Month: August 2013

Math 753 Background

In 2010 I team taught a class in the grad math/science program at Fresno Pacific University. My teaching partner (Dave Youngs) was more a mentor than a colleague at that point, as I had only recently finished my journey through the masters in education program at FPU. I benefitted greatly from the opportunity to work side by side with someone who knew the ropes, and I enjoyed that sort of partnership (first with Dave, and later with another mentor, Richard Thiessen) for three or four semesters. Afterwards, I tried my hand flying solo through a couple of courses.

When my wife and I had twins in November 2012, I took a break from the adjunct instructor gig. The girls are almost a year old now (and diapers are expensive!) so with my wife’s full blessing and encouragement I’m back in the classroom. This semester I’m teaching Math 753, Concepts in Algebra, to a small (but amazing) group of teachers whose positions range second grade to middle school. Our first session was this past Wednesday (August 28).

This is actually the same course I taught in my first semester as an adjunct instructor, working side by side with Dave, but I feel like it’s brand new for two reasons. (1) I’m no longer team teaching. All of Dave’s expertise is now an email or phone call away, rather than right there in the room while I’m teaching. (2) In the three years since I first taught this course, my philosophy and practice (as a teacher of adults, as well as a middle and high school teacher of mathematics) have shifted more than a little bit.

Why Post on the Blog?

“Great Mike, thanks for sharing. Um… why are you sharing this?”

After each class session I’ll post a brief summary or reflection, a small collection of links to resources used or discussed in the class, and—more often than not—a reading assignment (in the form of links to articles and/or blog posts). My purpose for posting these sessions (and hence this background) is threefold.

  1. I want the participants in the class to dip their toes into the mathtwitterblogosphere. I could easily share resources with my students another way (Moodle, Dropbox, Edmodo, Piazza, etc.) but by posting them here, I’m hoping to use my blog to draw them into reading more widely and exploring more deeply the strange and amazing community that I discovered back in March.
  2. By making the course goings-on somewhat public, I’m motivated to design a better course than I might if everything we did in Math 753 remained hidden in our own little corner of the world. It’s not that I would just phone it in, but in sharing publicly I’m putting a bit more pressure on myself to create an even more meaningful course.
  3. In the off chance that someone not in the class is interested in exploring what we explore… Well, have at it. 🙂

Links

These will all be dead links until the actual sessions have occurred (and the post-session writeup post has been written and posted), but eventually easy access to each session post will be found below.

Session 1 (August 28, 2013)

Session 2 (September 4, 2013)

Session 3 (September 11, 2013)

Session 4 (September 18, 2013)

Session 5 (September 25, 2013)

Session 6 (October 2, 2013)

Session 7 (October 9, 2013)

Session 8 (October 16, 2013)

Session 9 (October 23, 2013)

Session 10 (October 30, 2013)

Session 11 (November 6, 2013)

Session 12 (November 13, 2013)

Session 13 (November 20, 2013)

Session 14 (November 27, 2013)

Session 15 (December 4, 2013)

Session 16 (December 11, 2013)

Comments

I’ll close the comments for this post, but leave them open for the individual sessions (partially because I will share the course description/goals in the Session 1 post). If you have thoughts on how to make this experiment more useful to anyone involved, please share them. If you have recommendations for our reading assignments (articles, blog posts, books, Twitter chats, etc.), let me know. In the session posts, of course. 🙂

Transition to Integrated Course Sequence with CCSSM

This is the sort of post that in years past I would have scribbled in some word processor or private blog. I often write to clarify my thinking and set personal and professional goals, and I’ll do so again here. My reasoning for making this round of reflecting and planning public is twofold:

  1. It will force me to consider my assumptions, goals, and specific game plan even more carefully knowing that others might read what I write.
  2. It may help others process through their own transition, whether to an integrated course sequence or a more traditional slicing-and-dicing of the CCSSM content standards.

Whether the second of these two reasons will actually play out, I don’t know. But the value I’ll derive from the first (reflecting and planning publicly) is reason enough to proceed, so here goes.

My Schedule

Our school has seven academic periods during the normal 8 am to 3 pm day. A full teaching load is six classes, plus one period to prepare. In recent years I’ve elected to work during my prep for a slight pay increase (diapers are expensive!).

This year my schedule is filled with five classes and two periods we’re calling “Program Development.” During these two periods (2nd and 7th) my task is to redesign our 7-12 mathematics program to align with the CCSSM content and practice standards. That’s a lot of planning time each day, but it’s a fairly monumental task, especially considering that we’re transitioning to an integrated course sequence for grades 9-12.

My Assumptions

This could get out of hand (lengthwise) rather quickly, so I’ll jump right in with the bullets to share some of my assumptions:

  • An integrated course sequence in grades 9-12 will be more difficult to design and more difficult to teach, but (if done well) will provide students with a richer, more connected mathematical experience (provided I don’t settle for what @NatBanting describes here).
  • Due to the small size of our school and the constraints on budget and staffing (there are two faculty members—myself included—in the entire 7-12 math department), we need to make the transition to CCSSM content in grades 7-12 all at once. (In other words, we don’t have the staffing necessary to transition one course/grade level at a time, or to make the transition gradually over a number of years, essentially running two programs side by side in the interim.)

I’m calling these assumptions because that’s what they are, at least in part. It might be better to call them semi-researched opinions/positions. In any case, I hope some of you will push back and play devil’s advocate, especially on the second point above. If you think it would make more sense (in my small school environment) to roll out the transition one, two, or three courses/grade levels at a time, please share!

My Goals

By June 2014 I want our course offerings to include:

  • Integrated Math A
    (CCSSM Grade 7 content standards)
  • Integrated Math B
    (CCSSM Grade 8 content standards)
  • Integrated Math 1
    (CCSSM high school content standards)
  • Integrated Math 2
    (CCSSM high school content standards)
  • Integrated Math 2 Honors
    (CCSSM high school content standards, including STEM (+) standards)
  • Integrated Math 3
    (CCSSM high school content standards)
  • Integrated Math 3 Honors
    (CCSSM high school content standards, including STEM (+) standards)
  • AP Calculus AB
    (aligned to the College Board’s AP Calculus Course Description)
  • AP Statistics
    (aligned to the College Board’s AP Statistics Course Description)

Two notes:

  • Students who intend to take AP Calculus AB will be required to complete Math 2H and Math 3H (where, theoretically, they’ll learn the STEM (+) standards and other topics necessary for success in Calculus)
  • I’m not sure if we’ll offer a Math 1H course. If we do, it probably won’t include any of the STEM (+) standards, and I’m currently running short on ideas for how to differentiate it from the non-honors section of Math 1.

While aligning our courses to the CCSSM content standards will be an important task, I consider it even more crucial that we infuse all of our 7-12 courses with the eight Standards for Mathematical Practice. I want our courses to help students grow in their ability to make sense and persevere, reason, argue and critique, model with mathematics, etc. The content itself is important, but it’s the habits of mind that will last.

My Game Plan

It’s rather easy for my to become overwhelmed by the magnitude of this whole undertaking. But I also get incredibly excited when I think about chipping away at specific tasks in transforming our program, my courses, my teaching, etc.

With those two ideas in mind, I believe it will be helpful to break down the entire project into a sequence of smaller, more manageable tasks. In theory, this will keep me sane, on track, and encouraged. (We’ll see whether that’s the case.)

I also hope that by planning in this way it will be easier to share resources with others (in both a “give” and “take” sense), and that I’ll have more opportunities to collaborate. For example, if I ask on Twitter, “Who wants to help me develop a CCSSM-aligned course sequence for grades 7-12 with integrated courses for high school,” I’ll probably hear nothing but crickets. However, if instead I ask, “Who wants to help me create a concepts and skills list for, say, an integrated course for Grade 9,” I might have a few more takers.

So with that background, here is my plan of action, laid out more or less in the order I’ll proceed:

Curriculum (Draw the Big Picture)

  • Arrange the high school standards into courses (whether that involves adopting something like this as is, using or modifying California’s integrated pathway (see pages 95-123 of this document), or starting from scratch, I don’t yet know)
  • Identify the three or four “big ideas” in each course (and later, develop six- to 12-week units around them)

Note: I see myself reading more of this blog and these books in the near future.

Assessments (Set the Targets)

  • Develop performance task assessments for each of these units (emphasizing “synthesis skills”)
  • Write a “concepts and skills list” for each course (possibly by using these as a starting point)
  • Develop assessments for each of the items on the “concepts and skills list” (ideally, assessments worth posting here)

Lessons (Work Out the Details)

  • Create a list of individual topics (based on the “concepts and skills” list) for each “big idea” unit
  • Select, adapt, or create a rich task to launch each “big idea” unit (one that we can refer back to throughout the unit)
  • Sketch a rough outline of individual lessons for each topic
  • Write individual lessons for each topic (this should only take, roughly, forever)
  • Select, adapt, or create appropriate homework assignments for each lesson (though I probably should read this—currently sitting at my bedside table—before forging ahead)

That’s All for Now

If you need to tackle any of those smaller projects and you’d like to join forces for a bit (whether we collaborate through Dropbox, Google Drive, Hangouts, or some other tool), I’d love to have some help and/or lend a hand with your transition.

Drop me a line in the comments, or send me a note on Twitter (@mjfenton) if you’re interested.

Rich Math Tasks

Thursday evening I asked Frank Noschese (@fnoschese) and Elizabeth (@cheesemonkeysf) a question about whether they thought there was any value in students using a reductive, drill-and-kill math practice exercise platform, provided that it was accompanied by rich tasks and assessments in a classroom that demands synthesis and critical thinking, and provides students with opportunities to develop mathematical habits of mind.

I received a reply, but I’m more interested in a tangential question @NatBanting asked in the middle of the exchange:

What Do I Even Mean?

I’ve been throwing that phrase (“rich tasks”) around a lot more lately, in tweets, blog posts, workshops, and conversations at school and at home (my wife is either amazingly longsuffering or genuinely interested—maybe both?—when it comes to talking about math education). So what exactly is a “rich task”? What do other people have in mind when they use the phrase? What do I mean when I use it?

I told Nat that I’m still working that out in my own mind, but I think it’s time to clarify what I mean, if for no other reason than to have a better sense of what I’m looking for when I try to find, adapt, and/or create rich tasks for my own students.

Here’s What I Do Mean

A rich mathematical task is one that…

Has a low floor and a high ceiling

The first of many ideas I’ve stolen from others, this one from so many sources I don’t even know who to credit anymore. Most recently, Dan Meyer has me thinking about this in his Makeover Monday series. The bottom line: everyone can start, no one can truly say they’ve exhausted the problem’s potential (at least not in a 50-minute period).

Has multiple entry points, invites use of multiple representations

Student A starts by exploring numerically, Student B begins by investigating graphically, Student C jumps in by reasoning algebraically, and I don’t have to tell two of them that their approach is a dead end because—even if they don’t always make it—there is fruitful territory a little further down the path in any of their approaches.

Has multiple solution paths, provides opportunity for rich discussion

If there’s only one way to solve the task students lose out on the rich discussion of making connections between various approaches and teachers lose the opportunity to build a mathematically coherent, concrete-to-abstract storyline as they orchestrate these discussions.

Integrates multiple topics

I owe a lot of what I’m thinking here to a single word Daniel Schneider used in a post about assessment. After my initial foray into standards based grading left me dissatisfied with an overly fractured curriculum, I’m now placing a high priority (philosophically, at least) on tasks and assessments that bring multiple topics together. A rich task, in my estimation, should demand that students wrestle with multiple topics from multiple domains (if I can use the term in the CCSSM sense).

Engages student interest, is mathematically/cognitively challenging

I’m a little mixed up here, because I believe engaging students’ interest is massively important, but I’m not ready to throw away tasks that fail to generate buzz among students if I know they nevertheless provide great opportunities for exploration and discussion.

Here’s What I Don’t Mean

To clarify what I think a rich task is, I’ll share a few thoughts on what I think a rich task is not:

A well-crafted, but constrained guided-discovery activity

I value this kind of activity, but when students are guided along a specific path to a specific goal, it pushes the lesson into a different category for me.

A thoughtfully constructed lecture or an engaging presentation

If the instructor is doing the heavy lifting during class, I would say the students are not engaged in a rich mathematical task. I’m not opposed to heavy lifting, especially in preparation outside of class, but students need to play an active, central role in exploring/solving/reporting if I’m going to use the “rich task” label for an activity.

A challenging problem for which students already have a tried-and-true method

I have a large stack of started-but-not-finished books, some related to math and education, others not. George Polya’s How To Solve It is on the list, though I’ve read enough of it to be provoked and inspired, particularly by the distinction Polya provides between a problem (solution/method not known) and an exercise (solution/method already known).

I’ll Close with a Link…

Incidentally, after typing out the post, I Googled “what is a rich mathematical task” and found this.

…And an Invitation

I would love to hear what you think are the key characteristics of a rich mathematical task. Drop a line in the comments or send me a line on Twitter.

A New Kind of First Day

Today marked the first day of the 2013-2014 school year for me. It was, all in all, a wonderful day. Teaching at a relatively small K-12 school, I have an opportunity to work with some students for two, three, or even four years in their 7-12 grade experience. Seeing students who I’ve come to know so well over the past few years walk through my classroom door on the first day of the new year is a tremendous blessing, and it’s always fun to see how they have matured over the summer months in their transition from 7th to 8th, middle school to high school, or maybe even junior year to senior year.

The Highlight

I won’t bore you with the details, but the highlight of my day came in watching my AP Calculus AB roster (which appeared to have only 6 students when I checked online late last week) grow to 11 students by the end of the school day on Monday. This included three unexpected, last-minute additions, and I’m thrilled to have these students join our small but amazing group. (For reference, I typically have 10 to 15 students in Calculus, and our graduating class has been around 50 students in recent years.) I’m excited and honored that these students (all 11, really) have decided to challenge themselves with another year of math, and have even sacrificed other classes they were interested in to make it possible. Plus I think we’ll have a blast this year.

The Struggle Continues, Intensifies

Despite all the good vibes, I struggled through some parts of today. I’ve worked relentlessly over the past nine years to create as strong a math program as I could imagine at the school. If my today-self could time travel (with a USB flash drive or a link to a Dropbox folder) to meet, say, my 2006-self, that older version might think something along the lines of, “Wow! Most of what I’ve imagined for the math department is a reality. That’s super swell.”

Here’s the problem, though, and I have many of you to blame for it: The ceiling on what I can imagine has been blown off, and I’m now confronted (in the middle of nearly every class) by a dozen or so notions of how the lesson I’m smack-dab in the middle of could be improved, become less terrible, etc. These thoughts don’t even allow me the grace of finishing an example or an activity; they jump right to the front of my brain even as I’m presenting/discussing/guiding.

So after a few months of relatively stress-free hanging out in the MTBoS, I see the tension between what I believe should happen in the classroom and what I’m currently doing (the struggle between my philosophy and my practice) not only resuming, but (rapidly) intensifying.

Determined to Grow

While the MTBoS is largely to blame for this increased tension, it’s also likely to provide the inspiration for much of the personal growth I’ll experience in the coming months. It may be exceptionally frustrating at times, but I’m determined to make this struggle (my first full year of MTBoS-fueled, classroom-based struggling) exceedingly productive.

Goals for 2013-2014

I spent the summer alternating between tuning in to and checking out from Twitter and blogs, including my own. Inservice at my school begins in two days, and students will arrive August 12. As the summer winds down I’ve started thinking about my blog-related goals for the school year. This will be my first full year hanging out in the #MTBoS, so I want to be intentional about the ways I engage, particularly in how I use this blog to grow as a teacher.

These are subject to change throughout the year (and possibly even during the course of this post), but right now my framework for getting better has three five categories:

  • Implementing
  • Creating and Sharing
  • Reflecting
  • Collaborating
  • Transitioning

I’ll share a few goals in each category, not only to let others know what’s bouncing around my head as the school year begins, but also to force myself to organize my own thoughts and build in some personal accountability by leaving a paper (er, page) trail.

Implementing

In the few months I’ve spent engaging with other math teachers through reading blogs and following conversations on Twitter, I’ve been exposed to a wealth of rich mathematical tasks for the classroom. If the members of the #MTBoS are a chorus of angels on one shoulder, urging me to break out of my direct instruction-heavy approach to incorporate more rich problems and tasks, then my own experiences as a student, my initial teaching style, my tendencies toward control and perfectionism, and my at-times overwhelmingly-varied course load (typically four to six different preps) are a drove of naysaying demons on the other shoulder.

However, thanks to what I’m learning in Smith and Stein’s Five Practices (and reading on blogs), I’m gradually working up the nerve to take what I hope will be major strides this year. I’m finding the thoughtful intentionality of the five practices reassuring, as I’ve always feared relinquishing control of the mathematical flow of my classroom and assumed (incorrectly, I now believe) that this was a necessary part of implementing tasks and fostering student solution-centered mathematical discussion. As I try and fail and tweak and try again and retweak and find some measure of success along the way, I’ll reflect on these experiences here on the blog.

If you’ve had rich, engaging mathematical tasks on your “maybe later” list for a while, join me this year in making concrete plans to include them in your classroom on a regular basis. I hope you’ll reflect on your own experience, preferably by blogging about it, or at the very least by leaving the occasional comment on this blog. Speaking of concrete plans (and practicing what one preaches), here’s my goal:

One rich task each month in each course

Given my teaching schedule next year, that means 40 tasks. Excuse my while I go hyperventilate.

Okay, I’m back. And while I’m a bit freaked out by the prospect of shifting a core part of my teaching approach, I’m also excited about these 40 opportunities for growing in my craft next year. I think I’ll keep some paper bags in my desk at school, just so I’m prepared.

Creating and Sharing

The #MTBoS is full of amazing people. I regularly feel out of my league in this diversely awesome group, particularly in two categories: (1) thoughtfulness, completeness, and coherence in educational philosophy and (2) relentlessness in creating (and sharing) amazing resources. This year I want to shift my interaction with this community from primarily receiving to a combination of receiving and sharing. Not only out of a sense of gratitude for all of the excellent things others have made that I’ve enjoyed, but also because I think my quality as a teacher will grow through the practice of creating, sharing, receiving feedback, revising, etc.

As the school year begins, I’ll turn the lights back on at the Better Assessments blog. I have big plans for September (more on that later). I will also begin organizing a series of proportional reasoning challenges (tentatively titled The Running Game) so they’re available to other teachers as I create them throughout the school year for my own students. My 101qs radar will remain up, and I’ll try my hand at a few more Three Act tasks. This is distinct from my first goal since many of the bumps on the “creating and sharing” road will stem from my imperfect tasks (rather than imperfect implementation). At any rate, I’ll blog about both experiences here, and hopefully grow as a teacher through the process.

Reflecting

I suppose most of my posts in the coming year could be filed under this category. But it’s worth mentioning separately. When I started the blog earlier this year and saw a spot for a subtitle, I picked better through reflection. I want to get better at this teaching gig, and I know that reflection is a key means to that end. Over the years I’ve tinkered with different approaches to reflection, but nothing I’ve tried has been as helpful as working through my thoughts in a public forum. Knowing that someone else may read a post in which I reflect on the effectiveness of, say, my approach to homework leads me to be that much more thorough in my self-examination. I look forward to continuing more of the same this school year.

Collaborating

My first real #MTBoS buzz came from collaborating with Justin Lanier and Dan Anderson on Daily Desmos. Inspired by a tweet from Dan, I suggested a daily match-my-graph project. Several days later we had a head of steam, an unofficial endorsement from Desmos, and a growing team of collaborators. The entire Daily Desmos experience has been one of my favorite thus far in my #MTBoS tenure, probably because my involvement on this project fits more on the “give” side of the give-and-take scale.

While this next project has stalled (I’ll blame myself and summertime), I’m excited to kick start Better Assessments back into action. I hope others are interested in joining the conversation, but even if I have to fly solo for a while, I plan to forge ahead with some ambitious Algebra 1 assessment makeovers in September.

Transitioning

I’m looking for other ways to collaborate next year, particularly as I transition our department from the old Mathematics Content Standards for California to CCSSM. I’ll have some prep time set aside specifically for working through this transition (designing our courses, creating and curating tasks, developing SBG and performance assessments, etc.), and I’m hopeful that by collaborating with others on various projects (asynchronously, I assume) I’ll be able to multiply my own productivity and serve other teachers, school, etc., with the materials I/we create.

Join In, or Hold Me To It

So there you have it. My goals for the upcoming year. I invite you to join me in thinking about how to make the most of next year by writing your own Goals for 2013-2014 post, or by dropping a line (or link) in the comments. And I certainly hope people will hold me accountable now and again by asking how things (e.g., The Running Game, the Better Assessments blog, etc.) are coming along.