Baiting the Hook

This post has been sitting in my draft folder for over a month.  I originally stalled in finishing it because I wasn’t happy with my writing.  I’m working to stop letting “perfect get in the way of good,” and so I’m posting this to get back into blogging. -Kate

One of the reasons I asked to teach a class this year (in addition to my duties at the district office) was to be able to try out a bunch of different strategies with students.  I don’t want to be the leader that tells teachers they need to be using a strategy that I’ve only read about.  Today I took a cue from Dave Burgess, the author of Teach Like a Pirate, by using what Dave refers to as a Taboo Hook.  Dave writes that he has found making content seem taboo, secret, or otherwise off-limits makes students eager to hear it.  I adapted this for my class to be the Too Advanced For You Hook.

Today (9/4) was our first day of textbook-based lessons.  They’re not my favorites, but for some topics they’re efficient.  We covered powers and exponents, squares, and order of operations today.  (100-minute periods….tons of time for that much review content.)  Generally, my students don’t need review lessons.  But they do need a chance to develop note-taking skills with less demanding content.  To keep them engaged and challenged, I like to extend lessons to more advanced content, especially when a true conceptual understanding of the 6th grade content naturally leads to understanding of higher level concepts.  Enter exponents and the Too Advanced For You Hook.

After quickly covering the vocabulary and meaning of exponents, then working through a few exercises with students, I paused for a few seconds and looked at the clock.  I looked back and forth across the classroom and then said, “I don’t know.  I don’t want to overwhelm you guys.”  And that’s all it took.  I had 10 kids instantly insist that I couldn’t overwhelm them.  They didn’t know what I was going to give them, but they were already convinced that they wanted to get it.  So, with just a little bit of planning and some good theatrical timing, I had 33 students practically begging to be taught about negative integers.  During the last 20 minutes of the last period of the day.  And they loved it.

 

The Slippery Slope of Simplification

I’ve been thinking about making posters for each of the CCSS Standards for Mathematical Practice and used an image search to see what might already be out there.  Since I’m only teaching 6th graders, I tend to find myself in elementary land with all the cute stuff.  (Not trying to inflame anyone here…it’s the truth.  If you have missed the raging debate on the value of “cute” in elementary education, take a side trip to Matt Gomez’s blog for an update.)  Of all that I saw, I think the Grade 6 posters from Jordan School District in Utah are the closest to what I had envisioned.  I especially appreciate that they have customized their posters to each grade level, giving content-specific examples on each poster. Here’s a sample of one of the 6th grade posters:

What concerns me are the posters I came across that have tried to simplify the CCSS Standards for Mathematical Practice into single “student-friendly” sentences.  Let’s take practice #6, “Attend to precision,” as an example.  In the CCSS, “Attend to precision” is explained as such:

“Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.” http://www.corestandards.org/Math/Practice

The statement, “Attend to precision,” is purposefully broad.  It was intended  to include many different aspects of being precise; precise with language and explanations, precise with computations, precise with symbols and labels.  But many of the resources being shared online seem to focus only on one aspect of precision; precision with computation.  Some examples:

“Good mathematicians try to be accurate and revise their thinking when they make a mistake.”  Math Minds (Teachers Pay Teachers)

“I can work carefully and check my work.”  everybodyisageniusblog.blogspot.com

“I can check to see if my strategy and calculations are correct.”  Carroll County Public Schools

I’m sure that each and every one of these resources (and many more like them) were created with the intent of making a broad statement easier for young students to understand, but in doing so they have lost much of the meaning of the original statement.  In trying to simplify an idea to be “kid-friendly,” the opportunity for students to discuss and explore the meaning of “attend to precision” has been taken away and students are being given just one very limiting definition.

This is a slippery slope that elementary teachers have been on before.  Take the standard algorithm for division as an example.  A well-meaning 4th grade teacher may tell students, “The big number always goes in the house.”  (Translation: The dividend goes under the division bar and the divisor goes on the left.  You’re 4th graders and we’re only working with dividends that are greater than their divisors.)  But students are left thinking that this arrangement has more to do with the value (or length) of the number, and they have no understanding of the meaning of the procedure they are performing.  This serves the purpose of getting 4th and 5th graders to pass a high-stakes test that focuses on procedural fluency, but when 6th graders start working with division of decimals, their misunderstandings are unearthed and they start to fall apart.  This is just one example of a “trick” to understanding a procedure gets in the way of true understanding of a concept.

So back to CCSS Standards for Mathematical Practice.  Can we afford to allow students (or teachers) to believe that the eight Mathematical Practices can be boiled down to one kid-friendly sentence each?  I say no.  The Standards for Mathematical Practice are rich and deserve to be left as open statements that can be applied whenever appropriate.  I don’t condemn those trying to make it easier for their students, but I do challenge them to take a step back and ask themselves if what they are doing might, in the end, actually make understanding mathematics more difficult and confusing.

Day Two

We have a lot of work to do in my class this year.  After Wednesday’s reasonably successful problem-solving activity, I thought I’d give the students a few problems to solve from the Marcy Mathworks PUNCHLINE series while I dealt with first week paperwork.  I intentionally chose a set of problems from the set that calls for students to “Draw a Picture” as a solution strategy.  My goal was to reinforce the idea that even as they enter middle school, drawing a picture can be a great method of making sense of a problem.

After watching the groups attack the medicine problem on Wednesday, I thought for sure that this would be a simple exercise…a warm-up…but I was dead wrong.  Although several students jumped right in and worked efficiently to solve the problems, the rest had that dear-in-the-headlights look.  I reminded them to skip any problems they were stuck on and come back to them later, and I think there were a few that just kept skipping problems in a big loop.  Sensing that, I asked students with good drawings to put them on the board for others who might not know how to draw a situation.  That seemed to get the others moving, but some were still lost.

Some sample problems:

So, knowing now that this group will struggle with interpreting “story” problems, I think we’ll be doing a lot like this.  Probably not 7 at a time like today; the students don’t have the endurance yet.  Maybe just 1 or 2 for bell work, but then followed up with justification and critique.  One thing is clear, these students don’t seem to have had much practice making sense of problems and so that is where we’ll start.

Day One

Wednesday marked my first day back in the classroom since June 2012.  I was nervous.  Did I still know how to do this?  Well, I might…but I couldn’t stand the thought of just doing what I had always done.  Not so long ago, the topic of discussion for Global Math Department was the First Day of School.  Reading about all the different ideas, I resolved not to spend my first 100-minute class period just going over rules and dress code.  So after some reading about whiteboarding in class and researching some different problems, I chose the “When Should She Take Her Medicine?” problem from Robert Kaplinksy.

Over 10+ years of working with gifted and high-achieving 6th graders, I’ve noticed that they really struggle with patience when they get to me.  They can’t wait to have the right answer…and they’re used to getting that answer FAST because they’ve almost never been asked to look past the immediate and obvious computation-based “problem.”  That’s why the medicine problem seemed perfect for the first day.

To introduce this activity, I created a slide to display the problem.  When I displayed the “situation,” their hands shot up immediately because they were sure the answer was 35.  I apologized for misleading them to think that I’d be asking them to give answers to any obvious questions this year.  Then I showed the “problem.”  Of course, they thought they had an immediate answer for that, too.  Then I walked them through the estimation process (high, low, best) and asked about assumptions being made (I had to define that term since they kept trying to tell me that they were assuming the answer was 4.5 hours).  As soon as we covered the waking and sleeping times, the hands shot up again and giant 3s were being written on the boards.  I asked them to convince me that their answer worked…show me with a timeline, schedule, list, something to prove they had a good answer.  That’s when they started to unravel.  They tried to show me that doses at 7a, 10a, 1p, 4p, and 7p worked, but then I’d ask them about the assumptions we made about the dose schedule.  I asked if everyone in the group was 100% behind their answer and every time there was the one kid that said they weren’t sure it was a good solution for the person to be awake for 3 hours without getting any medicine.  Then I encouraged the group to come up with a better solution that would address their teammate’s concern.  (My favorite student work-around for this was shifting the doses up 1.5 hours to break up the three hour gap.)

Here are some photos from the group that fascinated me.

1) This was the group that was the first to arrive at the answer of 3 hours (and most insistent their answer was correct.)  I told them I wasn’t convinced and suggested that they find a way to convince me.

  2)  This is when I asked them to explain their dose schedule and how they arrived at this solution (every 3 hours).  It didn’t take them too long to figure out that they actually had 6 doses, not 5.  (If they had only seen that they had 5 intervals!)

3) Making progress.  Notice the repeated addition…they knew they needed to extend the interval, but unfortunately they were trying to add 2 minutes, 10 minutes, 15 minutes, etc.  I found it interesting that no group tried converting the times to minutes to use a division algorithm.

The hardest part of the day was not helping too much.  These kids worked on this problem in earnest for almost an hour and still didn’t get to a “best” answer.  At times I felt like a member of the “Who’s Line is it Anyways” cast playing the questions game; the students asked questions and instead of giving them answers I just asked more questions.  There were some huffs and sighs, some frustrated grunts, but they kept working.  They kept going back to the problem.  The different solution strategies were encouraging.  It was good to see that they had some solid understanding of how to approach the problem, at least once they resigned themselves to the idea of not having an instantaneous answer.

One thing is certain; this problem threw these kids for a loop.  I don’t think they knew whether to love it or hate it.  I heard from one parent who works at the school that her daughter was talking about the problem all afternoon, telling them all about the problem, how I presented it, and how her group tried to solve it.  I think I’m going to like this class.  And it’s good to be back.

Let’s take this blog for a spin…

After lurking and Tweeting in the mathtwitterblogosphere (MTBoS) for just over a year, I’ve decided to push myself to reflect and grow through blogging.  I’ve been wanting to jump in for some time, but just didn’t think I’d have much to offer after taking a position out of the classroom last year.  So when it came time to talk about this year’s assignment I did something a little different; I asked to stay in my special assignment (80%) and also to teach one period of 6th grade math (20%).  Much to my delight, my proposal was accepted and yesterday I started the school year with 32 gifted and high-achieving 6th graders.  With an alternating day block schedule, it’s less crazy than it might seem…I go to the office every morning and then every other day I leave at 1pm to teach my 100-minute class.

Part of my special assignment is to help my district with the transition to CCSS in Math.  With that in mind I have several goals for this year, most stemming from ideas shared by other math bloggers for whom I have amazing respect:

1. Make sure the students are doing most of the talking, thinking, and working.  This is something our county office is hitting hard with administrators and teachers alike.  As teachers, we can’t work harder than the students and expect them to learn.  To accomplish this, I plan on the students doing a ton of group problem-solving this year.  I’m excited to use the 5 Practices for Orchestrating Productive Mathematics Discussions to guide my work with the students.  I’ve also invested in some 24×32 showerboard panels for groups to use as whiteboards when they explore problems.
2. Be less helpful.  So many of my students have learned to be helpless.  They don’t get it.  They don’t know where to start.  They have no idea if their answer is reasonable or not.  And these are high-ability learners.  Not any more.  I can’t continue to feed this disease of apathy and feebleness.
3. Move towards standards-based grading.  I’ve questioned the meaning of class grades for some time, realizing that there are always students who manage to earn As, even though I know they don’t understand the content at the highest levels.  There are also those amazingly intelligent kids who ace tests after being absent for three days straight.  How can I convince my colleagues to stop giving points for Kleenex donations because it doesn’t represent mastery if my system doesn’t seem to be consistent, either?  (I would have SBG as a solid goal, but my school is a letter grade institution.)

I’m excited to get some feedback from the greater math community, even though I’m a bit nervous to open up and share more about my teaching than I ever have before.  So, welcome and thanks for visiting.  I look forward to your responses.