Data Landmarks – Educational Aspirations

One of my classes has been exploring box plots and data landmarks lately. Earlier in the year the class created histograms and found data landmarks on line plots. Box plots was not as easy as a transition as anticipated. There were a few roadblocks as students analyzed and created their own box plots while determining Q1 and Q3. Some students picked up on the concept quickly while others took more time. To help reinforce the concept I thought about bringing in a spreadsheet activity. I have been using spreadsheets quite a bit this year and it has been another medium in which students can experience statistics.

Students were first asked to create a question that they would be asking the class. The numbers could range between 1-51. I gave students free rein on what questions to ask and held my breath.. Here were a couple of the survey questions:

What is your favorite number between 1-51?
How many hours of sleep do you get per night?
On a scale of 1-50, what do you rate a cheese burger?
How many movies have you watched this year?
On a scales of 1-50, how well do you like dogs?
How many digits of pi can you recite?

Once students created questions they went around and surveyed everyone in the class. I gave each student a roster list so they could check-off who answered This took a good chuck on time – 10-15 minutes. Once the data was collected students grabbed a Chromebook and copied a spreadsheet that I had pre-populated.

Students took the data from the survey collection sheet and transferred it to column A. The data landmarks in row three were placeholders and awaiting formulas. Students then entered the minimum, median, maximum and mean formulas. They were familiar with those formulas as we explored them earlier in the year. I discussed with the class about quartiles and we put together a formulas for Q1 and Q3. We made predictions of what the vertical box plot might look like before finalizing. Students then entered the formulas for the quartiles and analyzed the box plot to see if it matched the data.

It was interesting to hear the conversations that students had as they compared the data to the box plot. The class had a discussion about interquartile range and variability. It was time well spent. From there, students shared their spreadsheets with me and I took a closer look to see how the data matched and if the correct formulas were in the appropriate places. Students seemed to grasp the concept fairly well. Feel free to use a copy of the spreadsheet by clicking here.

During the next day the class reviewed box plots and the spreadsheets that were created earlier. Students then complete the Desmos task Two Truths and a Lie. This is one of my favorite tasks for students to discuss box plots and use math vocabulary while doing so.

The spreadsheet and Desmos task took about 2-3 days to complete. The class took a unit assessment on Friday and I will be checking out how they did over the weekend. I put these two activities in a digital folder for next year.

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One of my classes is working on a unit related to data displays and number systems. Around a week ago the class was putting together sets of numbers to match data landmarks. This was a challenge as students had to think differently. The class was also asked which data landmark better represents a student’s performance. I was meaning to write a post then, but a number of things came up and it never happened. Fast forward a week and here we are.

Students were given two sets of scores from two different students.

Jack’s scores: 85, 81, 78, 100, 84, 89

Sonja’s scores: 55, 87, 91, 92, 68, 93

Students were asked to find the median and mean for each student. For the most part, students were able to identify both of these landmarks. Here comes the kicker … now students needed to determine which landmark better represents each student’s performance, mean or median? This was a challenging prompt for a couple reasons.

Students weren’t accustomed to using the word represent in this context. Students were taking the view that the students should get the higher grade and that would be the mean or median. They explained that the student should receive the higher grade because they (the person) is a hard worker and deserves to be rewarded with the highest score.

Students thought of the word represents as the typical score. When discussing the mean earlier in the year the word typical would often come up as a synonym.

Students looked at the last score as the most recent and thought that should be the final representation. My school is heading in the direction of standards-based grading so that’s maybe why students took that approach. I don’t know.

Students looked at the lowest and highest score of each set of data and reviewed the range to help them pick the median or mean

After struggling a bit, the class came together and we discussed a few possible solutions. The class agreed that the question allows a lot of room for interpretation and context certainly matters. The fruitful conversation brought about a change in perspective for some as students started to see this type of math differently than just numbers sprawled across a page. The numbers had meaning and the context drives the answer.

A little later in the week students were asked the following prompt:

If you were the teacher in Jack and Sonja’s class, would you use the median or the mean to calculate students’ grades? Explain.

This was a bit confusing at first, but students made progress in understanding the context and how it helped determine which landmark to use. Again, I had answers related to the teacher wanting to give the higher score to help students with confidence. Other students used the data landmarks to find the average. I felt like students were more comfortable using the average as they could say that they used every data point, therefore making sure all assignments counted for something.

I’m looking forward to next week as we dive into histograms.