cheesemonkey wonders

cheesemonkey wonders

Wednesday, December 12, 2012

Go graph yourself!

Yesterday I used masking tape to turn the floor of my classroom into a coordinate plane. 

Students had to graph themselves, then find the slope of the line between themselves and various other points in the room. A good time was had by all, and a few insights were had.

Today I think we will also graph all the bits of trash that usually get left on the floor by lunch time. That will give us time to set up for a fierce game of Coordinate Plane Battleship.

Oh, the things we do to promote a deeper conceptual understanding! :)

Friday, November 16, 2012

Standards-Based Grading, or How Teaching For Mastery is Different

Teaching for mastery is different.

Teaching for mastery especially means giving up a lot of old and cherished assumptions about assessment. Anybody who has adopted SBG in any way can attest to this. But I am continually amazed at how unwilling many of us can be to letting go of old, ineffective methods, beliefs, and assumptions about assessment.

At its essence, valuing mastery means not only tracking relative mastery but also accepting mastery as the measure of student success in our classrooms. And that means letting go of the value we have always placed on the routinized behavior of the the dutiful student.

This is is probably the hardest shift of all.

As I shifted over to SBG, I noticed how much of our system of math teaching is organized around students being merely dutiful: sitting still, listening quietly, practicing silently, accepting information without challenge. It's a model of student passivity that places everybody into the known and accepted hierarchy. The "good" students land at the top. The "middle" students land in the middle. And the "weak" students land at the bottom.

But as we all know from having inherited, taught, and assessed these students, this schema does not measure mastery, skill, or comprehension. Dutiful students often lack conceptual understanding or procedural skills. They often have distorted memories of algorithms they heard about but never owned.

Changing over to an SBG system of teaching and assessment has meant that I have to create conditions under which any student — even ones with problem behavior or lack of "dutiful-ness" — can achieve mastery.

To me, this idea exposes the biggest flaw in the existing system. If a teacher or administrator decides from the outset that a given student is a "B-" student, then what reason does that student have to make the effort necessary for improvement?

This system also fails to allow for individual (or group) movement up the fixed staircase of the classroom hierarchy, except for improvements in "dutiful-ness." And it seems to me that if we want to improve access and equity to mathematics for all students, this is the single biggest obstacle we face.

It also seems to me that we need to consider the possibility that any hierarchical model might be transformed from a staircase to an escalator, in which all students can be expected to reach the target floor or level of skills and understanding. And that means we will have to allow for the possibility that all students in a class demonstrate the mastery that is asked in a way that permits them to receive a higher score than the "B-" or "B+" that they have always been pigeonholed into.

Tuesday, November 13, 2012

A Day in the Life: cheesemonkeysf edition

5:59 am - Dog begins licking my toes and face insistently.

6:00 am - Shot out of a cannon. Or the alarm went off. Can't remember which.

6:01 am - Stand up to avoid falling back asleep.

6:02 am - Feed dog breakfast.

6:03 -6:13 - Shower while planning first two class periods.

6:14 am - Dog licks toes again.

6:15 am - Make coffee. Start drinking coffee. Assemble lunch. Check Twitter. Eat breakfast. Fend off further toe-licking. Read news.

6:40 am - Get dressed. 

6:45 am - Walk dog. 

7:00 am - Leave for school. Plan third and fourth class periods while driving. 
                Car dancing playlist: The Sign, Tweet Me Maybe, Theme to Sesame 
                Street, Crazy Little Thing Called Love, Shuffle everything else.

7:30 am - Arrive at school. Remember great lesson idea to steal from @samjshah. 
                Set an iPhone alarm reminder to steal great idea from @samjshah later.

8:00 am - Students begin pounding on my classroom door. They know I am hiding inside, trying to get some work done. They do not care. They want to change the origami flower indicator on my technology podium from gold to blue. This is our indicator of which color day (blue or gold) it is. For some strange reason, being the first student into the classroom and changing the flower has become a coveted job of honor. 

8:10 am - Give up and let students in. Student W wins the honor of changing the flower. Student X settles for writing the day's date and "BLUE" on the whiteboard. Turn on the school's morning newscast and figure out whether PowerSchool will cooperate in taking attendance today.

8:15 am - Morning newscast. Take attendance. 8th graders provide witty commentary during newscast, much like Mystery Science Theater 3000. Remind someone to close the door so we don't infect the 6th graders with our attitude. I think the 6th graders fear me. Make a note to ask someone why.

8:20 am - PowerSchool attendance module works - hallelujah. Submit attendance. Answer random unrelated questions.

8:30 am - First class period begins. This is English. We are doing NaNoWriMo - National Novel Writing Month. Thank God. Students take out netbooks and proceed to write for the next 45+ minutes uninterrupted. I do some of my own NaNoWriMo writing, read and make comments on their novels via Google Docs/Google Drive, then grade papers and record papers like a champ. This is the last week of the term.

9:35 am - Recess. I eat yogurt at my desk in the dark-ish classroom while simultaneously planning a third-period activity and grading papers for third period. Make a note to nominate self for Cirque du Soleil.

9:50 am - Second period class begins. Another English section, more NaNoWriMo. More great reads and comments, more papers graded and recorded.

11:00 am - Passing period before third period classes. Dash out as students enter the room, reminding them to "Please don't burn the house down." :)  They are good kids. When I get back, they are noisily but busily comparing Interactive Notebooks (INBs) for today's double INB check.

11:06 am - Algebra 1. Start INB checks while students complete reassessments and solo assignments. All INBs are checked successfully. The lowest score on any INB in this round is 95%. Several 7th graders ask, "Aren't you proud of me?" I assure them I am very proud of them. Make a mental note to buy @mgolding at least one beer at Twitter Math Camp 2013.

12:00 pm - Lunch. Conversation with other grown-ups. Fabulous cookies in the faculty lounge. A few very good laughs. I would really like a four-hour nap, but I think I can make it through the rest of the afternoon.

12:35 pm - Algebra 1. Same as the previous routine but with more reassessments and solo assignments. Many INBs are checked. Most are successful. Some students need to find or fill in missing assignments/pages. We have a brief discussion about whether or not to start a new INB with the new term. We vote and decide to start a new INB on Monday even though the new term starts on Friday.

1:20 pm - Directed Studies period. There is some silliness, but everybody has assignments to finish before grades are due. I have papers to grade and record before grades are due. Somebody asks a question about a musical group I do not know. Somebody else answers this question. Silence resumes. At the end of class, several students tell me they plan to sign up for my directed studies class again next term. I find this puzzling.

2:05-ish - Prep period. I open e-mail and discover 40 new messages, of which about half are from parents or colleagues that need to be answered before I leave. Click and type, click and type. As we used to say when I worked in the software business, first we put the bugs IN, they we take the bugs OUT. I feel that way with e-mail. Delete a bunch of silly Reply All messages. Grade papers and record them, grade and record.

3:10 pm - The end of school bell rings. I stay at my desk and finish grading and recording as many papers as I can. More e-mails. A few phone calls. Go to the office and sign my overdue attendance summary from last week. Eat a banana.

4:00 pm - Leave campus. Drive home while listening to news and music. No set play list for the drive home. 

4:30 pm - Find street parking. Walk the dog. 

5:00 pm - Move boxes in the garage to create a path for something that's supposed to happen later this week (can't remember what; must consult notes).

5:15 pm - Take out trash. Make dinner out of things that are lying around in our kitchen (crusty baked mac and cheese). Put mac and cheese into the oven to bake. Answer more e-mails. Read Twitter and math teacher blogs. Consult notes from this morning about what to steal from @samjshah . Empty dishwasher and reload with dirty dishes. 

6:15 pm - Eat dinner while watching news. Catch up with beloved partner during muted commercial breaks.

6:30 pm - Beloved partner goes off to get ready to do his radio show. Dog assists me in putting dishes into dishwasher. When I sit back down at computer, dog flops behind my chair and passes out. Some snoring ensues.

7:30 pm - Remember the Day in the Life teacher challenge. Decide to write up this summary even though it is boring as all, well, whatever. 

8:00 pm - Press the "Publish" button. Sneak off to watch The Daily Show before heading to bed.

Tuesday, October 30, 2012

What We Actively Value, Versus What We Tell Students We Value

Lately I've become acutely aware of what I actively value in my classroom, which has entailed an uncomfortable amount of noticing the conditioned habits of my teacher personality. I don't collect and stamp homework assignments. I don't have each day's agenda and objective for the day neatly written on the whiteboard by the time the first bell rings. My classroom is pretty messy most of the time. I don't have a good system for filing away those last three copies of every handout for future use. I took great permission from @mgolding's system of daily handouts using her Container Store hanging file system: basically, the handouts migrate downward one pocket until there are no pockets left, at which point they go into the recycling bin.

I've made my peace with these tradeoffs because I discovered early on that if I was allotting attention to those things, then that was attention I wasn't allotting to the things I actually do value.

I adopted an SBG assessment system because it aligns my grading/scoring system with the things I actually value: mastery, effort, and perseverance. And also presence — being fully present with the activity we are doing that I actually care about. And as I've noticed that, I have noticed something else I feel good about in my classroom: my kids know that those are the things I value. Which that means they don't waste valuable life-energy bullshitting me about the small stuff we all know I don't really care about.

This has led to a lot of interesting progress with students I didn't expect to make progress with. Less successful students who don't feel shamed stick around to ask questions and engage in meaningful academic inquiry. They come to my room during their study hall periods to follow up, get help on missed or misunderstood assignments, or ask for additional work they can do to improve their understanding.

Not their grade -- their understanding. Their performance.

I am not used to this, and it causes me a lot of inconvenience. 

Students who have a reputation for giving up and giving in ask me if they can write another draft, reassess their missed algebra skills/concepts questions, and take greater ownership of their learning in my classroom. My ego would like to think this is because I'm such a highly effective teacher, but in actuality, I think it's more that my walk is becoming more aligned with my talk. I care about mastery and effort and perseverance, which means that those are the things I respond to.

What I did not realize until this afternoon is that this also means that I don't respond to things that are NOT those things. Which means that my kids are not expending any effort pretending to care about things around me that they really don't care about either. There is a focus on the work, and there is not a focus on things that are not the work. This may sound obvious, but actually it's not -- or at least, it wasn't for me. It took me years to discover that I'd been walking around in a consensual trance all my life.

This kind of awareness is challenging, to be sure, but it is also incredibly freeing. Students spend a huge part of every school day pretending to care about things that don't actually matter to them. Fitting in, pleasing teachers, winning points. Some of it is necessary but much of it they know to be complete and utter crap.

Ten, fifteen, forty, or fifty minutes of being authentically engaged in something that matters to somebody is a huge thing. Ten, fifteen, forty, or fifty minutes of authentic interaction with someone who is trying to focus as sincerely as possible on what actually matters in this life is even bigger.

I learned this lesson from years of experience with my mentor and teacher, Dr. Fred Joseph Orr — mind to mind, and heart to heart, though it took years to digest, and quite frankly, I'm still digesting. I'll probably be digesting for the rest of my life. No one had ever paid that kind of focused, intensive, thoughtful, and bounded attention and awareness in my presence before. And it made me discover how it feels to feel alive. I only discovered how precious that kind of awareness was -- and still is -- once that chapter of my life ended and a new chapter had begun.

I was noticing all this today during a test in which some of my lowest-performing students were asking for "help" with certain problems. I noticed that each time I came over in response to their request, they were not so much asking for assistance as asking for a kind of authentic engagement and support that was neither judging nor doing for them but simply witnessing their effort with presence. What I noticed today inside myself — and what distinguished this from mere adolescent attention-seekig behavior — was my own felt sense of a embodied memory of seeking out this kind of authentic connection in my own work with Fred. And this felt sense gave me the motivation to allow that connection and that presence. I trusted something inside my own inherent, intelligent functioning that told me to allow the connection rather than to pull back and resist. It was a subtle and quiet movement inside me, and I'm still figuring out what exactly was going on.

How many times have I mistaken noise for the signal? Do discouraged students ask because they hang on to the sane and healthy hope that they can learn and connect and make progress? Fred always told me, "The organism moves toward health," and I grew to believe him. I wonder if this is what my discouraged students are really asking for when they ostensibly make a seemingly attention-seeking request for something called "help."

Friday, October 26, 2012

And this is why I teach...

It was another crappy Friday in an arithmetic series of crappy Fridays that were running together and threatening to define the limit of my patience for fall trimester as x approaches a mid-sized number that is nowhere near infinity. So I have no idea what possessed me to wake up even earlier than usual to pull together an extra day's practice activity for my right-after-lunch class of rumpled and discouraged algebra students — the ones who believe to their core that California's Algebra 1 requirement is God's own punishment for unremembered karmic crimes they must have committed in previous lifetimes.

But I did it.

The topic was solving and graphing compound inequalities — a skill set that must be mastered in order to have any hope of making sense of and mastering the next topic traditional algebra curricula force-feed to our students: the dreaded topic of absolute value inequalities.

There's really nothing I can say to convince a roomful of skeptical eighth graders that compound inequalities will prove not only useful in business planning (which, after all, is simply algebra writ large across the canvas of the economy) but also amusing and possibly even interesting little puzzles to delight the mind.

To this group of students, they're simply another hoop to be jumped through.

So something in me understood that I needed to reframe the task for them, and to do so using Dan Pink's ideas about intrinsic motivation from his book Drive.

Nothing unlocks the eighth grade mind like an authentic offer of autonomy. As I explained recently to a room of educators at a mindfulness meditation training, middle school students suffer emotionally as much as adults, but they have comparatively little autonomy. A little well-targeted compassion about this can carry you for miles with them, though I usually forget this in the heat of working with them.

For this reason, I like to save practice structures such as Kate Nowak's Solve—Crumple—Toss for a moment when they are desperately needed. I have learned to withhold my Tiny Tykes basketball hoop for moments like this, when students need a little burst of wonder in the math classroom. And so even though I was tired and very crabby about the ever-increasing darkness over these mornings, I pushed myself to pull together a graduated, differentiated set of "solve and graph" practice problems to get this group of students over the hump of their own resistance and into the flow experience of practicing computation and analysis.

And oh, was it worth it, in the end.

The boys who are my most discouraged and resistant learners came alive when they understood that a little athletic silliness was to be their reward for persevering through something they considered too boring to give in to. They suddenly came alive with cries of, "Dr. X— watch this shot!" from halfway across the room. One boy who can rarely be convinced to do the minimum amount of classwork completed every problem I provided, then started tutoring other students in how to graph the solution sets and perform a proper crumpled-paper jump shot.

The girls in the class got into it too, but they seemed more excited about the possibility of using my self-inking date stamp to stamp their score sheets. So I gladly handed over the date stamp to whoever wanted to stamp their own successfully solved and graphed inequalities.

I was far more interested in reviewing their mathematics with them. One of the things I love best about practice structures like this one is that they give me an excuse to engage one on one with discouraged students under a time crunch pressure that adds a different dimension to their motivation. Suddenly they not only want to understand what they have done, but they want to understand it quickly, dammit, so they can move on to another problem, another solution, another graph, another bonus point.

Ultimately, Solve—Crumple—Toss becomes an occasion for conceptual breakthroughs in understanding.

I can't tell you why this happens. I can only tell you that it does happen — often. It makes me feel lighter, more buoyant about teaching them algebra. And it makes them feel happier too.

I wanted to write this down so I could capture it and remember this for a few weeks from now, when it stays darker even longer in the mornings and when I feel crappier and crabbier and more forgetful.

Monday, October 15, 2012

Radio Silence Does Not Mean Nothing Is Happening...

Wow, did I ever fall off the radar.

Plop. That "splat" you might have heard was me, falling off the blogging radar.

But I'm back, baby.

Last night I had the most wonderful dinner with @btwnthenumbers and @woutgeo and @mythagon, who was in town for a conference/collaborative meeting, and I tell you, it pretty much restored my faith in teaching, in mathematics, and probably in all of humanity.

I have been working at a near-frantic pace these last five weeks, prepping, teaching, grading, not grading, having parent conferences, having meetings with parents and the principal, having meetings with parents and principal and superintendent, going to IEP meetings, collaborating with my department members to write goals that will help us to align our curriculum with the Common Core, and generally dealing with all those things that go haywire as soon as you start to nail down some satisfying, finite part of your teaching.

In other words, just like you, life has been kicking my ass.

But between last night and this morning's drive to work something shifted. Something sane and healthy intervened.

That something was my connection with the Twitter- blogo-sphere.

Whenever I'm feeling exhausted and run over with skid marks across my face and body, connection with my tweeps -- any connection -- seems to be the best medicine. I don't know why this is true; I only know that it is so. Remembering this makes me think of a quote I have from von Neumann hanging in the ring of inspiring quotes that encircles my classroom: "In mathematics, you don't understand things; you just get used to them." Some days that's how I feel about things in my classroom or in my school or in my life.

I only know that five or ten minutes of venting to my tweeps about an impossible situation -- even when @woutgeo is only half-listening because (a) the Giants are sucking pretty hard against the Cardinals and because (b) my venting is both predictable and boring -- it helped just to have reconnected with the connection. In Jakobsonian structuralist linguistics, this kind of communicative connection is known as a "phatic utterance" (look it up, Riemann, I have to look up all of your crap).

By this morning, I was feeling reasonably happy driving to work for a 7:30 a.m. meeting. I was not totally thrilled about the hour or having to buy gas at that hour or the price of gas for that matter, but I felt pretty great about car-dancing in the dark to Ace of Base's "The Sign" and remembering car-dancing at #TMC12 with @mgolding and @samjshah and @jreulbach and @ bowmanimal on the way to do Exeter problem sets. And I felt great when @rdkpickle's sweet soprano voice was joined by @SweenWSweens and @jreulbach singing "Tweet Me Maybe." And I even laughed when the theme from Sesame Street came on. iPod's "shuffle" feature has a somewhat perverse sense of humor.

OK, and one other thing I have learned is that my dog always knows when it's time for me to end a blog post. Just now he jumped up on my lap and pounded the laptop keyboard with his giant panda bear paw:
So that's my cue to wrap this up.

I just want to say, if you are feeling alone or frustrated or exasperated and you are reading this, then for the sake of everything we hold dear, please reach out to someone else who is of like mind. "It's hard to teach right... in isolaaaaaaaaation.... So here's some PD.... just like vacation!"

Tweet me maybe, tweeps. Over and out for now.

Wednesday, August 29, 2012

INBs Day 2: the Test & the Announcement of the INB Beauty Pageant on Friday

Students did pretty well on today's "Parts of the INB test." The lowest grades were low As, which made me very happy. I gave them five minutes before the test to quiz each other, and it was great to see how engaged and involved they were with their foldables. They are starting to really "get" the idea of the parts, the idea of the date stamp, and the Table of Contents. Today I gave our first Daily Date Stamps, and several students had to quickly fix mistakes they had made, such as taping page 2 of their TOC to page 3 (a LHS page) rather than to page 2 (a RHS page).

Not only does this process give students practice in following instructions (which middle schoolers sometimes have trouble with), it also gives them a chance to settle into the aggressive pace I am setting for the year. It also creates a culture of intrinsic motivation, with an emphasis on autonomy, even though they are following general instructions and interacting with their notes far more than they generally do. The amount of energy expended in handling their materials is really new for them, and nobody complains about writing brief reflections on a LHS page or redoing their table of contents.

So it was predictable that when I announced we would be having an INB Beauty Pageant on Friday with awards in a wide range of yet-to-be-determined categories, my students would completely flip their lids.

The time has been flying by, both for students and for me. It's a really lovely way to begin the year.

Tuesday, August 28, 2012

Day 1: INBs and foldables and tests, oh my!

Introducing the Interactive Notebooks (INBs) on Day 1 of school worked ALMOST PERFECTLY!

You should have seen the scissors and tape flying in there. :-)

I introduced the concept to my class of 7th graders very briefly, then quickly got them  busy DOING things -- getting handouts, making a foldable on the parts of the INB, filling it in, and setting up their table of contents pages. The homework tonight is to finish setting up the TOC pages and study the foldable on the parts of the INB in preparation for tomorrow's test. Yes, a test! On Day 2! I must be a maniac!

I did the same with my mostly 8th grade class, though we didn't get through quite as much as the earlier class. In their defense, they do have Algebra right after lunch and frankly, after all the rules and responsibilities reviews all morning, nobody is at their best right after lunch on the first day.

The funny thing, though, was that the activity instantly got everybody engaged in what was going on. Because no one had ever done it before, no one was at a particular advantage or disadvantage. They've all been cutting and pasting since pre-school, but never in the service of their more recent learning.

I used the document camera to model what we were doing and I found that the kinesthetic aspect added an extra dimension of interest to the activities. The foldable was on yellow paper, and my scissors have bright orange handles, and I was showing them where and how to fold and cut and snip. There were some misfires during the cutting process (which I had anticipated there might be), but I told these students to simply recycle the spoiled handout and get a new one from the hanging file because in mathematics making mistakes is a normal part of the learning process and we simply regroup and keep going.

I got the impression that no one had ever normalized the mistake-making process, and that made me even more eager to play The Mistake Game with our giant group whiteboards.

At the end of each class, I took a brief, unscientific poll and discovered that nobody in either class had ever done a foldable in class before! Egad! And they all really seemed to like the tangible nature of managing the learning of abstract procedures.

I'm excited to see what happens on Day 2. Stay tuned for more!

Monday, August 13, 2012

Life on the Number Line - board game for real numbers #made4math

UPDATE: Here is a working link to the zip file:

Last year I blogged about my work on a Number Sense Boot Camp, so I won't rehash all of that here. This year I want to give the follow-up on how I used it last year, what I learned, and how I'm going to use it this year in Algebra 1.

This was my breakthrough unit last year with my students. It anchored our entire Chapter 2 - Real Numbers unit and really solidified both conceptual understanding and procedural fluency in working with real numbers, the real number line, operations on real numbers, and both talking and writing about working with real numbers. We named it Life on the Number Line.

Here's how the actual gameboards, cards, and blank worksheets looks in action (sans students):

I sure hope I didn't make a bonehead mistake in my example problem!

The most effective thing about this activity was that it compressed a great deal of different dimensions of learning into the same activity, requiring learners to work simultaneously with the same material in multiple dimensions. So for example, they had to think about positive and negative numbers directionally in addition to using them computationally. They had to translate from words into math and then calculate (and sometimes reason) their way to a conclusion. They had to represent ideas in visual, verbal, and oral ways. And they had to check their own work to confirm whether or not they could move on, as no external answer key was provided.

Since they played Life on the Number Line for multiple days in groups of three or four players comprising a team who were "competing" in our class standings, learners felt that the game gave them an enormous amount of practice in a very short amount of time. Students also said afterwards that they had liked this activity because it helped them feel very confident about working with the number line and with negative numbers in different contexts.

I also introduced the idea of working toward extra credit as a form of "self-investment" with this game. For each team that completed and checked some large number of problems, I allowed them to earn five extra-credit points that they could "bank" toward the upcoming chapter test. Everyone had to work every problem, and I collected worksheets each day to confirm the work done and the class standings.

What I loved about this idea was that students won either way — either they had the security blanket of knowing they could screw up a test question without it signifying the end of the world, or they got so much practice during class activities that they didn't end up actually needing the five extra credit points!

Students reported that they felt this system gave them an added incentive to find their own intrinsic motivation in playing the game at each new level because it gave them feelings of autonomy, mastery, and purpose in their practice work.

The game boards were beautifully laminated by our fabulous office aide but do not have to be mounted or laminated. The generic/blank worksheets gave students (and me) a clear way of tracking and analyzing their work. And the game cards progressed each day to present a new set of tasks and challenges.

All of these materials are now also posted on the Math Teacher Wiki.

Let me know how these work for you!

UPDATE 10/27/2016: Here is a working link to a zip file of all the components for this:


  1. Am I missing something? I don't see what the rules of the game are. Maybe I have it. They roll one number die and two +- dice. They record the +- rolls first and then the number, so that they get (as in the worksheet shown) something like 0 (old position) + -5. Then they take a card (in this case an 'odd # task'), figure it out, and do what?

    This sounds great. I'd like to ask kids at my son's school if they'd like to play test it.
  2. I just just discovered the msmathwiki and in turn your blog. I love everything you have written. I have been teaching for 14 years, but this is the first time I've taught Algebra. I love playing games and am so excited I don't have to create them all from scratch. I will excitedly be checking your blog daily to see what other awesome activities you post. Thank you!!!! 


    1. Thank you! I'm glad these are helpful to you.
  3. Thanks for the feedback! In answer to Sue's question, the rules are, everyone works every problem. Each player starts at the origin, rolls the three dice, and moves where they indicate. Choose an even, odd, or zero problem card. Everybody works the problem and checks answers, then the next player rolls.

    It's only a game structure. I keep "score" by confirming how many problems each team has completed and checked each day.

    Hope this helps.
  4. I'll tell you how this goes when you send me a beautifully LAMINATED class set of these made by the lovely office ladies, okay?! C'mon now, sharing is caring. I wanna do this, but it's too much work to make. #cryingwahwah #stopthewhining
  5. Hi, I loved your idea. I am trying it over the summer. I have a question about some of the answers to the cards. On the 2-1 green and yellow cards, you have a few fill in the blank cards. What was your answer for them? For instance, one of the cards says "To avoid getting confused, we read the expression -w as _" The one that has been stumping me is, "The absolute value of ANY number is always _, which means that it is always also_"
    I know it is positive but what is the other blank?



    1. Sorry about that! I forgot that you weren't there in class when I was drumming these ideas into our collective consciousness.

      With regard to the first card, when we start out in Algebra 1, I always have students read "–w" as "the opposite of w" or as "opposite w" rather than as "negative w." This helps ground them in what a signed VARIABLE means, as opposed to a signed NUMBER. If the value of w happens to be (–2), then –w is opposite-w which is –(–2) which is going to be a positive. Because they ground themselves in thinking about the opposite sign of the VARIABLE (rather than as a negative number), they get less confused as they evaluate expressions using different values for "w."

      With regard to the second card you mentioned, I also have students actively use the definitions of positive and negative — i.e., a positive number is defined as being greater than zero while a negative number is defined as being less than zero. So in the case of that card, I would hope they would say that "The absolute value of ANY number is always positive, which means that it is always greater than zero."

      Since definitions are our bedrock for the axiomatic aspects of algebra, this practice grounds them in thinking about whether a number lives to the left of zero (in the world of negative values) or to the right of zero (in positive territory).

      Hope this is helpful. Let me know if there are any blanks I can fill in!

      - Elizabeth
    2. Thanks! This helps a lot! I came up with numerous possible answers but I couldn't sleep without knowing your right answer! lol

      Thanks again!
  6. In the example you showed, did they just chose whether to go to positive or negative 5?


    1. Chelsea — They rolled three dice: two + / – dice and one six-sided number die. If they roll + — 5, they move 5 in the NEGATIVE direction (i.e., to the LEFT of zero). If they were to roll a + + 5, then they would move 5 spaces in the positive direction.

      Hope this helps!

      Elizabeth (@cheesemonkeysf)
  7. Greetings everyone,
    Enjoy the shared learning and knowledge.
    I am interested in using this to model rational addition and subtraction - i.e. -2.45 + 3.6 or -3 and 1/4 + 2 and 7/10
    How would you incorporate this in to the game?

Monday, August 6, 2012

WEEK 1: 'Words into Math' Block Game | #made4math

In keeping with my Week 1 emphasis in Algebra 1 on activating prior knowledge of how to translate words into mathematical expressions, equations, or inequalities (or at least gelling some of it back into place), I've also created a "Block" game for practicing 'Words into Math' in my Algebra 1 classes. There are two levels of game cards that correspond to Lessons 1.3 and 1.4 in McDougall Littell Algebra 1 California edition (for those of you playing along at home).

This is a variation on Maria Anderson's wonderful, tic-tac-toe-style "blocking games" (Antiderivative Block, Factor Pair Block, and Exponent Block — using her generic gameboard, rules, and my own game cards for each of these first three games of hers on her web site).

The game can be played in any number of ways — either competitive or collaborative. Students can compete against each other — tic-tac-toe style — to get four of their counters in a row. Or they can simply take turns choosing the problem and working on solving each problem on the whole board.

I've created two levels of "Words into Math Block": Level 1 (purple problem cards) and Level 2 (green problem cards). I use Maria's generic PDF gameboard and print or copy them on colored cardstock or paper. I have learned the hard way to give each level its own color ID as soon as I create the game cards so I can easily recreate the card sets later whenever I need to.

I allow students to use whatever resources they need to during practice activities, so I expect to see those nifty Troublesome Phrase Translator slider sleeves flying during these two days. :-)

All of my materials, plus the photo above (in case you need a model) are on the Math Teacher Wiki.

Students really love these block games! I have a bunch of different "counters" that they can use as their game board markers: little stars (Woodsies from Michael's), circles, and hearts, colorful foam planet/star clusters, and various kinds of beans.

I'm hoping to get my students to be less flummoxed by mathematical language by giving them practice in using it early and often. Enjoy!

Starting the New Year Right — Buckle Up for Week 1 #made4math

This is my second year at my new school, which I guess technically makes it no longer my 'new school,' huh. *facepalm*

This matters because Year 1 in a new place is always a time of establishing a reputation, but my reputation got totally screwed up last year because this year I am being positioned by the kids as cool flavor-of-the-month "nice teacher" everybody wants to have.

So to protect my street cred, I need to ruin my reputation at the start of the school year — and fast.

"INB Overview" foldable glued into my sample INB
I'm introducing Interactive Notebooks this year in my math classes, so everything during my Week 1 this year is going to revolve around that.*  Day 1 will be my "Introduction to the INB," including The Ceremonial Decorating and Labeling of the INB Cover, The Death-Defying Gluing-In of the Table of Contents (TOC) and other general reference pages, and most importantly, The Making and Filling-In of the "Rules & Parts of the INB" Foldable (photo at right).

This is the most important thing on Day 1 because I am giving a test on the INB Set-Up and Use bright and early on Day 2.

The test covers the six key things about INBs that I want students to have down cold from the start: the TOC, LHS and RHS pages (plus the LHS and RHS acronyms, which will be useful in working with equations and inequalities), The Rule of the Page (i.e., the fact that everybody stays on the same page), The Rule of Attachment (the fact that nobody leaves until (a) everything is glued into INBs and (b) INBs have been put into their zipper bags and hanging files), and finally, the purpose and importance of the Daily Date Stamp.

The message I want to send here is that, in Dan Meyer's words, "We use time well in this class." I also want to communicate that I am a badass unicorn who gives a test on Day 2 on actual material that is vital to your survival in my class and isn't that totally unfair and OMG. So let the word go forth — stay on your toes in my class and do not be fooled into complacency by my seeming niceness or my obviously wrongheaded reputation.

Using the set-up and use of the INB as my core "Day 1 Lesson" also allows me to teach classroom procedures through a foldable, which means that students learn how to use and study from a foldable right away. It also gets everybody onto the same page and creates that sense of shared suffering at the hands of a crazy teacher that is so vital to classroom community-building. ;-)

It also lets me put some teeth into the bellringer activity on Day 2. The test will be time-limited, so there will be no time for screwing around at the start of class.

The test will be a "trade and grade" affair, so that all I have to do is enter the scores into Power School and hand them back. While someone collects the tests, everybody will glue their INB Overview foldable onto page 7 of their INB.

Then I'll stamp page 7 of their INB and we will move on to creating some Chapter 1 pages and getting down to the business of Chapter 1.

DAYS 3, 4, and 5
The Day 2 Test will be taped into the INB first thing after the bellringer on Day 3. Taped in and date-stamped. No monkey business.

These days will cover Lessons 1.1, 1.2, and 1.3, complete with in-class activities and homework. It's important to establish our routine right away so I can jump on any students (and parents) who need a nudge to get with the program. By the time we have our Back to School Night, I expect parents to have seen, signed, and checked a number of activities and documents that will become part of their student's INB.

My thinking about homework is to deal with it separately. I'm going to set up a file box for each class with a hanging file folder for each student. Since INBs will live in the classroom and can only be brought home to study for a test, the hanging file will provide a home for each student's INB Ziploc bag as well as their archived loose HW papers.

To carry materials back and forth between home and school, students will use a two-pocket folder that contains their current chapter HW assignments as well as a stash of binder paper. I want to use the LHS pages for higher-level processing work rather than simply pasting in HW.

That also allows me to use bellringer time for students to do active processing of the previous day's material on their LHS pages. I'll keep you posted on how well this works, and I'll be curious to hear how others deal with the LHS pages.

By the time we reach Day 4, we'll be deep into mathematics. That is the best way I know to communicate my in-class goals and values to students.

More on the opening lessons and materials in my next post.

*I use the acronym INB rather than the more common IN or ISN because my school is acronym-heavy and both of those acronyms already stand for other things at our school. For once, I'm not intentionally trying to be a cheesehead.

Friday, August 3, 2012

#made4math | Words into Math - Taming Troublesome Phrases with an interactive foldable translator

It's been busy here in the Intergalactic Cheesemonkeysf R&D Laboratories
(see trusty assistant hard at work, right). Ever since Twitter Math Camp 12, I've been working on implementing all the lessons and activities I learned about in person from my fabulous math teacher tweeps!

I'm using the Interactive Notebook structure that Megan Golding-Hayes showed us, and I'm also incorporating a lot of Julie Reulbach's foldables. The most helpful insight (out of many) I received from Julie was the idea of using a foldable as a way of getting kids to SLOW DOWN and trust the steps of the process as they're working on word problems. So I've made a nifty little foldable like hers that will go into an INB pocket the first week and will be usable on all quizzes and tests.

One of the reasons I like having students develop tools they can use on tests is that many of the discouraged math learners just don't trust their own learning. They have a habit of "collapsing" when they encounter a first speed bump. So from the perspective of encouraging students' courage in problem-solving, it is good to allow them to have tools they can use, even if the tools are sometimes nothing more than a security blanket — a talisman or a good-luck charm they can touch as a tangible reminder of their own courage and resourcefulness. So a four-step problem-solving foldable serves double duty: it acts both as a checklist (as in Atul Gawande's New Yorker piece and book) and as a reminder to have courage and perseverance in working through problems.

However many students have a habit of either not using the tools or finding the tools too complicated or frustrating. Nowhere has this been more evident than when I've given them approved lists of words and phrases they should stop, consider, and look up if need be. The charts and lists seem to turn into giant floating word clouds that signify nothing. So I wanted to come up with a slightly more interactive than usual foldable that students could use as a way of isolating and decoding some of the most troublesome words and phrases they get hung up on. Not only does it slow them down, it gives them a focal task that redirects an anxious mind.

After a lot of research on both blogs and on Pinterest ("PINTEREST!" #drinkinggame), I came up with the idea of a folded sleeve with a sliding chart insert, containing the phrases that often confuse kids or cause them to second-guess their translations from words into math. Here's what the finished product looks like:

Here is a close-up:

I used OmniGraffle to make the sleeve template and I used Pages, Preview, and Adobe Acrobat to make the insert. I'm linking to the Troublesome Phrase Translator sleeve, a generic sleeve you can customize for your own fiendish purposes, and a PDF of my exact insert (Troublesome Phrase Translator INSERT). 

If you want to make your own inserts, you'll need to set up your own table (Word, Pages, Excel, etc) making sure that your row height is exactly 1/4 inch. Your LHS cells should be 1 9/16" wide and your RHS cells should be 1/2 inch wide. You can have about 19 or 20 rows, depending on what you put in them.

Sometimes a little magical thinking is just the thing to displace a discouraged learner's anxiety (or freaked-out-ness) for that extra second it might take to recommit to the process of solving a problem. If that helps me hang onto just one extra student a day, it's a win. But usually I find that a tool like this will encourage multiple students to encourage each other's confidence as well, which is an even bigger win in my book!