Wednesday, December 6, 2017

PBL in Algebra Days 2 and 3


Here is a link to my previous post about our launch and QFT to start the project.

Days 2 and 3: Histograms and Boxplots

After the project launch and QFT on Monday, we jumped into the 'content' on Tuesday. The content goal of day 2:

c  I can create a dot plot or box plot given data.
c  I can describe the shapecenterspread, and outliers of data given a histogram, dot plot, or box plot.

c  I can compare the shapecenterspread, and outliers of two sets of data given histogram, dot plot, or box plot.

I didn't expect students to master all this in one day! But this lesson introduced univariate statistics being represented using a histogram or dotplot. On Tuesday a period is 90 minutes and I planned to have about 40 minutes of content (traditional) and 40 minutes of project time.

I also put students into groups on Day 2. At the start of the lesson, I gave students a survey asking a few questions. I had planned to give the survey on Monday, then make groups after they left. However, we ran out of time on Monday for the survey. I'm fortunate to have a student teacher, so while she gave the histogram notes, I looked at the survey results and used the student responses to build groups.

The survey was 4 questions:




I used the broad categories from the QFT for the 1st and 2nd choice project questions in the survey. 

After students finished the content portion of the class (notes and then partner talk and class discussion to practice describing and analyzing histograms), they were given data from one of my classes (data I pulled from the survey mentioned in this post) and asked students to make a histogram of the data and then analyze the histogram. 

example of the type of graph of made using the class data

This is a huge improvement in how I've taught this in the past. We've always done notes, but then we look at random histograms that I pull of the internet for practice. I LOVE that we were looking at the data. 




Students created the histogram in their project groups. While this was part of the project work time, this work didn't directly relate to their project--though it could. And it wasn't a group grade; while students worked in their groups and could support each other, they were individually accountable for turning in this work.  The reason behind this is I want to make sure I can assess students individually for content as well as assess students as a group for the project.

What I loved is that students were so engaged during this work time. I think the engagement happened for a few reasons:
  • they used their class data, not random data from the internet.
  • they had choice: they chose the data they wanted to use, they could also choose where to sit with their group. 
  • they could choose when to turn the histogram in. It was due at the end of the block, but students could also turn it in the next class for full credit if they felt what they finished at the end of the block wasn't high quality. About 25% of the students wanted to keep it to finish and turn in the next class because they wanted to create a high quality product. 
The other thing I loved about this lesson is how the open-ended structure of the group work created a need. For example, as students were working on their histograms in small groups, the inevitable problem came up of which bin to put data that falls on a border of a bin. If the bins goes from 10 to 15, where would a data point 10 go? In the previous bin or the 10 to 15 bin? I LOVED that students would call me over because there was a need and I would fulfill that need.

In previous years, I would just share that info with the class and 2/3 of the class would not hear me, etc.

Day 3: Boxplots

Day 3 looked a lot like Day 2 except the learning goal was boxplots instead of histograms. 

c  I can create a dot plot or box plot given data.
c  I can describe the shapecenterspread, and outliers of data given a histogram, dot plot, or box plot.

c  I can compare the shapecenterspread, and outliers of two sets of data given histogram, dot plot, or box plot.

We did notes on boxplots, then students described boxplots I made from our data with partners. Finally students got into groups and created a boxplot using data from our class.

example of the type of graph of made using the class data

Reflection

There are definitely improvements I want to make to this unit next year. I don't think what I did is perfect, though it is better than how I taught this unit in previous years. I'm looking forward to continuing this process--and I'm thinking a lot about how to incorporate more PBL into my curriculum. My only problem is that I think algebra, or at least how algebra is taught at my school, isn't a good fit for my PBL. 

More to come! 



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