## Carl's Teaching Blog

#### Category: Clog (Page 4 of 6)

Yesterday in class we had a day of getting kids on board with the technology and ramping up for our final project. For this class, students write a little research paper about what their peers beliefs on, well, anything. Prior to this class I looked at the calendar and freaked out a little after realizing that we need to get this survey drafted and out to the school ASAP.

But Before We Start On The Project…

Before we get started on the project I want to bring back the conversation we have been having about outliers and review it a little. I had an idea for a review “game” that was slightly more interactive then asking kids to do a bunch of problems and could also serve as a reference for finding outliers with Standard Deviation and the IQR. I made little cards that kids could work in pairs to see if they could put the steps for finding those outliers in order. It was cute, check it out, let me know what you think in the comments.

The next part of the lesson was to have students learn how to do all of this statistical analysis we have been doing by hand on our good buddy Google Sheets. I asked the kids to learn average, median, mode, min, max, range, quartile 0-4, Standard Deviation, and Variance.

Whenever I do this kind of thing, flashbacks of the age old ‘calculator’ debate echo through my brain. Visions of my old professors glowering at me appear like a bad dream alongside images of students understanding withering from the glow of their computing devices. I’ll probably never get rid of the dirty feeling associated with replacing by-hand work with computing devices. I think when it gets down to it, kids need to be able to explain the purpose of all the statistical tools that they are going to use in the future. They will get to have more practice explaining if they do more calculations done on computers than if they only did work work by hand.

Starting the Survey Project

So I was about to teach standard deviation today, and from the beginning of the unit I had planned to revamp this power point that I originally made sometime before 2010. Unfortunately the revamp didn’t happen, so I got a little flashback to what my teaching was like in the naughts, and it wasn’t pretty. I mean it wasn’t bad, it was a Powerpoint where I go step by step through what Standard Deviation was using an example comparing two sets. There are lots of discussion prompts that get at why standard deviation is useful. Here’s the file if you want to check it out. LINK TO CARL’S OLD SCHOOL POWERPOINT Because my day was busy, I had no choice to but teach it pretty much identically to how I taught it at that time.

#### Stepping back in time

Teaching this lesson was like taking a quantum leap back in time to my previous teacher self. As I was teaching it I realized that I had not built in a way to see if students really understood the reasoning behind the the calculations, there were a few students who answering the discussion prompts in the class, but the rest mostly stayed silent. I tried to think of a way to modify the lesson on the fly instead of just using the results on a worksheet where they practice finding the standard deviation. I thought up  some different writing prompts that would be good ways to see if students understood why they were doing what they were doing, and I offered the class the following choice.

“Either do this worksheet, which asks you to calculate a lot of these giant standard deviations by hand…or answer some reflection questions that shows that you really understand standard deviation. Worksheet? Reflection questions? You pick!”

Would you believe that they picked the worksheet???

#### Why did they pick the worksheet!?!?

Having my reflection questions rejected was a pretty shocking occurrence in my classroom. One of those things that makes you suddenly question your whole approach in the middle of a class where you don’t have time to flesh the ideas out. Here are some of the things that ran through my head.

Should I let them choose? It wasn’t unanimous, the kids who were really into the lecture were the ones who were the ones who would write the reflection questions everybody else wanted the worksheet. Would allowing people to choose really result in everyone thinking about the ideas equally? (I said no)

What if they just didn’t get it? My first thought was that the pro-worksheet students might be students who may not have gotten much out of my Powerpoint, or any powerpoint in general. How many other times has an oversight on my part prevented a group of students from getting access to the big ideas.

Should I just do more practice? Should I allow students more opportunities to practice computations instead of asking them to describe big ideas? If I do, will math class turn into this thing that everyone hates (including me)?

How do I make reflection more natural? Students in the class need to be able to explain the ‘why’s’ behind all of the ideas in the class, so reflection should be though of as something as important as practice. Should I be doing more to change students thoughts about what math class is about?

Perhaps I am over thinking it. The fact that I had so much to think about made me glad that I am much more reflective teacher than I was when I originally made the worksheet. At the same time, I’m sure it’s unanswered questions like these that I need to reflect on if I want to keep getting better.

Today’s class began with the awkward dance of finishing what we left off the last class. The source of the awkwardness 40% of the kids unaware of what we did yesterday and needing to get caught up.

To combat the awkwardness I typically try and quickly get those 3 up to speed, but the students were responsible, and did what they had to do the day before end up sitting their bored. Today that wouldn’t work because it would require too much circulating. Instead I tried to do a comprehensive recap of what happened last class, and then ask the absentee kids to ignore front page of the assignment and instead join the rest of the class on the back page. Instead I caught all of them working on the front because they wanted to work linearly. What ended up happening was the worst of both worlds, where I had to wait for the whole class to finish so I could have the discussion, leaving some of the other students doodling in their notebooks for longer than I’d like. Guh.

Luckily, the discussion was great, as kids were saying exactly the things I hoped them they would say. I felt like Hannibal at the end of an A-Team episode when it was all said and done.

5/30

Today we worked on reviewing average, median and mode before talking about how to use those tools to make arguments around a set of data. Students were given basketball statistics and data about restaurants in NYC and a set of statements that weren’t correct about the data and asked them to reword the statement so it actually reflected the data. After that I wanted to get into the “Hot Dog Festival” worksheet when my teenagers started acting like teenagers and nothing got done.

Hopefully we can finish the hotdog activity on Thursday, and then we can get into the outlier activity. This activity is another one that I did last year. Naturally, I will spend much more time preparing for Thursday’s class than I did today. (I might even write a blog post about it.

Are you wondering what the joke was? Ask me in the comments!

3/3

Edit, ok here is a link to the worksheet, you can see what threw them off in there: https://docs.google.com/document/d/1afWGNu0PtdxchiSRnP4jHBD7lHcNFVBQnRkDW0aol1Y/edit?usp=sharing

We have spent our time this past few weeks turning an interest in patterns into an interest in modeling. Each day we have done activities to get the students to think about number sense, and also about relationships and functions. Next we will focus on linear and quadratics simultaneously and look at both as examples of functions that we can use to describe how things grow and change. Teaching the two functions simultaneously will hopefully strengthen kids’ understanding of what functions are and what they could be more so than focusing immediately and solely on linear.

I taught my class twice, as per usual. The way our school is scheduled, we only see kids on Tuesdays-Thursday classes for 90 minutes each. The class has only met on 6 occasions (and one of those was taught by a sub who wasn’t given my subplans). At times it feels like we should be further along, but I want to remember to be patient.

Tuesday we looked at the penny circle on Desmos. We also opened up class with three visual patterns, one linear, one quadratic, and one exponential followed by a Contemplate then Calculate activity from math.newvisions.org. This helped going into the penny circle because they were familiar with the types of equations, and also with counting things. The best part about Desmos activities are that it let’s the students work independently on tasks, and learn from each other. It is certainly because of these benefits that the universe conjured up a perfect storm of misplaced computer cart key and a soft lockdown drill kept me from actually using computers with my kids, and I ended up having a few kids walk through it with the smart board. Luckily I made a worksheet so I could see what kids are thinking about the activity, and the kids could still engage in this whole-class format. The students were able to see how the different equations look on a coordinate graph.

Following the activity we did an Interpreting Distance Time Graphs from the Shell Centre, which we did not have time to finish.

On Thursday we started with a visual pattern that worked out pretty well. This was the 5th one of these that I have done, but it was the first time I asked for symbolic equations for the patterns. I was surprised that students didn’t offer some kind of equation earlier, but I still wanted to wait until this point because we could start working with equations soon. To formally begin working with equations we looked at a modified version of Tina’s quilt squares, which has been a staple of my introduction to quadratics for years. Kids then worked on finding the number of grey squares and the number of white squares and eventually we had time to talk about the equations.

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