Hi, I'm Hollylynne Lee and I'm here again with our expert panel, Chris, Webster, and Susan.  And we're going to be focusing on the idea of tasks.  So, when you design tasks for students, what are some of the key things that you think about in how you design that task and how you kind of envision it playing out in the classroom for different levels of students?

You want me to go first, okay, I'll go first.  Well, I think one of the first things you do is you need to state your goals and your objectives for the task.  I think so often we start writing a task, but if we're not really clear in our mind as to what we want the learning outcomes to be for the task, that runs into problems.  I think it's also important that we scaffold within the tasks.  So, in other words, make sure that you're getting entry points for all your students, whereas some students may go more quickly than others through a task, but you don't wanna lose some of your students that may need some additional entry points.  One of the things that I have really started  focusing a lot on with my tasks in recent years is an assessment piece.  And so, one of the things that I also try to incorporate into the task is certain assessment questions and put those throughout the task to help the students kind of check point.

Self-check.

Self-check where they are and as I work with pre-service teachers at the University of Georgia, as well as, in professional development, I really try to emphasize to the students and the teachers what we call the DOK levels, the (Depth of Knowledge Levels).  I know at least in Georgia this is becoming a very big component of the professional development training with the teachers there at K-12 and helping students how they can write a DOK I Level question, 2, 3, even 4, and what's the difference between the different levels in terms of how much you are hoping the student will understand.  So, those are some of the first things that I think about when I'm writing a task.

Okay, good.

Also, how long the task will take.

Ahh, yeah,.

And oftentimes, I'm not very good at judging that.

I was going to say I tend to be a very poor judge of that.

Task or right tell.

Right tell.

Some students take much longer than others.

I'm a bit better than I used to be, but I still misjudge a few times.

Yeah, so we maybe need a...we need to plan for the variability too.

We need a plan, I'm a bit optimistic sometimes.

Right, right.

But time is very important because as teachers that are gonna use your task, that's gonna be one of the first things they're gonna ask you is how much class time am I going to have to devote to this task?  And so, trying to pilot the test is very important to get a good sense of that.

Yeah, nice, nice.  So, thinking about designing of tasks.  Do you guys have anything that you'd like to add to that?

I would say I just have very specific learning outcomes that I intend for the students to get out of the tasks, so, one of my favorites is, "Why should I always do a bar plot, almost always do a bar plot rather than a pie chart?"  So it's a very simple task and look at some pie charts I have on the screen and try to answer a few simple questions, do the same thing with bar plots, and they see the error rates like over 50% using a pie chart, whereas, it's zero, no errors when you look at the bar plot.  So, very concise activity, you know, if I can get students to never produce a pie chart I've probably done the world a favor.  And so, I'm very focused on that particular issue, so that's something I think most of my activities or tasks have as a key component.  Very, very focused.

So I would like that activity, I know I tell my students all the time or teachers, statisticians don't like pie charts and yet, every school curriculum includes pie charts as...

Yeah, we need to be able to read them in the newspaper at least.

And they have them on their state tests so then it's like, well then they have to learn how to use a pie chart so, we need to match, but.

But we do need to move beyond them.

Right.  So in doing the connected math curriculum, I mean, what I kept hunting for interesting data sets, real data sets, and then once I found something that I was working with, I would play around with it to see what kinds of concepts come out of it easily, and sometimes it was productive and I could hang on to it, and sometimes it wasn't so productive and I had to let it go in terms of that.  So one of the contexts that I did a lot of data collection on was I made this wonderful database of steel and wood roller coasters and I...it took me about a year, a year and a half to research all of the...

Did you have to ride them all, I'm a huge roller coaster fan?

No, you go to the roller coaster database and there was another database that used to be online that was really good and it went offline right in the middle, but I used to go in and get all my data from these databases and there's a lot of roller coasters in which they don't have enough data so you have to find the data that's pretty complete in terms of that.  And it is really interesting data and so I got this whole set of data on steel and wood roller coasters and I updated it a couple of years ago and probably will update it again because of newer coasters.  But I remember then showing it to Cliff Konold, and he said, "Yeah, so what are you going to do with it?" And so, it ended up, it is a sample of what I've done, more of a convenient sample than anything we use that, but there are some interesting things to do to compare steel and wood roller coasters that you can and actually, if you look at speeds of steel and wood roller coasters, the curves are pretty normal, the means and medians for both fall in almost the same place, but steel, because steel can control the speed of its cars as more slower roller coasters and definitely has more faster roller coasters than wood coasters.  So you can ask the question, I like to ask this question because it really confuses kids, which is faster, wood or steel coasters?  And they have to come back and qualify it in terms of, you know, it doesn't have an either/or answer, it's related to how you look at the data and how it's spread out, and then you really, and kids do know coasters and so they can tell you.  You have to be able to go in and do what I just did, well, what did steel do to make a difference so that you've got these incredibly fast, you've got major speeds that are damaging to people now when they ride coasters that didn't use to the be case?"  And so, we use it in that context actually is about the only place that I've used the data set, but it was fun to try.

It was worth it to collect all that data.

Oh and I started, well, actually there's a couple other problems about relationships to speed to the height of the coaster and stuff, and the scatter plots you get are very interesting because there's a speed when things all of a sudden shift in terms of the height and speed and things like that so there's some really interesting.  But I collect the data, look at it and then figure out what of the goals we have to address this might help me address.  I don't...I mean I know what I have to do, but I first go hunting for data, I'm a data snoop.

Okay, so if we're going to use a statistical investigation approach to our stats classes, and you're going to do a task that has all the phases of the statistical investigation, what does it look like, what does it feel like in your class?

Well, I'll talk about one thing, I'll put a plug in for a resource that I think that would be great for teachers to use and this would be more appropriate most likely for high school.

They actually do have the elementary and middle ones.

They do have the elementary and middle ones, but the task that I am going to reference is actually in the high school and that is the NCTM Navigation books.  And the Data Analysis and Probability NCTM Navigation books are excellent.

Yes, they are.

And the one that I'm going to mention is in the 9-12 book, it's the chapter on the discrimination activity.  And the goal of this chapter was to basically take the student through the four steps of the investigative process, it's a very nicely laid out task, it has transparency sheets with all your questions so you can very easily use it in your classrooms.  This is actually a task that in my first week of my intro courses I used this task.

At the collegiate level.

At the collegiate level.  And as I said, you could easily use it at the high school level, and what's wonderful about this is because of technology, because of simulation, you're able to take the students through all four steps.  And it has to do with a research project that was actually conducted here in North Carolina with banking managers and the idea that women are discriminated against in terms of promotion practices.  And it was an actual experiment that was conducted, so you have this research question that you're trying to answer.  The kids, I call them my kids, my students, I'm showing my age...they very quickly get into the notion, "Oh, discrimination" you know, this sounds kind of interesting.  And so we talk about how they actually conducted the study, the experimental design that was used and then we actually think about sort of the idea of a null and alternative hypothesis, you know, what is it that we're assuming before we begin the study, what is really the researchers question here?  And I actually had the students go through and think about, what would your results look like, in your mind, what would they look like if there is no discrimination?  What would the results of the study look like in your mind if there is clear cut evidence that there is discrimination against women?  And then I have them think about, what would it look like if it's kind of in a gray area, that is, well, I feel like there could be discrimination, but I'm not for sure.

I can't say for sure.

I can't say for sure, and then that leads into the idea that we need to do a statistical investigation.   And I send them home with decks of cards and they carry out the simulation.  Under the model of randomness, the idea of what would happen with random variation, which is what statistics is all about, trying to figure out if it's random variation or if there's a real fact.  They come back with their results, we create simulated sampling distributions, we actually go through and create simulating P values, this is...this is intro college stuff here.  But by the end of the task, they're on board, and they've seen the big picture of statistics, and where we're headed for the rest of the semester.  And I like to tell them that you've now seen the big picture, what we're going to try to do is we're going to try to fill in your tool box for the rest of the semester, and I think, it's just been a great task.  It's one I'm very proud of actually.

Cool.

But it's in the NCTM Navigation 9-12 Data Analysis book.

Yeah, good.  You were mentioning using this particular task in your collegiate level settings, in your college level intro stat classes, kind of what is it, what does a statistical investigation look like and feel like in that class?

Well, I'll start, I sort of try to bring this in by coordinating task activities across several class periods.

And it seemed like that was similar there, it was over several periods.

Yeah, one of the things that I do just as part of the examination process is have two versions of an exam.  So I have a yellow version and printed on yellow paper and a version printed on white paper.  And so, my students when they take Exam 1 on graphical and numerical summaries for data, they're going to take that exam on yellow and white paper, now, little do they know that that's actually part of a bigger activity.  So immediately after that exam we're going to come back and look at the data, we're going to summarize it, we're going to look at the scores on the yellow compared to the scores on the white.  And then, later on in the semester we come back to another activity where we're going to actually see if there's any difference in the typical yellow score and the typical score on the white exams.  So we're going to do that with randomization and simulation later on in the semester.  And in between there I'll talk about what my goal was with having the different colors and my research hypothesis and things of that nature.  So, you know, really beginning with that first exam and then a couple, two or three more activities over the course of the semester, they're going to see how that all comes together, that's my goal with that particular activity.

Yeah, and I've sat in on your Introductory Statistics Courses and seen how you kind of transition from, you know, when you've got 80, 90, 100 students in your class and you're transitioning from these whole group conversations and you give them, they're going to do a hands-on simulation, and you have your packs ready to go with these cards, and you're handing them out and they're working in groups, you know, and they're kind of clustered together working in groups generating their data.  And as you mentioned in a prior conversation, that they then kind of enter their data live with the technology and you have access to that, and I just think that this is so cool that, you know, yes, even in a large lecture session we can do these types of investigations and make it manageable.

Yeah, and there's a hands-on component like you said and some technology that comes to the aid as well, so, yeah, I think those are all sort of very key components.

Right.

So, Susan, do you want?

Well, I think the components that they're talking about would be in any level task.  So a middle grade task that you do your work on or an elementary task and it seems to me that they, I call it, we, in our curriculum call it, launch, explore, summarize in the sense of you setting up the task without a huge amount of direction, but they get engaged in it, but the explore phase which will take and you have to give time for it, and so, if you're even doing any explore phase with elementary or middle school kids, you talking about taking a reasonable amount of time, and you have to be going around, this is where differentiation comes in , you may have some extra tools you give some kids, you're going around thinking having thought carefully about the questions you're going to ask as they're exploring because when you get to the summarized phase you pull back together and you try to pull together the responses to what your goals were and what your intentions were so that happens in our classes all the time.

Yeah, yeah, yeah, and so, I mean, without I hear them...the students are working in groups and the teacher is really walking around and kind of thinking about what each of these groups are doing and then that teacher, you know, can give them some prompts and pushes in different directions, but then also kind of, you know, in the end when they have to make their judgments and their interpretations that that teacher has a glimpse of the kinds of things that the different groups have been doing so they can orchestrate a conversation.

And actually, one of the ideas is to actually sequence the presentations and you build from the simpler to the more complex so everybody has access to everybody else's thinking at the same time.

Right, right, yeah, good.  So when we're doing statistics investigations and we're also charged with, you know, students have to deeply understand what the concept of a mean is or deeply understand the difference between a pie chart and a bar chart and then kind of affordances or constraints with different representations.  We're charged as teachers to do both of that, we want them to engage in statistics as an investigative process, but we also need to make sure that they understand some concepts. How do we balance that?  What's the role of a statistical investigation in helping students conceptually, build conceptual understanding, and what's the role of conceptual understanding in helping do statistics investigations?  Chris, I'm going to come back to you.

I think you can actually design tasks that are aimed at understanding the concepts.  So it's not that you're actually necessarily trying to go through the four stages of the statistical investigative process, but you have a specific task that's aimed at understanding a particular concept.  And to me, that is well worth your class time because once the students have the conceptual understanding the content and how to use the different statistical ideas as tools becomes much more natural for them.

Right, exactly.

Constantly revising.

Constantly revising.  

I've never done the same task twice.

I haven't either.

Yeah, because they could be tweaked.

They always get a tweak.

Well, and when you choose context you have to think about accessibility to students too.  So one of the things that we do up front to work on measures of center and general distribution stuff is look at name lengths of students from different countries, they're talking with pen pals and name lengths from China and U.S. and Japan and things like that.  And every time I get working on trying to figure a context I always go back to that and I know that people sometimes roll their eyes at me about that context, but it is very useful, the kids understand it, they can put it in their own data and it's very useful to go after these primary concepts that we're after, will not take a lot of time and they will not get confused by the context, they understand it.

Yeah, nice, nice.

Can I say one more thing about task, in terms of we're constantly revising, you know, one of the things, maybe I'll put a plug in for STEW, which is the Statistics Education Website and Hollylynne is the editor now, but if you find that you have a task that is really rich and that is really working well, write that task, write it up.

Write it up and share it.

Write it up and share it with other teachers because I think one of the hardest things for practicing teachers, they barely have enough time as it is to prepare for their classes and with everything that they're responsible for, starting from scratch, try to help them out to where they don't have to start from scratch, share what you know works.

Right, right, yeah.

Yeah, and I think that's one of the biggest lessons that I've learned about tasks.

Yeah, yeah, and through this MOOC we're actually going to actually be sharing a lot of things with you and hopefully you'll walk away with a nice little stuck in your back pocket.

Right, that's right.

Good, thank you.