This summer, as part of my professional development, I am taking an online Stanford course entitled "Mathematical Mindsets". This is a course developed by Jo Boaler, Cathy Williams, and others at YouCubed.org, a part of the Graduate School of Education at Stanford.
As part of this course, the question just posed to me was, "Do you think you could teach to big ideas, instead of all the isolated content standards? Why or why not?" For some reason, I have been working on this course through the lens of my 10th grade integrated math course. But, this question resonated with me in regards to AP Statistics.
One of my great difficulties in my first two years of teaching the course was getting through all of the content in time for the AP exam in May. I have been relying a lot on our textbook. So, my goal has largely been to cover as much of the text as possible. The book is broken up into 12 chapters and each chapter has two or three sections.
Each chapter has its own main idea. But, each section within a chapter has its own ideas. So, I feel like I have been teaching AP Statistics by focusing a lot on the isolated content standards.
I know there are big ideas in this course. Without looking it up, I think there are four. So, I wonder now if I could teach AP Statistics better focusing less on the nitty gritty and more on the big ideas and then study problems and ideas in each. I may not get to every individual smaller idea, which might cause some problems on the multiple choice problems. But, I think this approach might help students do a lot better on the free response questions.
Teaching this way certainly seems possible. I wonder if anybody reading this understands what I am writing and has any experiences that they would be willing to share. Have you tried teaching AP Statistics by focusing on the big ideas? Was it successful? Did you try this multiple times? Has anyone tried this approach but thrown it out because they felt it didn't work?
There has to be a balance of both, I think. I definitely think a focus on the big ideas is crucial. We have analysis of population data (assuming you're using TPS, that is chapters 1, 2, 3 mostly), experimental design (chapter 4), probability necessary for inference (chapters 5 and 6), and statistical inference (chapters 7 through 12). But really, I see this all going toward one big idea: how do I design, carry out, and analyze the results from a study or experiment? Chapters 1,2,3 and 7-12 are all about different ways to answer that last comma, the anaysis. Chapters 5 and 6 are, frankly, only important in and of themselves as background information for chapters 7-12. (I think the AP exam needs to focus less on probability for the sake of probability; I feel it detracts from the thematic consistency a bit). Finally, chapter 4 is remarkably short to be so important, but its ideas should resonate throughout the rest of the book (or if you do it first, as many do, it should resonate throughout the course).
ReplyDeleteI don't think its a bad idea to start the year from that end-goal perspective. Show (but don't really assign) a typical medical trial or other experiment and look at the big ideas. Here's one I found comparing allergy medicines: http://www.jacionline.org/article/S0091-6749(98)70172-1/pdf . There is information about how the subjects were gathered, how the experiment was formed (chapter 4). There are data tables and charts to visually represent the data (chapters 1-3). And of course there are lots of technical terms - most importantly for our class, "p-value" - that require statistical expertise to understand, but it can be pointed out that without those terms and the underlying analysis the article would not have been published and the medicines might not have been approved for sale at all. This is, of course, fairly dry and technical, but you can then also show something from fivethirtyeight.com or another public-facing data journalist site to show how it might be prettified and simplified for the public; but without the technical stuff there would be no data for those writers to work with.
Thank you so much for the detailed comment.
ReplyDeleteI do use TPS. This year, I am going to start with chapter 4.
I completely agree with your comment about probability problems.
I really like your idea about looking at a big medical trial. I will probably use the one you shared. What a great way to motivate the entire course.
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