The Timeline of Awesome

Friday August 12, 2011

Kate poses a great problem.

Thursday, November 17, 2011

Dan asks a great question.

To which I responded something like, "yeah, prolly, but it'd take a bunch of brute force."



Saturday, November 19, 2011

I forward it to the GeoGebra Forum.

Sunday, November 20, 2011

Raymond responds.  

This flow of information absolutely amazes me.  I mean, I loved the question after Kate posted it.  In fact, I immediately created an applet and had used the problem with my advanced class early in the first quarter.  They struggled a bit with it, but then when Dan asked about highlighting the squares and doing some of the counting, things changed.

I consider myself to be a little better than average when using GeoGebra, but Raymond is a freaking Jedi. Take a look at his stuff.  He takes an applet that I thought would require a number of tedious steps and bangs it out using 6 steps--and within 24 hours.  That's ridiculous.

The applet is here.

Mixed Up Mixture Problems

A former student of mine (and future math teacher) just posted this problem on Facebook:

Soybean meal is 16% protein and cornmeal is 8% protein. How many lbs. of each should be added to get a 320 lb mix that is 14% protein?

I've never been a big fan of 8th grade students having to work through mixture problems, but maybe that has to do with the way I've taught it.  

Every year I would come up with a new way to encourage students to set up equations to solve these problems but we'd always end up with some variation of this:

Let x = lb of cornmeal

Let y = lb of soybean meal

  x + y = 320

.08x + .16y = .14(320)

Solve for x and y. 

And for my advanced classes, that was fine.  They already knew how to solve systems of equations and it just became another jumpable (yeah, that's a new word. Deal with it.) hoop.

It never set well with me.

This year, it kinda pisses me off.  I've got kids who are able to think, but this kind of abstraction just kills them.  It may seem intuitive to freaks like us, but for most kids, it's just a ridiculous application of an already ridiculous skill.

Enter proportions.

We live in the agricultural capital of the world.  People mix stuff here all the time--and they don't use systems of equations to do it.  They use common-freakin'-sense.

Mira.

 Step 1

 Step 2

Step 3

Step 4

 Step 5
Sit back and relax while the other losers diligent students are using systems of equations to solve this disaster challenging problem that includes not only rigor but relevance.

I find this not only easier for students to do, but it appeals to a skill (proportional reasoning) that they may actually use 10 years from now as opposed to a skill (systems of equations) that they will use for about however long it takes to pass the test.  


Question
How do I introduce this so that it appeals to my students' intuition  in a way that keeps it from being just another trick they learn?

Applet is available for download or online use here.

This is Gonna Hurt

These kids aren't dumb.  But they think they are.  What's dumb is the way math has been done to them.  I didn't think so before.  I do now.

I made a commitment to do a few things differently this year.

Consistent Format
I've created a lesson template in SmartNotebook that is really quite simple.  Each file contains lessons one week at a time (even though I may only lesson plan one day at a time).  Files are named Week1, Week2, etc and slides are named Day1, Day2, etc.  Each day contains a slide for the Opener, Number Talk, Lesson for the Day, Homework Assignment and Exit Slip.  Any handouts, links or any other resources I need for the week are attached to the notebook file.  I've linked the previous day's homework slide to the current day's opener slide--mostly because I have a tendency to forget to talk about homework.  Another cool feature I've started to utilize is the ability to link to these resources from within the actual Smart slides. Now, I can access the web, applet or any other resource with just a click on the slide.

This has been really good for me because it's allowed me to really focus on the content of the activity which ends up paying dividends for the students as well.  This makes the design a non issue as I'm just replacing old with new and everything has it's place.  Next year it will be nice as well because my resources will all be aggregated.

Opener
I've always been a believer in having something for students to do at the start of the period but having things structured has helped me be more focused on my daily first impression.  These problems usually contain a review problem, some sort of pattern recognition problem and a maybe random fact involving numbers that I re-word so students have to make an educated guess.

Number Talk
I read about these in What's Math Got To Do With It and it immediately clicked.  I've been wanting to help kids with their basic numeracy and tried to deal with it as it came up.  Having a daily Number Talk has embedded it into my lessons.  This has paid off greatly in the first few weeks of the semester.  Metacognition is one of the bonus words in the faculty meeting bingo game and it gets thrown around like LMNOP in a pre-school class.  We think we know what it means, but really have no idea.  Metacognition isn't something you can talk about, it's something you have to be about. (h/t @jybuell)  A Number Talk is all about Metacognition.  I'm sure there could me more done with it than what I'm doing, but so far, so good.  It's a travesty that so many kids haven't learned to decompose and recompose numbers.  It's almost like I've had to give them permission to do so.  And there's a positive correlation between kids who struggle and kids who don't know how to break numbers apart and put them back together.  These kids are what we've begun to call "Stackers."  They want to mentally stack the numbers they are adding or multiplying and work the standard algorithms mentally which is the most difficulty way to do mental math.

This activity has "win" written all over it.  Not only do kids have to think about their thinking, but they get a chance to discuss it with others in a pretty non-threatening way.  I can already see the culture of the classroom changing.  I still have kids who are resistant because they are painfully afraid to share their thinking, but more are jumping on board than not.

Context, Context, Context
I've made a conscious effort to introduce everything via some sort of problem solving context. These contexts are sometimes application problems but, more often than not, they have been in the form of some sort of problem that gives students the opportunity to identify a pattern and use multiple representations to describe the pattern.  I started this very early because I want them to realize that words, pictures, tables, equations and graphs are just different ways to tell the same story.  I'm finding that kids who have scored very low on standardized tests have been very successful in taking a pattern and generalizing as well as graphing with not much trouble at all (which just further demonstrates that it's not the kids failing math, it's the math failing the kids).  I've also found that it's much easier to differentiate when you have students engaged in an activity than it is when you're in the middle of a lecture--news flash, right?  I'll go into more detail about the actual activities I've had students do in a future post.  But, suffice it to say, I'm convinced that these kids can do math.

Things That Need Work
I've been spoiled over the past five years.  The kids I've had come through my class have been extremely mature and hard working.  I would still have kids who would lose focus and say and do things they shouldn't, but the overall direction of the class has always been pretty easy to maintain.  But again, that mostly has to do with the fact that the advanced kids usually have parents up in their grill about anything less than an A.

First quarter just ended and, while we are still having our ups and downs, I can see some adjustments I need to make.

I have to be more mindful of the timing of things.  I'm still having trouble determining how long an activity should take.  As a result, I'm either running out of time or expecting things to go longer than they actually do. It's a different type of planning for sure.

I can't expect all these kids to be mathematicians. Yet. Yesterday, I had one of my advanced kids discover the point-slope form of a linear equation.  All I did was give the class a point and a slope and asked them to figure out a way to show me the equation.  It was beautiful.  And messy.  And it was all his.  In fact, instead of using (x₁,y₁), we used (c, a) for the given point for no other reason than those were the kid's initials.  I can't just drop a problem on my other two classes and get out of the way.  I can however, offer opportunities for them to engage in math in real ways.

It's not their fault. I'm all about kids taking responsibility, but I have to remember that they have been forced been trained learned to wait for directions.  I have to help them unlearn this learned helplessness.  But I also have to be gentle when pointing it out.  I'm not very subtle at times and I think that's done more to hurt the progress of some kids than help.

I have to find a balance between context and abstraction. Even my struggling kids can take a context and have a decent discussion on how the graph helps tell the story.  But if I give them the exact same equation to graph without any context, I get a bunch of I've-never-seen-this-before looks. This isn't a matter of not being able to do it; it's just a matter of recognizing it when there isn't a context.


I'm probably not going to fix all these things before the year's out, but that's ok...there's always tomorrow.

The Un-Lecture

Pretest

3x - 5y = 15

x intercept:  ______

y intercept:  ______

Results

0% correct

The Non-Khan Academy Un-Lecture Prompt  

Me:  Tell me what to do.

Them:  Put the red dot on ____ and the blue dot on _____.

Gentle Feedback for Misconceptions 

Encouragement 

Scaffolding

And Finally

Hit the refresh icon and Repeat




Exit Slip

7x - 3y = 21

x intercept: ______

y intercept: ______

Results

90% correct

 The applet.  (includes original .ggb file as well as jar files.)

Time to Stretch

The thing that convinced me to leave the high school classroom was the chance to work with a bunch of precocious pre-teens and follow them through middle school, hopefully sending them off to the big bad world of high school a little better off than they were when we met.  This opportunity, coupled with meeting y'all has created a professional development explosion.  It was a perfect storm of honestly asking the question: "how can I make this matter?", a group of math educators willing to push back on ideas while simultaneously offering unconditional support, an administrator willing to let go of the leash and a group of kids who constantly push me to be better.

The tough part has been the assumed disqualification when it comes to conversations about pedagogy because the stuff I do only works for "my kids." Let's just say, I feel Shawn on this front. This year, the gloves have come off.  I have two completely heterogeneous classes with skills ranging from Advanced to Far Below Basic (see Jason for explanation) and 2/3 of the kids are less than proficient based on previous years' scores. So, basically, this year I have to put up or shut up.  And some things have to change.

Let me be clear:  I'm not changing my expectations; I still believe that all kids can do math. But my planning has to change.

In my experience, "advanced" kids fall into one of two categories:  Advanced duplicators and advanced thinkers.  Advanced duplicators are the kids who take copious notes, ask if "this is going in the grade book", want to retake tests minutes after turning the original test in and will do absolutely anything the teacher asks.  They are compliant.  Advanced thinkers will often be the kid who gets labeled as lazy and distracted because, well, they are lazy and have distracted.  Problem is, they aren't lazy, the lesson just sucked.  We ride the backs of these advanced duplicators because they are good for test scores.  They make up for everything that a teacher lacks because they don't necessarily need a teacher to learn skill duplication (see:  Khan Academy) and they are willing to do it because, well, that's what good students do, right?

I've spend the better part of that past five years trying to find ways to have students explore, invent and discover while maintaining fidelity to our state standards.  My focus has always been on pushing kids beyond--but I've ended up learning as much from them as they have from me.   My goals have been singular in that my planning has been framed by the question "how far can we go with this?"  I've really learned a lot about exploring the right side of the bell shaped curve.  Keep going until maybe only three kids get it. Forget Madeline Hunter, I'm using the Daniel Tosh lesson planning model.

Now it's time to look at the other side of the curve.

Time to Breathe

So, I planned on writing a really nice reflective post on the past school year which turned into a based-on-last-year's-experience-here's-what-Imma-do-next-year piece which became a Start 'o the School Year Here's What's Happening that morphed into a Dude, Do You Still Have a Blog? kind of thing.

I missed the deadlines. But I have a note.  Ask Alex.

Last year, the district bought my afternoons so I could get out there and work with other teachers in the most organic way possible.  It really looked like an opportunity to be part of something pretty cool in that there really wasn't a detailed description other than "let's try to get teachers talking about best practices."  The flexibility was what drew me to this but it also scared the heck out of me.  The problem was that I had "technology" attached to my name and began fielding questions like "how do I turn this thing on?"  Not what I signed up for. But, all in all, the conversations I had with teachers and administrators were very good.  Based on the feedback they received, the district office wanted to keep it going this year, but my site took a beating in the afternoons.  Class sizes were high and test scores were low due to the fact that the sections I'd normally teach were just absorbed by the other teachers.

I learned a lot about myself and the profession last year.  I learned that I love to talk about teaching and really trying to figure out the best way to help kids understand this thing we call math.  I also learned that many other teachers don't like to talk about it quite so much.  But I can't really blame them.  The system we are in has made many teachers feel like Big Brother is looking over their shoulder.  This creates quite a dilemma in that innovation is not a chance many are willing to take.  We've created a system where teachers want to be told what to do so that they are covered if it doesn't work.  Tough to grow in that soil, let me tell you.

I learned that I'm not really interested in being a "tech guy" although I do believe that technology has it's place and if it can be a conversation starter, then I'm for it.  Some of the things I saw in the classrooms I visited showed me that elementary teachers work their butts off.  I don't see how those people do it.  But it was also apparent that we need vertical articulation.  We have to have a common vision K-12 with respect to how we have our kids do math.  We have pacing guides, benchmarks, common formative assessments and even a standards based report card, but there's really not much continuity between how kids approach mathematics from elementary to middle to high school.  I think that needs to change.  We can spend all the time we want on unpacking standards and developing assessments, but somehow, it has to affect what happens in the classroom.  We have to go beyond using the ancillary materials that come with a textbook adoption and start teaching our kids to do math. Now, if that job opens up, I'm interested.

Even though there is a lot of potential with having a teacher have some flexibility in the schedule, my site needed a full time teacher and the district wasn't ready to make what I did a full time position.  So I'm back in the classroom full time this year.

More to follow; gotta get the kids to bed.

Adventures in Pedagogy: Units Matter

Nevan is measuring the length of an aquarium when he exclaims:

"Dad, this thing is 3 feet long!"

"No it's not, its 36 inches."

"Hmm." *looks at the tape measure* "Oh, 36 inches and 3 feet are the same."

"No they're not. One is 3 and the other is 36. 36 is waaay bigger than 3."

"Dad. Look. Inches are smaller than feet. There's an amount of inches in a foot."

"Oh. How many?"

"12."

"Ok."


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