Monthly Archives: June 2012

Letters to a First Year Teacher: The Compilation

Dear First Year Teacher,

We have all been in the same place as you as your are about to start your first year teaching and we wanted to give you some thoughts and advice from our individual perspectives. Below are 19 different letters from teachers of various subjects (mostly math and physics). The letters are also compiled as a Google Doc or pdf for those who would prefer the advice in that form as opposed to clicking through various teaching blogs. If you are looking for great teachers to follow on twitter and great blogs to read, this is a wonderful (though of course not complete) list that would be a great place to start.

*Note 1: If you would still like to submit a letter, go for it! I will update, and Drawing on Math will still compile them here.
*Note 2: The quotes I picked for each post are not the titles of the original posts as written by the writers – they are somewhat random quotes from somewhere in their letter that I thought were poignant, unique, or interesting.

Sam Shah, @samjshah, on Continuous Everywhere But Differentiable Nowhere

Daniel Schneider, @MathyMcMatherso, on Mathy McMatherson

Jason Buell, @jybeull, Always Formative

Grace Chen, @graceachen, on Educating Grace

Kelly O’Shea, @kellyoshea, on Physics! Blog

Breedeen Murray, @btwnthenumbers, on The Space Between the Numbers

Mimi Yang, @untilnextstop, on I Hope This Old Train Breaks Down

John Burk, @occam98, on Quantum Progress

Sophie Germain, @sophgermain, on A Brand New Line

Bowman Dickson, @bowmanimal, on Bowman in Arabia

Michael Pershan, @mpershan, on Rational Expressions

Fawn Nguyen, @fawnpnguyen, on her Untitled Blog

Tina C, @crstn85, on Drawing on Math

Joe Kremer, @josephlkremer, on Observations First

Renee, @approx_normal, on Approximately Normal

on Room 289 Math

Stephen Lazar, @SLazarOtC, on Outside the Cave

Emily H, posted here on Bowman in Arabia

Tom H, posted here on Bowman in Arabia

[Updated 7/2]

 Kate Nowak, @k8nowak, on f(t)

Laura Kinnel, @LauraKinnel, on Continuous Reflection

Jackie Ballarini, @jackieb, on Continuities

Lance Bledsoe, @bledsoe, on his Untitled Blog

Guest Post: Letter to a First Year Teacher from Emily

*I had a few friends submit letters that do not have blogs, and I couldn’t figure out a great way to include them other than just making a post on my blog with their awesome advice.*

This is from Emily H, who teaches history at the same school as I do in Jordan and is a dear friend of mine.


Dear first year teacher,

I’ve heard somewhere that the first three years of teaching will determine whether or not someone stays in the profession – if you make it past three years and still have a passion for it, then chances are you will remain a teacher for the majority of your career. I suppose it is because I just finished my third year of teaching that this fact came to mind when I thought about what to write in this letter – why is it after three years I have decided to continue teaching? Why has it not lost any charm, and in fact why do I feel even more secure about my decision to be a teacher than I did my first year? Because I can tell you that I had some experience teaching at university before I chose to teach at a high school, and when I put my pen to my contract and decided to teach at a high school, I had literally no idea how I was going to feel about it, or whether I would stay longer than a year. So now, as twenty-seven months or so of teaching are behind me, I want to reflect on why thankfully this has been a successful journey and offer advice to you, because in all honesty I am not sure this profession would have been as rewarding without the help and advice from the other great teachers, both young and old, that I have had the privilege of working with. The organization of my ideas below is rather random, but I hope they provide you with both theoretical and practical advice.

There is only one word you need to know about teenagers: “I”
Before I left my former job to start teaching high school, I had a lovely farewell lunch with my employers, one of whom had a wife who worked as an educational consultant. Her advice above in bold was one of the first I ever got about high school age students, and it has proven to be extremely helpful to remember the image of her telling me this over our food. The essence of her advice is that teenagers are going through a phase of their life in which everything is about them – they will make mountains out of molehills because they can only see a problem from their own point of view, and they will explain everything from only their point of view. This little piece of advice has helped me find eternal patience when dealing with students who are otherwise frustrating – it helps me to remember that they are (depending on the extent to which their parents have encouraged this kind of self-involvement) incapable of thinking beyond themselves sometimes.

Don’t get me wrong – this isn’t the case with every teenager, but it does help to remember that it is our job as adults to not only provide them with the ‘traditional’ education of knowledge and skills, but also with a moral compass that guides them to thinking that the world is in fact not always just about them. So when you find yourself completely unable to fathom why a student is behaving the way they are, it is helpful to remember this little piece of advice and have a little patience, because in fact it is often those kids who are most self-involved that need the most mentoring.

Classroom management
Do not underestimate how important it is to set the right tone the first week of class. The most important thing you can do from the start is to get the students to trust you. You need them to trust you both in terms of knowing that your class will be productive and that you will, in general, be predictable both in expectations and content. So put time into thinking about how you will structure the class – will you give them a guideline at the start of every week that explains what they will learn and the homework in advance? Will you always write the topics to be covered on the board before class? What routine can you create so that students know it is time for class to start?

Think of yourself as a coach more than a teacher. You want your class to work as a team as much as possible, so don’t ever have what’s meant to be a class discussion, for example, without the whole class listening. In fact, that will role model that you want them to practice the skill of listening.  The more you can create a climate in which everyone feels like they are responsible for the material, the better your class will run.

Don’t be afraid of silence! If you ask a question and there is an awkward silence, have patience. The students may simply be thinking. This means you want to avoid calling on the people who immediately have their hand up (if I don’t have to think because I know someone else will always be chosen to answer, I won’t) and when lecturing don’t hesitate to pause and give students a chance to write – it may feel awkward for you up front, but for the students it shows that you value their ability to be engaged.

Be aware of what every single student is doing during class. This is easier said than done if you are in a room with over twenty students, but the more you are able to do this, the more your students will come to trust that you are there to ensure they are learning. If students know they can get away with playing on their computer for half of class, they will. If they know they can disappear to the bathroom for over ten minutes, they will. Students know in what class a teacher is more likely to be aware that they are engaged, so do not get so caught up in getting through class that you lose what is even more important: as much of their attention as possible.

If students are chatty in your class, it is completely unproductive to yell over them. One of the best methods of classroom management that I learned before I started, and which has proved completely invaluable to me, is using silence as a way to control the room. It may seem counterintuitive, but the best way to get students to calm down and focus is to actually remain silent in front or use less hand gestures to individual students so that they are quiet. This strategy is also great because it role models calmness and patience rather than frustration, and it also allows the leaders in the class to silence their own peers.

Get advice from other teachers
I was lucky to work with colleagues who enjoy talking about teaching and who offer practical feedback. If you have others as a resource, take advantage of them! Visit their classes, talk about your problems and or successes over dinner – this has probably been the greatest key to my success because the ability to bounce ideas off of people helps us get excited about getting back into the classroom. If you feel embarrassed to either ask for or share information, this honestly may not be the right profession for you. And don’t just talk to people in your field – some of the best lessons I have ever developed came from talking to teachers in completely different subjects.

Think about who you are
I was once told that in high school the teacher’s personality is of fundamental importance to how much a student will engage in a class. Now I know that may sound awful, and it’s an ugly fact, but to a certain extent it is true. As I said in the first bolded bullet point, teenagers are very self-involved, and so they will allow themselves to gravitate toward those whom they feel they can be most comfortable with, and they will be less forgiving if they do not like you, even if we all know that is very selfish. So it is really important that you are comfortable with yourself before you step into a room of teenagers – you will be dissected more than you have probably ever been, more than even on any first date, but if you are ready for it and can remain true to yourself, I can guarantee the students will like you. It is when you are uncomfortable, or try too hard, or try too little, that they get turned off.

Variety doesn’t mean effective teaching
Don’t feel like your lessons need to have a huge amount of variety and don’t be afraid to be simple. While it is smart to have lots of tools when making lesson plans, don’t be too experimental and irregular your first year because it could make you lose what really matters. Always focus on how your plans allow students to most effectively: 1. understand your expectations 2. reflect on and 3. be able to articulate and/or apply what they have learned. Students may say they want a lot of song and dances in order to do this, but really what they need is a good framework into which they can put content and skills. Mike Schmoker is an author with good advice on this.

Be ready to change the way you teach a subject every year. This doesn’t mean that you completely revamp a class every year, but my best teachers have always been those who constantly reflected on their classes and tweaked it both during and after the year was over in order to consider what would actually work best given new circumstances or information. My worst teachers were always those who stuck to a formula and never changed it – firstly that is bad role modeling if we expect our students to become reflective adults, and second that will make this profession a lot more tedious.

Be ready to think on your feet
This is advice that applies particularly during your first year, but then also for the rest of your professional life. I think the best teachers are those who find the somewhat paradoxical balance that leads to structured classes which encourage the development of organic discussion and learning. You can’t hesitate to let go of what you may have planned nor of letting the class develop into a student-centric place, but you also can’t hesitate to rein in students and know when it’s time to take the lead as well. Finding this balance may not come immediately, but with practice it will become easier.

Don’t hesitate to listen to students
Teaching requires thick skin – there are days when students will validate your very existence with their profusion of gratitude, and then there are days when you feel like you are achieving absolutely nothing and that your students are unbelievably frustrating people. Yet overall it is important that you listen to them. Don’t hesitate to give anonymous surveys in the middle and end of the year – you will often be pleasantly be surprised by how helpful student feedback can be, particularly if you have created enough trust as a team that they are unafraid to offer both unconditional praise and productive criticism. Yet I will also recommend you design the surveys yourself and tailor it to your class. Do your research and consider what kinds of questions make for productive feedback.

Don’t expect immediate results
If you are someone who wants immediate results, whether it be in expecting students’ writing and thinking to improve or to know that you have made an impact on a student in some way, this may not be the right profession for you. This is not to say you won’t actually witness such transformations – I certainly have and they have made this job incredibly rewarding – but you also need to remember that you may be doing a lot of good that won’t be recognized for years to come, so always keep that perspective in mind.

Finally, to end, I will offer one last piece of advice: keep a journal of how your teaching went. There are a couple of ways you can do this, I am sure, and I will suggest two. First, you can try to update it daily, even if it’s just a few sentences, so that you can reflect on what worked and what didn’t. Or, secondly, one friend of mine keeps a journal only with those teaching moments that were positive. She decided to do this because anytime she got frustrated she could pull out the journal and remember why she is doing this, and her journal has gotten pretty long. May that will be the case with you as well, and good luck!


Guest Post: Letter to a First Year Teacher from Tom

*I had a few friends submit letters that do not have blogs, and I couldn’t figure out a great way to include them other than just making a post on my blog with their awesome advice.*

This is from Tom H, a friend from college who teaches middle school in China. His advice isn’t written out in prose, but the way he organized I thought was really interesting – problems he was initially having, how he addressed it, and what happened from there.


Student Actions (initial):

1. Seldom engaged in class. Misbehavior negatively affects other students in a serious way.

2. Misbehavior spreads throughout the classroom. Other teachers become involved and punish students.

3. Students act like little kids.


Teacher Actions (my reaction):

1. Consistently maintain high standards, both behaviorally and academically. At the same time, differentiate work and goals for students that really struggle.

2. Emphasize student successes/improvements over student failures/shortcomings – both publically and privately, both in terms of behavior and academics

3. You can’t force change in your students – be a positive influence and then be there for them once they show a willingness to improve


Student Actions (after above teacher actions):

1. Students begin to quiet down in class and engage in the material. Students that were previously misbehaving misbehave less. Students that were distracted now have a healthier classroom environment and can concentrate better (and for those that were influenced to misbehave, they became more interested in the content and began to do better in class).

2. Instead of students talking, randomly switching seats or throwing things to get attention, they sit quietly and do their work to get your attention. Students who do well see that their success, whether behavioral or academic, has positive outcomes. Seeking recognition, students work harder.

3. Students naturally mature throughout the year. It’s our job as teachers to be patient with students, be a good model for them to look up to, and eventually help them to change when they feel they’re ready. We can influence them in small ways and encourage them to change, but I haven’t had much success with any method other than ones that require patience. We have to be there for our students when they’re ready to change.

My Advice For a First Year Teacher

A few things before I get to my letter to a new teacher… first, I must give credit where credit is due for “Letters to a First Year Teacher.” This was not really my idea. I was trying to collect advice for a friend of mine who is beginning to teach and crowd sourced Twitter for ideas. I was going to collect these ideas in a document and send them to her (and post on my blog for others to use).  And then this mini conversation happened… while I was asleep (read from the bottom of course, like on Twitter).

I know that some people get their best ideas when they are asleep. I guess I do too – they just happen to be from other people.Thanks to Sam and Tina for the inspiration and really thanks to Bree (@btwnthenumbers) for the actual brilliant idea.

Also, I will compile the submissions in the next few days into both a blog post and a pdf. I picked a really silly time to do this – I’m leaving Jordan tomorrow for the summer and have to pack for 2 months of traveling around and seeing friends before making the basically day-long trip back to the US and then dealing with crazy jet lag when I get there. So the compilation might take me a few days. But first, I have to submit my letter! A lot of the other ones do a great job at helping teachers prepare for the psycho-emotional-roller coaster that is your first year of teaching, so I am going to focus more on the mechanics of teaching (and essentially post the document of advice I was going to create anyway instead of a real letter).


Dear first year teacher,

It’s almost silly to wish I knew what I know now when I started teaching. What a dumb cliché the more I think about it. No matter how much you read now, or think you know before you start, teaching is hard, and the best way to learn it is just to get out in the trenches and do it (though I might be biased as someone who loathed the undergrad education classes I suffered through before I changed my major from education to math). That said, it doesn’t hurt to have an idea of what issues you are going to face, and I think that’s the real power of reading letters of advice from current teachers. I’m going to split my advice up into the three real areas of day-to-day teaching life: planning, teaching and reflecting.


Focus on how students are learning the content more than the content itself. Despite what first year teaching Bowman might have thought, a 2-3 page narrative of what you are going to say in class not only takes forever to make but isn’t really that useful in the end. The content is important, but the hard part of teaching any subject isn’t the subject itself. So instead of poring over the content, try to develop a grab bag of learning modes that will help you teach the content (like in Sam’s Virtual Filing Cabinet or Kate’s various review modes or some of my skills instruction ideas). The more structures you have, the quicker planning will be and the more students will learn.

Plan in 10-15 minute chunks. I use a table in Microsoft Word to plan, and each new chunk is a new row in the table. This is for a few reasons. First, you have no idea how long things are going to take in the classroom your first year, so planning in chunks allows you to move stuff around easier, like moving something to the next day if you don’t finish, or starting something up that you thought you were doing to do tomorrow. Second, the attention span of teenagers humans is about that long, so planning in chunks allows your classroom to flow more easily and keeps students engaged. Lecturing isn’t bad, but lecturing for 45 minutes is. Having students do practice problems alone sometimes works great, but expecting them to sit there and practice alone for 45 minutes is asking a lot. If you follow the previous bullet point and get a tool box of learning structures, this makes planning in chunks even easier.

Beg borrow and steal. It would be fun to try to figure out how many times the class “Algebra II” has ever been taught – not only are other teachers okay with you stealing their ideas, they really encourage it (and they probably stole said ideas from someone else in the first place). I love trolling around blogs for ideas (again, Sam’s Virtual Filing Cabinet is a good place to start for math), and really wish that had  done more of the same idea-seeking with the teachers in my department at my school my first year. Observe lots of classes and ask, ask, ask other teachers for ideas all the time. No one will think you’re stupid for asking. In fact, they will think you’re smart. Also, if you are looking for some books to read before you start with some steal-able practical nuggets, two I would recommend are Lemov’s Teach Like a Champion and Wong’s First Days of School. Both can be cheesy at times and have some dud advice mixed in with good tips, but I remember reading both of them and being so thankful that they got me thinking about the right things and gave me some practical ideas to try.

Assessment is part of planning – consider Standards Based Grading. A real game changer in my classroom was switching to Standards Based Grading (SBG), which is a system of grading where students are grading on specific learning objectives (rather than a percentage on a test) and those grades evolve over the course of the term based on student learning (instead of grades reflecting how much you knew at the time). Even if it is too much to adopt in your first year, reading about it is so worth it to think about the role assessment plays in the classroom. My favorite takeaways: learning objectives should be clear and well defined, assessment results should be used to guide both student learning and your teaching, and learning should be thought of as a process instead of a one time thing.


Be flexible. Despite all the planning you do, very few things in a room full of teenagers go according to plan. I am still so bad at this, but I’ll say it anyway – be prepared to change your plan on the spot to adapt to what has happened in the classroom. My first year, I taught 3 sections of Physics, and no matter how bad a lesson plan went in the first class, I would do the same thing again in my other two classes and have another two painful 45 minutes. Why Bowman, why?

Be positive and patient and don’t take things personally. I used to pretend every morning that I was putting my “patience pants” on, and even considered writing the word “patience” in the waistband of all my pants. Kids do all sorts of annoying things, and it’s almost always just because they are in their own little world. It’s almost never a personal attack on you, though it often feels that way (“I put all this work into this lesson plan and they are ruining it by doing blah blah blah, they don’t appreciate my work”). And even if it is a personal attack or they are being annoying beyond belief, getting angry and impatient never solves the situation. You set the tone in your classroom with your demeanor, and the more positive that can be the better.

Don’t forget to teach them how to be real people too. Far more important than the content you teach are the “habits of mind,” as my headmaster would call them, that students learn from your classroom. Teaching students how to organize themselves, take notes, ask questions, receive feedback, work in groups, be real people etc. felt like a huge waste of time at first (we must cover more material!) but I have come to understand more and more its importance over the past three years. By the way, this is really really, really, really hard at first before you get a sense as you see kids succeed and fail what habits of mind are important.


Change how you view mistakes. I wish I had known about Dweck’s Growth Mindset before I began teaching, because I think I wouldn’t have been so hard on myself about all the mistakes I made my first year. Some things will go as you planned, but others will be really messy and still others will go horribly wrong. It’s all about how you react to these mistakes. View everything as a chance to improve, a learning opportunity, rather than a moment of failure.

Find ways to document your work. I think the most important thing I did my first year was organize myself very, very meticulously. I had every lesson plan, every worksheet and every assessment saved on my computer and carefully organized by unit. This helped so much in the year after in planning class because I could see what I had already done. What I wish I had done in addition (and will start this next year) is spend 2-3 minutes at the end of every class just writing a quick reflection about what had happened. I think that will make old work even more useful.

Solicit lots of feedback. If you view mistakes as opportunities to learn, you can become more comfortable asking others for feedback on your teaching (PS I am really good at giving advice about things that I still struggle with myself). Invite other teachers to your classroom and then ask them lots of specific questions about what they saw (don’t let them get away with a simple “it was great!”). Poll your students often (every couple of weeks) about various things. Ask them specific questions about things you feel like you are struggling with and give them opportunities to make observations of their own. I still find this painful at times, but it is so helpful in improving my teaching that it is totally worth it.

Take time off. Period. I take every Friday off as a rule (before you think I am crazy slacker, our weekend is Friday-Saturday over here in Jordan). Teaching is so consuming, and is one of those jobs where you could fill up any amount of time that you have with work. I knew I was going crazy at one point last year when I started having dreams about catching my Physics students drinking. If that starts happening, chill, work out, read books, watch TV, hang out with friends (but don’t talk about school) – even if it means your lesson plan wont be as meticulously planned as you hoped.

Best of luck,


Call for Advice for New Teachers

[Edit: Here is my final compilation of the letters, also available at Drawing on Math]

I have a few friends that are starting to teach this upcoming school year and they emailed me asking for advice. It feels a bit strange being asked for this advice, as I still feel so new myself, but I realize that there is so much that I would want to say to someone starting teaching to help them along what is inevitably a difficult experience. From a quick poll on twitter, I realize that everyone else has so much to say too… and it’s not always the same things! So, with some encouragement from twitter colleagues, I am collecting advice for new teachers.

Please help the first year teachers in the world by writing a letter to a new teacher.

Include advice, anecdotes, resources – whatever you want! It could be as long or as short as you want. I’ll give everyone a little more than a week for submissions, and then I’ll compile the advice in a blog post with links to your blog (which could be a really cool jumping off point for someone trying to join the blogosphere) and also in a document if you have new teachers that you want to just send something.

Just make sure to mention me on twitter with any submissions (@bowmanimal). I’ll compile everything between blog posts and tweets (and @crstn85 will compile blog posts at Drawing on Math’s #matheme page too, so it would be good to add that hashtag too). If you don’t have a blog or twitter, feel free to email me submissions to me – bowman.g.dickson at gmail dot com.

Epic Ginormous Math Portrait… of me.


Okay, this was EPIC.

After the seniors graduated, I had about 2 weeks of class remaining, the only problem being that I still had three juniors to teach… I needed to do something with them, but pushing forward in a math curriculum didn’t make any sense. Instead, I wanted to do something fun and give them a chance to be creative and do something they could be proud of, so I proposed that we partake in some sort of epic math art project. I gave them tons of ideas from MArTH Madness at Saint Ann’s (and they loved the word MArTH), but they eventually decided on doing something completely different…

Behold the final product!

What is it? A ginormous mathy portrait of my face (if you were thinking about saying something snarky about me being egotistical or something, you’re too late, everyone in the math department has been ribbing me for a few weeks now, but I SWEAR they insisted on doing my face). It is 60 inches by 40 inches (yeah… I said ginormous) but it’s made of 1080 small pieces of paper that are 1.5 inches square. We colored each piece of paper individually using oil pastels and put a math symbol on each one then arranged them and glued them on a canvas. So it’s a math teacher’s face… made of math symbols. YESSS.

It looks better the further you walk away from it… here is a zoomed out version (feel free to squint too, if you are so inclined):

But it’s also pretty cool close up… here are some close up views:

20120606-121215.jpg    20120606-121226.jpg

20120606-121201.jpg        20120606-121236.jpg        20120606-121136.jpg

The students finished it today while I was proctoring an exam, and left me this sweet note at the bottom – so nice! What a fun way to end the year. Now I just have to find an appropriate place at the school for a 5 foot tall picture of my face…

Goodbye Card for Seniors

I had a really rough two weeks or so with my seniors before they graduated. There was a lot of tension over stuff that needed to happen for class that wasn’t happening, and a lot of annoying things that I admittedly I was taking far more personally than they were meant. Taking inspiration from Sam’s annual senior letter (because basically half of the things I do are from Sam), and some of the nice ideas expressed in Elissa’s post about Seeking Your Own Compliments, I decided to write quick handwritten notes to all of my seniors to give us BOTH a chance to express how we really feel before they left. It was really fun because I got to reflect on my whole time with them and got some really sweet responses. Also, I love drawing and had a great time drawing this, and coloring it in with Photoshop! I should have done these on real paper, but I was too shy about giving them cards in person, so I made a pdf for each student and wrote on them with a pdf editor and emailed them. I’m too awkward for real life, as are many people in my generation.

Here it is:

(It’s a picture of me in front of my board, and in my speech bubble is the word “مبروك” which means “Congratulations!” in Arabic)

Project Implementation Reflections and Questions

I really enjoyed doing final projects with the kids this year (which may be patently obvious considering that this is my 6th post on the topic). It’s such a fun way to end the year, seeing them get excited about doing something interesting with Calculus and coming up with ideas about math that I never would have even dreamed of.

But projects can also be very frustrating, and hard to implement. Here are the things I struggled with this year. I’d love any feedback or tips.

  1. Since these projects were very open-ended, some students felt a bit lost, and I struggled a lot with how much guidance to give and similarly, how much to let them struggle. I just find it so hard when we have such a short amount of time to see them getting thrown off in a crazy direction, especially if it’s going to lead them to a lot of useless work. I tried so hard to “be less helpful” but I just couldn’t resist sometimes! Part of me feels like I am stealing a bit of a learning opportunity from them and part of me feels like I am just advising them to help guide their crazy teenage thought process. Also, some students just started working on their projects without really knowing why they were doing what they were doing (they just wanted to do “something about optimization”). I wanted to help them do something for their idea without turning it into my idea, but I’m not sure how well I did at that.
    THOUGHTS: I think that I am going to try to have them submit proposals next year where they present some sort of thesis, or a guiding question they are going to answer in their project. This might get them to plan out their project a bit better before starting, give me a chance to give good feedback and also give them an overall question which will really guide their whole project.
  2. One thing that I was continually frustrated throughout the week in class that I gave them to work on the projects was that students did not work very efficiently, leaving much of it for the end. Part of it was that they just had so much time in class, but part of it was that I have no idea how to help them structure their own project to use class time well. I had tons of students show up without materials to work on their projects, and even some who would sit there and do nothing telling me that they were just going to finish at home.
    THOUGHTS: I wanted to do a midpoint deadline of some sort, but because all the projects were so different, it seemed really weird to me to organize something like that. I might try having them make a schedule in the beginning of the project, but I’m not sure how to help them stick to that, or if that is even worth all the work that it would be.
  3. Similar to supporting them in organizing their time, I struggled helping them work well together with each other. I think group work like this is crucial in high school to learn how to structure time with someone else and communicate about a project, but the students were terrible at this. They would do things like not show up to class without telling their partner, even though they had all the materials. I even had to mediate an email war between two girls who were flipping out at each other about who was doing less for the project.
    THOUGHTS: Maybe this isn’t something that I need to do something for, and maybe this is something they just have to learn by doing the project, but perhaps I could find ways to help them structure their roles in the project beforehand, or maybe just do more long-term projects like this over the course of the year.
  4. Last, I really want them to show off their work to each other, but I’m not sure how to make class presentations anything but the boring yawn fest that they tend to be. Students did some really cool things, but were really bad at explaining those things in a way that the class could understand. Also, it’s really hard to listen to two full class days of presentations, even for me, and it’s really hard for students to get anything out of the presentation when they are not really expected to engage in a meaningful way (not one of the presentations was interactive in any way).
    THOUGHTS: I’m looking for some sort of other structure to make it more interesting. Maybe some sort of gallery walk type structure? And I also want some formal way to get those listening involved so that they really pay attention and learn – some sort of commenting system, or interactive component. It’s very hazy in my head, but this is something I am going to try to flesh out over the summer.

Any ideas would be greatly appreciated!

(Also, below is my rubric for grading these projects)

Calculus Final Project Spotlight: Packaging Consultants

And the last project I am going to detail…

A few students did a pretty standard, but well done optimization project investigating different can shapes to find which one is the most efficient (Sam profiled his kids doing a very similar project, I loved reading his students’ reflections on it!). Then they redesigned the cans to help companies lower cost. The reason that I am profiling this because it made me realize what students find interesting in this whole optimization nonsense – I brought in cans in the winter when we first learned optimization, and we did something similar, but we never talked about the issue that really got other students’ attention…. money! I had been focusing on the shapes, but I should have been focusing on money! (Seems like a super “duh” in retrospect, and it’s not anything original, but helpful to realize nonetheless).

The students did tons and tons of calculations, but what I really loved is that they compared the price of producing the current can that the company produces and the price of producing the ideal can. They looked up the price of aluminum and estimated (or looked up? I’m not sure here) how many cans per day a factory would produce. After a bunch of multiplication, they showed that tiny, tiny changes in the shape would result in savings in the hundreds of thousands of dollars range for a year (see red number below), which is super cool.

Also, they had a really nice framework for their project. They pretended they were a packaging consulting company and even came up with a logo and a name that combined their names. I thought that was great!

NEXT YEAR: I am going to frame my optimization unit much more in the way these students went about it. I feel like this is a complicated mini experiment in terms of #anyqs – the students found for me what the actual interesting question is. For me, the shapes of the cans themselves is interesting (especially that it ends up being such a beautiful ratio), but I think a lot of kids were really amazed at how a small change in the size of the cans can result in huge savings and led them to wonder why all cans aren’t shaped the same way. So, thanks for helping improve my curriculum, (now former) students!

Calculus Final Project Spotlight: Math of the Pilgrimage (Hajj)

A student’s mother is completing the Hajj this year, the pilgrimage that Muslims take to Mecca. This is one of the five pillars of Islam (along with prayer, fasting, charity and testifying that there is only one God). All physically and financially capable Muslims must carry out this pilgrimage at least once in their lifetime. This student based her whole project on the Hajj and calculated many different things about it. Specifically, she calculated:

  1. How long it would take to complete each part of the Hajj (once you get there, there are certain rituals during which the pilgrims walk to various places). She used aerial photographs and official information to measure the distance (around 40 km!) and then used an average person’s walking speed to estimate that each pilgrims walks for around 10 hours during the Hajj.
  2. How many people can be expected to attend the Hajj in the future given data from the past 10 years and assuming exponential growth. She used previous data and the basic exponential growth model to make predictions for the next 30 years.
  3. How large the current area around the Kaaba is (the holiest site of Islam around with the Hajj is based). She used GeoGebra and Google Earth software to measure the area.
  4. And how much the area will have to increase in future years to accommodate the extra pilgrims. Based on her predictions of the increase in the number of pilgrims, she mapped out how big the area around the Kaaba will have to be for the pilgrims to all have the same amount of area. She thought it was cool they they would have to restrict the number of pilgrims, or knock down highways in order to keep the area per person the same.

The math wasn’t perfect and there were some crazy assumptions made, but I absolutely loved this project. It was from someone who had told me in the beginning of the year that math wasn’t her thing, and it was really cool to see her get excited about the project because it applied to something really interesting. All the math was very well motivated and taken from a wide range of things that we did this year. Great stuff!

NEXT YEAR: I could see doing some sort of city planning project involving Google Earth that somehow involves population growth. It would be really cool to look at current rates on population increases in areas and see what that would mean for the physical space. I am so happy that a lot of these final projects have translated into great teaching ideas!