What is a Statistical Question?

As I approached the start of a unit on data, I spent a lot of time thinking about how I was going to meet the needs of two very different students.   I didn’t want this unit to just meet the needs of some “average” or “typical” student.   I was pretty sure I could do that.   I was less confident that teaching to that “typical” kid was going to be enough for these two kids.   Naturally, the two kids were diametrically opposite.   Both of the kids are pretty extreme on the conceptual/sequential cognitive style and have been struggling.   Unfortunately, they are extreme in diametrically opposite directions.   One of them is very sequential in his thinking and tends to compartmentalize information and ideas.   The other one is very conceptual in his thinking and has difficulty managing details and sequential processes.

If I am going to reach both of these kids (in addition to everyone else), I am going to have to build a really good “big picture” that shows the connections between the different ideas very clearly and then fill in the details.   My conceptual thinker needs the big picture to give him a framework on which he can hook the ideas.   He is also going to need some instructional supports to hold on to those details.   I’m going to have to find some ways to help him remember the sequential steps in the processes we address.   My sequential thinker has a hard time building that big picture from the details.   He stays within the details so I have to build the big picture and bring out the connections or he is not going to be able to put the whole picture together.

I decided that I wanted to “start at the very beginning” because “that is a very good place to start”.   (My students had to watch The Sound of Music in their band/orchestra class this week when their teacher was absent.   Being 6th graders, naturally, some of them felt the need to enter class singing.)

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I also created some resources to help give the big picture and explicitly bring out those connections.   Those are things I will write about in coming days.

I started by giving the students a quick overview of the unit and then moved into the first lesson.

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I decided the very beginning was the question of what exactly is a statistical question.     I wanted my approach to the topic to have a lot of support for a particular student with visual processing challenges.   That meant I needed to make sure there was a lot of verbal discussion and clarity brought forth to enable auditory processing.   It also meant that anything I had on the promethean board was also in some form of a handout (it can be hard for kids with visual processing challenges to read information off of a board).

I started the lesson by presenting my students with a set of about ten questions.   I told students that I wanted them to decide which of those questions were statistical.   They needed to use a Think-Pair-Share technique.   I wanted them to come to their own conclusions first (Think).   I wanted them to discuss their thinking out loud with a partner (Share).   This would help my student who needed to process auditorily. It would also de-privatize mathematical thinking.   I would have a better sense of what my students were thinking as I listened to their discussion.   Struggling students would also have access to the thinking of students who were more readily grasping the idea.   Finally, the whole group discussion would provide the opportunity to clarify the concept.   I wanted everyone engaged so I used a Thumbs Up/Thumbs Down formative assessment to structure the discussion.   For each question, students had to “vote” whether the given question was statistical (thumbs up) or not (thumbs down).

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Then, we talked about why the question was or was not statistical.   I was intentional in who I selected to speak.   If there was disagreement, I asked a student from each perspective to justify his or her thinking.   I wanted student voice to drive the conversation and was careful not to tell students what makes a question statistical.   I let students bring out the idea that a statistical question has to be something that would create a table or a graph when answered.

I wanted students to refine their understanding, so I had them do a Write-Pair-Share in which they had to explain what makes a question statistical.   This would require each student to refine his or her thinking, give them the chance to express that thinking and hear the thinking of another student, and then for me to ensure that everyone got the full picture in the whole class discussion.   It also would give my student with visual processing challenges the chance to hear the idea explained several times, several ways, in several different voices.

At this point, I was fairly confident that everyone in the room had a working understanding of the concept.   I wanted to step up the cognitive demand a little bit, so I gave them a second set of questions.   Once again, they had to identify whether each question was statistical.   However, this time, they also had to explain why a given question was not statistical and then re-write the question so that it was statistical.   For this activity, I wanted to ensure that each student did their own thinking but also had the chance to have real discourse.   I decided to have them use the Kagan Numbered Heads Together Cooperative Learning Structure.

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In this structure, students work individually on the task.   When a student has completed it, he or she stands up (giving them a chance to move a little bit).   When all the members of the group are standing, the students in the group discuss their responses. (I circulate, listening and sometimes asking a question.)   Students in the group are mutually accountable.   That is, one member of the group will speak for the group, but they don’t know which one.   When the groups were all ready, I led a whole class discussion.   I selected students to explain their response for each question based on seat position within the group.   (By the time class was over, every student had to respond to a question).

Based on student responses, it seemed that students had a good working knowledge of what makes a question statistical.   So, once again, I wanted to increase the cognitive demand.   I gave students a set of four different data representations.   I told them that they must write a statistical question that could have been used to create the data representation.   This was trickier than it might sound.   At first, a lot of the questions were questions that could be answered by analyzing the data rather than questions that would generate the data.   After discussing this subtle difference, things proceeded fairly well.   Again, I had students use a Kagan Cooperative Learning Structure to give a structure for the discourse and to ensure mutual accountability.

I followed up the lesson with an Illustrative Maths performance task.

I feel starting the unit “at the very beginning” was the right place to start.   I was happy with how the lesson seemed to be working for both of my distinctly different students. However, it is early days yet and I have only begun to implement some of my ideas on how to build that big picture and the connections between concepts.   I will have to give it more time to see if my ideas about how I can support these students play out the way that I hope.

While I am generally happy with how the lesson went, there are a few things I want to change for next year.     I gave students a handout with all of the questions and prompts for the lesson.   However, it was pretty cumbersome, taking up multiple pages.   Some   students did all of the work on the handout, folded up the handout and taped it into their interactive notebooks.   Some students cut up each question and then taped it into their notebooks to answer.   I felt like the students who taped the whole handout in probably won’t go back and look at the whole thing to study and those that cut each part out just spent too much time cutting.   I decided that I wanted to use the same structure, but refine the way I gave the information to the students.   For the first set of statistical questions (while they are exploring the idea), I created a card sort with the questions.   I will have students cut out the cards and put them into their interactive notebooks in the form of a T table (Statistical/Non-Statistical).

 

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I then took the next part of the lesson and created a foldable.   I have two versions.   The first version is my standard version.   It requires students to write their explanation for what defines a question as statistical.   The modified version is a cloze activity in which students need only fill in some blanks.

Identifying Statistical Questions Foldable

Identifying Statistical Questions Foldable Modified

 

 

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