Friday, August 11, 2017

Math Songs to Calm the Amygdala

(cross-posted on

I have been reading Culturally Responsive Teaching and the Brain and it is fantastic. Lots of nuggets to apply immediately in the classroom, as well as a bigger picture to think about. One of the early gems from the book was about how many cultures are still steeped in oral traditions, and the effect of that is that -- depending on their home culture -- some of our students' brains are primed to learn that way even in the classroom. When we provide instruction primarily through writing, not all students process it at the same rate depending on their home culture's dominant way of passing along information. I was on the plane when I read this particular part of the book, and I thought about how I find myself repeating the same information often to groups of students, instead of resorting to music to help them encode that information. I put the book down and wrote three songs to use with my students next year, that encapsulate some of the basic information that I think everyone should really internalize. I don't think teaching by song is in contradiction to "Nixing the Tricks", because really a song is not able to provide the student with all the things they will need to be able to do. They still need a lot of knowledge and understanding outside of the song to be able to flexibly and accurately execute the skills, but if they can memorize the song, then maybe it will provide them with a starting point to be/feel less helpless when approaching intimidating problems. That's all. It's a way of quieting the amygdala and to encourage students who learn through a different sense, to be more independent.

Here are my songs! I wrote one for linear functions, one for math faux pas's (the mistakes that kids often make in simplifying expressions), and one for solving equations. I am not the most musical person, so they are written to mostly kiddie tunes as I sing kiddie tunes to my baby everyday. My thought is that we would sing them as a class sometimes, and I would give extra credit to students who wouldn't mind performing it in class on some days before the assessment. The idea is really to encourage the kids who struggle with tests to learn the songs by heart before the end of the unit, so that it can serve the purpose of building their confidence before the test. 

What are your thoughts? Do you think they are too procedural still? Do you think that songs can be used in the classroom to complement student understanding, rather than to take away from it?

Saturday, August 5, 2017

Brainstorming for a Mini-term Course

(cross-posted on

To the two of you who still have my blog bookmarked, I am back! Back from maternity leave (see picture below of a tiny person I am now responsible for), and back in school mode now that The Precious has started daycare.

One of my first orders of business is to research options for teaching a new class during a two-week mini-term in the 2017-2018 school year. The format is going to be as such: two weeks straight, 6 or so hours a day in that same class. This mini-term is a feature that is new to our school calendar, and in spite of having some anxieties surrounding teaching a new course in such a compacted time frame, I am excited about the possibilities! As far as I understand, the students don't get graded, so it is purely for enrichment. Which means: 1. Anything goes, as long as there is educational value. 2. No alignment to an existing curriculum is needed. The format also means that it needs to be deeply engaging - because can you imagine being stuck with kids for two weeks doing something that they think is boring?

Okay, so my three ideas thus far are: 1. a coding course 2. a robotics course 3. a social justice and math course. I researched these options and want to just lay out the details, both for me to come back to and to gather some feedback at this pre-planning stage.

Option 1: Coding

I reached out to my friend Sam C., whom I had met at PCMI a bunch of years back. He had recently mentioned on social media that he taught a course using the curriculum, and that it was fantastic. I looked into it, and it is! They have a free curriculum called CSP, Computer Science Principles. For a two-week course, I would start with Unit 3, which is introduction to computer science. The lessons are thoughtful and accessible -- for example, Unit 3 starts off with kids writing verbal instructions for their partners to draw basic geometric shapes on paper. It is like that build-a-PBnJ-sandwich activity that is very popular. It then progresses to the students drawing basic shapes by giving instructions to a computer -- a smooth transition from paper to coding. Then it asks the kids to find the lowest value from a physical row of cards (as manipulatives), and then again to teach their algorithm to a computer. Slowly, it starts to introduce more functional concepts such as parameters and encapsulated logic. All of this within Unit 3! Then, because of the nature of the mini-term lending itself to doing projects, the kids would move on to Unit 5, which gets the kids to start building apps. Sam also did the same with his class, and he said the kids got really into it! (My husband, who also builds apps and writes software professionally, thinks it's not only an essential skill for our students, but also something they would surely get excited about. He had independently recommended teaching a Build an App course to me, before I talked to Sam!) Anyhow, makes it really easy. They have a sandbox called App Lab that basically allows kids to drag and drop visual elements (such as buttons) onto a page, so that kids can focus their time on programming the desired reaction in response to the user-action. (Here is a video that gave me a good idea of how it works.) The programming concepts can ramp up fairly quickly from there, which allows for both differentiation and creativity in the students' apps. (I would have to do more specific playing around prior to teaching this, so I know what is realistic within the time frame.) Sam also recommended a similar sandbox from MIT, called App Inventor. I haven't had a chance to check it out yet, but Sam C seems to prefer it a bit more to App Lab. 

Bottom line: Since I have some coding background (it was my undergraduate study and I had worked in the industry for a bit) and the curriculum is so kid-friendly already, I think I can already hit the ground running and teach this course with fairly high chances of success. It would also give me a chance to brush up on my Javascript programming skills, which admittedly I am very rusty with. (I have been teaching for over a decade! Can you believe it? I have hardly programmed at all in that time.)

Option 2: Robotics

So, back when I first went on maternity leave and thought that it meant that I would have copious time to learn extra skills (Ha! Ha! I die laughing...), I had borrowed a Lego EV3 robot from my friend Danielle, whom I had also met at PCMI. (I mean, if this is not good advertisement for PCMI, I don't know what is.) Danielle, if you don't know, is one of the baddest mofos ever. She went to a robotics camp as a newbie some years ago with Zero prior experience in programming or robotics, and now teaches a robotics course and advises her school's award-winning robotics team. If that's not badass, I don't know what is. Well, back to my efforts to learn robotics. My motivation comes from seeing the cool things Danielle's students do with their robots, and now that our school has hired a couple of new teachers who have experience already with Lego, it seems within the realm of feasibility for us to agree to invest in other teachers to build out our program. 

Bad news: I tried looking at tutorials online, but they're really hard to follow unless you already have a full EV3 set at home (complete with the connectors, which I didn't get from Danielle) and are tinkering along. But even then, I wouldn't feel comfortable running a robotics workshop unless I have BEEN to one, amirite? It just makes sense to me that I would want to see how the pros train teachers to teach robotics, before I would want to turn around to run a workshop for kids. So, I looked into the pricing of such training. I'll list them all here for your convenience. It costs $999/teacher to go to a full-week training course, which has the benefit that they provide all the hardware and run the workshop in person. The drawback is that they don't offer these training courses during the school year, so I would have to wait until Summer of 2018 to go to one. (This might happen, if I get approved.) Alternatively, you can also take an online course, which costs $499/person. The caveat is, of course, that it's online and you have to provide your own hardware. These courses run often, so I could take one as soon as the fall (I think September-October 2017). They also go once a week from 3pm-5:30pm PST, for a bunch of weeks, which is a little hard on the childcare side. (I would probably have to get my husband to pick up Sir Poops-a-Lot from daycare on those days.) Lego also offers trainers to be flown out for a one-day $2500 workshop for up to ten teachers on your own campus, which sounds like it could work out to be a better deal for our school, but my husband reminded me that there is no way they could cover the same depth in one day as in a week or a recurrent class, so it could be pretty rushed. 

Bottom line: I am still super interested in this option, but more as a long-term thing, maybe as a mini-term in 2018-2019. If the staffing numbers work out for me to help teach this course alongside someone who is already fully capable of running the course, that would be fantastic, because then I can learn alongside the kids and maybe run the course the following year. I also think it would be a good idea for our school to really invest in people to build out our robotics program, particularly seeing how it is project-based and goes along well with the mini-term format.

Option 3: Math and Social Justice

One of the visions laid out in the mini-term program is that our course offering is inter-disciplinary. Okay, that makes sense, and it seems to me that our school can really use a bit of social justice math. I know, social justice, so vague and broad. But I sat down and tried to brainstorm today, and I think if I were to choose one issue to focus on, I would choose housing. This is because in Seattle, where I live, housing has reached a crisis point. It's so unaffordable for the average person to live here, and minimum wages are not even close to cutting it.

Okay, so I sat down and did some rough math. Obviously if I were to teach the course, we (maybe the kids) would have to get better numbers. But, just hear me out.

I assumed that a median individual salary in our city for a person seeking to buy a house is $60,000. (In reality I know that there is a huuuuge disparity between people who work in tech, and everyone else. When I looked briefly into it, the median household income is $65,000.) I listed some very conservative annual expenses and concluded that the person could save a maximum of $17,500. (In reality, we know that that's not really possible. That's VERY aggressive saving for this salary. But, let's just say that that's the ideal case.)

It would take this person 10 years to save $175,000. At 20% down payment, this person would technically be able to afford a house that is valued around $875,000. In Seattle, a house can easily cost this much today. (When I looked it up, our median single-family home now costs $700,000 before taxes and fees.) So, assuming that this person borrows $700,000, then his monthly mortgage payment would be close to $3,500. (The standard estimate is that for every $100,000 you borrow, you pay $500 in mortgage per month. So, for $700,000, you pay roughly $3,500 per month. Of course we would do the real math in class assuming 4% mortgage and either 25- or 30-year repayment plan, but it does work out to be roughly the same.)

This causes a problem for the person buying the house, because although technically they had enough down payment, their monthly expense now exceeds what they make after taxes. So, we can work backwards with their new expenses (some good ol' middle-school math) to see how much bump in salary they would need, in order to sustain this lifestyle. It turns out that in my model, the person now needs to be making closer to $80,000 in order to make this happen! WOW! Big salary jump.

So, how can people afford to buy houses? Besides the obvious options (buying a starter property or  pooling together resources with your domestic partner), some people are fortunate to have initial help from family, particularly relevant because I teach at an independent school. We can do the work to see how the math changes if you have more down payment. Obviously, this raises the issue of privilege, and that can lead to a discussion of why economic advantage is a legacy that is often passed on from generation to generation.

This should lead into discussions/research about the rental market. I haven't yet looked, but I think we can pull together some stats on how quickly rental prices have grown in Seattle. We can graph them and research whether that outpaces the general trend in income. In general, as the property value rises, the landlords would need to keep raising the rent in order to keep up with the mortgage on their investment, which exacerbates the displacement of families and communities.

What if someone waits to save up more money to buy a house later? Assuming that the market continues to grow the same way it does (which is exponential and ridiculous... something like 25% or 30% in two years), your savings account which is growing roughly linearly from your monthly contributions, cannot hope to catch up to the market. So you would end up in a worse state in a few years unless your income level changes drastically. That is a very real use case of function models.

(Of course, the argument can be made that that's why couples combine incomes to purchase a home. But it comes back to considering that the median household income in our city is $65,000!)

Other aspects of Seattle's housing crisis that I would want to touch upon in the course, should I actually teach the class, include: gentrification, segregation, and homelessness. 

I found a link from Rethinking Schools that paints some personal perspectives behind gentrification. Why do people sell their house in a neighborhood of rising values? This gives me the idea of reaching out to the community activism groups to bring in housing advocates who work on this on a day-to-day basis, to shed some light on the narratives that affect our specific POC communities. In the article, they also do some easy discrete math — great opportunity to incorporate technology! (A few years ago I worked with my Precalc kids to write explicit equations from recursive forms of similar complexity, and it was challenging but great, because it was anchored in real-world math! That can be a possible math extension for this.)

A little while ago, my husband and I watched a mini-series called Show Me a Hero, that I would love to also show my students as a multimedia link to this topic. It has 6 episodes, so it would take basically one whole day. The show is about how there was an attempt in the 1980s to build affordable housing in a middle-class white neighborhood. It became a racial issue, and (I will spoil the ending for you if you read on...) the experiment worked and the project was a success. I am hoping to use this as a segue to talking about the current homelessness in Seattle, and the various challenges surrounding the sanctioned homeless encampments in our neighborhoods. Granted, I am not very good at leading this type of discussions, so I would probably want to partner up with a humanities teacher for this course in order to up the rigor of our structured sharing sessions.

Ideally, the class can then take a service trip to one of these local encampments! In my neighborhood, there is one such area called Nickelsville. I know that volunteering there is possible, because I have a friend who used to do it often. (Our school's ethos goes along with doing such trips as well. We regularly take kids to food banks to help out.)

So far, all of these are just rough thoughts. If I did such a course (which I would like to at  some point), I would like some project that ties it all together. It could be a reflective assignment, or it could be something like interviewing adults and kids to incorporate their thoughts and voices into our class. It could also be a math project, looking at data from different cities and trying to coalesce them somehow into a meaningful conclusion.

But, regardless of which routes I go down, I would love it if you could point me at any resources that you think might be helpful! What are in my blind spots? I know that, for one, I have not yet considered the appropriate audience for these classes. I vaguely think they would be more appropriate for high-schoolers, but is that necessary and true? Have you taught a mini-term before, and do you have any tips for me in terms of structuring each day? Thanks in advance for any tips you might have!