Authentic Learning at Its Finest

Devon (*Name changed) was the kind of student that every teacher dreams of having. He attended study hall every week, whether he was on the list or not. He was extremely well organized with his time and used study hall as an opportunity to get all of his work done. He worked ahead when he knew he’d be missing class. He also genuinely wanted to learn. If he was unsatisfied with a test score he would ask questions about his wrong answers. We worked through them together and when he got it he grinned broadly and nodded saying, “I see, I see!” He also readily participated in classroom discussions. In my statistics class he had some of the deepest insights of all of my students and demonstrated that he really understood the big ideas deeply, not just on the surface levels of formulas and equations.

When Devon told me that he didn’t want to take the AP Statistics test, I was disappointed to say the least. Devon came to Wasatch as an athlete. He was an extremely talented point guard and will be attending an awesome California school on a basketball scholarship. He valued his education above all but I think he often doubted his ability as a learner and a mathematician since he had most experienced praise for his athletic ability rather than his academic ability. No matter how hard I tried to convince him that he would do well on the test, he wouldn’t budge. I had told my students that if they opted not to take the test, they would need to do a project while the rest of the class participated in test prep. The effect that this had was to scare most kids into taking the test, thinking that a project would be harder. Not Devon, he was so set on not taking this test that he was willing to dive into project mode. While I wanted him to try the test, I commended him for his willingness to do some hard work and I wanted to help him have a great authentic experience. Every class thereafter, I would spend the majority of the time getting the larger group grounded in review and self directed test prep and making a schedule of small group conferences with students but I made sure to set aside 10-15 minutes with Devon as well (class periods were 90 minutes long).

I asked Devon if he wanted to do a project about basketball and he immediately lit up. We only had a few weeks so he couldn’t do an experiment to gather data. I asked him what data about his team he could gather. The next class, he came in with 10 years with of summary statistics for players that had been on our high school team; averages for each player with respect to 3 pointers, rebounds, assists, field goals, steals and more. He said he could also get data about how much weight each player could lift. “What do you wonder about this? What questions do you think this data can help you answer?”

Image from NBA.com

Devon put his headphones in started scribbling in a notebook. The next class period he had a list of questions. Just a handful are listed below.

1. Are more three pointers associated with more field goals?

2. What positions have the most field goals?

3. Does height affect the number of field goals?

4. Does the weight you lift affect basketball success?

5. Is GPA correlated with number of field goals?

6. Is GPA correlated with basketball success?

Devon was visibly excited by the last two questions.

“I really think that the guys that do better at school do better on the court.”

“Why do you think that is?”

“They work really hard. They know how to put the effort in.”

We tried to work with the last question since it had excited Devon most. We quickly realized, that the key to breaking it down would be to answer the sub-question, “What does basketball success mean?” If Devon wanted to measure the correlation between basketball success and GPA he would have to define “basketball success” and in this case put a number to it, using the data he had.

This became his focus for the next couple of days. I asked him, “Does high field goal percentage mean that you’re a good player?” He answered right away, “Not always. There are players that have low field goal percentages because of the position they play. Centers will have a lot but guards will have a fewer. Good guards will have more assists.” AHA! We were getting somewhere. We decided that it would help to figure out how the NBA ranks it players. This was key to the process, we were both in it together. Over the weekend we emailed each other articles that we had found about statistics that were being used to rank professionals. In class, we sat down together with a white board and tried to figure out what each part of the statistic was doing. Devon was able to tell me why certain inputs should be weighted more heavily than others and I was able to help him understand the mathematical operations that were being used to combine these inputs. It was truly a collaborative effort. We ended up discussing some really deep mathematics here, like weighting and normalizing. The concept of normalizing is key in statistics. The equations that we looked at normalized with respect to the amount of time that players were on the court and with respect to the intensity and speed of the game (of course more field goals would be scored during a fast paced game). Seeing this mathematics in a context that he deeply understood really cemented the ideas for Devon. It became intuitive for him.

In looking at the statistics used to rank NBA players, Devon quickly noticed that they did not account for what position the athlete played. This deficiency was reinforced when Devon looked at the list of ten top ranked players and didn’t agree with it. We also didn’t have the data to simply plug into the ranking equations that we had researched. Now Devon had a goal: create a summary statistic for basketball players that would accurately rank them, based on their position.

He quickly got to work with some equations. He used each one to rank the players on his team. He was originally doing all the work by hand so I showed him how to use a spreadsheet to do things more efficiently. He caught on quickly and loved how simple it was. It seemed like magic to him at first. He began recording all of his progress in a google sheet. (Link to Devon's Spreadsheet) As he worked we also had conversations about weights and how he the key to differentiating the statistic by position would be to weight each input differently. For example, assists should be weighted more heavily for guards than they should be for centers. We also talked about dummy variables which allowed Devon to have one single equation that worked for every player, regardless of position. The dummy variable would be used to “turn on” or “turn off” certain parts of the equation depending on position. These are econometric concepts that are not required at all in the AP Statistics curriculum. I didn’t learn them until I was two years into my economics major in college. We talked about partial derivatives and how the sign of the partial derivative shows the direction of a correlation in a multivariable equation. Devon had not even taken calculus and yet these discussions were coming up and he was understanding the value! I excitedly adapted mini-lessons for him every day based on questions that came up as he was doing real research.

He ended up using NBA data, recognizing that having more data points would make his work more precise (another important concept in statistics).

Here is a reflection that Devon wrote at the end of the assignment:

To compensate for not taking the AP test, I decided to create my own project based on what we’ve learnt this year in our statistics class. When trying to figure out what to do, miss chiappetta and I figured that it would be most relevant to create a project that revolves around basketball which is also very entwined with statistics. Doing this allowed me to discover some new things and to realize how statistics is applied to real life situations. Primarily, I intended on creating a hypothesis test that would show whether or not the GPAs of the players on our team would have determined their performance on the court. This was where I learnt my first lesson. I realized how tests like these don’t always go as planned. It turned out that I ended up having to change plans completely. I had no access to the necessary statistics of our team to follow through with this idea. I decided to let go of that idea and go with something that I could have access to. It made perfect sense for me to base my project on NBA statistics instead. I decided to create my own statistic that would allow me to create my own top 10 NBA players ranking and to compare it to the actual NBA top 10 ranking in order to see how accurate my own statistic was. This was very interesting to me because I managed to evaluate my own work and see where I could make adjustments in order to make the most accurate statistic as possible. In this project, I combined my basketball knowledge with my knowledge in statistics to come up with an equation that would work best to accomplish my task. It turns out that I ended up touching the surface of some calculus while trying to discover a way to break down the equation that I ended coming up with. I also managed to play around with tools that I was given this year in AP statistics.

Overall, this project was a lot of fun and I learnt a lot from it. I feel like combining statistics with a real life situation that is relevant to me was the true meaning of project based learning because it has helped me see what the material we are given is all about.

I am so proud of the work that he did and I am so grateful for the experience. I learned a lot about the true nature of learning, about the value of context, and about the benefits of modeling to a student how to think critically and to roll with the punches. I look forward to more opportunities like this.