy costs $2.82, how much does one ounce, or one unit cost?
It was multiple choice with the choices being A) $0.34 B) $2.91 C) $3.09 D) $0.27
Any one with conceptual understanding of a unit cost would know that B and C can not be correct since they are greater than $2.82 which is the cost of 8.2 units. However, most of the incorrect responses were in fact B) $2.91 while the correct answer is A) $0.34 because if you see it has a ratio of ounces to cost being 8.2 : 2.82, then dividing both sides by 8.2 would give you 1 : 0.34 which shows the cost of one ounce as being $0.34.
However, if a student has only learned the procedural way to solve this problem, they might realize this is a division problem and then simply start dividing numbers. Since 8.2 is listed first in the question, and 2.82 second, they might simply enter 8.2 and divide that by 2.82. This would give us an incorrect answer of $2.91 per ounce.
Now here is where student understanding is shown to be either procedural or conceptual. A student with conceptual understanding would notice immediately that this answer is wrong. A unit cost should be less than the cost of 8.2 units, so this answer must be wrong. However, the exams I graded showed that these students didn’t notice the contradiction implying that they merely understand the procedures for such problems.
However, this failure to notice an answer that doesn’t make sense could have surfaced for many reasons. Perhaps one student guessed wrong and everyone else managed to copy their answer, or the students typed in some numbers into their calculator and happened to have 2.91 pop out as an answer. But I fear the answer is that the students don’t know the concept behind finding unit costs. Their procedure was simply to divide some numbers until you see your quotient is one of the multiple choices.
This blog will storitize my semester of Teacher Assisting at Riverside MS under cooperating teacher Mr. Kim Stevens and with fellow TA Alissa Zalewski. I will also make up words, such as storitize (verb, to make an event into a story). We work with 6th and 7th grade students teaching mathematics. Unfortunately I have started my assisting at the end of the 2nd marking period for the students so most of my first week has been spent working on review for the mid year exam and on test taking strategies.
Good news is this past week has allowed time for contemplation about assessments, especially summative. On Tuesday we will be starting a new unit. I look forward to watching a unit form beginning to end and to posting further stories from my perspective.