When schools from Boston to Texas are missing school,teachers may start thinking about how to tune up the tasks they give their students. Some recent blog posts, and one from the past, can show different ways to think about the tasks that we assign our students.
What are you students bringing to your task?
In Andrew Gael‘s blog there was an interesting post about describing a number of ways to present students with a task that asks them about area while keeping in mind each of his students’ “mathematical strengths, goals and cognitive pathways your students use to access the content.” In “There’s More Than One Way to Skin a Task” he effectively makes a framework for thinking about task in terms of the kinds of thinking students would use to finish the task.
What do you want your students to do?
Kate Nowak described a framework which explores another way to improve a task in her January post “On Making Them Figure Something Out.” When teaching a concept to a student, Kate implies that in the worst scenario you could “Tell Them Something.” Better than that, you could “Make Them Practice Something”, and perhaps even “Make Them Notice Something” or “Make Them Do Something”. “But lots of times, the learning that comes out of MTDS and MTNS doesn’t really stick that great.” Kate writes, “They can maybe do an exit ticket, but ask them a question that relies on The Thing in a week, and you just get a bunch of blank stares.” In this post she explains how she turned a MTDS task about the discriminant into the penultimate type MTFSO, “Make them figure something out”.
How Mathematically Complex Is The Task?
If you want one more way to look at tasks, and don’t mind looking at a post from 2009, Mr. Vasicek wrote about the “Task Analysis Guide” which was originally published in a mathematics journal and looks at problems in terms of cognitive complexity. The different scales in this guide include “Memorization”, “Procedures without Connections”, “Procedures with Connections”, and “Doing Mathematics”.
If you want to give some of your tasks an upgrade, all of these teachers give you ways to think about tasks that can help illustrate tangible next steps to improve student learning.
“Look around at your groups guys, all of these people are going to work with you to get your work done, so make sure you get them to come!”
That was the last thing significant thing I said to my “Understanding Data” class on Wednesday before my typical end-of-class chatter (i.e.”put each folder in the box, and your assignment in your bags bag and trash in the trash can etc.). As I walked back to the room I thought to myself “Great Scott! I may just have hit on a secret attendance improving strategy!” As a transfer school full of kids who most often have a checkered history with school attendance, we are constantly looking for ways to keep kids from back sliding and having enough attendance in classes to avoid it feeling like a drop-in session. “If kids are in groups,” I thought to myself, “and accountable to their groups, then they may be motivated to come to school!”
When today’s class started and I’m looking at a class with roughly half of the students that I had the last class. Every group was missing at least one member, a couple groups only had one member! Last class there 28 kids There were only 2 groups of four, the one that begged me to let them have a fifth member, and the group students who weren’t here in the last class and had no idea what was going on. It was a little sad, but after trying to arrange the groups into mostly pairs and threes, and postponing some of the task for Monday, it was still pretty nice to have the kids work in groups. Once groups finished work they worked on some reflection writing.
Students were brainstorming different methods of determining whether something is an outlier using sets of data that I prepared. The group part of the task would have been to compile all of everyone’s data so that they could look at which of their so-called outliers really lie outside of everyone’s data, and which ones actually look normal when placed around the larger set of data. Instead, I asked the smaller groups to work on clearly defining a mathematical test that they could all agree on which would show why the outliers are outliers. Some groups said “If it’s more than 1000 higher than any other number” or “twice as much as the other numbers.” I think this could lead to an interesting conversation about why we need the Mean and the Standard Deviation, as well as the Median and the IQR. We will soon talk sample size and the law of large numbers, and having these posters around the room will be good references for putting large groups of data and reducing error.
So, as sad as it was to only see a fraction of the students I was expecting in my class, it should not affect the momentum of class too much. The kids who missed will get an email asking them to essentially do the same task on their own, and we can do a nice gallery walk at the start of Monday’s class about everyone’s ideas. When we have them work on further group work, it will be good to have this experience to look back on. Maybe next time I’ll require them to exchange emails or whatever else in order to stay in touch with their group. We can still make this experiment work!
So in my class I thought up a good uses of technology in a “flashes of insight” late last night. One idea was to come up with a way to have the students play around with the ideas of what mixtures of juice would be orangey-er than others.
I had my Transition Math students work on this yesterday, but I didn’t have a lot of success. This class is for students who typically “get-by” in math, and will probably have trouble understanding the basics of algebra, like proportional reasoning. Virtually all of them have said some form of “I never understood fractions!”
The trouble yesterday was partially because so many kids only saw me as an answer, and didn’t trust each other enough to justify one juice mixture being more “orangey” than the other. Without a way to really check and see if their strateg was right, they didn’t really see a way to reason through to deciding which cards should be in what order. So I tried a couple things. One thing was showing a video of orange juice concentrate just to make sure they weren’t confused by the concept of juice in a can (a student yesterday was horrified by it). I also had them do a gallery walk of each others work, and I tried to talk through a comparison of a few juice listings on the board.
After class today I created the little tool so that kids could experiment with the different colors and test to see which is more “orangey”. I think I will have students get on their laptops and compare two different versions of the tool and compare their answers in that way. I still need to do some work on it but It seems pretty useful.
Now I need to work on what happens when students use this to compare different kinds of juice mixtures. I will come back here and post some results and student thinking when I can. Let me know if you can think of any intersting questions that could be explored by using this.
Today in class I was teaching the “Mixing juices” task and found out that kids don’t know about concentrate cans of juice. This is the part of the task where kids are given a number of cards with various juice mixture recipes.
Kids kept saying they had difficulties, and it sounded weird that after five or ten minutes of talking about, the language kids used didn’t really relate to the problem. Instead of saying cans of juice, or cans of soda one kid would say “the grey cans” or the “The empty ones.”
After class a student came up to my desk and I was explaining again the task and she legit didn’t undrerstand. “You know, when you make juice from a can?” I said. “Like this.”
Then she recoiled back with a look in her eyes that was a mix between disbelief and disgust as she said “I don’t even know what that is!”
Unfortunately, I think students had a similar response to the talk about ratios. Representations of a rational relationship between juice and water was treated pretty differently by the students in both of my classes, and not just because of the orange juice in a can business. I think the concept of a rational relationship, the need for it and the usefulness of it, is one that doesn’t make sense. Scores of kids immediately turned the ratios into fractions, decimals, and percents when thinking about the order the cards would go in, but not seeing how that number makes sense. One girl in particular took a card 2 juices and 3 cups of water on it and came up with 66%, but on another card 1 juice and 2 cups of water she wrote 33%. I figured this out at the board, 10 minutes after this task was supposed to end and had to tell kids we would come back to this. In my head I realized that this could have been a rich conversation at the board, or in groups, but I didn’t have the time, I wasn’t prepared for the variety of responses that I would see, and I was worried about what this student would think if we dissected her thinking in front of the class on day 4. It was pretty rough.
So my understanding data class basically needs to take a quiz soon and but I wanted to build in a little review and preview some of the concepts from the next one. I also for some reasons wanted to have a joke in the class, so I created this worksheet about a barbecue. Analise knows that 200 people are coming, so she asks 20 of the people how many hotdogs they will eat, and then afterwards the uses either the mean, median, or mode to come up with an estimate of the amount of hotdogs they will need and how much they will cost (if they are $4 for an 8-pack).
The catch? Oh right I forgot. One of those twenty people is 2011 hotdog eating champion Kobayashi. So while the rest of the twenty people in the group tell Analise to order 1, 2, or at most 5 hotdogs, Kobayashi plans on turning the barbecue into some kind of super-competitive “sausage party.” The kids notice the problem with Kobayashi in the sample and suggested that we remove him from the data set. In order to compare they find the mean, median and mode for both scenarios and see what is going on.
Towards the end of the lesson when students were talking about the eliminating Kobayashi from the set one student angrily asked/questioned the title of this clog. I didn’t engage her blurt, but I kind of smiled, for a second. It was like when someone validates how hard you worked on your outfit with a compliment. At the same time, I would feel weird if students see some of these assignments as labryinths that I create to direct them to one place. How do I let them know they are discovering mathematics authentically and not doing really convoluted “answer-getting”? I’ll let you know if I figure it out.