Tuesday, December 5, 2017

The Stats Project Part –1

I've wanted to try PBL in math for a while now. Two things were holding me back. First, there is a lot to PBL and I wasn't ready as a teacher to tackle all that until this year (maybe...we'll see). Second, I don't think PBL is a natural fit for mathematics. It is hard to have authentic, public projects that align with some of the content I teach in algebra--solving for example.

However, last year I realized there was an opportunity for me to teach my Statistics Unit using PBL. Stats is real life! What a great opportunity to come up with an authentic, public project that aligns with the content.

In January 2018, I'm going to teach the Stats Unit via PBL for my Sheltered Algebra class. Sheltered algebra is for recent immigrants to the United States. The students have low English proficiency in reading, writing, speaking and listening. Some students speak conversational English, some speak no English. Most of the students are Latino, however, I also have students from China, Vietnam, Japan, the Philippines, and Palestine.

Thus, any blog posts about the Stats project are "pre unit". Here is a link to my first post on this project.

I expect this project to be messy. There is a lot I've thought about and planned for; but there is a lot of things that I know will catch me off guard and I cannot plan for those things. I will be sharing my experience (good, bad and ugly) on my blog.

Language is Messy

One of the biggest parts of this PBL Unit on Immigration will be teaching EL students that language they need to discuss and make sense of the different representations of immigration statistics we will be looking at. 

In anticipation of this, I have been showing students complex graphs in class and on homework and asking them things like "what does this graph tell you" or "what questions do you have for this graph".  Here are a few examples of the types of graphs we've looked at:




The reason I am doing this is so I can get a sense of what language they know and what language do I need to teach. 

Some of the graphs have been class discussions and students just look at the graph and then discuss with a partner and then the class. Some have been on homework and I ask them to write a response. 

One of the biggest things I've learned (so far) is that the graphs we usually look at in class are not the kind of graphs that are in the media. Accordingly, the language I usually teach in terms of how to describe graphs isn't useful. 

For example, we talk a lot about y-intercept aka initial value in my class. And several students pointed out that the graph below does not have a y-intercept. I know that seems like a small thing, but for students that speaks little to no English, identifying the initial value from a graph is a great use of language and it is important to them as they make sense of a graph. I never taught them how to think about a graph with no initial value! 


Also, very few graphs from the media are perfectly linear! So my usual sentence frame of "as the inputs increase by ___, the outputs increase/decrease by ___" isn't useful.  

But this is good to know! I want to know where they struggle and what language supports I can put in place to help them.  I developed the following sentence frames to help students analyze the graphs we are currently looking at.  The big difference is how we describe linear v. non-linear graphs. This is something else we've gone over in class.


And students started using the sentence frames "the function is increasing for x values" and "the function is decreasing for x values" to describe graphs! Here is some of their work (good and bad).






Formative Assessments

The point of all this is to say that sometimes a teacher needs to formatively assess students so the teacher can determine next steps. None of the assessing I did with these graphs was graded; that's not the purpose. I wouldn't know what language students need, and I wouldn't think through how to teach that language, if I hadn't done these activities.

Lots more to come on this project! 


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