Catching Up and Looking for Some Ideas

There are a few ideas/questions banging around in my brain. No school tomorrow here so I can relax a little more than usual on a Sunday night. I’ll try to be coherent and I hope to get some feedback here or through twitter (where I can be found as @mrdardy)

On Friday our school had the day off and we have been encouraged to use this as a professional development day by our administration. I chose to travel a few hours to visit a school where an old friend is working. The school does some interesting work in the STEM arena and they balance an IB program as well as AP expectations. I gathered some ideas that I will be bouncing off of my colleagues and administrators, but more importantly I just felt energized. I walked away excited to have made some new contacts, happy about many of the things we do at our school so well, interested in figuring out how to develop cultural pieces to support some ideas that work there, and filled with some ammo to talk about the need for schedule changes at my school. As a young teacher I never visited another school. I have long had the habit of visiting other classes at my school and I never feel like I do that enough. It has only been since I moved north 8 years ago that I started making the effort to visit other schools and I cannot recommend this enough. Where I live I pretty much have to drive two hours or so and I have done that the past two years. Every time I have reached out to another school I have received nothing but positive responses and a generous  expense of energy in making the visit happen. I also want to take this space and time to extend an invitation to anyone who wants to come and see our school in action.

On Thursday my AP Stats classes had a group quiz. I stood at the door with playing cards in my hand. Students took one (blind) from me and were randomly assigned to groups. Each class had four groups and each group had a different quiz. There was one question in common to all quizzes but otherwise they each had five different questions. It was SO much fun to listen in as they wrestled with these questions and as they explained ideas to each other. There were some healthy debates but it never got tense or unpleasant. Our school has a very international flavor and I was especially pleased to hear the voices of my international students in these conversations. So much of the material in this course is based on careful reading and vocabulary and I sometimes worry about whether this gets in the way of these students accurately showing me what they know. Have not graded them yet – that is tomorrow morning’s task – but I fully expect them to shine.

On Thursday my AP Calc BC class took a test on integration techniques. The last question on the test was this – Divide a pizza of 14 inch radius into three equal portions with two parallel lines. Most of my students wisely chose vertical lines. Two chose lines in the form y = mx + b, a bad choice. I went into this intending to give full credit even without a numerical value for the line equations. Setting up the integral appropriately is where the calculus is in my mind. Here is what I find myself wishing after this test and after looking at their work – I wish that they had access to desmos or geogebra while they were taking this test. I wish that they had something much more powerful than their TI calculators to visualize this, to try out ideas, to narrow down where the solution needs to be. I had to struggle through some ugly algebra and some calculus that should have been cleaner and more obvious. I’m impressed by the patience and perseverance I saw but I am frustrated since I know that better tools can help them work smarter on a problem like this one. How many of you out there have a setup where your students have access to these tools on assessments? Am I overthinking this by worrying about internet access during a test? Should I just trust that reasonably written questions can allow them to show me what they know and allow me to judge my students’ progress? I’m thinking hard about this and I would love some ideas.

Great Follow Up Day

On Friday I wrote about a pretty terrific conversation that came up at the end of our BC class. We had tackled a particularly gruesome integral – (tan x)^5 and I had done so by repeated patience substitution and I chose to let u = sec x and look for combinations of sec x tan x as the du piece. One of my students stayed after and showed me his work where he shoe u = tan x and du = (sec x)^2 He was frustrated and told me that he spent about a half an hour trying to figure out why his answer was ‘wrong’. So, I typed up my solution and had it on one side of a page. (This document and the graphs I created are all linked on my last post from Friday.) I typed up the solution my student arrived at and placed it on the back of the page. I had my students working in teams so they each had my solution and their classmates’ solution in front of them simultaneously. I asked them to examine each of them and explain why they did not agree. I heard some pretty good conversations, most of them simply concentrating on making sure that they even followed each of the solutions. We had talked about it on Friday so it was good to hear them reflecting clearly on that experience. After a couple of minutes, one of my students announced that he proved that both solutions worked. I played dumb and asked what he was talking about. He explained very calmly that since one answer was based on even powers of tangent and one was based on even powers of secant, we could show that they were nearly equal. They seemed to differ only by a constant. I then showed them the Desmos graph I created and the GeoGebra graph I created. Both programs were happy with my solution and with my student’s solution. Neither program was happy with the difference between them. But I showed them that every x input we could guess at in the difference function yielded either an undefined answer or an answer of -0.75

I used this conversation with a number of goals in mind. I want them to get in the habit of talking to each other. I want them to see that there is not just ONE way to do math problems – especially ones as sophisticated as the ones we talk about in BC Calculus. I want them to think about graphs. I want them to utilize resources such as Wolfram Alpha, GeoGebra, and Desmos. I want them to notice and wonder about relationships. They are not yet where I want them to be in these terms, but the more often I remind them and the more often I model this behavior, then the more likely they are to adopt these behaviors.

If I did not believe this, I might not have the energy to keep on keeping on in this job. But I do believe it and I do keep on keeping on.

Thank you world of math resources for my students! Thank you world of recourses for me!!

We Broke Graphing Technology Again – A Success Story

In AP Calculus BC we are doing some pretty unexciting stuff right now – techniques of integration. The problems are (sort of) fun little algebraic puzzles but I find little room for conceptual conversations. Maybe I am just missing something obvious. But today was a bit of a revelation and I wish I knew better how to try and insert equations to tell the story. I’ll just have to use some tortured syntax to get my point across. I put up three pairs of integrals and told them that one in each pair was something they knew how to do before they met me (our school does BC as a second-year calculus course) while the second was one they needed my help with. I had an integration by parts example side by side with a boring old u substitution (the integrands were x cos(x^2)  versus x cos x) and they knew which one they COULD do and we talked through integration by parts. I had a partial fraction problem side by side with a  natural log problem (the integrands were (x – 2)/(x^2 – 4x + 3) versus (x + 1)/(x^2 – 4x + 3)) and again they knew the difference and we talked about partial fractions. I had a trig substitution problem against a boring old square root (this time it was sqrt (9 – x) versus sqrt (9 – x^2)) Then someone asked me a HW problem. They were asked to integrate the fifth power of tangent x. I took off writing and trying to get buy in at each of the many steps. I told them at the end that they knew each of the steps they just did not know which direction to move. I assured them that this was a process they would master with a bit of practice. As I was working, I made the decision to substitute for sec x and set up the answer in terms of that function. A student asked me why he could not use tangent to substitute. I did not have a bunch of time left so I asked him to hold his thought and talk to me at the end. He did. As a result, I made a document we’ll examine as a class on Monday comparing his solution and mine. You can grab that here I went through with math type to show his solution and mine. I’ll leave it to the students to determine why they look different and I hope they come to the conclusion that they are NOT different. To help push the conversation I created a Desmos graph and a GeoGebra graph to show my function (called d(x) in each case) and my students function (called j(x)) in each case, I will erase the f(x) that you can see by following these links because I don’t want to give the game away immediately. What troubled me was that each program dealt with my function and my student’s function just fine. When I combined them the graphing technology broke. I tweeted out to @desmos and received – as usual – a quick and helpful reply. In this case, the reply was simply ‘Thanks for sharing. This will help us make better graphs for the future.’ This is the second time this year that we have found a little glitch and I could not be more pleased with the response I have gotten each time. It is such a great way to emphasize to my students what a connected world we’re living in and how they can reach out and find help. My student said he spent a half an hour trying to figure out why his answer was ‘wrong’ since it disagreed with his text’s answer. I hope after Monday that he will begin to internalize the idea that he can check his answers in pretty powerful ways. Ways that I did not dream of when I was learning this stuff in 1982. What a fun fun experience seeing his work and getting the reply I did from Desmos. Add in the fact that I get a date with my wife at a local farm to table restaurant and the day could not get much better.

Progress Report

It has been, as usual, a busy year. It seems that this is absolutely the norm in our professions, isn’t it? I am teaching three classes this year – AP Calculus BC, AP Statistics, and Geometry. In the next few days I want to comment on all of these classes as time allows. Unfortunately, this is the week we are working on midterm grade comments for every one of my 68 students AND my mom arrives tomorrow night for a visit as this is grandparents’ weekend here at our school. The two things I want to share today are reflections on the progress of my Geometry class and a class visit I made last week. I’ll tackle last week first.

We have a number of students who finish the Calculus curriculum before they graduate here. Those students – who have has two years of AP Calculus (we teach BC as a second-year course) move on to an Applied Differential Equations class taught by our school’s President. He is a retired Army engineer and he teaches a lovely Problem-Based curriculum using Mathematica. He ran into me in the hall last week and mentioned that his students were presenting the results of their first research problem and he invited me to join them on Friday. I was able to watch as two of my former students presented fantastic work that they had done on their own on a research topic of their choice. One was presenting a supply and demand curve. She explained her choice of parameters and shared the results. Her classmates made note of the similarities to a predator-prey problem that they had worked on together. She eloquently addressed the similarities and differences between the problems, but what most impressed me was her response after one of her first graphs. She remarked that the graph did not fit what she suspected should happen and her slide suddenly displayed the phrase “Question Results” and then she moved on to discuss her modification. I loved the directness and the simplicity of this message. Just because a fancy machine, and Mathematica is a VERY fancy machine, tells you something, it is not necessarily true. I have to incorporate such a simple response into my repertoire when looking at surprising or counterintuitive results. The second presentation was analyzing the forces involved in walking on high heels. It was a fun discussion and I was impressed by the depth that the student found in examining this situation. Unfortunately, our school President is retiring and I suspect that our new administrator might not have an engineering background. It’ll be up to me as department chair to find someone capable of carrying on this kind of high level work with our best math students.

I start each day with my Geometry class. We have had a blast so far playing with GeoGebra in the lab, discussing reflections, rotations, and vector transformations, talking about distance and Pythagoras. I have been pleased with the level of engagement I have seen from the students. They are reading the text (and finding typos!) and they are engaged in class discussions. Now we are getting ready to begin discussing proof. So I want to sloooow their brains down a bit. I borrowed (okay, maybe it is just stealing) an idea from Max Ray in his book Powerful Problem Solving. I asked my Geometry students to write directions for making a peanut butter and jelly sandwich. I wanted to show them just how hard it can be to carefully describe something. I did not have people act out the descriptions, though. I was a little worried about embarrassment. So, I dealt out cards at random to sift the kids and I had plates, paper napkins, knives (plastic ones – just to be safe!), peanut butter ( one table had sunflower butter due to allergies) , and some jelly. I bought both grape and strawberry. I shuffled the instructions and handed them out and we had a terrific conversation about the assumptions made and about being careful with details. We had some laughs talking about how peanut butter might magically appear on knives to be spread and what side of the bread gets put together. Then we came to the description made by a student I’ll simply refer to as E. She typed her description ( which can be found here ) and she did such a lovely job. Her list is detailed and she took great care to break down the actions involved. All of the class agreed that hers should have been the first one read since we decided to go ahead and eat as soon as we dissected hers. She seemed really proud when I asked her for her copy to share out.

i’ve been thinking about this all day. Remember, this is my 8 AM class. I have resisted some activities like this in the past thinking it just was not my bag. However, I am working closely with two terrific colleagues in Geometry this year and they sort of encouraged me to try. I stepped out of my comfort zone and the result – at least this time – was a relaxed and fun class. Kids were engaged, they supported E and gave her some real praise and after class one of my students who has been struggling so far came up to me to tell me how much fun she had. I think I may have earned some important personal capital in working with her and this may be a gateway to building a relationship with a student who does not seem to have much inherent love for my subject.  I also think that some valuable points were made about the challenge of explaining what you know to someone who does not know it. I am optimistic that this will help build a bridge toward understanding some important principles of proof in the next week or so. So, thanks to my colleagues for encouraging me to try something that seemed a bit silly to  me. Thanks to E for being a model of thoughtfulness and detail. The rest of her work this year has been uniformly outstanding, so I was not exactly surprised by this. Thanks to my students for trying an assignment that probably seemed a bit weird. Finally, thanks to Max Ray for this thoughtful book that got me going on this path.

A Geometry Revelation to Remember

We are working with isometries in our Geometry class right now. We are looking at vector translations of objects, rotations (primarily around the origin), and reflections over horizontal or vertical lines. I am only teaching one section of Geometry so sometimes I feel like if I don’t get it right, I’ve missed an important opportunity. There have already been a couple of instances where I explain something after school in a way that I wish I had done the first time around. I am trying to keep note and be a smarter Geometry teacher next year.

Today when we were wrestling with rotations about the origin (I am sticking mostly to 90 degree increments) there was a bit of a clamor with the students begging me for rules about how to transform a point in the general (a, b) form. I really want them to try and develop a better intuition so I have resisted the call for these shortcuts. One of my best students, a boy I’ll refer to as M, pointed out that these rotations always maintain distance (again, we are rotating about the origin) so I pointed out to my class that this really limits our choices. We were looking at rotating the point (4, 2) 90 degrees counter-clockwise. Everyone agreed that this would put us in the second quadrant and I used M’s idea to suggest that our destination was now restricted to either the point (-4, 2) or (-2, 4) since the distance was the same and the second quadrant has negative x values and positive y values. A quick sketch convinced us all that the target should be (-2, 4). I felt like we were in sync with each other and that my sketches convinced my students. A group of them came after school to work to get ready for tomorrow’s quiz and they all confessed to not being convinced. I pulled up GeoGebra and tried to show them what would happen. I referenced M’s idea about distance and one of the students reminded me that I had been emphasizing the Pythagorean Theorem more than the distance formula earlier when we talked about distance. This was the breakthrough that I should have had at 8:30 am instead of 2:45 pm. I drew a right triangle on GeoGebra, called up a slider to rotate the triangle and showed where the vertex originally located at (4 , 2) ended up. Then I reminded this gang of help-seekers that points on the x-axis move to the y-axis under a 90 degree rotation. So I convinced them (and this time I am pretty sure that I DID convince them!) that the side of the right triangle corresponding to the distance 4 represented by the x coordinate of our original point now HAD to represent a y quantity after the rotation. We tried a few other points as well and we were humming along. I tested their wits by asking them one more question before they headed off – I asked about a 270 degree clockwise rotation. I was thrilled that one of the guys quickly pounced on this and said it was simply our 90 degree counter clockwise example again. VICTORY!

At least it feels that way now. I’ll see (and report back) after our quiz tomorrow morning.

Progress Report

A beautiful Monday here – the heat finally broke and fall is beginning. I just want to take a few moments to share what’s been happening with two of my courses. I am teaching AP Statistics (my 5th year doing so now – I am finally beginning to feel comfortable), AP Calculus BC, and Geometry, I have already written about my Geometry book that I wrote this summer (you can grab it here if you have not done so already) and I am pretty pleased so far with how the students are responding. We just spent two days in our computer lab so that they could get their hands dirty working with GeoGebra. In my book, Sect 2.4 is the hand-on intro. This section has the fingerprints of @jensilvermath all over it. It was fun to watch the kids poke around and try to discover. It was a refreshing reminder that all of the talk about digital natives needs to be taken in context. There are certainly tech skills that feel more natural to my students than to me. Hell, there are things my 11 yr old son knows better than I do on our laptops. But this kind of exploration does not necessarily come naturally. I also am reminded of the relationship between comfort with material and comfort with exploring. Some of my students accomplished so much more and were so efficient compared to their peers. I saw a direct relationship between kids who feel confident that they understand directions like – create a regular hexagon and then create a circle that contains the vertices of the hexagon. The students who were willing to simply poke around on the pull down menus were quick and happy to execute some simple commands while others just stared aimlessly at their screens. I led class very directly on Friday in the lab and intentionally did not do so today. I have had a couple of students comment that they are enjoying the text and that it feels easy to read. I have also had a few tell me that they do not like my habit of asking questions for which there are multiple correct answers.

I spent about 5 or 6 hours this weekend reading short essays from my AP Stats students and responding to them. I had them read How Not to Talk to Your Kids an article that I first read about 7 years ago. It was my first encounter with the ideas of Carol Dweck regarding mindset and praise. It changed my thinking as a parent and as a teacher. I gave my students two sets of quotes that I found memorable and asked them to pick one from each set to comment on. I also asked them to find a meaningful quote of their own. I was really proud of them. I got some thoughtful responses and quite a bit of personal reflection. When we debriefed in class today most of them said that the article really made them think about their own childhood, what motivated them, and how their parents treated them. Could not ask for much more than that. I also shared with them a brief video from an interview with Richard Feynman. In it Feynman discusses the distinction between knowing the name of something and actually knowing about that something. My students reported, as expected, the depressing news that they feel that their job is often complete when they know the name of something. I was pleased that they expressed, pretty unanimously, that this is not the way it should be – just the way it is.

That Visible Learning Business Again

I gave my AP Calculus BC kiddos some rough problems to deal with on HW last night. On one of the problems they were asked to consider the greatest integer function – to be called the floor function from here on – and they were to graph the relation (floor(x))^2 + (floor(y))^2 = 1. A tough problem for sure but a couple of students nailed it. Most did not, so I fired up Desmos to show them the graph thinking we’d spend some time discussing why the graph was what it was. Desmos gave a nice graph but one of my students insisted it was not quite right.

 

So, I told them (kind of bragging, honestly) that I had met Eli this past summer and I would tweet out our issue. My last blog post was about sharing my learning with my students and here was another great opportunity. Eli tweeted back with another go at the graph – found here

 

This happened while we were still in class! I got to show my students this graph and it still was not quite right. I wrote back to Eli again and his response was awesome. He tweeted back that this problem would be a lunch time conversation at Desmos World Headquarters. How fantastic is this? I get to share with my students tomorrow that a problem we shared out to the world was going to result in some brilliant guys reprogramming their fantastic tool so that it would tackle this thorny problem. Don’t know that it gets much better than this. Oh yeah, as an added bonus I was sent another take on the problem by Christopher Danielson. Here is his take

 

Days as a teacher don’t get much better than this. Oh yeah, I should note that I got so wrapped up in these tweets and talking to my Calc students after school about this problem unfolding that I was late to get my children from their bus. A friend had to call me to get me out of my classroom building to go grab them. For one afternoon math seemed more exciting than seeing my own children.

Making My Learning Visible

I am in my 28th year of teaching high school math (with some overlapping years of middle school math thrown in as well) and some would think that I should have it all down pretty well but his point. Luckily for me, this is only partially true. Also, luckily for me I have a great community of support online (I’m looking at YOU #mtbos.)

In the spring of 2010 when I was interviewing with my current school I was told that one of my tasks was to teach AP Statistics. I had never taught stats before at any level. There was a time in my life – in 2001 as a matter of fact – when I stopped talking with a school about a position because they needed a stats teacher. This time I was more confident and more interested in the school so I took on this challenge. I enrolled in a week-long summer institute taught at Fordham in Manhattan by Chris Olsen. I’ve really enjoyed teaching this class but I still feel far less confident in Stats than I do in any of my other classes. I gave our first quiz of the year last Friday over Section 4.1 of the Starnes, Yates, and Moore 4th Edition of The Practice of Statistics. A number of my students were engaged in a pretty heated debate outside the classroom. I was pretty sure that I knew what the answer was but students in favor of two different answers both made compelling arguments. In the past, I might have dug in my heels and stood by my initial guess. Or I might have thrown he question out. Or I might have given everybody credit regardless of their answer. In any of these situations I would have felt pretty unsatisfied and I would not have been any smarter. I was tempted to go to the AP Community page where I have found some pretty helpful folks. However, the feedback cycle there is not particularly rapid and I have to remind myself to go back and check in. Twitter to the rescue! I sent out a plea to Hedge (@approx_normal) and to Bob Lochel (@bobloch) sharing a link to my quiz and begging for help. Hedge replied in a series of about 8 tweets and Bob replied as well. Hedge suggested that I also reach out to Shelli (@druinok) Temple for help as well. In the end, I felt smarter, I realized that my students who had a misconception (a) had a very reasonable misconception and (b) had that because of something I had said earlier. I now know to be more careful with my use of vocab, I know that there are folks who have my back. I was able to show my students the twitter transcripts of these conversations so that they can (a) see that learning keeps on going on even when you are a supposed expert like they see their teachers to be and (b) they (hopefully) see that I am trying my best to be clear and fair in how I evaluate their work. The fact that Bob suggested that each of the two hotly debated answers should be accepted certainly helped.

 

Back in the Saddle … or Back in the Classroom

Yesterday was my 5th opening day here at my current school and my 28th overall as a teacher. I was speaking with a senior who was a little melancholy that this was her last first day of high school. I let her know it was my 32nd first day of high school so she might have more ahead if she chooses.

There are quite a few changes this year for me. Last year our parents association agreed to help fund an AppleTV cart for my room. I now have an iPad that I am trying to learn to navigate and I have a lovely color TV to project GeoGebra, TED Talks, my new Geometry book, class notes and activities, etc. I rearranged my room for maximum viewing space, got rid of two clunky old file cabinets, and I fully intend to get rid of at least one bookshelf soon to create more space. I rearranged my AP Stats curriculum based on helpful suggestions by Josh Tabor and @majorfstats. I have never been much of a room design guy but the fantastic @mathymeg07 designed some fantastic posters for me so my room is adorned with messages for my students. The biggest change and challenge for me by far will be my Geometry course. I blogged about this recently. I wrote a text for our school’s students to use. This summer was taken up with trying to blend years of thoughts about Geometry with recent advances in my own understanding of GeoGebra. Thanks to the help of some twitter pals (especially @jensilvermath, @mathhombre, @mathbutler, and @a_mcsquared) I’ve been making some progress in my mastery of GeoGebra. I hope that my flashy new AppleTV, my PDF text with link outs to applets on GeoGebraTube and to blogs with great activities, and my enthusiastic younger students will lead to a great year in this course. I already have my first piece of editing advice from a student about one of my diagrams. I’m going to work hard at not being thin skinned and looking at all suggestions as ways to make this a terrific text.

So, we’re only two days in but I already have had a number of really terrific conversations with my students. A couple of Calculus BC kids have especially wowed me already. I hand out a problem set on the first day and ask them to work in small groups. I’m not a fan of going over a syllabus on day one. It bores me to tears and I suspect it saps a good deal of enthusiasm from my students as well. This problem set is designed simply as a way to shake off some rust and give me an opportunity to eavesdrop and begin to understand how my Calculus students think. I wrote last year about how I had one VERY quiet class and one interactive class. This year I only have one group of BC students and I think that they’ll be willing to share. I did two of the ten problems on the board and students did the other eight. I was thrilled to see some students use old precalculus knowledge on the ellipse problem and I saw a couple of different approaches to the logarithm problem. My favorite work that I saw from them today involved a minimization problem and a square root curve. I had a student solve this minimum distance question with no calculus at all. He wrote the appropriate distance formula and made a substitution so it was a square root with a quadratic function inside. He then completed the square to factor the quadratic and said ‘I know that this square expression is never smaller than zero, so the distance is smallest when the square quantity equals zero.’ Lovely, lovely work and I appreciate that approach rather than the automatic reaction of differentiating. Don’t get me wrong, I want my students to remember their calculus from last year, but this kind of analysis really makes me happy.

I start my day with my younger Geometry students and they too seem more than willing to engage in conversations so far. It is fun to teach a class that doesn’t feel quite as serious and important as the AP classes can sometimes feel. I’m especially excited to think about the fact that I’ll et to spend time with them watching them develop into better thinkers and then I may get to see them on the other side as they prepare to graduate. I have not had that opportunity as often recently as I want to.

So, nothing major here (yet) but I am certainly happy to be done with meetings and get back to the classroom.

 

How I Spent My Summer Vacation…

One of the committees I serve on at our school is a group consisting of department chairs and other academic leaders at the school. Late in the winter of this past school year our administration approached this group with an offer/request. A little background first will set the stage. A number of years ago our current science department chair wrote his own set of class notes for his Chemistry Honors class. Since I have been at the school I have seen students with three 3-ring binders (one for each trimester) that contain their Chem Honors notes. These are legendary at our school by this point. Our administration approached this curriculum group and asked if anyone was interested in creating something similar for one of the courses in their department. My department was already in the process of searching for new texts for Geometry and for Precalculus Honors. There were some precalc texts which made us happy enough, but there was little agreement for the Geometry search. I have also been trying to move myself in our curriculum so that I would teach some younger students. I have mostly been teaching AP Statistics and AP Calculus in my four years at our school. This offer seemed like a way for me to work with younger kids AND begin to create a Geometry book that we would be happy with. One that would grow and adjust as we worked with it. So, I took on this challenge and spent most of my summer writing a Geometry book. I leaned heavily on the wisdom of our MTBoS army and I scoured the web for activity ideas (many of which are living in my Virtual Filing Cabinet here) to try and enrich the book. I have always been bothered that students seem to treat their math texts as simply a source of HW exercises and not as a resource to help learn the material. So, I chose to include very little in the way of practice exercises in the text. I will be working with two of my department colleagues to put together HW assignments and activities to help make this course come alive for our students. Writing this was a great deal of work and I am reasonably proud of it at this point. It’s not a work of art yet, but it is my hope that this text will morph and become more meaningful and beautiful in the next few years. This is where you, my dear readers, come in. I want to share my public dropbox link to a PDF of this text. I want to encourage all of you to look it over when you can, to borrow any ideas that seem helpful, to point out where I goofed, and to share your experiences and activities that will make this a better experience for my students. I will keep updating this text based on our experiences teaching it and based on the suggestions/comments.compliments/complaints I receive from students, from colleagues (both here at school and out in the world), and from the parents in our community. 

I am excited to launch this project. I am thrilled to share it with some of the people who have shared so many ideas already with me. I am anxious about the warts we’ll discover as the year unfolds. I am too exhausted by the whole project to have a clear eye for it at this point.

Thanks in advance for any wisdom and advice you are able to share. August 25 is when we launch – this will surely be a regular topic of conversation on this blog for the upcoming academic year.

 

I would be severely remiss if I did not make a special thanks to Jennifer Silverman (@jensilvermath) for her inspiration throughout this project. She gave me the first significant nudge down this path.