# Explore Math (Reprise)

At the beginning of the 3rd quarter, I did an experiment in my Advanced Precalculus classroom: Explore Math. This post is the compilation of the survey results from my kids on this experiment. So if you don’t know what the activity was, read up here, and then see what this survey is all about. I will share examples of some of student work for this experiment later. Part of the assignment for students included submitting one exploration to our school’s math-science journal, Intersections. When this year’s issue of the journal comes out, I hope to link to my kids’s explorations!

The question in the survey:

The “Explore Math” project is something I’ve never done before. I explained my reasoning behind it — which is I wanted to encourage you to see that there is so much more than our curriculum covers, and let you just have fun looking at math stuff outside of our curriculum… and get some easy credit for it (almost everyone is getting full credit for the first batch of things I’ve seen). However, as a teacher, I know something like this could easily be seen as busy work, and that was my big concern — that it would feel like a chore rather than something you actually want to do.

This is me laying my cards on the table. If I came to you in the student center and told you this and asked you for your thoughts, what would you say?

Every Student Response In Entirety:

I really liked the Explore Math project and I definitely would say it was an overall success. I loved how many options we were given for what we could do, and the fact that you gave us the options was great because otherwise it can feel like you are just trying to desperately research and find a topic to write about. My Explore Math topics I thought were extremely interesting, and it was cool to even connect some to the stuff we were learning in class. It was a lot of writing, which is something foreign for math classes, and also made it kind of difficult to grasp exactly how to format what we were writing (five page essays for each topic?). One other thing that was a little stress-inducing was the deadline and I know it was for a problem for most people that it often happens that when there are multiple assignments due on one day, students leave them all and do them in bulk. Because of this, having the deadline of the first three due in February was definitely helpful. Overall, I really loved the assignment.

I really liked this project! I found a lot of things about math that I would have never known about if we weren’t assigned this project. I learned new formulas, new (very addictive games), great youtube channels and informative popular articles. I found an entirely new community online that I did not know existed.

At first I expected it to feel like a bit of a chore but when I actually sat down and did it, it was pretty fun. I think it was great that there were multiple ways you were allowed to “explore math.” I also thought it was amazing I could play around with the project a little bit to find areas of math that are aligned with my personal interests. Being able to think about how math affects our society, in a math class, was an amazing interdisciplinary activity. I think it’s good that not every option was a math puzzle — that would have felt constrictive.

I would say as long as the students are innovative, interested and patient people the project sounds wonderful. The student, if very interest in math, should be encouraged to further their mathematical understanding, and find means in which math is even more interesting to them as it was prior. Emphasizing the point that one (the student) does not need to seek the more difficult problem or most tedious theorem is also very helpful, as the student will be encouraged to explore areas of math in which really interests them.

I would say that I absolutely love the explore math project. I have always been a person who enjoyed math that connected with the world. Being in a classroom memorizing formulas was never my interest and I was psyched when you announced the project. I think that this project can be very helpful in putting math on the global scale for students who only see it as a class in a school. This opens their eyes to new heights math can taken and how much math actually helps outside of the classroom.

I agree it felt like busy work some. I find it weird that something that’s supposed to be us having fun exploring math had a grade and time constraint attached to it. That’s one thing I didn’t like.

All I have to say is that this was not busy work; in fact it was productive and learning work. I found this to be incredibly intensive and interesting, and it broadened my horizons of the understandings of applied mathematics and sciences, and introduced me to things that I had previously trembled [at] before, like string theory, for instance. I thought this was a great project and a simple and easy way to get us thinking in a mathematical mindset, and I am definitely reaping the benefits from it, because I have come away with much more knowledge about certain aspects of math that I had previously not known. I really wouldn’t know what to change because I liked these individual explorations so much and they intrigued me so much. Thank you for giving a projected that I was thoroughly interested in, seriously!

For someone who is very interested in math in and out of the classroom, I am generally engaged with math concepts that are not a part of our curriculum. Thus, this was a good experience for me in that I was able to get credit for simply enjoying and exploring math; it also perhaps pushed me a little bit to go further than I normally would in exploring mathematical concepts online. However, for students who don’t love math outside of the classroom, I could definitely see how this might have seemed like busy-work. If you don’t genuinely enjoy math, then writing a lot about it and research about it is going to be cumbersome, but if you do, it’s enjoyable.

I really liked doing the explore math assignment. I liked that you were giving us an outlet for us to not just do the math that needs to be done in order to complete the class. This assignment allowed me, personally, to dive deeper into how math can be applied to the world and that math is actually occurring all the time. Also, I remember not really understand[ing] infinite series and then I did an explore math with infinite series that really helped me because it was a visual representation that really clicked with me.

I think that initially I thought the project might just be busy work and I didn’t really understand what we were expected to be doing. Once I read over the assignment and saw the scope of the projects we were allowed to do, I was much more interested and saw the project completely differently. I think that it is important to highlight, when giving the assignment, how broad a range of options you have when doing this, and that there are so many math projects that relate to everyday life that could be interesting if you just think about it, rather than relying on the assignment sheet completely to guide you.

Personally, I have enjoyed what I have done so far. Just recently, I voiced my concerns about the state of math in America and was able to comprehensive research about the bitcoin that I would not have done on my own. That being said, some of this has seemed like busy work and stuff “I just have to do for credit.” Since it seems like you genuinely want us to enjoy the project, it might be made better by making it extra credit. That way, we could be able to explore as much as we want without worrying about our grade.

I had a really awesome time doing my Explore Math assignments, but the one thing you could do to make it less busy work is make it 3 different assignments, rather than 5, and make them a little more in depth, and more interesting in that regard. I think that if the students only had to do 3, they could expand more on what they were interested in.

I really like the idea, but for me personally, it turned into busy work. Not because I find it boring but because I have so much other work that it gets pushed back towards the end of my load. I would like to spend more time on them, so possibly have it on top of the nightly work for math, designate a night specifically to explore math.

This is practically the farthest thing from busywork we can do! Repetitive problems often seem like busywork. Practice is always good, but once you have something down, it can be quite annoying to practice it over and over again. Sometimes i feel that way about homework, but with this project we’re choosing any math-y thing that interests us! We have a lot of freedom, and hopefully it piques an interest in math outside of the curriculum. This project is great, personally, I wish I had taken more time with it. As long as you don’t procrastinate too badly with it, I don’t see how this project could be a chore, unless you claim to hate math.

I LOVED this project, and I wish we got to do more things like this throughout the year. (I know we can do things like this whenever we want, but it’s really nice to get some recognition and the chance to formally share your math ideas with others.) As a side note, this project was also interesting to be doing while looking at colleges for the first time. I know that sounds like a really strange thing to say, but getting to enjoy math in new contexts, such as music theory, has given me new ideas of things I would like to pursue and take classes [on] while I am at college because we don’t always get to learn about things like this on a daily basis in high school.

I do admit that I wasn’t very enthusiastic at the start of the project, but as soon as I started I completely changed my mind. Most of the work that I did was stuff I had never done before and might never do again. I was genuinely interested in what I was doing, and it was great to be able to choose what I focused on instead of being told what to look at.

I understand why you assigned this project, and I think it is very important to see the relevance math has in the world. This breathes life into the abstract “why are we learning this” type that doesn’t appear to have anything to do with life outside the classroom. However the problems with this assignment are that I didn’t know what I was searching for. When I found the Sloane’s Gap video and paper I felt like I struck gold after seemingly endless mining. However the mining part is very un-exciting. Not un-exciting enough to undo the excitement of finding the cool stuff, but it’s not very encouraging either. I wouldn’t want this assignment to turn into a chose 5 of these pre-determined projects because that wouldn’t make anyone feel like anyone feel like they’re venturing outside the classroom. I’m not really sure what I would do to change this assignment, but I think it really is a good idea that with some refinement could become a really dynamic way to get into math. I think keeping it low pressure and “easy credit” is the way to go because stress + ambiguity about an assignment is a terrible combination that would only end in resentment from your students, and students not enjoying their work.

Honestly, I had quite a bit of fun with the “Explore Math” project as I saw many cool analogies of real-world applications of math. For example, one of my five “research topics” was the probability and randomly guessing on every SAT multiple choice question. I learned that the probability is horrifyingly low — I already knew this, but not to such an extent. Furthermore, I saw some very cool analogies in this SAT topic; for instance, if a computer were to take the SAT 1 million times a day, for five billion years, the chance of any of the SATs resulting in a perfect score on just the math section would be about 0.0001%. Crazy, I know!

## 3 thoughts on “Explore Math (Reprise)”

1. Meg says:

What perfect timing! I stole this idea and assigned it to Honors Precal, and the first round was due today. I have gotten such wonderful responses back! Students have been coming in every day this week with something new they want to share with me.

I added another option of reading Lockhart’s Lament (I let it count as two explorations). One of my students told me he read it and that “it was beautiful.” I think that made the assignment worth it to me even if everyone else thought it was busywork. :)

I have another round due in a couple weeks and then I may try asking them the same question. I’ll let you know what responses I get. Thanks again for posting this!

• This is a super late response, but I love the idea of including “Lockhart’s Lament”! I whipped of a digital page I may use next year (http://explore-math.weebly.com/) and added that in!

2. […] felt like my first venture into “Explore Mathematics!” was so successful last quarter with my Advanced Precalculus kids that I wanted to build upon that. So this is what […]