Thursday, June 21, 2012

The Efficient Grader

These questions were floating around Twitter yesterday:

Will it take more time to grade reassessments in a SBG classroom? 
How long will it take to get used to it?

The answers take more than however many characters Twitter gives you.  Let me take a break from my patio obsession to address them.

My answer to the first question is this: If you do it right, it should be faster, not slower, than traditional grading.

BUT, notice I say if you do it right.  In my building, it took us a few years to get it right.  So how do you do it right?  Here are a few rules to live by.

Keep the number of learning targets manageable in number.  As I've previously mentioned, we began the process with wayyyyy to many learning targets.  We as teachers felt like we were so focused on assessing and reassessing that the teaching and learning was secondary.  We decided that this needed to stop.  We combined, condensed, and made our assessments more efficient, so that we had 10-12 learning targets per trimester.  With fewer assessments given, we were able to spend more time giving quality feedback to the students on those assessments.

Assess kids where they are at.  Do your best to assess kids where they are at, not above or below.  With regard to question difficulty, traditional tests do one of two things.  They (a) attempt to assess at some point in the middle, or they (b) attempt assess all difficulty levels.  Both of these are inefficient.  If you can assess kids where they are at you'll grade fewer wrong answers; and as any teacher knows, grading goes fast when the kids get it right.

SBG allows us to use a "build" approach: give different tests at different times in an attempt to meet the kids where they are at, students constantly building their learning.  In my classroom we have C, B, and A level questions for each learning target.  On a 0-4 scale, C=2, B=3, and A=4.  For each learning target (LT) a student needs to work their way up.  They have to pass the C-level before attempting the B-level and have to pass the B-level before attempting the A-level.  We have multiple versions of each so a student can take a level more than once.

The one exception to this is the first attempt for each LT.  We give them the C and B levels at the same time initially to expedite the process for our faster learners.  Same rules apply though - if they want to get a B on that test they need to do the C and B-levels correctly.

Here are some examples of what C/B/A levels might look like: C / B / A

Be clear with what you expect for each level on each LT.  Outline very clearly ahead of time what kids will need to do to reach each level.  Students should not be surprised come test day.  We hand out skills sheets ahead of time with examples of leveled problems, along with a description of what they'll need to do for each level.  This makes it much more likely that they will pass the first time.  Less grading.

Shift your thinking away from partial credit.  Although we do give 2.5's and 3.5's occasionally if they get close to achieving the B or A levels but not quite, the way we think about giving that partial credit is very different from a traditional tests.  In a traditional system, we usually deduct a half a point for this mistake, a point for that mistake, etc etc etc.  SBG forces you to use a holistic approach.  Assuming the assessment is well-constructed, all you need to do is ask yourself, "to what level do I think this student mastered the material?  That goes much faster than hunting for partial credit.

Consider requiring an "opportunity cost".  Make students do some sort of problem set or worksheet before allowing them to retake.  This almost ensures they will pass. Again, less grading.

Be patient. At first it's going to take you a little longer to grade, mainly because you're not used to it.  Be patient with the process.  Also, with many different versions of different levels of multiple learning targets, the main challenge is organization.  Find a system that works for you.  Leverage technology (and student aides) when you can.

So to answer the second question, "How long will it take to get used to it?" I'll say 1-2 months to settle into your sweet spot.  It'll take getting a few learning targets under your belt to find that spot both with grading and organization.  And it will get even better over time as you continue to think of better and more efficient ways to do things.

Monday, June 18, 2012

Walmart on Crack (patio math side note)

Not anything groundbreaking here, but when I ordered the shade triangle, I was offered these options for shipping:

One day for about $25?  Seemed unreasonable.  Then I got this:

This shipped pretty much when I expected it to, not otherwise.  Why why why? Who at Walmart is holding the crack pipe?

Monday, June 11, 2012

Patio Math, Part 2

We are putting a shade triangle over the right section of our patio.  Remember, the right section looks like this:

You should know that the front of the house is due north and what you're looking at is the very south side of house.  The neighbor's house (red) is directly east.  The morning sun rises in the east, obviously, so this section of the patio is sunny until that bit of shade you can see on the left creeps over in the evening.  Sitting out here on a summer afternoon can be very hot without shade.

I'd like to order this triangle because it's cheap and my wife likes blue:

Coolaroo 9'10'' Triangle Party Sail in Blue

What I want to do is find a way to rig it up so that I can have it in different positions in the morning and afternoon.  The far vertex will be held by a moveable pole with two possible hole anchors in the ground.  If we don't want shade, we can simply pull the pole out of the ground and let the triangle hang by the house.

Also, I am making some assumptions.  I am assuming this triangle is equilateral.  They are not very clear about that.  Also, I am assuming that 9'10" is the length of a side of that triangle.

Here are some drawings of both the patio and the triangle to give you an idea of what I'd like to do:

They are roughly to scale.  So if you put the triangle over the porch, that's how much it'll cover.  The green lines represent where the ropes must go to keep the triangle taut.  They don't necessarily have to be perfectly perpendicular with the opposite side, but that is the most efficient way to do it.  (Vectors, anyone?)  The little circles on the house represent where I'd anchor the ropes onto the house.

In the morning, I would like the the configuration to be something like this:

And in the late afternoon, I'd like it to look a bit like this:

So the question I have is this: are there two spots where I could put the anchors so that moving the triangle is a simple moving of the third corner?  That should look something like this, where the top vertex will move and the rope connecting the other two sides is one length going through the loops that are the anchors:

Is it possible?  Might be cool to make a Geometer's Sketchpad or Geogebra drawing of it, which is a whole other challenge in itself.

UPDATE 6/18: Creating the Geogebra document is more difficult than I thought.  Maybe it's because school just got done and my brain is mush, but I haven't been able to get my head around it's a file with the patio; you just put the triangle over it:


UPDATE 6/19: I got close.  After some thought, I constructed a Fermat Point.  Sadly, it doesn't keep the length of the rope constant.  Click here to download the file.  It's close enough though to let me know that it is not feasible to keep the ropes perpendicular to the opposite side.  So the challenge changes.  Can we do this where the rope could be anywhere BETWEEN the extensions of the sides?  In a picture:

Rope should be somewhere between the two yellow lines for each vertex.

Sunday, June 10, 2012

Patio Math

I have been pondering what blog posts will look like in the summertime when I'm not in full-on teaching mode.  And then I started thinking about my summer projects.  I am pretty handy and love to do/create/construct things myself.

So last year I put in a patio.  Here's a picture of the first major gathering:

Those are pretty much all teachers at the school I work at - we were celebrating the last day with students.  Turns out English and Social Studies teachers can be cool too.  BTW I still have a ton of leftover beer if anyone wants to swing by.

The origins of this patio began years ago when my wife told me she wanted one.  And finally I gave in and decided to build her one.  I began with this rough plan.  There are actually two parts of the patio: one for the table (left) and one for lounging & reading (right).

It's not to scale.  The only thing I failed to estimate well was the amount of work it would take!  Before I could even start on the patio I needed to remove a whole bunch of bushes so that I could transplant the sod from the area I was digging out to the ground where the bushes currently were.

bush roots
The plan then was to excavate and move the turf to where the bushes used to be.  I had to dig down 6 1/2+ inches total since I needed 4 inches or so of base material, at least 1/2 inch of sand, and 2 inches for the patio block.  I'm skipping ahead a bit, but when I'm done it should look something like this:

So after a LOT of sweat, I finally got all of the sod out plus a few more wheelbarrows of soil and I felt like I had 6+ inches pretty much everywhere.  Then I framed it in.

At this point I thought I was in the homestretch of this project, but NO!  Maybe halfway.  My next job was to order the base material and start scooping it in there.  How much to order?  Well being the good math teacher I am, I estimated the volume needed by taking the the square footage by 1/3 (4 inches) for a total number of cubic feet.  I looked around town for the best deals and decided to have local company Hedberg Landscape & Masonry deliver some.  I looked on their website and found what I was looking for:

Buff Limestone Class II

Problem.  This stuff is sold by the TON!  How many cubic feet are in a ton?  This is summertime and I am supposed to be off duty!

Well with the help of the salesman at the company we figured out how much I would need.  After delivery and taxes I spent $293 and started scooping:

first scoops
right side full
left over base material

Next, we leveled and compacted the base material, and it was time to start laying sand and leveling the block.  Luckily my best friend's dad was free and he came down to help.  Notice our choice of orientation for the pavers.

As we went, we wanted to make sure that the patio pavers were almost level, but not quite.  They needed to slope just a little bit away from the house.  Laying the block was a real killer - it's a slow and tedious process, and there really isn't any room for error because every small mistake turns into a big one in our Minnesota winters.  My buddy Matt came over too and lended a hand.  After a ton of hard work, we were close to being done. 

Maybe got a little more slope than I wanted on the right side...

And here's the block we had left:

Finally, the finished product.

What really struck me as I look back at this project was how much math was really involved.  Measurement, area, volume, unit conversion, 45-45-90 triangles (yes I did multiply by the square root of two and divide to calculate how many blocks out I should go...), slope, estimation, cost comparison, rates (how about carbide vs. diamond-tip blade to cut the blocks?..they both dull at different rates and the diamond is way more expensive).  Yeah a crapload of math here.

Maybe next time I should do this project with my class and I could justify using them as manual labor?  Just a thought.

Wednesday, June 6, 2012

Adjusted GPA's?

I must confess that I've never valued grades or grading.  As a student, I didn't care ONE BIT about the grade I received (still don't in grad school).  What was important for me was my learning, and in my opinion I am the best judge of that, not a teacher or anyone else.  This approach certainly did not help me get a great class rank or GPA, but that was never a goal of mine.

Fast forward to today.  Finishing up my eighth year teaching.  All the learning is pretty much done and kids are taking their finals.  I have some scores to put in and some grades to assign.  I don't really care all that much about what those grades are.  The learning is what is most important and the learning is done.

So keep that in mind when I make this proposal.

Problem: Our district is in the early stages of transitioning to Standards-Based Grading (SBG).  This year we mandated an equal-interval scale and next year that scale must be 0-4.  The data shows that although the average GPA is within 0.01 of last year, the spread of GPA's is more compressed.  That means we have more B's and C's and fewer A's and F's.

Parents are a bit angry that their high-flying A-achieving can-do-no-wrong "geniuses" are not getting the A's they used to.  This is because of a couple of factors: their grades have been inflated for years, there is a transition period for students, and there is a transition period for teachers.  This will affect college entrance and scholarships, they say.  It's unfair that our kids are caught in the transition.  Fair point.

Solution: Adjust the top half of the GPA's (those above the mean, since they are roughly the same) based on a 4 year rolling average of where the distribution of GPA's "should" be.  Phase it out after 4 years, one trip through the high school.

Example with made up numbers (I don't have the exact numbers in front of me):

2009 Mean GPA = 2.41 Stddev = 0.96
2010 Mean GPA = 2.43 Stddev = 1.12
2011 Mean GPA = 2.41 Stddev = 1.06
2012 Mean GPA = 2.40 Stddev = 0.89

Based on the above data, it should be obvious that there will be fewer A's in 2012.  Is that fair?  To a point yes, to a point no.  So my proposal would be to take in aggregate all of the data from 2009-2012  and use the z-scores from just the 2012 data along with the mean and standard deviation from all four years to calculate an adjusted GPA.  And as the years progress into full and good implementation, the calculation will in a sense "phase itself out" and necessarily should be gone in 4 years.

I'm not suggesting individual grades change, just the way GPA is calculated.  And this should only happen for those with a positive z-score.  We are not in the business of changing D's to F's!

This would ease transition with grades and allow the SBG process the breathing room it needs to develop.

Just an idea here, and admittedly I haven't thought it all the way through.  I may bring the proposal to the curriculum fat cats at the district office and see what they say.  My guess is that it'd never happen, but who knows?

Am I over-thinking this?

Tuesday, June 5, 2012

Who Cares?

I'm a big fan of resolutions, New Years in particular. I try to come up with a meaningful resolution every year. Here are a few that have stuck:
  • One year I resolved to give people complements if I thought of them.  Even people I didn't know.  So often we think of complements and don't voice them.
  • I resolved to floss consistently in another year.
  • And one year when I was busy busy busy going to college and working full time I resolved to go on one date per month.  My wife was my April date.
Pertinent to this post though is my resolution from about 4 years ago: to focus my time and energy on what is most important.

Let me be frank.  Teachers deal with so much bullshit, it's easy to get sucked into conversations and work that in the end isn't meaningful.  And when that happens, the "who cares?" switch in my brain gets flipped and I either move onto something more meaningful or try to steer everyone else onto a more meaningful path.

This composition is the first in a series of "who cares?" posts.

Our lunch conversation from yesterday revolved around how we deal with scores from our final test  Here is what we tell them about the final:
Final Exams: Your grade may be adjusted up or down 1/3 of a grade based on your performance on these tests. If you do well relative to your LT grades, it’ll be adjusted up. If you do poorly, it’ll be adjusted down.
In a perfect world, we'd compare their current average to their final test score and if it is a certain amount above or below their current average then we'd adjust their grade up or down.  Turns out this is a major pain in the ass with our gradebook.

So it was suggested that we adjust it upward for A's and downward for D's and F's.  And then someone said we should bump it up for B's too.  And maybe we split the D's and a high D would not be adjusted down.  Blah blah blah.  Argument ensues.

WHO CARES?  IT'S A THIRD OF A GRADE!  It has no influence on learning what-so-ever.  I'm not sure what was decided, but I was pretty sure I didn't care all that much.

Sunday, June 3, 2012

SBG In Practice

I have been reading a lot of the blogs lately and maybe it's because it's the time of year when grades are given out so naturally there is a lot of talk about tests, but there seems to be a lot of chatter about assessments and making sure kids are prepared to move on to the next course or (gasp) life itself.

Exhibit A: misscalcul8 describes her End-of Course (EOC) exams and the way her school uses them as a bar to see who moves on to the next course and who does not.

Exhibit B: John Scammell opines: "Raise Your Standards. Don’t Give Zeros. Expect More" and "School Isn't Like a Job."

And of course Shawn Cornally bangs his drum on the issue fairly often as well.

These along with my recent tangle with the school board, the subsequent fallout, two recent one-on-one conversations with individual members, our recent grading and reporting committee meeting, and me giving my own finals and dealing with kids still trying to demonstrate some level of competency for our trimester learning targets...all of this compels me to say a few words relating to Standards-Based Grading (SBG), how it should work, and how it relates to comprehensive finals.

The top question I get when I ask critical question of others' grading systems is this: "OK wiseguy, if you're so smart, how do YOU do it?"  So here's how we do it.  These are things we live by.

1. Learning targets must be clearly defined and manageable in number.
Way back when we started this process of defining learning targets, we had 30+ per trimester.  That's around 100 per year!  Absolutely unmanageable for the teacher and barely manageable for the student.  We spent a good deal of time this year combining, condensing, and cutting learning targets to make our teaching and assessing more efficient.  What we came up with was a list of learning targets (LT's - about 10-12 per trimester) with embedded skills that relate to the LT.  Here's an example of what we did for trimester 3. The amount of testing we are doing has dropped dramatically and we still feel that we are getting an accurate measure of student learning.

2. A student must meet a basic learning goal for EVERY learning target.
The basic learning goal generally simply asks the question, "Do you understand the concept at the most basic level?"  If a student does not demonstrate basic understanding, they need to retest until they can demonstrate some basic understanding.  At no time will a student be allowed to pass the course without demonstrating that basic understanding for every single learning target.  Students struggling to meet a basic learning goal are funneled into special intervention time for extra help.

3. Use a "BUILD" approach, not a "SNAPSHOT" approach.
Traditional tests/assessment systems take a Polaroid of what a student knows at a moment in time.  A good SBG system should encourage an ongoing development of skills and continual learning throughout (even beyond?) a course.  We scaffold a student up from the basic learning target to the advanced learning target.  We have three levels: C (basic LT), B (LT), and A (advanced LT), and students must work their way up.  There are no D's.  We have multiple versions of each test and students have multiple opportunities to demonstrate understanding at each level.  [For example, here are some of our tests for using scale drawing: C Level / B Level / A Level.]  We have "test-up" time built into the schedule.

4. The final test is deemphasized, but still important.
Because all students have demonstrated learning for each LT along the way, it isn't exactly "mission critical" that we assess them again at the end.  Yet, retention is important and should be measured.  This final test score causes a shift upward or downward of 1/3 of a grade if someone does considerably better or worse than they have all trimester.  This is certainly not the only way to do it, and I really believe there is more thinking to be done on this issue.

There are definitely other pieces to this: I consider a student tracking sheet critical, and how to deal with homework is a whole other conversation (although I will say it's really important that HW be used as a vehicle for feedback of some sort).  There should be an "opportunity cost" (remedial practice) after failing a test and attempting to pass again.  And good parent communication is super-important too.

Current ideas to make it even better: measure the advanced learning goal (A Level) in a format other than a test and use computer testing to generate an unlimited amount of retests for the basic learning goals.

To me, what we have represents something that is very close to what we are aiming for.