The Calc unit is fairly straightforward: here are some of the big ideas, hey lets learn some notations, oh noes division by zero?!, take some deep breaths it’s just a limit stop freaking out type of stuff. After doing some work with the delightful Chris Sangwin, I have chosen to play around with the following piece of information (and hopefully some geogebra modeling) to take polynomial long division to a new level in precalculus:

Given a polynomial P with degree n ≥ 2, the remainer when P is divided by (x – a)² is the equation of the tangent line to P at x = a.

Boo Yah. Go try a few examples–it’s rather fun. I am going to set up the kids w/ the long division and then have them graph the original equation in geogebra along with the remaider equation and then have them write down what they notice. I have yet to come up with anything practical as it’s not all that useful for finding extrema, but I need to think about it some more.

Oh, and please feel free to shoot me down if this is wrong. My working knowledge of Taylor Series is rough at best and that’s where this idea comes about.

I chose prezi as a presentation format. You can find my prezi here. I tried to keep the text minimal and just use the presentation to make points and show a few graphics, so I’m not sure how easy the prezi will be to follow without having seen the actual talk.

the highlights

I stumbled onto blogs in a move of desperation my 3rd year of teaching. I’ve talked about this before, though, so I’m not going to belabor the whole story here. Suffice to stay, I found online professional development that wasn’t about clock hours that I could partake of on my terms. A few summers later I got to go to PCMI and Sam Shah got me into the world of twitter and blogging myself, instead of just lurking. I hadn’t really looking into twitter outside as something I would see occasionally on blogs or mentioned in the news media in a joking context. Sam also gave a presentation on twitter and blogging at PCMI that you should really go read/watch.

Twitter has been an amazing experience me both professionally and on a more personal level. I have people I consider friends (as in, I would let them sleep in my guest room if they needed a place to stay) all around the country and several outside of the country due to twitter. I find this very cool.

the links

During the presentation I showed a variety of links of places to start for new twitter/blog math people.

First off, if you want to really leverage twitter, you will need to go and make an account. Once you have a twitter account, check out this great list of tweeps compiled by @Fouss.  You can follow as many people as you like and you can make lists if you only want to read certain things at certain times.

I also recommend checking out the hashtag feature. Hashtags are a way to tag your tweets for a specific channel of conversation. For example, #mathchat is something you can search for and see just tweets about math education. #anyqs is another great channel of people sharing videos/pictures of mathematics in the world. Check out Dan Meyer’s post for a great explanation of this channel.

For blogs, I use WordPress, but there are other sites out there. If you want to find blogs to follow, you can start with the blogroll I have at the right of my page. From there, follow their blogrolls, and so on and so on. There’s really all I did in the beginning and it’s lead to a pretty filled reader that I turn to for inspiration weekly. I’m not as good about blogging as I want to be, but I’ve always felt when I do get a post out there it’s really helped me think about the issues and then any comments I get are just icing on the reflective process I’ve already taken part of.

One other thing I shared out was the Virtual Filing Cabinets people have created. Sam Shah has one of the larger ones I’ve come across. Bowman in Arabia even shares out some sweet Geogebra resources in his. If you just want a place to start reading some quality posts, go check out Riley Lark’s Conference on Core Values from this past summer. The topic was about what is at the center of ones classroom and posts came in from all over.

And if you’re wondering how to join in the conversation, don’t feel like you have to do something like write some amazing blogpost and submit it to a virtual conferences. Just get out there and post on peoples’ blogs. Give feedback. Ask questions. Be respectful. In short, come enjoy being a professional with people who are as dedicated to this profession as you get. It’ll change how you teach in the best ways because there’s nothing like knowing your tweeps have your back, good days, bad days, and all the grey in between.

goals of the project, as I understand them
How many of us stay in tune with the maths we did in college? My own background is mostly theory. I have pretty distinct memories of taking writtens and orals my senior year, proving most of the underpinnings of calculus in Real Analysis and studying groups and rings in Abstract Algebra. Number Theory along with Combinatorics/Graph Theory were some of my favorite classes. I have forgotten more mathematics than the majority of people will ever know and I suspect a lot of teachers are like that.

I used to spend hours every day reading/practicing/explaining math. Unless I am willing to do that again I doubt I will get back to being as in touch with higher level maths as I was back in college. On the other hand, I’m amazing at just about all aspect of precalculus. I can glance at student work and spot the problems with minimal effort. I know how to question kids to make them think and prod them to a point that they crave understanding and not just answers. It’s a trade off that I’m just fine with as a math teacher, but that doesn’t mean that I don’t miss the higher level stuff.

The Klein Project is trying to help high school teachers stay connected with research-level maths. I am not going to take the time to wind back up to my senior math major glory days, but I will totally sit down and read a short paper explaining tandem rigging for crew. These papers, or vignettes as they are being called, are meant to be 4ish pages taking a view of a specific topic with a message about the math. A vignette is meant to be read seriously–have out a pencil, paper, maybe even geogebra, and be ready to dig into the topic. While working through Bill McCallum’s paper I chose to prove a few of the equations to myself and it was rather satisfying. I also mocked up a few of the ideas in Geogebra. Outside of PCMI, I don’t often get that feeling of satisfaction with my mathematics anymore. My teaching, sure, but not my math ability.

A goal with these vignettes is to show teachers something beyond what they know. The math detailed in a vignette should be explicit. It should be modern (okay, last hundred years may not sound modern, but for math is totally is). It should have the reader convinced of the importance of the math. Now, that’s not to say that everyone will find every topic riveting or personally important to them–Graeme’s paper on rowing configurations is probably not something I will ever use (more of a single-person kayaker, myself), but that doesn’t mean it isn’t a great read about the mathematics.

One part of the project that I really appreciate as a teacher is that these vignettes are not curriculum. They are not telling me what or how to teach to my kiddos. They are for me as a professional mathematics educator. I love to be treated like a competent professional. I feel like these vignettes will be for me what modern medical journals are for doctors–a way to keep up with the mathematical world. I have things like Mathematics Teacher (which I would like, but NCTM seems to be offline right now), but this is something different that satisfies the mathematician in me.

events from the week and a call to arms. or pens. or tablets.
For five days at the American Institute of Mathematics in Palo Alto, CA, a group of about 30 math researchers, teachers of teachers, and high school teachers worked together to bring the Klein Project out of the planning stages and into the writing/publishing vignette stage. A lot of the talk centered around the content of vignettes; their size, their message, their accompanying materials. The organizers put on a good conference and I think steps were made that will keep the project moving forward. I also think there is a long way to go in regards to how the Klein Project will be brought to the attention of teachers, but it’s all a work in progress.

I am away at a conference right now (it’s super cool, but that post will have to wait for the week to be complete), and I made sub plans for 4 days. I had a folder for each class for each day. Seating charts. Annotated keys. I left cocoa for my sub as a thank you.

Tomorrow the kids are taking a midterm. I know it’s more than awkward to have them take a midterm when I’m not around, but they know exactly what the problems are and have spent the past two months working with them. Each day was planned out with review problems like ones they had seen before to practice and a full key to check their work with at the end.

But that’s not the distressing part of this tale.

Today after school some students talked a custodian into letting them into my class, at which point they took a book (I don’t know which one) off my from stand and some papers out of my desk. One of those papers has been identified as a test given last week. I’ve not been given a clear picture of what happened next, but it sounded like the custodian realized he’d been led astray and reported the incident to the VP. I worry that they took more than was seen, as I know exactly where my key for the midterm was located. At this point in time, I don’t know who the kids are, and a part of me never wants to.

It’s such a breech of trust. It’s such disrespect to the dignity of the class. It’s compounded because I know teenagers; two did the deed, but how many were in on it? How many know, but will never say a word. And if these kids are willing to lie to an adult in order to steal from another adult they see every day, what will they be willing to do when they get older? That’s the real problem I have with the culture of ‘don’t snitch’. What do kids who get away with cheating now do when they are older? Clearly their integrity already doesn’t mean much to them. Will they go on to cheat at other things? Cards? Significant others? The secondary mortgage market? Maybe it’s old fashioned, but a person’s honor should mean something. I cannot comprehend their actions so I feel a bit at a loss to repond to them.

I’m completely re-writing the midterm tonight. In the daily emails I send home I’ll be letting parents and students know what happened. But beyond anger, I’m heartbroken. I work so hard to build up trust in my classes and try to connect with my students beyond the superficial student-teacher dynamic. To have students do this tells me how badly I failed at truely connecting with them.

Too much to think about. I’m not entirely sure how to deal with everything and I’m glad I have until next Monday to think about it. Right now my thoughts have too much vibration to them. Typing this out has helped calm down my physical vibration (I don’t respond well to strong, negative emotions). I work hard to not respond emotionally to students. They deserve to work with an adult. And that’s what I keep reminding myself: I am the adult, I am the adult, I am the adult…

spurs
From pg 13: ”A numerical score or a grade does not tell students how to improve their work , so an opportunity to enhance their learning is lost.” I feel that if students are paying attention to what the 0-4 system I use means, the numerical score does give feedback, but it’s not very specific. Sort of like I’ve told them the answer is on that bookshelf over there, but I didn’t say what shelf to look on.

And then you read stuff like this:

Research experiments have established that, while student learning can be advanced by feedback through comments, the giving of numerical scores or grades has a negative effect, in that students ignore comments when marks are also given. (p.13)

…

What’s worse is that I know that is true. I don’t think I’d ever thought it consciously, but I know it. I’ve watched kids get their skill quizzes back, glance at the number and then toss it away. How many of us have spent too much time writing comments on tests that we know our students will never read? But how much of that is our own fault? Why should the kid bother reading comments if they can’t do anything to make it better? (yes, yes, I know there is an answer to that but I don’t think my students do)

One of my goals this year is to make feedback useful. I’m honestly not entirely sure what that is going to look like, but to start I’m changing the format of my skill quizzes and how my kids line up to retake them.

I know, earthshattering, right? The above would fill the top half of a regular 8.5×11 sheet. Those are the first two skills I started out Precalculus with last year as the vectors until let into trig nicely and checking to make sure they remember squaring negatives in the calculator blindly is problematic is a good thing.

The purpose of the middle column is to give real feedback; “think about…”, “did you consider…”, “what if…” I will not put a grade onto this page, but I will put one into my gradebook that will get entered into the online student/parent accessible gradebook after students have been handed back their skill quizzes. If a student gets a perfect, the comment will reflect that. If a student doesn’t get a perfect, then they need to retake the skill and the feedback will direct them towards what to do to get ready for that. I plan to have some page numbers written down to direct students to examples to read or practice problems to prep with. Perhaps even online options

The last column is to help me enforce my policy that students prepare for the retake. In order to retake the skill, they must show me their corrections. I’ve been very lax on this in past years but I think with the feedback column I can help students be more self-sufficient with how to prepare.

Self-sufficient. Isn’t that what we want all of our students to learn? I feel a bit like a parent telling a kid to look it up in the dictionary, but I don’t think that’s a bad thing. If the kids know they can figure it out and where to look, that’s half the battle in math (read: life) sometimes. I know I’ll be facing kids who completely believe they cannot do math without ridiculous amounts of help and I am hopeful that good feedback will help them learn skills to help themselves without clinging onto those they deem ‘experts’.

future thoughts
I also have thoughts about changing my grading system. As it stands, I take the highest score and it stays no matter what happens. Kid could get a 3, 1, 2, 1 and their score would stay a 3 and that’s bothersome to me. I’ve swept it under the rug a lot because it’s a quiz system for me and I give regular tests and we do projects, but if my grades are going to accurately reflect what a student knows and is able to do, then that is definitely not happening. The strongest contender for replacement is Kate Nowak’s system from back in the day, but that would involve switching to a 0-5 system. I still have about 3 weeks to think this over, though, so I’ll keep y’all posted.

I am not a fan of quiet classrooms. I like it when students are willing to talk, ask questions, and put their thoughts out there. My room is in table groups of 4 so my students have to face one another and, *gasp*, discuss the math they are working on. Now I’m not trying to say I do good group work because I am not that awesome yet, but I do believe that I do a good job creating a classroom environment where students are willing to talk about the math at hand and ask each other questions.

At PCMI Bill Thill put together an evening of 10 minutes shorts for people to sign up and share something they do in their class that they love. I got to go first and my short was entitled “What’s the Question?”, which is a warm up format I came up with second semester last year that I loved and I think did a lot for creating a classroom environment of discussion. Note: I don’t think this is an activity I ‘borrowed’ from anyone, but if you read the following and know of someone else who does something similar please let me know so I can give credit.

the general set up:

Let’s say you are in my Precalculus class and we’ve been working with trigonometry. At this point you pretty much know what sine and cosine look like, you got right triangle trig down, and you can plunk down a 16 Point Unit Circle down in under 5 minutes (yes, I do make my kids do this). Now as my student you walk into class and see the following on the board:

Here’s how it works. Underneath each of those blue tiles is an answer a la Jeopardy. I pull off the first blue tile to reveal the following:

I give students about 30 seconds to absorb the solution and think of a question that it answers. They are allowed to talk to their group mates, but no cross-table talking. I use a die to randomly pick a table. I write out every question students say under the answer. And try not to offer too much commentary. I do this again for B and C.

what actually happens:

I often pull answers from the previous night’s assignment, so kids learned quickly to have out their homework. Since I don’t assign many problems it’s a quick skim before one of them is bouncing in their seat with “what is the solution to number 3?” Sometimes interesting discussions about why that is the solution to problem 3 happens and I will ask other students to work through their logic in explanation. I also accept non-math questions unrelated to our current studies. “What is the scariest expression I’ve ever seen?” “What is the most awesome looking rollercoaster ever?” “How many servings of ice cream did I have last night?” “What is can I phone a friend?” If something like the last one comes up, I move onto another group. I once had ‘2’ up on the board and had a student pull out “what is the only even prime?” That kid is made of win. I also have no problem hinting them in the direction I would like them to take their questions *cough*trigratios*cough*

There is a lot of group debates, good-natured heckling for comic answers, and positive phrase for the groups with mathematically relevant solutions. Sometimes they surprise me with things they learned the previous year. Sometimes they surprise me by not coming up with anything relevant, but that’s useful information to have heading into a lesson. There were a few times the blank faces helped me insert a ‘hey, remember this stuff?’ mini-lesson to get those light bulbs to go off.

my goals:

Priority number 1 for me in doing this is to get them talking in math class. How often do we as math teachers face a sea of silence? I don’t want words to be like pulling teeth. The kids need to see that my classroom is a safe place to talk and be wrong and be silly and say the most dreaded three words: “I’m not sure.”

Priority number 2 is about making connections. Want to make sure they remember some important skills they are going to need from yesterday/last week/last unit/last year before you head into the topic of the day? Sure, you could ask, but kids are remarkable at faking knowledge and faking themselves into believing they actually have things down.

My third priority is inspired by Stephen Colbert’s The Word. For those not familiar, it’s a monologue with text offsetting what is spoken in a humorous way. But the kicker is that the first line of text is always the last line of text, thereby linking the beginning to the end. Here is a shot of what’s under C:

Now, I don’t need to tell math teachers how much the Pythagorean Theorem plays into trig ratios, but the kids? They didn’t even know there were trig identities before today. Now they’re primed. Now they know that Pythag is a key, so now they’re looking for where to make that connection in the lesson. And I have no problem with my kids beating me to the punchline of a lesson.

some fun stuff:

Why put just math stuff? Why not steal vocab words from English class? Plan mini-WCYDWT videos behind the blocks to see what questions the kids have? Something from current events, perhaps? Your own brand of geekery?

technical notes:

Now, I have a SmartBoard, but this works under a doc cam with a sheet of paper and sticky notes or on a whiteboard with three sheets of paper labeled A, B, and C taped to the board. Smartboard is just easier for me to make a page for each class and then compare guessed from the classes at the end of the day (Mmmm, data).

unintended consequences:

At PCMI the teacher topic is always “Making Connections”. The morning session crew do an amazing job of this and it made me want to spend more time on working those connections in between lessons. I cannot wait to do a better job working with complex numbers and vectors and rotation this upcoming year, but that is a topic for another post. What making up the A, B, and C’s did for me was provide a format for focusing on the connections. This is something I suspect we all try to do when we’re lesson planning, but by thinking about necessary skills from the lens of what type of questions do I think the kids will come up with was really inspiring to me. I also kept better focus on only one or two big things per lesson, which for my non-linear self was quite helpful.

But the laughter! How much laughter do you think the average person on the street would say is in math class? These kids are hilarious and creative and geeky and amazing. Kids that would never talk eventually started speaking up with some prompting and even though it often started with “what is 1 plus 1?”, at least it’s a start! I’m torn that I didn’t keep up with this warm up. I used it consistently for the first part of the semester and then I started panicking about time and getting through all the things I wanted to do and it fell by the wayside. Looking back now I can see how powerful it was for the class and I didn’t realize it at the time. One of my goals for this year is to do this at least once a week. I believe it will keep me focused and keep the formative feedback-loop going. I’ll keep you posted.

Before we get into the week, let me be the first to say that I have no grandeous dreams of students going forth into the world and using their ability to long divide polynomials or sketch them from factored form by hand. Polynomial Long Division (henceforth referred to as PLD) is a way for me to do the following:

1. Check on and improve student ability to add/subtract positive and negative numbers as well as distribute them
2. Improve mathematical endurance (why yes, those last two problems may take up a whole page each)
3. Improve student understanding of how the equation, the factors and the graph work together with higher order polynomials
4. Create an opportunity for my studens to feel like mathematical Rock Stars

Let me explain that last one. It goes back to my drive to help students see themselves as being ‘good at math’. PLD is impressive looking.  I mean, really impressive. Especially when you start with a 5th degree, have students figure out the zeros, create the factors and then do multiple rounds of long division in order to come up with the factored form which they then must graph by hand labeling all intercepts. Then they can check their work with the calculator. Yay for instant feedback.

At the start of last week the kids had only worked a day or two with PLD. By then end of the week, with some group assistance, they were all working through these massive problems. They’ll whine that the problem’s huge and takes up too much space, but they’ll do the whole thing and then just kind of sit back and stare at it with this look of ‘did i actually just do all that!?’ on their faces. There were lots of “got it!” mumblings while they worked. It’s not the crowing cheers you get with, say, WCYDWT problems. I liken it to the satisfaction of a job well done. Because what is the true hold up for a lot of students in math? The concepts, or the grammar? Is it that the kid can’t understand what’s going on, or that they are so hung up on the symbols and the difference between coefficients and exponents and plus’ and minus’ that their brain is spinning? I think it’s the latter much of the time that shuts off the student mind.

So here’s the worksheet given out to each table group. I put them in a plastic slip so the four students in each group would have to share. Maybe even, I dunno, read a problem to the group. Work together.

Monday
I started by laying the ground rules. Students were to work with their tablemates to solve the groups of problems: sketching a polynomial, identifying rational zeros, and writing factors given zeros. For each group a set of 5 side-problems needed to be answered using short sentences. I told them I was worried they were not reading problems in full and that the 5 questions were to help give them things to ponder when they approach a problem. The 5 side problems were:

(a) What is the problem asking?
(b) What is the problem giving you?
(c) What are the essential features?
(d) How are the first and second problems in this group similar? Different?
(e) How do you know your right?

Once a table finished the first three problem groups they are to call me over to get checked off. More on how I did that later. I also noted to the classes that I didn’t expect any group to finish the first page today. The problems are about bringing together several of the ideas we’d been working with (factors, zeros, rational zero theorem, PLD, sketching from factored form).

They set off Monday and most tables got through the first group. I was able to meander around the class and ask questions, rephrase problems, and, my personal favorite, listen to students argue about problems.

Tuesday & Wednesday
Set the students straight to work this day. I should also note that it was AP testing week, so I had gaps in many tables. I ended up taking tables of two and splitting them into other groups. This was actually a really effective way to share ideas between groups because when they were put back together on Wednesday they spent time comparing answers. For me, Wednesday was more listening and giving little kicks when they would get stuck. Often it would be pulling the page of one of their tablemembers to the middle for all to see and pointing at what they had written. Then a reminder that they should always ask their table first. Yeah, I’m one of those teachers that if you call me over with a question I will ask the person next to you what the question is. I’m not perfect at it, but it’s something I work on and the kids expect.

By the end of the day I had about a quarter of the tables in each class checked off or ready to be checked off first thing the next day. The check off worked like this: table calls me over. I randomly pick a student’s work to look through. While checking through I make comments about little stuff (“your graph is naked–you should give it labels to cover up” or “I like how you _______” or “that’s a great way to phrase what’s going on there. Thanks.”). I also directed follow up questions towards different members of the table to poke at what I know are common misunderstandings. I learned that side question (b) is badly phrased and students didn’t get that it was meant to be very general. (c) was asking for specifics. Will need to clarify that for later.

I really like the check up since I got face time with every single student. With classes hovering around 32, I often feel like I can go over a week without talking one-on-one with some of my quiet ones. The randomness of the check also keeps groups at the same pace. Yes, there was definitely some copying of a neighbors’ work going on, but I heard far more demands for explanations than I saw copying of work.

Thursday
By this day almost all tables were working on the last two problems (I had a few tables disproportionately affected by AP testing and one that was slacking a bit I had to crack the whip with). This is where the dividends of the previous week and the first three day’s payed off. More times than I can count a table would call me over to ask a question about the last problem group only to end up talking me through each step making connections to the problems on the front page while I just stood there with a carefully blank expression. They would then wave me off. I love that.

So much good practice on fundamentals. Precalculus students would never accept me giving them a quiz on addition/subtraction/multiplication/division, but man, if they didn’t get one while working on PLD. Some confusion over what factor to divide by first, to which I would always ask “what’s 24 divided by 2? then by 4? what about 24 divided by 4? then by 2?” They were able to work from that to figure out that it didn’t matter and then set upon the polynomials using PLD until all that was left were a set of factors they then used to make a sketch. It was awesome to watch.

Probably my biggest role that day was helping tables find the little errors in the basics. I’d have tables get stuck on why they have a remainder and that they know something is wrong but none of them could find it. Heck, sometimes took me over a minute to spot the error. Stupid negatives. It’s always a negative.

Tables that finished earlier were set up with skill quiz questions to work on. I also sent a few off to other tables to help out. Mmm, peer tutoring.

Follow up Thoughts:
For those wondering why I havn’t said anything about synthetic division: I have nothing against it, but I like having students divide by x-squared and the like. I am also unconvinced that students understand what it’s doing.

For bringing together a bunch of ideas, I think this type of table-work/discussion/check-in is great. The side questions had the students using the vocabulary of the unit and focusing on what’s important. I’d like to do more of this in some of my other units, though I’d also like to incorperate more of the PCMI flare of important stuff/neat stuff/tough stuff.

I think my classes are more comfortable working with larger equations now and dealing with longer problems. I really hope that this work pays off when they move on to AP Calculus or AP Statistics. Or just when they are confronted with large problems in general. Break it down! What do you need to do first? Are you double-checking your work? How do you know you’re right?

And how awesome is it that at the beginning of this week you looked at the back problems with wide-eyed fear and now they lay defeated on the page in front of you? Rock on, kiddo.

————————

Student: reads a problem. Attempts to solve. Completely bombs. Ignores order of operations. “I suck at math!”

Teacher: sits down with student. Breaks apart the problem, giving it verbally to the student.

Student: does perfect, exclaiming “That was so easy! Why didn’t I get it the first time? I must suck at math!”

Teacher: *facepalm*

————————–

On facebook there are a variety of little polls that go around.  Right now there is one that looks like this:

Now how many people who got the ’1′ are thinking “my, goodness, look at all the idiots who don’t know simple mathematics!”

And how many who got the ’9′ are thinking the same thing about the people that picked ’1′?

Me: *facepalm*

I feel like that’s the same as making fun of a lady for not knowing the sign said ‘men’s room’ when it’s in Japanese and the lady in question only reads English. If some helpful soul had read it out loud and translated, of course that lady would have chosen the other door. It’s not willful ignorance, here, it’s that smart, hardworking individuals never figured out how to read math. Or if they did, it was short term omg-there-is-a-test-tomorrow learning which does not stick. Especially if sleep deprivation is invovled. But that’s another post another time.

I suspect I could grab just about any individual off the street and walk them through it and they would get the right answer. Possibly with some finger counting.

So does math illiteracy = not able to do math? No. Not any more than reading illiteracy = not being able to discuss complex ideas. It’s useful to write math down because when large problems are being worked through, it’s a rare individual that can keep all the number straight. The visual form of mathematics (equations and graphs and tables) give a clear why to communicate mathematical ideas just as words do for language.

Now, teaching a language that pulls from multiple alphabets, where position is important, and multiple symbols are in play? Including three different ways to indicate multiplication? That’s a part of my job. Not the biggest part by far, but one that can cause an avalanche of problems.

Kids can do math just fine. But how much of the lack of mathematical self efficacy is from young kids deciding they suck at math because of a click on Facebook?

And which did you pick? the 1 or the 9?

This partly goes against the grain for me. I like time being a variable. I like being able to sit down with kids and have them show me that they ‘get’ the concepts and who cares if it took them a little longer. But there is also the practical me dressed in beige and pearls with a clipboard on my shoulder saying am but mortal and having students from four classes wanting to retake skills at the end of the year because they don’t know how to not do things last minute is a Bad Idea.

Yes, it is definitely my fault for not instituting a ‘only one skill a day’ rule (though I do have the ‘you may only try this skill once today’ rule).  I really need to do that next year. But then would their grades reflect their organizational ability or their mathematical knowledge?  Dog, meet Tail. Tail, Dog.

Anyhoo, in the past two weeks I’ve seen a lot of my students outside of class. I’ve had great conversations and learned so much more about what THEY know based on the skills they sunk on and the skills they flew over. On the progress reports that went out a bit ago every student had a comment with what % of skill quizzes they needed to come in and work on by today. I’ve harrassed kids in class, in the halls, and over emails. My class skill chart will have a lot more blue’s on it come Monday when I get around to updating it (blue means >90% average in the class).

But better than anything, I feel like my skill grades are more accurate now. In example: expected value (skill 17): not too good. I really need to work on that unit and come up with something better for next year because it felt like a total swing-and-miss this year and their skill scores reflect that. Writing and solving permutations (14), combinations (15), and isomorphic situations (16): awesome. Need to keep that around. Possibly should add a joint skill where kids have to write/solve a situation that demands both types of counting. Needs must ponder.

At the end of the day, I have these little slips to mark what was done. These are from the last 24 hours and represent every skill retake. It’s been a good day.

I feel like this short video series could be very useful in teaching, but I need another week to digest it fully. Some quotes  that I like with following thoughts:

“…when you have one thing leading to the next leading to the next you can feel inherently that you are on a train that has a destination and that [your] gonna find something.”

“The other thing that that little anecdote has is that it’s raising a question from the beginning. And that is the other thing that you want: you want bait. You want to constantly be raising questions.”

“Everything will be more compelling if you just talk like a human being. If you just talk like yourself.”

Ira Glass has quantified ’storytelling’ into two main things: the Anecdote and the Reflection. In thinking about how storytelling is done in a math class, I want to say that it’s my job to get the story going. It’s my job to show a picture or a video or bring up things in the news and get the Anecdote rolling, but I want my students to do the Reflection piece. I want to hear their conclusions about facts they have been presented with. I want to help them reach toward beautiful mathematics which we can then put on paper and solve and then sit back and be all ‘wow, that’s neat’ together.

How often do we see teaching where one or both of these components is missing? I know that I’m guilty of teaching students to work through a variety of mathematics and then missing out on that Reflection piece. Or trying to get students to be Reflective when I’ve not presented enough of an Anecdote for them to be even a little curious. How does this stuff connect? Where is it used? Why do I care?

I think my favorite part in the 4-part video is from #3. Glass is talking about video makers, but I feel it rings to true to teaching.  The following is transcript from the video that I’ve edited slightly:

“Nobody tells people who are beginners,and I really wish somebody had told this to me, is that if you’re [teaching] you’re somebody who wants to [inspire], right? And all of us who do creative work like, you know, we get into it and we get into it because we have [a passion for it]. Do you know what I mean?

Like you want to [teach] because you love [education and learning and the kids]. You know what I mean? Because there’s stuff that you just like love, OK? So you’ve got really [strong passion] and you get into this thing that I don’t even know how to describe but it’s like there’s a gap. That for the first couple years that you’re [creating lessons], what you’re making isn’t so good, OK? It’s not that great. It’s really not that great. It’s trying to be good, it has ambition to be good, but it’s not quite that good.

But your [passion], the thing that got you into the game, your [passion] is still killer and your [passion] is good enough that you can tell that [the lessons] you’re [teaching] are kind of a disappointment to you, you know what I mean? Like you can tell that [they're] still sort of crappy. A lot of people never get past that phase and a lot of people at that point quit.

And the thing I would just like say to you with all my heart is that most everybody I know who does interesting creative work, they went through a phase of years where they had really [amazing passion] and they could tell what they were making wasn’t as good as they wanted it to be. They knew it fell short, you know, and some of us can admit that to ourselves and some of us are a little less able to admit that to ourselves.

But we knew that it didn’t have the special thing that we wanted it to have and the thing what to do is… Everybody goes through that. And for you to go through it, if you’re going through it right now, if you’re just getting out of that phase or if you’re just starting off and you’re entering into that phase, you’ve got to know it’s totally normal and the most important possible thing you can do is do a lot of work.

Do a huge volume of work. Put yourself on a deadline so that every week or every month you know you’re going to finish one [amazing lesson or unit]. You know what I mean? Whatever it’s going to be. You create the deadline. It’s best if you have somebody who’s waiting for work from you, somebody who’s expecting work from you, even if it’s not somebody who pays you but that you’re in a situation where you have to try not to work. Because it’s only be actually going through a volume of work that you are actually going to catch up and close that gap. And the work you’re making will be as good as your ambitions.”

I’m currently working on making something amazing for Rational Functions to try to inspire a room full of anti-math, bored seniors and help them see that they have mathematical ability, but it does take work and they can’t slack off. Right now I’m trying to use some technology to get them to see the problems through a different medium. I also decided to start with adding/subtracting instead of multiplying/dividing because I didn’t want them thinking it was some factor-and-slash cakewalk.  We’ll see how it goes.