Political Numbers Game

So this weekend the Wildrose party held a march on the legislature for people who want a “back to basics” math approach.  I tried to find a panoramic shot of the crowds to get a better idea as to numbers in attendance but this was as close as I could get….although I may have missed something somewhere….

Image

 

Some news outlets reported “dozens had attended”, others reported about 150, I saw the number 200 somewhere and David Staples from the Edmonton Journal swears it was about 400 over the course of 2 hours.  He says he personally did a head count.

“When will the government stand up and listen to us?” seems to be the prevailing question.  Well, we all know that politics is a numbers game.  So let’s crunch some numbers.

The “Back to Basics” math petition has been signed by just under 13,000 people I believe.  It has pretty much had it’s day I think.  While there are a few more signatures added each day, I think we can say that in terms of it’s momentum, it’s pretty much done unless there is a resurgence.  I’ve looked at the signatures.  Not all of them are Albertan.  Heck, not all of them are even Canadian!  But let’s use that 13,000 to say that there are 13,000 “Albertans” who want action.  Well that’s 13,000 people out of a population of about 3.8 million people.  Now not all of those are adults.  So let’s say that half of them are children under the age of 18 (or non-voters).  That takes us down to about 1.9 million.  So 13,000 signatures out of a potential 1.9 million is roughly 0.68% of the Alberta population.  Yikes….not super overwhelming…..

Let’s use Staples’ number of 400 attendees at the march on the legislature.  400 people out of a potential 817,000 (roughly the size of the city of Edmonton. But again, let’s assumer that half of that number is the non-voting population.  Oh, but wait….I see kids in the photo so nope, we have to include everyone.  So 400 out of 817,000 people were counted as attendees.  That would be roughly 0.05% of the population of Edmonton took the time to come to the march.  And you have to wonder how many were there because they were legitimately interested vs. dragged there by family/friends/etc…. vs. how many people came over to just simply take a look at what the heck was going on while they were out for a walk.  But again…not super overwhelming.

Anyways…..like I said though, politics is about numbers.  And based on these numbers I think the Wildrose Party is about to turn their attention to something else.  Because clearly this “flavour of the week” battle isn’t going to gain them the votes they need to win the next election.  Especially since they likely acknowledge that most of these people supported them already anyways.

It has been posed that parents are speaking up against “discovery math” and they are making sure their voices are heard.  Where are the voices of those in favour of it? We’re not hearing THEM speak up!

Well it’s simple really.  It’s also a very common trend.  Our school used to hand out surveys to parents and the results were seriously depressing when we looked at them.  There were some very negative comments and it seemed like no one had anything positive to say about our school.  And then I was told, “You have to remember, we rarely hear from the people who are happy.  The ones who have a complaint or a criticsm are usually the ones who take the time to fill out the survey, because they want to be heard and this is their opportunity.”

Those who disagree with the current math curriculum have definitely made their voices heard.  If you live in Alberta and don’t know about this issue, it isn’t for their lack of trying.  It’s had media/press coverage, a full online petition, numerous blog postings, and has ruined my Facebook feed numerous times as well.  And you do need to hear from these people.  They are the ones who will provide you with a different viewpoint.  We can’t live in a vacuum.  So no, I’m not at all saying that these people should be ignored or that they are not important.  They are definitely passionate, I will give them that.

But numbers are numbers and we all know that political parties are about the numbers.  So as far as being a political issue?  I have a suspicion this will likely be regarded as little more than a blip on their political radar.  Come election time the focus will likely turn to health care, the oil sands, and other more high profile issues.  Based on the people behind “Back to Basics”math movement, I think it’s likely to be shuffled aside.  Oh I’m sure it will get a nod and a mention, but it isn’t likely to be the driving force behind an election campaign.  Does that mean the debate and the conversation is not important?  Absolutely not.  But as a political bullet…….?  I think it just doesn’t have the power.

That being said, I don’t have a degree in political science.  My assumptions could be dead wrong, after all….they are only inferences based on what I know from the past and what I see happening in front of me.  I would call myself politically aware but certainly not a political expert.  But then again, I don’t seem to be an expert in anything.  Not even education.  Nope….my 12+ years of classroom experience, my degree in education, the hundreds of parents I have talked to over the years, the 1000+ students that have walked through my classroom…..none of it seems to count.  I am dismissed as “just another teacher” who “doesn’t get it.”  I was referred to the other day as a teacher with a “cute” little blog and a nice “smattering” of followers.  Ouch.  I’m 37.  I’m far too old to be “cute”.

But as far as my teaching math goes….

One of the proudest moments I’ve ever had was a couple years ago when I was in the middle of teaching a math concept when one of my students put up her hand.

“Mrs. Olthof, I normally like the way you teach math but today I don’t like the way you’re teaching this.  I’m not getting it.  Can you teach it different?”

Talk about the level of trust it takes between a teacher and a student in order for THAT to happen mid-lesson.  And I stumbled for a bit and thought for a second before I said…..”Sure, let’s try it this way…..”  But what if I hadn’t known another way to teach it? Or had the freedom to teach it another way?

Hm.

“If a child can’t learn the way we teach, maybe we should teach the way they learn.”  This notion holds true for BOTH sides of the debate….those who push the “back to basics” approach AND those who support inquiry based teaching.

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Game Changers

While media and public critics curse Inspiring Education and say it is going to bring about the downfall of Alberta Society, I would ask you to keep this in mind…..here are a list of people who were also accused of trying to destroy society in past history:

daVinci

Galileo

Newton

Copernicus

Stay calm and carry on?  Forget that.

Raise hell and change the world.

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Endless Debates

I seem to keep engaging in what I call “wrap around debates.”  You lock horns with someone who has a different opinion from you and you hash things out. Like the debate Alberta Educators are having (as well as many others) around the issue of how best to teach math.

The problem with wrap around debating is that it never gets anywhere.  In my mind there are two types of people who like to debate:

1.  Those who are only debating to force their own views and agenda.  They will never really listen to what you have to say, they seek only to poke holes in your theory and wait for opportunities to prove yet again why you are wrong and they are right.  They will throw the same lines at you over and over again and just when you think you are getting somewhere, you circle back to the beginning and start again.

2. Those who debate for the purpose of thinking.  They will challenge you.  You will challenge them.  You will both cause each other to think and in the end someone might shift or you will both stick to your own thoughts and agree to disagree.  But the conversation is key because each side has made the other think.

Some people exist inside a vacuum.  They surround themselves with like minded individuals who will agree with whatever they say.  I feel sorry for these people because when they “debate” they might as well be having a conversation with a mirror.

I like it when people challenge me.  It causes me to consider things I might have neglected to think of before, or reveal information to which I was not aware.  Either way these conversations help me to grow as a professional and as a person.

Some people I refuse to talk to anymore though.  They aren’t interested in hearing what I have to say.  They’re only waiting for the chance to prove me wrong.

The problem with talking to these sorts of people is that after awhile you feel like you’re bashing your head against a wall.  In that situation, the only thing you are doing is hurting yourself.

But we must speak up against those who are have it wrong!

No you don’t.  You won’t convince them anyways.  They have a core set of unalterable beliefs and you will come to realize after awhile that really nothing you say is ever going to change them.  That’s when it’s time to move on.  For someone that deeply entrenched in their beliefs they experience a phenomenon known as “cognitive dissonance”.  This means they will dismiss or discount any evidence that is outside of their belief system.  It doesn’t matter what you put in front of them, they will argue it away.

Head…..meet wall.

Where is your time best spent?  It isn’t with these people.  Debate with those for whom the debate will be meaningful.  Everything else is just simply arguing for the sake of arguing.

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You Will Memorize…….

The Globe and Mail reads this way this morning:

http://m.theglobeandmail.com/news/national/parents-push-alberta-back-to-math-basics/article17654746/?service=mobile&cmpid=rss1&click=dlvr.it

I’m disappointed.

Not by the requirement that kids will “have to” memorize their times tables in the fall, but rather by the belief that this is a means to fix what parents are angry about.

And I have several questions for Mr. Jeff Johnson….

1)  What happens with the kids who won’t have them memorized?  Just because you “require it” doesn’t mean every kid is suddenly going to develop the ability to do it.  And so what?  What happens when I fail to recite my times tables back to you like a trained monkey?  You certainly aren’t going to hold me back a grade because we just don’t do that any more.  So what does this “requirement” fix?  Nothing.  Absolutely nothing.

2)  When will you follow suit and make learning the alphabet mandatory?  I’ve got kids in Grade 6 who are struggling readers.  Some of them are still having trouble with letter recognition.  So I’d like you to make learning the alphabet mandatory too please.  Maybe I should start a petition…….?

3)  What are you going to do when this band aid solution doesn’t meet with the demands of the public.  Sure, some of them are now going to go away.  The majority of the public who truly believe this is what they have been fighting for.  But what about the others?  The “pressure you are bending to” isn’t about multiplication tables and if you think you can placate the public with this move, I think you’re in for a surprise.

I think this was an interesting move.  Because really many elementary teachers are already doing this.  They may not all be doing mad minutes but they are all promoting the memorization of times tables in some way.  So I think this move was entirely political.  I’m going to get the public off my back by SAYING we will make this a requirement, even though secretly we know this really won’t change much of anything.  But it will appear we are working with the public.  Great.  Then when PISA scores do what they do and the public gets all antsy again you can throw your hands up and sluff off responsibility by saying, “But we made multiplication memorization MANDATORY!  What more do you want?”

Well Mr. Minister you had my respect for a moment.  Two steps forward, three steps back.  Let’s see what happens after the Leadership Race shall we?

My fellow educators, get ready to duck.  The pendulum has once again been set in motion.

 

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Read Out Loud Every Day

I read an article in Educational Leadership about the 5 things that we should be doing with kids every day.  Unfortunately I have since misplaced the article and so I only remember a few….

1 of them was that kids should be reading something they have chosen themselves.

1 of them was that they should be given dedicated time to read each day (in our school we start every day with 20 minutes of reading).

And 1 of them was that a child should be read to out loud by a competent adult each day.

In my classroom we have just finished our 6th read aloud book.  We started with the Gordon Kormon series “Island”.  And the kids loved his books so much they wanted another series by him.  So I read them the “Dive” book series.  Now we have started the “Kidnapped” series.

I love reading to them.  And they have come to demand it.  When I walk to the front of the room and grab the book, excited whispers start to filter through my room and they put away their “school” stuff and get ready to listen.  I leave them at cliff hangers and they beg me to read another chapter.  I read for half an hour and they will say….just five more minutes!

Not all my kids in my class are confident readers.  Some are struggling.  But they all love to be read to and so they are actively engaged in literature.  I think this is incredibly important because when you struggle to do something on your own, it’s easy to drop it and let it disappear.  Now that we are writing stories, my struggling readers are actually still finding it easy to come up with story ideas.  Why?  Because they are pulling things from the stories we are reading in class.

I read until my throat is raw some days.  And I was so broken hearted to hear another adult refer to that as a great “time” waster.  It’s not a waste of time.

If we want kids engaged in reading, sometimes it starts with simply hooking them into the stories.

And how do I know it works?  Because my struggling readers are starting to get sneaky and look for the books in the series ahead of time and read them.  They come to me with little looks the next day and say, “I know what’s going to happen next!”

Every kid should know the joy of having an adult read out loud to them, I don’t care what the age.  I teach Grade 6 now but I used to teach Grade 8 and I did this with them too.

It’s so worth it.

What books are you reading with your class?  I would love to know!

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The Myth Around Multiple Choice

I just recently marked a test I gave my class surrounding area of a rectangle.  I don’t like giving tests and I avoid them when I can just for reasons like the one I’m about to show you.

I pulled a question from one of those highly regarded specialists in the industry that are so touted about by media personalities and whatnot…..Pearson.  This is their test question……

Which rectangle has the greatest area?

a) Rectangle A: length 20 cm and width 5 cm

b) Rectangle B: length 13 cm and width 12 cm

c) Rectangle C: length 36 and width 9 cm

I’ll give you a second to come up with the answer yourself.  Most people who look at this question would say that it assesses a student’s ability to calculate area of a rectangle, that this is a “reliable” test question.  And looking at the results, 82% of my students got the question right.

Except for one little problem…….take a look at some of their answers to the follow up question of “How do you know?”

Student A:  Figures out the area of each Rectangle (100, 156, and 324 respectfully).  Then she said that she chose C because it produced the largest area mathematically.  Smart girl.

Student B: Adds the two given sides for each rectangle ( 25, 25, 45 respectfully).  He says, 45 is the largest number so that’s the biggest rectangle.  Uh oh.

Student C:  Figures out the perimeter of each rectangle (50, 50, 90 respectfully) and says C has the largest area by comparing the numbers.  Oh boy. Got perimeter mixed up with area although I never would have known that from multiple choice alone.

Student D: Says, “Because I guessed.  It looked like it would make the biggest rectangle because one side was way bigger than the others.” Crap……..

Student E takes the time to actually draw the rectangles with her ruler and then by comparison deems C to be the largest and therefore the one with the most area. She’s correct but this isn’t because she knows how to calculate area.  It’s because her measurement and comparison skills are spot on.  I actually admired this student the most because she clearly found a way to answer the question even though she didn’t know how to directly calculate area. Good for her!  I didn’t even teach this as a strategy, it came from her head.

Yikes………..my kids aren’t as good at this as I had originally thought.  Good thing I asked that follow up question.

If I hadn’t asked the question “How do you know?” I would have congratulated myself on the masterful teaching of area of a rectangle and moved on.  This actually shows me I have to go back and reteach the concept.  Of my 82% of the kids who got it correct, only 40% of them identified a “correct” method.  Although I do admit that at least 5 of them left the follow up question blank so I have NO idea where their thought process is.

But I’d like to point out that of the students above, their “basic math” was spot on. The ability to multiply, add……none of them had any issues.

Is it really the “basics” that are getting lost in education?  Or is it the ability to do something with them?

Now if you’ll excuse me, I must go plan my re-teaching lesson for tomorrow.  Because truly this is the purpose of assessment.  It’s to inform ME about how I’m doing as a teacher.  And I’m sorry, but had I relied on the question alone, I would have thought my kids had mastered the material and skipped right along ahead.

The truth is, multiple choice doesn’t “assess” anything.  It’s just an easy way to give statisticians some data they can go play with and then journalists and media and political personalities can take it and distort it to scare the heck out of the general public.  They use it in a game where they convince you that these numbers actually support some kind of argument they are making.

Numbers don’t always mean what you think they mean.

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My Return To Blogging – Math Wars

Many of you may have noticed I took a hiatus from blogging this year.  This wasn’t intentional, life simply got in the way.  I took on a new grade this year after having taught Grade 8 for literally my entire career (12 years).  It effectively made me a first year teacher all over again.  This and my ageing children who are now involved in extracurriculars plus school pursuits have kept me busy.

It’s no excuse.  Blogging is a huge part of my professional development and I’ve been neglecting it.  So what has brought me out of my siesta?  Math Wars.

There is this prevailing idea that is being perpetuated that “basic math” has been replaced by so called “Discovery Learning” math.  And for the most part I’ve ignored it and shrugged it off and I have been unwilling to engage in debate.  My friends are debating this on their facebook pages.  My news feed is filled with people sharing videos and pictures of mostly very complicated things that have been simplified to the point where I shake my head.  My twitter feed is filled with teachers defending and parrying attacks of the general public and local media who have turned an accusatory finger towards them under the grounds, “PISA standings are dropping…..YOU FIX IT.”

And the math teacher inside me sighs.  At least the part that knows you can take statistical results and manipulate them any way you want to prove your point.  Yet people are taking the information at face value and no one is delving into the deeper issue which is, “What does it mean to teach math for the purposes of understanding?”

I have said it before and I will say it again, memorization of the times tables is great.  Unless you are presented with a problem and you have no idea you need to multiply to solve it.  And what about the understanding that dividing is the opposite of multiplying.  I’ve got kids who say they love multiplying but hate dividing.  They have no concept that one is the reverse of the other.  These kids are products of Mad Minutes and “basic math” gone awry.

We also get kids who are so focused on process that they don’t stop to think about the answer they have come up with.

Is 90 divided by 1/3 = 30 or 60 or 270?

So here’s the process.  When we divide fractions we invert the second fraction and then multiply.  (Do you know why?)  At any rate 90 divided by 1/3 becomes 90 X 3/1 = 270

So now look at this question……

Kenny had 90 jelly beans.  He gave away 1/3 of his jelly beans.  How many jelly beans did Kenny give away?

And here’s how one of my students solved the question…….

Well, Kenny is dividing up his jelly beans so this is a dividing question.  90 divided by 1/3 is 270 so the answer is, he gave away 270 jelly beans.

Mathematically sound in his process of dividing fractions.  Except there was an error in logic.  Did you catch it?  Well let me ask you something….he started off with 90 jelly beans but somehow gave away 270?  How is that possible?

But this kid has been taught when you divide fractions you invert the second fraction and then multiply.  Go!  Basic math skills at it’s finest.  Too bad he didn’t know he needed to multiply to answer this question, not divide.

So let me back this up and say that yes we will drill kids with basic facts until their eyes bleed.  They will be able to recite the times table up to 12 like robotic little monkeys.  Fantastic.  And this will be great for the grocery store.  When we need to know how much 5 jars of pasta will cost us when they each cost $3 on sale.  Fabulous.

But what about when we are building a house and the lot is only so big and we want to build a house that will maximize square footage while only taking up X percentage of the total lot size?

Knowing 9×7 = 63 doesn’t exactly help with that now does it.  Rats.

There is an argument that 9×7 = 63 is the foundational skill you need to build on.  Ok, I can see that point.  And to some extent I agree.  But when kids ask you WHY does 9X7=63 you can’t just say, “Because.  Now go memorize that.”  They want to know about the process.  Math is about process, not about memorization.  Kids want to UNDERSTAND the process.

Getting the public upset about this so called “lack of basic math” is a distraction technique.  The purpose?  To make you think the current provincial government is evil, that are kids are becoming stupid but that’s ok because provincial party X has all the answer.  What is the answer?  A return to basic math!  Which appeals to voters because after all, that’s the way they were taught and look how they turned out?  Right?  Right?

Problem.

The world I grew up in and entered into as an adult is very different from the world my children will enter.  Kodak was one the leader in terms of camera technology.  They aren’t anymore.  Why?  They held the status quo, failed to innovate and other companies rose above them.  We don’t need basic fact regurgitation, we need kids who can think.  Do I think kids need to be able to multiply 5 x 3 without the aid of a calculator?  Yes.  But “basic math” goes way beyond this.

Another scenario for your consideration……

You’re in a mall and your favourite pair of pants which was $80 are now 25% off.  So you think….

1) Well 25% is a quarter and a quarter of $80 would be $20 off.

Or possibly…..

2)  10% of 80 is $8 so 20% is $16 and then half of 10% is $4 so 16 + 4 = $20 off…..

I’m willing to bet very few of you went……ok, so change the percent to a decimal (.25) now multiply by 80 which gives us $20.  And yet that’s how you would be taught to do it in school.  It’s how I was taught.  That’s “basic math” for you.  And how many people in order to do it that way would have pulled out a calculator?  The very thing the public is ready to string me up for?

Math is nothing more than logic puzzles at work.  It’s so much more than basic math.

Anyone who has you convinced that kids are no longer doing “basic math” has done you a disservice.  And if they have used a standardized test as their “proof” you should be asking more questions.

Test scores went down, our ratings are dropping, teachers and the government who invented the curriculum are to blame.  It’s an easy leap to make.

You got into a car accident, your car is totalled, you’re a bad driver, insurance rates are sky rocketing because of bad drivers like you.  What do you mean the accident wasn’t your fault?  That the road was slippery?  That YOU were actually hit by the other driver?

There’s always another explanation.  Instead of pointing fingers, I’d like to encourage you to ask questions instead.

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Asking Fair Questions

My Grade 6 students completed a lesson on asking fair questions on a questionaire.  This is what they came up with:

https://docs.google.com/forms/d/1LwHdsGjucXiCr_MjcXrWIldSD0kmD5eXl3Ta3jRiKCE/viewform

I can’t wait to see what they think of the questions they asked.  They had 3 pieces of criteria.

1)  The question must be clearly understood by all.

2)  The question must be fair (not leading).

3)  The question must be set up so anyone can answer it.

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A Child’s Choice: Grade 3 PATs

My daughter is on the verge of turning 9 and is in Grade 3 this year.  She’s a very bright kid who does very well in school and her skills are strong.  She would do very well on the PAT, of that I have no doubt.  I was adamant that she would not write her PAT tests but my husband thought she should have the choice.

“Maybe she wants to write them?” he suggested.  This gave me pause.  Although I disagree with them fundamentally, taking away her right to choose is a bigger issue with me.  So I sat down and had a conversation with her.  This is how it went.

“Hey Kate, do you know about the tests at the end of the year?”

(Eye rolling) “Yes mom, I know.  We’ve been practicing for them in class.”

“So do you want to write them?”

“Don’t I have to?”

“No, mommy could give you a note so that you don’t.”

“You can do that?”

“Yes, but do you want to try them?”

She sat and thought about this for a moment, twirling her fork around on her plate and bumping her food around.  “I think that no, I don’t want to write them.”

“Ok,” I said.  “How come?”

“They’re boring.  It’s the same questions over and over again.  What are they for anyways?”

“Well, it’s supposed to tell daddy and I what you can do well in school and what you can’t.”

“Can’t you just ask my teacher?”

Good question Kate, good question.

I didn’t tell her that PATs are actually supposed to test to see how well curriculum is being covered because with the way that the data is being used nowadays, that isn’t how people view them.  The public sees PATs as a chance to rank schools and to judge the quality of the teacher.

Why are PAT results made public?  Parents have a right to know, is the typical answer.  But do they know what that information is really telling them?  Are they using the information in a critical thinking context?  Or is it being used to fuel negativity and criticism about school and teachers?

But it’s neither here nor there.  My husband asked me to give her the choice.  She chose.

Her answer is no.

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Who Will Pack Your Parachute?

Battle River School Division I applaud your new grading system.  I have a few slight issues with how you really are still using percentages, but on the whole you are breaking new ground and I applaud you.  You’re trying to change the system and that needs to be acknowledged.

When we changed our grading system in  my middle school from percentage based reporting to skill level based reporting there was huge backlash from our parents.  They said that percentages were much more accurate and this new system was “wishy-washy”.  As a teacher I knew the real truth….the percentage system is actually the easy way out, while the skill based reporting is far more work and requires much more effort on the part of the teacher.

Concern #1:  This promotes teacher laziness.

Here’s me teaching using percentages.  Assignment, Assignment, Quiz, Quiz, Test….aaaaaaand marks plunked into a computer based reporting system that spits out an average.  Little to no effort on my part really, other than the time to physically mark it.  And I can get around that by making it mostly multiple choice so a machine can do it for me.  And so simple to justify because when a parent says….how did my kid get this mark?  I have 5 marks to show them.  And our entire conversation revolves around that – the mark.  I don’t even need to show you the assignments because when I put a mark sheet in front of you that a computer program processed for me, you won’t even question it.

The skills based system requires that I have much more knowledge of my learner because if I am called to justify the mark I have assigned I must be able to provide evidence in the form of the child’s work.  And I must be able to clearly demonstrate what your child CAN and CANNOT do.  It’s the reason my students put together portfolios of their best moments. Because then our conversation is around the skills of the child and not the mark.  Each time your child hands something in I must sit there very carefully and really look at what your child has proven himself capable of.  This isn’t so easy.  Throwing your kid’s multiple choice test through a scan tron machine takes me 10 seconds.  The funny thing is….parents will accept this as a more “truthful” assessment.

Concern #2:  Why change the system that works?  Can’t teachers stick with percentages but just add comments?

Dylan Wiliam has 5 strategies to improve student learning.  None of them involve percentage based grades.

Wiliam has shown in previous research that when students are given a grade along with feedback that students only look at the grade.  They asked students with this type of assessment two questions, “What was your grade?” (Pretty much all of the students reported back immediately and accurately.) “What did your teacher say about why you got that grade?”  (More than half the students were clueless because they hadn’t read it.)

Other researchers have shown the same findings (as evidenced in this blog post by Joe Bower.)

Concern #3:  Although not said outright like this (because it would be mean), basically the concern is….but how will I know how my child compares to others?

There’s a danger in comparing kids using percentages.  When we first switched our system we used this example to say to parents…..who is the better student?

Student A:  Unit Test Mark – 75%

Student B:  Unit Test Mark – 75%

The parents had no response.  Was this a trick question?  And so I said to them, what if I could tell you that one of these students is clearly ahead of the other?  They were confused.

So I provided slightly more information.  Both these students wrote a test on adding, subtracting, multiplying and dividing fractions.  There were 5 questions in each section.  Each student got 5 questions wrong.  Who has a better grasp of them material?  No one knew.  So I went deeper.

It was revealed that Student A’s mistakes were quite minimal.  A few calculation errors here and there.  The mathematical reasoning behind their skills with fractions was sound, he was making simple mistakes like multiplying 4 and 6 and accidentally writing 20 instead of 24.  But on the whole, clearly understood how to add, subtract, multiply, and divide fraction.  Got 1 wrong in each section, 2 wrong in multiplying fractions.  All errors that the kid recognized immediately and had nothing to do with process.  5 minutes of corrections and it was done.

Student B got everything correct……until it came to dividing questions where he got every single question wrong.  He didn’t have a clue that the second fraction needed to be inverted BEFORE multiplying to find the answer.  This is a processing error.  And since the outcome clearly states that students need to be able to add, subtract, multiply, AND divide fractions…..?  This student would not receive a passing grade in my class.  He clearly cannot do all four and we need some extra work here.

Same mark…..but 2 completely different students with 2 completely different grasps on the concepts.  The problem is that when a kid goes home and mom says, what did you get on your test?  Kid responds with 75% and mom says, “That’s great!  Go get washed up for supper.”  Conversation over.  Kids usually don’t flip open the test to see why they got the 75%.  The scary thing is that many of their teachers don’t either……

In the new grading system when mom says, “What did you teacher say about your test?”  My student would respond with, “I need to practice dividing fractions.  I did everything else right but I got all those questions wrong.”

See how the conversation changes from what the mark is to what the skills are?

THE ANALOGY

Everyone is always so concerned about how we can possibly know who is on top, who is the best, and who is clearly on the bottom.  The problem is that percentage grades don’t give us the whole story, especially when we bring averaging into the mix.

I heard this story once and it really hit home with me.

Two students take a course in parachute packing.  At the end of each week they are asked to pack 5 parachutes and then they are tested for effectiveness.  If the parachute was packed in such a way that it would fail to open when the string is pulled, the student is give 0.  If it would open, the student is given a 1.  Marks are reported like this…

WK1 WK 2 WK 3 WK 4 WK 5 Course Mark
Student A 4 4 4 4 4 80%
Student B 1 3 4 5 5 72%

Student A has learned nothing in 5 weeks.  His accuracy is the same at the end as it was in the beginning.  1 out of every 5 parachutes he packs still won’t open.  Student B finished with a lower mark and started off really poorly.  But consistently packed every parachute accurately in the last two weeks of the course.

But if all you were given was their grade in the course to choose by……who would you have chosen?

Student A has the better mark?  I’ll pick him.  (Good luck with that, hope the odds are in your favour!)

Neither!  I’m not taking anyone unless they got 100%.  (Fair enough, you’re missing out on the experience then.)

And this would be my answer….I’ll take Student B.  He’s proven he can learn and improve and now has a 100% accuracy rating.  Let’s go.

Obviously analogies are meant to prove a point and this wouldn’t really happen but think a little deeper about what the question is asking of you.  It asks…..which student is truly the stronger of the two?  The one with the better mark?  Or the one who has proven he can learn and improve even though he started off as a failure?

As a teacher, my dream class is the one filled with Student Bs.

Anyways…..just something to think about…….

All I know is this.  When I began skill based reporting I found that as a teacher I knew my students far better then I ever did when reporting percentages.  My time spent assessing increased under this system as did my time spent preparing quality learning assessments.

Who’s being lazy?  It sure as heck isn’t me.

Confession:  It’s those days when I’m tired and exhausted that part of me wishes we had a percentage based system.  Because that was SO much easier than what I’m doing now.  And I rarely had parents question my marks.  Then I remember that the way I assess now is far more valuable and I suck myself back up to return to what I know is good teaching.

Posted in Assessment, Grading, Math Reasoning | 6 Comments