A Day In… Honors Precalculus with Trigonometry

A Little Introduction for “A Day In…”

Today was the first day back from spring break. I decided it’s time to take the subtitle of my blog (better through reflection) seriously. How so? By writing a recap of one period for each of my classes, including things that went well, things that didn’t, things I can do to get better, and any other takeaways (or questions to consider) that come to mind.

This is the first installment. More will follow as time and energy allow.

The Setting

4th Period, Tuesday, April 2, 2013

Honors Precalculus with Trigonometry

How Things Went Down

As students walked in the room I welcomed them back from spring break. This semester I tweaked how I enter things in PowerSchool (assignments get grouped by chapter now, rather than entered individually), so I’ve been brainstorming how to help students keep track of their assignments without the same level of detail online. My most recent (and I hope final) attempt is this handout. I spent two minutes explaining how it works and how I expect them to use it. It’s pretty easy. They just copy down whatever it says under “Do @ Home” on the Daily Plan. As an example, here’s today’s:

P4 Daily Plan.095

I suppose that slide won’t make any sense unless I share the Course Outline. (I used to call it the Assignment Schedule). Students get one of these on the first day of the year. It’s my wonderfully lazy way of communicating assigned homework.

Alright, back to today. We then played SET for two or three minutes. For the first round students had 60 seconds to work quietly in small groups to find as many sets as possible in the Advanced Puzzle Mode (12 cards, exactly six sets are present, no cards are removed when a set is found). When the 60 seconds were up, each group had an opportunity to share one of the sets they found by recounting the card positions (e.g., “1-5-12” or “3-4-9”) of the. For the second round students had 60 seconds to find as many sets as possible in the Basic Classic mode (12 cards, three cards removed and replaced when a sets is found). The students did a great job, finding 17 sets in 60 seconds, a record for the week. The record for the year—held by 7th period AP Calculus AB—is 20 sets found in 60 seconds.

I was excited for today for a number of reasons. One, I typically love my job (even though I’ve had some rough stretches this school year) and I’ve missed the students after 10 days of no school (honestly). Two, I was a little bit excited about today’s lesson because I took what I thought was a rather lackluster notes handout and spiced it up tried to spice it up with some Desmos graphing action. (As it turns out, the “supplementary” handout was garbage. More on that in a moment.)

After playing SET, I grouped students in pairs, gave every student a copy of the supplementary handout, and had each pair grab a laptop (either of their own or from the laptop cart I checked out for the period). I expected this part of the lesson to last about 5 minutes, but with some typical tech-related delays many students took closer to 10 minutes to finish. (And it didn’t help that the handout lacked a clear goal. More on that later.) While waiting for the last few groups to wrap things up I invited other students to write their responses to questions 1, 2, and 3 on the board.

After the supplementary handout, we turned our attention to the notes handout. (I’ll share my frustrations with and potential fixes for the handout below.)

As we finished Example 3, the bell rang. I would have liked another 1-2 minutes to debrief, summarize, etc., but I didn’t manage class time particularly well today.

What I Liked

It was good to see the kids again. They did a great job playing SET. Some students made important connections in spite of my poor sequence of activities. Did I mention they found a lot of sets?

What I Didn’t Like

This could drag on for a while if I’m not careful. Time for bullets!

  • Kids were bored (not everyone, but definitely some; and not just bored, but bored!!!)
  • The school laptops take multiple minutes to start up (those who used their own laptops finished the entire “activity” in half the time)
  • The first half of the supplementary handout didn’t have a clear purpose; the second half didn’t provide students with any engaging tasks (kids need a longer leash for healthy/rich exploration, not 60-second tasks that need teacher intervention before students can move on to the next mini-task)
  • The original notes handout starts with two big ugly definitions/properties boxes (Ugh! don’t lead with this kind of thing, Michael!)
  • I should point out that students had already discovered the content of the first box in a previous investigation, so I’m not totally opposed to including something like this as a summary in a later handout… But to lead with it? More ugh!
  • I blew right by the second box (“These are not the properties you’re looking for…”), deciding to introduce/develop these properties with the help of a right triangle in a two-layer Cartesian/polar coordinate plane (is that even mathematically sound?), but in a very “lecture-y” manner, where my students could have developed these properties on their own with a well-written sequence of questions
  • Example 1 could be improved (ideas below)
  • Example 2 requires completing the square, the kids were super shaky on this, and I wasn’t prepared for their confusion (in every other year that I’ve taught Precalculus, I had taught most of the students the year before in Algebra 2 or Honors Algebra 2, so I usually have a good read on their algebra skills; I didn’t teach any of this year’s Precalculus students last year, so I’m not as in tune with their strengths and weaknesses as I have been in years past)
  • Example 3 was rushed (by me, to finish before the bell rang)

How I’ll Get Better

Alright, the point of this isn’t to stew but to reflect, and through these reflections to get better. So here goes (bullets again to avoid turning this long post into a truly gargantuan one):

  • If kids were bored, that’s (usually) my fault. Here, it definitely was. I failed to give them an engaging sequence of tasks. Too often they were just waiting for the next teacher-led portion of class. With some extra time in planning the lesson, I could design something where students work primarily in groups and we only do the whole-class thing for a very brief introduction and a more detailed (student-led, teacher-facilitated) debriefing session.
  • I can’t do anything about the school laptop frustrations. However, I could plan ahead and tell students when to bring their laptops to class (or have them bring them every day just in case). More and more students are bringing laptops and tablets to school. Maybe 25 to 30% now? As that grows, it becomes easier (at least for me) to incorporate web browser-based activities into class.
  • The supplementary handout suffers from a lack of clear purpose. Was it supposed to help students learn some general graphing basics (toggling on/off, sliders, domain restrictions, etc.)? Or was it designed to have students explore a particular graph? Or to graph three on their own?
  • When I think about it some more, the entire lesson suffered from a lack of clear purpose. Are we focusing on graphs and the impact of parameters (our conversation drifted there today)? Or is the goal to convert from polar equations to Cartesian? To be honest, I need to rewrite the entire sequence of polar lessons to give students more practice graphing, making observations about the impact of parameters in polar equations, etc., before asking them to convert polar equations to Cartesian form. So next time? Here’s what I envision: A handout with 12 images (six on the front, six on the back). Students working in pairs (each with a handout, one laptop per pair). The directions: Use sliders on my pre-made graphs to match each graph. Write down the “winning” equations. Explain how you did it. Then, on the following day we can focus on converting the equations to Cartesian form to have the “a-ha” moment(s) of “Hey, that really is a vertical line/horizontal line/circle with center (#,#) and radius #!” (Oh, reflection! How you resemble rambling!)
  • Example 1 would be much better if it took over an entire page with: (1) A big fat polar coordinate plane so students can sketch what they see on Desmos or their calculators and (2) A big fat table for students to complete (theta values given, r values missing) so students can see clearly/numerically where r first becomes negative and what happens on the graph at this point. (Do I need to bring in auxiliary Cartesian graphs from the get go? Sam’s link to this applet has me wondering if that’s key early on and if I maybe wait too long to draw it in…)
  • Example 2 would be much better if we first developed the properties (rather than giving students a pathetic box o’ properties (“Hey, where did those come from?” “Pay no mind, pay no mind! Back to the examples!”). This could be done with a mini-investigation.
  • Example 3 would be decent if it followed the revamped Examples 1-2, provided that I move to the back of the room and have students wrestle as a whole class with how to make the conversion based on what we’ve done in Example 2.

Most of the rambling above, while helpful (I think), is focused on just a couple of lessons in a single chapter. But I’m similarly dissatisfied with a lot of the lessons in my Precalculus course. I don’t own it the way I do my Algebra 1 and Algebra 2 courses (despite their many and sometimes deep flaws). Algebra 1 and Algebra 2 are the classes for which I put the textbook on the shelf and wrote my own curriculum (here and here if you can bear to look). Did I mention the many and deep flaws?

At any rate, I know my Algebra 1 and Algebra 2 courses inside and out. I’ve wrestled with the sequence of topics, the sequence of lessons, the sequence of examples within those lessons, and I look forward to wrestling with how to turn these teacher-centered lecture-heavy courses into ones packed full of activities, investigations, explorations, rich problems, engaging tasks, etc.

Is it time to chuck the textbook for Precalculus? Can I even afford to make a move like that? I’m not exactly running around with heaps of free time these days, thanks to four beautiful little kiddos. Maybe my days of writing entire courses from scratch—flawed as they may be—are numbered? I don’t know. But I do know this. I want to get better, and I think know that I can. Reflection is time-consuming, but so worth it.

And the best wisdom I’ve heard so far on this issue (but the hardest thing for me to be satisfied with)? Baby steps. Just keep taking baby steps.

Thanks for reading! Wisdom and insight welcome in the comments as usual.

A Further Call to Arms

Entering the Discussion

Two Thursdays ago I jumped in the middle of an ongoing discussion about assessment by posting this. It was essentially a call to arms, a request to join forces in strengthening the quality of our assessments.

Then, just after midnight on Saturday morning Daniel Schneider blew my mind by posting this. If you haven’t read it yet, stop messing around on my blog and get yourself over to his. Make sure you follow all of the rabbit-holes provided in the links. (He wasn’t kidding when he said he was a master aggregator.)

(Update: While I was fiddling with this draft, Daniel threw this down as well. Go ahead and put another educator on the list of people I want to be like when I grow up.)

What’s Next

So where do we go from here? What should we do with all of the interest and enthusiasm surrounding assessment? I see one thing as a no-brainer:

Let’s create a centralized location with links out to quality posts and articles about creating excellent mathematics assessments.

I’m hopeful that a certain master aggregator will lend a hand here. (Update: He will!) Over time we can add more links to resources and even invite members of the so-called better assessments movement to write articles addressing specific topics of need.

Archive or Conversation?

Beyond that, I see two lines of attack: (1) Build an archive; (2) Foster a conversation.

Let me explain.

It would be incredibly valuable to have access to a well-populated, easily-searchable database full of rich assessment questions.

It would be even more valuable—incomparably so—if we learned, as an entire community, to write such rich questions.

In the first case (the archive-building scenario) the focus is more on writing and/or gathering good questions and assessments, and then serving them up in a helpful way. A noble task, to be sure. One I hope others will take up and carry to great heights. (By the way, if that’s you, check out OpusMath, follow them on Twitter, and start uploading like crazy.)

But more than a comprehensive archive of excellent problems with a slick user interface, I think our most essential need right now is to develop an army of amazing assessment authors.

If you agree that the ongoing, teacher-developing conversation is at least as important as the creation of a fantastic archive, then I invite you to join me in the following challenge.

Write An Assessment You’re Proud Of

In a recent email exchange with Daniel, I shared a massive vision I have for creating this group of great assessment writers. He suggested starting with something smaller (something vital, yet attainable) and building from there.

With that in mind, here is my/his/our challenge to ourselves and to you:

I want to challenge the blogotwittersphere to write an assessment they’re proud of. To pick a skill/concept/objective and write a targeted assessment that measures this objective at various depths. Or, if they already have an assessment they’re proud of, to share why they’re proud of it—what is it about this question/this series of questions that makes this assessment meaningful? That finds a way to assess both procedural and conceptual understanding. That gives students an opportunity to exceed expectations. That has an ‘explain’/’justify’ component. I don’t know if these things are possible for all skills and objectives, but this is why I want others to be thinking about it too.

The end goal is: create an assessment you’re proud of in terms of format or questions or depth or all of the above, and explain why you think this is something worthwhile.

(I tried to recast his challenge in my own words, and realized I was better off stealing the thing wholesale, with his permission, of course.)

Where Do I Sign Up?

If you’re interested in playing along at home, start with a one-minute survey. Then hop on the Twitter and spread the word! The more voices we have in the conversation, the better we’re all going to get.

What You Can Expect From Me

Once this blog post goes live, I’ll do the following:

  • Set up betterassessments.wordpress.com (the “home” for the better assessments conversation)
  • Gather already-existing resources together in an Assessment Authoring Boot Camp section of the blog (Daniel Schneider has agreed to lend a hand; additional volunteers welcome)
  • Put out an official “call for assessments” over a two week (?) period in the near future, including submission guidelines
  • Feature a small number (one to three?) of these assessments each week as guest posts on the blog (including the “explain…” bit from Daniel’s challenge), and invite the “better assessments” community to offer feedback, constructive criticism, etc.

As with any group project (and I hope this turns into a massive group project), better ideas will come as soon as brains other than my own start their wheels-a-turnin’. I’m not married to any of the details sketched out above, so long as we find a way to establish an ongoing and positive conversation about assessment.

The Dailyness is the Key

I feel I should explain the last bullet under “What You Can Expect From Me.”

Let’s dream big. Imagine that 100 math and science teachers from all sorts of different grade levels and courses submit assessments when the call goes out. The assessments range from decent to amazing, and we’re all stoked because 100 people (100 people!) played along with this little experiment and we have heaps of assessments to look at and learn from.

If we’re not careful, we’ll squander most of the opportunity for conversation presented by 100 such submissions. My intention is to highlight a few assessments at a time so that busy teachers (that’s us!) have an opportunity to dig into each assessment in depth, over the course of an extended period of time. (Whether or not my suggested approach will achieve the goal is open to discussion.)

I think we’ll experience the most growth as a community if we employ a slow-and-steady approach, rather than go after this all at once. It’s the reason many of us find blogs and Twitter more powerful tools for sustained professional growth than fantastic-but-isolated conference experiences once every year or two. The dailyness of our practice is the key to our growth.

What To Do With a Head of Steam

If this project isn’t dead in a few months, then I’ll share some details of the bigger vision I have for this assessment conversation. It has to do with recruiting and organizing people at various levels and in various subjects into assessment-writing cohorts. They’re exciting plans (at least to me), but possibly unrealistic. In the coming weeks I’ll invite some of you to tell me what has potential, what’s a waste of time, and what needs tweaking to become realistic.

Some Closing Thoughts

I think multiple-choice questions are generally inferior to free-response questions. I also think that both styles of “one-off” question are completely inferior to well-crafted performance assessments. However, I also believe that poorly-written MC and FR questions are inferior to well-written MC and FR questions. With that in mind, I think it’s entirely appropriate to allow MC and FR questions into the discussion at betterassessments.wordpress.com.

With that said, I think the MC/FR/Performance Assessment classification of assessment questions isn’t as helpful as the conceptual/procedural/synthesis approach described by Daniel here and here. I certainly like this latter three-part structure better than then conceptual/procedural/application framework I’d been mulling over prior to reading all these great blog posts on assessment.

Comment Time

Heart beating with uncontrollable excitement? Bored out of your mind and wondering how you made it to the end of another lackluster post? Have a suggestion? A critique? An idea? Drop a line in the comments and keep the conversation rolling.

Expressions Challenge

The Four Fours

In my first year of teaching I came across the Four Fours challenge. I loved it. I’ve always considered puzzles, brainteasers, and trivial challenges of that sort to be rather entertaining, so I went to town on the Four Fours right away. The problem gets better as you go: easier target numbers are out of the way and the real mental effort begins as you look to fill in the gaps.

Beyond the personal puzzle perspective, as a brand new teacher (my course load then was split 50/50 between 7-8 and 9-12) I considered this challenge to be a gem for my middle school students. Here’s a few reasons why:

  • Mundane-yet-necessary practice is made more engaging in the context of a challenge (just like in this problem).
  • Shifting the task from evaluating expressions to writing expressions ramps up the critical thinking component of the task. Students have to look for and make use of structure in order to bend the expressions to their will.
  • The problem is flexible and can be presented to individuals, small groups, entire classes (class vs. class challenge, anyone?), or with a twist (find as many expressions as possible with a value of, say, 23).

And Then It Happened: The Internet Failed Me

I’m sure there are more reasons why the Four Fours is awesome. If you think of any, share them in the comments. But I know of one reason why the Four Fours is not awesome. In fact, I know of one reason why the Four Fours is worthless. That’s right, useless. Totally devoid of any value.

Wait? Just a minute ago I was singing the problem’s praises. Why the dramatic turn? One reason:

The Internet

I typically love the Internet. Defender of the integrity and usefulness of Wikipedia and all that. But not this time. Here, the Internet failed me.

See, someone decided it woud be a good idea to ruin the Four Fours by posting entire solutions all over the place. Now any time I give this problem to students, they’re one Google search away from Four Fours glory.

My Solution

So what do you do if the Internet robs you and your students of a great problem? Make another one. Keep the good stuff (see the bullets above) and tweak the parameters.

Flash back to my first year. When someone told me the full solution to the Four Fours was online, I rewrote the rules and called it Expressions Challenge. Once I got going, it was easy to make additional versions. I’ve included the directions (and handouts I mocked up this year) for the first three versions, as well as some comments on how to tweak Internet-proof the problem further.


Here are the directions for the first three versions of the Expressions Challenge. Note that there is only one difference between the three: Use the numbers in (1) any order, (2) increasing order, or (3) decreasing order. Obviously, versions 2 and 3 are more challenging.

expressions.1 expressions.2 expressions.3


Just to be clear on the order element of the directions, here are examples for each version (1, 2, and 3, respectively):



And the handouts (nothing special):

Further Defense Against the Evils of the Internet

If the Internet destroys any of the challenges above, no problem. Just tweak the problem again. Use the numbers 1, 2, 3, and 4. Or 1 through 6. Or the first four odds (or evens). You get the idea.

Also, you could change the word “numbers”  in the directions to “digits” to open up some additional possibilities. And for the record, whether your students should be allowed to use decimals, percent signs, radicals, ceiling/floor/rounding functions, etc., is totally up to you.

Let me know in the comments if you find any of this useful, or if you have a similar challenge you use with your students.

The Great Blog Exchange

All Your Blogs Are Belong To Us

Strange as it may seem, the impending death of Google Reader has me on the hunt for more great blogs. I know I could go to a few of my favorite blogs, check out their blogrolls, and go from there. But personal recommendations feel so much more… personal.

With that in mind, I hereby announce the inaugural edition of The Great Blog Exchange.

From Me To You

My favorite three blogs Three Four of my favorite blogs are:

  • http://blog.mrmeyer.com/
    Not exactly a hidden gem, but prior to finding Dan’s site I didn’t know there was such a thing as a math blog. Great place to start, continues to inspire and challenge.
  • http://mathymcmatherson.wordpress.com/
    I’ve been thinking about assessment lately, and so has Daniel Schneider. Only, his thoughts (and performance assessments) are miles ahead of mine. Good reading!
  • http://christopherdanielson.wordpress.com/
    If there was nothing else on Christopher’s blog besides the conversations with his kids, it would still be one of my favorite blogs. (P.S. There is much, much more.)
  • http://onegoodthingteach.wordpress.com/
    Had a tough month teaching? Me too. Reading One Good Thing is like group blogging therapy. Three posts and you’ll feel better already. I promise. (And if you start looking at each day through the lens of what you might post as a guest-blogger, you’ll feel even better.)

From You To Everyone

Ready to play along? Leave a comment with your favorite one, two, or three math/science/tech education blogs. Add a (brief) note about why you like each one, or just do a drive-by link drop.

P.S. Feel free to share old blogs, new blogs, famous blogs, or hidden gems. If no one shares this or this because they’re not obscure enough to mention, then we’ve collectively missed the point. Let’s share it all, and help newbies like me get to 100 amazing feeds in our soon-to-be-dead Reader lists. (Don’t worry, I’ll have an exit strategy soon too.)

Tasks and Assessments

More Awesome, Please

Either I’m a glutton for punishment, or there’s just too much awesome on the Internet and I can’t help myself. Whichever is true, I want to build something, and I need your help to do it. Here’s what I propose:

Let’s do for assessment what Dan Meyer, Andrew Stadel, Fawn Nguyen, and countless others are doing for rich, engaging tasks.

Here’s what I mean. As a math teacher, there are two things I need more than anything else: awesome tasks and awesome assessments. And maybe it’s because I just joined the party, but it seems like people are absolutely killing the task-creation side of the equation right now. The number of people creating tasks, as well as the number and quality of the tasks they’re creating, is exploding. And with some recent changes, Dan’s 101qs.com appears to be morphing into a place where entire tasks can go to live. I hope I’m right. If I am, the proliferation of creators and their creations will only accelerate.

But that’s only half of the equation. I need more than great tasks. I also need great assessments. I firmly believe that the quality of my courses will rise or fall with the quality of my assessments.

Why is my AP Calculus course stronger than my Precalculus course? The assessments my Calculus students take (throughout the year, as well as in May) are better than the ones I give my students in Precalculus.

Why am I stoked about the Common Core? It’s not because the standards are better than my state’s old standards (which they are). It’s because the assessments promise to be worlds better than the CST (fellow Californians know what I mean).

Weak assessments allow me to teach a weak course and get away with it.

But awesome assessments force the issue. If students aren’t doing some serious learning, we’re going to know. And it’s going to be uncomfortable. And we’re going to have to get better.

So Let’s Get Better (By Sharing Like Crazy)

So what if we all started sharing more of our assessments? What if they had a place to live, with room for rubrics and commentary and comments and suggestions for improvements and whatever else will make it easier to share and steal and tweak.

Let’s share the ones we think are fantastic (like this one from Daniel Schneider) so others can learn from our best moments. Let’s share the ones we’re embarrassed by so others can tell us why they’re terrible and how to make them better. Let’s share the ones we’re not sure about, so others can tell us what works and what doesn’t, what to keep and what to throw away.

Let’s start sharing. And giving feedback. And revising. And making our classrooms better by making our assessments better.


Are you in? If so, head down to the comments, hit me up on twitter (@mjfenton), or drop me an email (mjfentonatgmaildotcom). And by all means, let’s all use our megaphones to get others involved.

I’m next to nothing without you guys. But together… This could be exciting.

More than Skillful?

I’m new to the standards based grading world. I’ll share more in another post about what I’m loving, what I’m struggling with, what I’m dreaming about, how I want to use the power of the Internet to make all of my assessments fantastically awesome, etc.

But a question just popped into my head after a rather successful (though entirely skill-focused) class period in Honors Algebra 1:

How do you use standards based grading to help your students become more than just skillful?

My current implementation is heavy on skills, and I’m having trouble moving beyond that (more a shortage of time than vision, but my vision is lacking as well). I have some ideas of my own on how to use SBG to create a classroom where skills are the launching point, not the end goal (again, future post forthcoming), but I’m curious to hear what others think as well.

To the comments, if you please!

Quadratics Matching Activity, Take 2

Visitors and Commenters? Woohoo!

I’m amazed anyone reads this blog, and even more blown away that people have posted so many thoughtful comments. Shortly after my long-winded sky-is-falling post, I added a quick note about launching an activity with as few words as possible. There were a few great comments on this shorter post about how to improve one particular activity (matching equations, intercepts, and graphs of quadratics).

The comments that caught my eye include:

Could you build on the task with an addition to the end where they create their own quadratic and then write up a key for the graph, intercepts and factors? They could switch it with another group and verify their answers? – Dan Anderson

One thing I’ve done occasionally with matching activities is deliberately leave one out. So they end up with an equation that has no graph, or vice versa, and have to generate the missing one. For added chaos, leave out one of each – just let them know that this was done… – Gregory Taylor

Love this activity! I think the concise written directions are a good idea, too. On my first day of Algebra 2 class, I had a similar but less pretty handout where each quadratic has a graph, an equation (in some form or other), a table of values, and a word problem. Each kid as they walk in the door gets one, and they need to find the others who have the same quadratic in order to form their groups of 4. – Joshua Zucker

Activity Revamp

So tonight, while standing guard next to the boys’ bedroom door (they have a tendency to leave their beds when they should be drifting off to dreamland; my wife calls it whack-a-mole, probably because of this)… Where was I? Oh yeah, standing guard…

So while I was standing sitting guard next to the boys’ door I revamped my rather unassuming matching quadratics activity to include some of the suggestions above. (Disclaimer: My activity doesn’t include Joshua’s table of values or word problems, but I think those are awesome ideas, and will probably find a way to include them in another activity, either for linear or quadratic functions.)

For reference, the old activity handout is here. And for what it’s worth, the new one is here. My game plan is to start with an entire-class matching activity and follow it up (either on the same day, or on another day for review/additional practice/to beat a dead horse) with a small group activity (groups of two or three students, matching at their tables). For my students who don’t hate school and who think meaningless competitions of an academic nature are enjoyable (read: third period, not fifth period) we might play three quick rounds of “fast as you can” matching. Fist bumps to the fastest group in each round, and fame and glory for the fastest time of the day.

I think the new wrinkles make it a much better activity. We’ll see what my students think/how they respond. If you use it with yours, let me know how it goes.

P.S. The handout no longer includes directions, as I’ve included those on a slide that can be displayed for the entire activity. (Once we start cutting up the old handouts, the directions made their way to the blue bin by the door pretty quickly.)

Pockets of Time

I’m a little worn out after my last couple of posts, so I’ll aim for something more cheerful today.

Several years ago (okay, maybe closer to 20 than several) my mom went on a trip with a friend to Monterey. She stopped at a game shop, picked up this little gem, and brought it home for me and my sisters to play.

set_box_ over25

The game consists of 81 cards. Each card has four attributes (color, number, shape, shading) and each attribute has three flavors (red, green, purple; 1, 2, 3; squiggles, ovals, diamonds; and open, striped, solid). The goal:

Find a set of three cards where each attribute is either all the same or all different on the three cards.

If that explanation isn’t sufficiently helpful (it usually isn’t enough for my students), then check out the online (semi-creepy; I usually mute the audio) tutorial here.

At any rate, I have since played untold thousands of games of set, first with the physical deck of cards, then using the (free) online daily puzzle, and more recently on the iPad app. Partway through my first year of teaching I began playing the daily puzzle with nearly all of my classes nearly every day of the week. This year I’ve begun using the iPad app (since it offers a few additional ways to play, including a basic mode where the shading component is simplified by using only the solid cards). Regardless of how I’ve accessed the game, here are a few of the benefits to my students, at least as I see it.

  • When we start with Set at the beginning of class, nearly every student is engaged.
  • It’s a great way to develop spatial reasoning (probably a weak part of my courses, aside from this game/puzzle).
  • With a little bit of thinking it can be turned into a competition between classes.
  • After teaching the kids how to play, it lasts only 60 seconds (for basic) or 90 seconds (for advanced).

This last point is really what inspired me to write this post, as I’ve been searching for short, engaging activities to weave into my classroom this year to fill out the pockets of time at the beginning or end of class. While I’ve been using the Set Game to start class for years, the online puzzle only offered one game per day, so repeats in a given class period were off limits. With the iPad app, I can pull up as many puzzles as I want, so when students are finished with an assignment and there are two minutes left I can fire up the app and challenge them to another game.

Two other great ways to fill those extra minutes (whether they fall at the beginning, middle, or end of a period) are Andrew Stadel’s Estimation 180 and Fawn Nguyen’s Visual Patterns. They’re not quite as short as a game of Set, but in just a few minutes I can have the students doing something far more interesting (and mentally profitable) than sitting quietly while they wait for the bell to ring.

So here’s my list o’ questions to you:

  • Have you ever played Set? If so… Cards, online, or app?
  • Do you use Estimation 180 with your students? If so… How long do you spend on a typical estimation challenge (start to finish)?
  • Do you use Visual Patterns with your students? If so… How often do you use them and how much class time do they take (once your students have become familiar with the concepts/format)?

And if you just answer one question, make it this one:

  • What do you do with your students when your students finish an activity or assignment and you look up at the clock to realize you have two minutes left?

P.S. If you’re interested in hearing the three ways I play the game with students in class, just holler in the comments. I’m happy to share, but this post needs to be done and I need to be in bed.

Launching an activity: Cut to the chase!

Howdy. If you’re reading this and you haven’t read my super long post from last night (technically, it went live early this morning), this post might not have enough context. At any rate, I’m aiming for a better day today in fifth period (Algebra 1) and my game plan is this: When giving directions for a group activity, cut to the chase.

The original activity is here. In the past, I’ve introduced this activity with a minute or so of verbal directions and then cut the kids loose. I fell on my face yesterday using that approach (verbal directions as the means of launching an activity), possibly because I haven’t spent the necessary time clarifying in my own mind both the goal of the activity and the directions for students.

My attempt at more concise directions (in non-verbal form) comes in the form of these slides:

activitylaunching.003 activitylaunching.004

I’ll probably let you know how today goes in another post. I’m hopeful that this new wave of constant reflection will provide my students (at least in the long run) with a better teacher. In the meantime, feel free to comment on what you like/dislike about the activity and the “launching” (key question and directions) of the activity.


Blogging as Therapy

My Inflated Sense of Awesomeness

I used to suffer from an inflated sense of awesomeness. I blame my honors students. Now, stay with me for a moment. I don’t dole out blame like this too often, but I think I have a case here.

Picture this daily routine from my not-so-distant past: I bring mediocre to a classroom full of awesome kids on a regular basis. The experience is, well, awesome. Such regularly fantastic interactions lead me to believe my teaching is, well, fantastic. Little do I know, the awesomeness is often in spite of my efforts, rather than a result of them. Things only go swimmingly because my kids are so swell.

Reality Settles In

I mentioned that I used to suffer. No longer. In fact, my sense of awesomeness has been plummeting for a couple of years. I’m so mixed up right now that it’s about to crash into the floor. Here’s a graph of my current crisis in confidence:


Good News, Bad News

So the bad news is this: I’m not half as good at this teaching thing as I thought I was, and that’s more than a little discouraging.

Here’s the good news: I’m not a quarter as good as I think I could be, and that’s more than a little exciting.

More good news: I’ve realized that my primary teaching style (I’d call it “conversational direct instruction” with a lot of “What do you see? Why does that happen? How can we generalize?” in an all-eyes-on-the-front-of-the-room style) is seriously limiting my students’ potential.

I think the “What do you see? Why does that happen? How can we generalize?” elements of my teaching are incredibly valuable. I don’t plan on throwing those out, and I only hope to get better at creating opportunities for students to ask and answer questions like these.

But the all-eyes-on-the-front-of-the-room style is starting to kill me. What’s worse, I expect it’s been killing some of my students for a while. The delay in seeking a remedy is because my mostly-honors students have been so amicable and cooperative that they haven’t pushed back through bad behavior, inattentiveness, or poor learning results.

Enter this year’s course load. The pushback is alive and well. I have a few classes this year that are helping me see through the mirage and have given me a clear view of my strengths and weaknesses.

Class Portraits

Take today’s classes in fifth period (Algebra 1) and eighth period (Honors Algebra 2) as portraits of what sometimes goes wrong in my room.

In Algebra 1 we’re making connections between the x– and y-intercepts of the graphs of quadratics and their equations (in factored and expanded form). At least, that’s what we’re trying to do. Today was an absolute train wreck of a lesson. Their attentiveness during yesterday’s lesson (where we reviewed some factoring techniques to prepare for today) was so poor that I decided to transform today’s direct instruction lesson (remember, they’re almost all written that way right now) into a small group activity. I figured if they spent less time listening to me walk through problems and more time thinking their own way through problems that they would have a better chance of making the relevant connections (which are not terribly profound). We eventually got there, but I felt like a slave driver while giving what should have been 30 second “getting started” directions that lasted far, far longer because I couldn’t hold their attention for the life of me. I left class thinking “There must be a better way.” So what is it? Type the directions on a Keynote slide and keep my mouth shut? Type more detailed activity directions out at the top of the handout so they don’t have to wait for me to get started on the activity started? Would they even jump into the lesson right off the bat without any teacher explanation? Is it even possible to train a class to become self starters when they’ve always relied on me as their teacher taking the lead? I expect that it is, but how?

Just to be clear, as I tried to move away from direct instruction today, we couldn’t even get past the directions for their small group task. At the risk of sounding conceited, I feel it’s appropriate to note that outside of this group of students my classroom management is typically stellar and discipline is a non-issue. With that being said, it’s still on me to make things work with this group of kids. It’s just going to take better lessons, better ideas, better systems, etc.

In Honors Algebra 2 I fight another battle. These students are noticeably more interested in the mathematics, and their behavior is mostly excellent. However, they struggle to remain focused, partially because it’s the last period of the day but also (I think) because the pace of our discussion is just right for about one third of the students, too fast for another third, and too slow for another third. I want to break out of direct instruction mode so that students can proceed at their own pace. I expect all of the students would learn at least as much as they do now, and a full half of the class might have an opportunity to learn a great deal more because they aren’t tied to my pacing for the entire lesson. But I don’t know how to make this happen.

More Bad News and a Plea for Help

As you can sense, there’s some more bad news: Even though I’ve identified what I want to change (my teaching style) I don’t know how to get from here (“conversational direct instruction”) to there (something better than what I’m doing now), or really even where “there” is.

So here’s what I need from you. I need some help vision casting (what could my classroom look like). And maybe more importantly, I need some advice on how to get there.

A few things to keep in mind while you’re dishing out the good stuff:

  • I typically teach 4 to 7 different courses, so lesson planning, activity creation, and so forth, is a challenge.
  • I desperately want to design a curriculum where the most challenging thing for students is to think about the interesting, non-trivial tasks they have been given. I do not want to remain mired in a curriculum where the most challenging thing for students is to pay attention when every part of their being is shouting “Boring! Don’t pay attention, it’s boring!”
  • A part of me wants to go all Sam Shah on my students with guided discovery packets like this, but I’m terrified of the monumental task of transforming my direct instruction lessons.
  • I want to include more open-ended problems in all of my courses.
  • I think well designed three act tasks are the bee’s knees, but I’m currently more of a stumbling bumbler than a Dan Meyer when it comes to creating my own.
  • About four years ago I shelved my Algebra 1 and Algebra 2 books and wrote my curriculum from scratch (lessons, homework, and assessments, the whole shebang). The curriculum is heavy on concept and procedure, but light on application (i.e., problems in genuine, engaging contexts).
  • I still use a textbook for Precalculus (Foerster), Calculus (Foerster again), and AP Statistics (Starnes), though I may “escape” from the Precalculus book when we transition to Common Core in 2014-2015.
  • I’m trying to build a Pre Algebra course from scratch, aligned to Common Core standards, but it’s been an uphill battle (and until recently, almost entirely based on direct instruction for new content).

So there you have it. I’m in trouble. And you can help. Get thee to the comments!

(By the way, if you made it this far, you deserve a gold star. Two gold stars for anyone who leaves a comment.)