The Mastermind Project, Day 3: Gathering and Organizing Data
Lesson 5 of 11
Objective: SWBAT differentiate between qualitative and quantitative data as they begin to gather, organize, and synthesize each kind for the Mastermind Project.
Today's class begins with a 5-minute Check-in Quiz on the topic that we began to study during the previous class: comparing measures of shape, center, and spread on two box plots. As students enter the room, I hand out index cards and tell them they have 5 minutes to tell me as much as they can. The quiz prompt is posted on slide #1 of today's Prezi.
Among other things, this is an exercise in abstract and quantitative reasoning (MP2), because students are asked to talk about quantities that lack context. This is in contrast to the highly-contextualized data with which we've been working so far. I considered not even labeling the number line, but chose to so students can get comfortable with what it looks like to put two box plots on the same number line.
When I collect the index cards, I explain the above thinking to my students, by pointing out that this data has no context. "In other words," I say, "we have no idea what these box plots actually represent. In the Mastermind Project, on the other hand, there's context, and that means you'll be interpreting the data as well."
As students work today, I can sort through these index cards during my free moments. I'm looking for a few things:
- Can each my students identify the measures of center, spread, and shape?
- If so, are they making accurate comparisons between these measures?
- To what extent do students report specific values (such as "the IQR of the blue data is 35 and IQR of the red data is 50") or give general statements (like "the median of the blue data is greater than the median of the red data")?
- Is there any evidence that students are trying to interpret these data sets and their differences, even though no context is given?
As students get to work on their Mastermind Projects, they will need to apply this skill, and this check-in allows me to see how I'll need to direct my attention.
I post slide #2 of today's Prezi, which lists all of the data sets we've made so far. "Here is all the contextualized data we've created in just a few days of class," I say.
The purpose of this slide is to help us have a short conversation about some key takeaways from our first week plus of class. At the bottom of the slide, are two questions that might get us started. If there are no immediate answers to these, I name the sets one by one, and ask for volunteers to summarize where each set came from and what we've done with it.
After this conversation, I say that our work will continue (slide #3). Today, we'll complete Trial #3 of the Mastermind Project, and tomorrow we'll continue our adventures in statistics by kicking off a new round of data set creation.
Framing the Project: Qualitative and Quantitative Data
"Before we run our third Mastermind trial," I say, "I want to introduce the first part of the Mastermind Project." I distribute copies of MM Part1 Gathering Data, and I move to slide #4 of the Prezi, which shows the front the handout on the screen.
The title of this part of the project is "Gathering and Organizing Data," and that's exactly what is to be done on this part of the project. In addition to providing a space for students to collect some data from our experience playing the game, this handout guides students through the distinction between quantitative and qualitative data.
With a couple of nifty Prezi tricks (see slides #5-7), we briefly take a big-picture view of the course syllabus, where one of the guiding questions for the class is "How can we collect and organize qualitative and quantitative data?" I tell everyone, "In order to address this question, you first have to know what the words qualitative and quantitive mean."
Introduction to Part 1 and some Work Time
All three parts of the project include a reference to the first Mathematical Habit: "I can make sense of problems and persevere in solving them" (MP1) and three questions that students will address using data. While the content of this project has to do with collecting data and using to make a point, on another level this project is introducing the idea of perseverance and the role it plays in the success of each student.
As a class, we read through this introduction at the top of the page. Moving down, students can see the first task, which is to draw box plots for each of our three Mastermind trials, then analyze them by recording measures of center, spread, and shape for each.
Without too much more guidance, I tell students to get started on recording their first two box plots and filling out the chart at the bottom of the page. Depending on the pace of class so far, I'll give students between 10 and 20 minutes to work right now, after which we'll move on to Trial #3. While they work, I have time to take a peek at their check-in quizzes, and to circulate and check for understanding.
Right around the half-way point of the class period, I call students to attention and say it's time for Mastermind Trial #3. "But before we get started," I say, "we're going to make some predictions."
I post slide #13 of today's Prezi and instruct students to take a look at Part 1 of the Mastermind Project. With two trials in the books, what does everyone think will happen with Trial #3? I wear my poker face: I don't want to influence student thinking at all, even if they start saying brilliant things. I defer to the question on the slide, "What will the box plot for Trial #3 look like?" Students can answer this question in words or by sketching their thoughts.
This prompt is a scaffold on the way to a more complete treatment of Mathematical Habit #3: "I can construct viable arguments and critique the reasoning of others" (MP3). Making a prediction now allows students to establish some of their thinking. When it comes time to write about what actually happened on all three trials, students will be able to consider what they thought would happen, and to use their prior expectations as a piece of qualitative data.
I give students about 5 mintues to record their predictions before we move on to the game. Today's Record Sheet prompt will ask them to revisit and make an initial assessment of these predictions.
As trios of students complete their Mastermind Trials, I distribute Stats Problem Set 2. When I give the handout to each group of students, I tell them that this is a chance to practice some of the skills they've been learning so far and to think about measures of a center.
As with all problem sets, this one is due a week after I hand out it out.
Today's class ends with another Record Sheet prompt. Here is today's prompt (it's also on slide #15 of today's Prezi):
Does it look like your predictions for Trial #3 will be correct? Why or why not?
It's unlikely that students will have had time to take all the data from Trial #3 and turn it into a box plot, but students will be able to reference the experience they just shared with their partners and to take a glimpse of other data as it comes in. This is question is about initial impressions, and it will add to the body of qualitative data to which students can refer as they complete their projects.