Our Youth Deserve Better – Computer Based Learning

There has been a push for computer-based learning in public education for about a decade or so now.  The thinking is that students can go at their own pace, have optimally focused and differentiated remediation and instruction, and thus, students will perform better.  That’s the sales pitch, anyway.

I teach remedial math courses part time at a community college (the observations made here pertain to all of education not just math), the shift was made so that 100% of these remedial math courses were taught on such computer programs.  Students take placement tests where their strengths and weaknesses are accurately identified and they then work their way through lessons and assignments, with help along that way that addresses their specific short-comings.  If students grasp something easily they can move quickly through the curriculum.  Students that need more time can go at their own pace.  At the end of the section (or chapter), students take a test and must show a predetermined level of accuracy before they’re allowed to move forward.

It sounds great, but it doesn’t work.  Even if it did work and students could pass these classes in a way that prepared them for higher level classes, it would be a failure.   The purpose of education is not future education.

The ugly truth here is that we’ve lost sight of the purpose of education.  Education has become a numbers game where schools receive funding based on graduation rates and percentages of students passing multiple choice tests that have mysterious grading schemes behind them (70 multiple choice questions will be graded on a scale of 450 points, for example).  We lull ourselves into believing we are servicing our students if they graduate or our school surpasses the state average on these tests.

The truth is that the quality of education is rapidly decreasing, seemingly in direct response to the remedies that seek to reverse this trend.

The question often asked by students, in minor rebellion to the tasks at hand in class, “When am I going to use this in my real life,” needs to be carefully considered, with honesty, by the public and by educators.

The particular skills and facts being tested are of little to no importance.  What is important is the ability to be teachable, the ability to learn, which requires a lot of maturation, determination, focus and effort.  The purpose of education is to create an adaptable person that can readily latch onto pertinent information and apply previous learning in new ways.  An educated person should have the skills to adapt to an unknown future, a future where they are empowered to make decisions about the direction of their own lives.

Absolutely none of that happens in a computer course.  The problems are static, scripted and the programs are full of basic “If-Then” commands.  If a student misses this question, send them here.  There’s no interpretation of why a student missed.  There’s no consideration of the student as a sentient being, but instead they are reduced to a right or a wrong response.

What do students gain from computer courses?  They gain those specific skills, the exact skills and knowledge that will serve little to no purpose at all in their lives after school.  But, they’ll gain those skills in a setting with a higher student-teacher ratio (fewer teachers, less students), and where the teachers need not know the subject or how to teach.  That’s right, it’s cheaper!

But the cost is enormous.  Students will be trained how to pass tests on the computer, but will not be receiving an education. They will not develop the interpersonal skills required to be successful in college or in the work place.  They will not develop as people.  They will miss the experiences that separate education from training.  They will be raised by computers that try to distill education down to right and wrong answers, where reward is offered for reciting facts and information without analysis, without learning to consider opposing points of view, without learning how to be challenged on what it is they think and believe.

Our youth deserve better.  They deserve more.

Not only that, our young teachers (and we have an increasingly inexperienced work force in education), deserve better support from within education.  Here in Arizona the attitude from the government is that the act of teaching has little to no value, certainly little to no skill, and that anybody can step in and perform the duties of teaching in a way that services the needs of young people.

And while those in education throw their hands up in disgust, they follow suit by finding quick, easy and cheap solutions to the ever-expanding problem of lack of quality education, especially here in Arizona.  Instead of providing meaningful professional development and support for teachers, teachers are blamed for their short comings.  Instead of being coached and developed, they are being replaced by something cheaper and quicker, something that is fully compliant.

I fully believe that a teacher that can be replaced by a computer should be.  I also believe that a computer cannot provide the inspiration, motivation, the example, mentorsing and support that young people need.

The objection to my point of view is that teachers aren’t being replaced, they are still in contact with students.  This is true, the contact exists, but in a different capacity.  Just like iPads haven’t replaced parents, the quality of parenting has suffered.  The appeal of having a child engaged, and not misbehaving, because they are on a computer, or iPad, is undeniable.  But the purpose of parenting is not to find ways for children to leave them alone.  Similar, the role of education is to to find ways to get kids to sit down and pass multiple tests.  Children are difficult to deal with.  Limiting that difficulty does not mean you are better fulfilling your duty to the young!

The role of a teacher in a computer-based course is far removed from the role of a teacher in a traditional classroom.  While students are “learning” from a computer, the role of the “teacher” is to monitor for cheating and to make sure students stay off of social media sites.  Sometimes policies are in place where teachers quantitatively evaluate the amount of notes a student has taken to help it seem like a student is performing student-like tasks.

Students learning on computer are policed by teachers.  The relationship becomes one of subjects being compliant with authority.

The most powerful tool a teacher has is the human connection with students.  That connection can help a student that sees no value in studying History appreciate the meaning behind those list of events in the textbook.  A teacher can contextualize and make relevant information inaccessible to young learners, opening up a new world of thinking and appreciation for them.  None of that is tested of course.

A teacher inspired me to become a math teacher, not because of her passion for math, but because of how she conducted her business as a teacher.  Before that I wished to work in the Game and Fish Department, perhaps as a game warden.  That would have been a wonderful career.  Consider though, over the last decade, I have had countless students express their appreciation of how I changed their thinking about math, how I made it something dynamic and fluid, something human.  Math went from a barrier, in the way of dreams, to a platform, upon which successful can be realized.  Those things happened because of human connection.

We owe our youth more.  They deserve better.

It is time to unplug.

Math is Hard

Math is Hard

A typical conversation with a failing math student, with a failing math student’s parents, or with a counselor or administrator about a failing math student either directly sites this, or is pulled in a direction like driftwood in a tide by the fact that math is hard.

A common conference would go something like:

Parents:  Why is my child failing math?

Me:  Well, let’s ask your child.  Why are you failing math?

Child:  Because math is hard.

Parents and other interested parties accept this as sufficient reason and place the onus back on me as though I can alleviate the very nature of the subject.

I am completely fed up with the observation that math is hard.  And while refraining from profanity in response to this excuse should award me man of the year, I get it.  Math is hard.  No kidding!

It doesn’t matter what innate abilities someone has in math, eventually it will become difficult, confusing and … well, hard!  It is something everybody that learns math must face.  They must learn how to learn something that is hard, demanding and elusive.  That whole experience of, “Oh, I got it,” and then ten seconds later, “Wait a minute, I don’t get it anymore,” is something we all suffer.

When I was taking math courses in college I was certainly challenged.  At one point a formal proofs/topology class was really destroying me.  It was designed to be a bit of a gate-keeper of a course.  If you failed to posses the ethic and fortitude required to be successful in mathematics, this class would ferret out such things.

While taking this class my birthday rolled around.  I am the oldest grandchild on my father’s side and share my birthdate with my grandmother.  I am the oldest grandson.  So birthday parties are kind of a special thing for the two of us!

At the party I showed up with a small dry-erase board, a marker, rag for erasing and my book.  I didn’t have an assignment, no test coming up soon, but was well aware that I “didn’t get it.”  While friends and family hang out enjoying themselves I sat in a room with the door closed and practiced.

To be clear, I wasn’t struggling for mastery, I wasn’t fighting to get an A.  I was struggling just to get by, just to get a C in the class.

So yeah, math is hard.  Education changes you, or it should.  I’d argue if it was easy and didn’t change you, what is the purpose?  Sometimes you have to fight to get things done.

Think math is hard, try beating addiction.  How about facing cancer?  Raise children.

The difference between those that get math and those that don’t is a simple one…some are fighters while others site difficulty as sufficient reason to surrender and quit.  While that may sound harsh, there’s a little more to it than just that.

Fighters have faith and patience.  They have faith that through perseverance they will overcome.  They have the patience to persevere through hard times, knowing that it will pass and the result will be worth the endeavor.

By facing the struggles presented in math that perspective can be gained.  If math is hard for you it offers you an opportunity to learn that if you persevere, keep faith and have patience with yourself you will overcome.

Why Remediation Fails

Why Remediation Fails

Students that struggle unwittingly do two things that ensure they continue to struggle with concepts and procedures.  Students can go to tutoring over and again, and sometimes it works, but it’s a long and frustrating journey.

I’ve fallen victim to these two habits myself, we all have.  How students learn in school is not any different than how adults learn outside of school.  Learning is identifying something that’s wrong and replacing it with something that is right, or at least more efficient.

It is the act of identifying something that is wrong that is the hitch here, the hold up.  The first of the things students do when presented with remediation, that is review materials or a review of what went wrong before, is they morph what they’re seeing to fit what they know.  Of course if they did that the other direction, things would be great.  But that’s not how we learn.

It is imperative to recognize that we develop new learning by relating it to old knowledge.  We don’t just replace all that we’ve developed over time with this new thing.  Instead, we create connections between what’s already in our noggins and what is new.  The more connections we have, the stronger the new learning is and the more quickly it happens.

Consider someone learning to cook.  Say, they learned that Worcestershire sauce is yummy and delicious on steak.  Some spills over into potatoes and that’s not too bad either.  It’s not even unpleasant when it mixes with green beans or broccoli. With some experimentation we can learn that it’s good with chicken, rice and mushrooms.

What’s the thing we know?  Worcestershire sauce makes things taste good.  Not wrong, but not a very deep understanding, right?

Now let’s say this person want to make some desserts.  Someone hands them some cream and tells them to whip it up, so it can top a pie.  Why, they might ask.  Well, to make the pie better, of course.

This whipped cream is new information, it’s something different than what they know.  It’s fundamentally different than Worcestershire sauce.  Yet, whipped cream is supposed to make food better, just like Worcestershire sauce does.  So what students do, in effect, is say, oh, whipped cream is the same as Worcestershire sauce, and I’m used to Worcestershire, so let’s just use that instead.  Same thing after all, right?

A similar thing happens when trying to train someone to use the computer.  They know how to do a set of things and try to use those processes to manipulate this new software.

That is, instead of seeing the new protocol for interfacing with the software as completely new, they instead relate it to what they had done in the past.  They fail to replace old knowledge with new.  Instead, they see the new information as the same thing as what they already have at hand.

How do we, as teachers, combat that phenomenon?  Well, we have to expose what they believe as fundamentally different than what’s right.  We have to expose their misconception as being, well, a misconception that is not aligned with reality.

That’s a tricky thing to do, especially in math, for two reasons.  The first reason is that often in math we are dealing with abstractions.  We can’t have them taste Worcestershire topped cherry pie.  The second reason, especially for math, is that when students see a procedure performed, they feel they understand if they believe they’re able to follow that procedure. (That is not that they are able to perform the procedure themselves.)

That second reason that it is tricky to expose misconception is the second thing that students do, they latch onto procedure.  It makes them feel grounded, even if they are obviously off-base!

How many times has this happened?  You, as the teacher, review a quiz question with students.  They sit there, take notes as you work through a problem.  They all exclaim they can’t believe how dumb they are, how could they have missed that?  They get it now, right?

No.  They don’t.  They followed what you did, you doing all of the thinking along the way.  A large percentage of students will be no better off than before the review.  In some ways, some will be worse because they’ll now think they understand.  Before the review, they just knew they were wrong, probably had no idea why.

What can we do?

This is a tricky thing to answer, dependent on too many variables to articulate a clean protocol.  However, I think I have some ideas that will help in general.

First, when developing a review lesson, test or quiz review, or remediation lesson, you need to have students confront some mistakes.  Maybe they need to try a problem and get it wrong.

Once the misconception is exposed, address why it’s wrong, what’s wrong with it.  Don’t discuss what is right immediately, they’ll translate that to fit what they believe (and that is wrong).  Expose why the misconception is in fact wrong, on a fundamental level.

Next, if possible, arrive at the right conclusion without process or procedure.  Is there a way to think through the conception at play and arrive at what is right?  If so, that’s beautiful.

The last thing is that this new learning will be soft in their heads, a fragile thing.  They need to make a record of what they’ve learned, in their own writing, preferably on the old quiz or next to the thing they used to believe was true.  It’ll be a reminder, because they’ll go for that Worcestershire sauce again when they shouldn’t!  Old habits, they die hard!

I tried something along these lines in a video I prepared for a remedial math class at a community college.  The topic is fractions.  I tried to show how common denominators work without treating them like they were stupid, because they’re not, they just never had to learn fractions, and tried to do so without use of a process.

As I explored the inner workings, and why various things were wrong, I began describing what needed to be done, but the focus was conceptual.  The video is posted here at the end of this article.

This is a topic I hope to explore more in detail, how to help promote the efficacy of remediation and tutoring.  I am working on some experiments I’d like to try to determine more closely the behind the scenes workings here.  Until that time, thank you for reading, thank you for your time.

 

Philip Brown

 

The Toaster Problem in Education

It’s easy to talk about shifting education towards a more concept based approach.  But it’s hard to see what that really means in practice.  I’m not a betting man, but would be willing to bet that upon inspection there are many things you think you understand conceptually in your topic, but you just feel that way because you understand procedure well enough to always arrive at correct answers.

I can offer an example in math:  Why does the order of operations work?  Why does the structure in the order of operations guide us to the correct calculation?

Let’s use a mathematical way of thinking to approach this problem of understanding what conceptual approach education looks like, compared to our current procedure based approach.  (Tell-tale sign that you’re procedurally based is if your students cannot remember how to do something big a year later.  Or, do you consider the work assigned before your lesson?)

Imagine you want your students to know how to make toast.  You could introduce them to a toaster.  Then, demonstrate how the bread-item is dropped in the slots on the top, the little knobby is turned to select the desired level of darkness, the button with the picture of the type of bready-material being toasted is pushed, and the lever is depressed.

If it’s an advanced class, maybe some discussion is given to what to do if the toast gets stuck, and why you should always unplug the toaster when finished with it because toasters have notoriously cheap circuits that short out, causing a fire.

Oh, one last thing.  All toasters are good toasters.  There are no bad toasters.  Some make light toast, some dark toast.  If you show preference to one kind of toaster, you’re then the exception to the rule because we tolerate everything except intolerance.

That’s a very typical American style of teaching something.  We cover how to use a tool and throw in a little social justice message to boot.  (That is not a comment on the need for awareness of social issues except to say that math textbooks are inappropriate platforms for them.)

Imagine that instead of wanting your students to know how to make toast, you wanted them to know about toast.   You teach them what it is, previously cooked bread that is now slightly, but evenly, burned on the cut-faces making a slightly stiffer, crunchier piece of substrate for the delicious spreadable material of your choosing.

For the sake of this thought experiment, let’s say you also show them a toaster, but that’s it.

Now consider a pair of students.  One who learned the first method, and the second learned about toast, but spent little time with a toaster.

Which student could make toast if the toaster broke?  Which understands what a toaster really does?

Teaching how to use a toaster is procedural, while teaching what toast is would be conceptual.

Education is a HUGE industry with an enormous amount of inertia to overcome before change is realized.  There are jobs at stake if responses to changes go wrong.  Companies invest millions to supply the desires of schools.  And what do schools want?  They want to be like everybody else, because it’s safe!

We have these methods, that if not effective, are at least safe because we have used them for a long time, so has everybody else.  So if we’re close to the average, we’re okay.

But don’t get me wrong, things in education will change.  Pretty soon curriculum will be all conceptual.  Kids will be reinventing the wheel at every turn.  We see some of that in the elementary levels right now.  That’s truly a shame because it’s harmful.  Young kids do not yet possess the faculties for abstraction!  They need to know how to use a 3rd grade toaster, if you will.

I am NOT a doomsday preacher here, but I do not believe education cannot fix itself.  It is so established in the way it operates that the path we are on will remain until something really big from way up high changes.  The likelihood of that being a good change is slim because politicians aren’t educators.  Even if the idea is good, from above, the execution will be poor because it’s ideas, not how they play out, that gets people elected.

But, the change from teaching how to use a toaster to teaching what toast is, well, is needed.  Even for students to pass the new style of standardized testing they need to know what toast is.

Beyond that, for them to be successful in college, the nature of toast must be understood.  To change math from a hurdle to an opportunity, they’ve got to know all about toast, not just how to use the toaster.

It is these last two things, the belief that the education system cannot right itself, and the need for conceptual understand, that has motivated me to step outside of education for my project.

Why Good Lessons Fail

Ever had a lesson you were THRILLED about?  You loved it, it was fantastic, interesting, crisp, approachable and ... wonderful in every possible fashion.  And yet, when you delivered that lesson, it flopped!

What gives?  What was wrong with the lesson?

In reality, there was probably nothing wrong with the lesson.  Sure, all can be improved, but the lesson wasn't the problem, the delivery was.  It seems there exists an inverse relationship between how much I love a lesson and how well received it is.  The more I love it, the more students hate it!

What it really boils down to is engagement.  We are so sure that what we have to say will blow minds, that we forget our number one task ... making sure we are teaching students, not just covering material.  We assume that because we find it interesting and fascinating, and because we had such a grand time putting the lesson together that they'll gravitate towards it.

But gravitate towards it in favor of what?  What captures the attention of students?  Drama at lunch, fights with family members, changes in weather, they might be tired from staying up and watching the new season of Stranger Things on Netflix ... we don't know.  But whatever has their attention, we must wrestle it away.

In a normal lesson we are usually vigilant and on top of distractions and such.  We work hard to make the lesson itself interesting.  But in a lesson that needs no such adornments, we fail to sell it.

So regardless of whether you think it's great, they need to be sold on the fact!

There are a couple things that you can do, at any point in time, if they're not engaged.  These work for average and poor lessons, not just the great ones that we hope will inspire a future generation of (whatever it is you teach).

Before I share with you three ways to quickly grab their attention, let me say that once you have it, you can just jump right back into the lesson.  You'll have their attention, they'll not even notice that suddenly they're learning stuff!

My favorite, go-to, method of grabbing attention is with a quick, cheesy, usually Dad-Joke.  I sometimes look up a bunch of them, print them off and have them at the ready.  There are a few that I have on the ready at any given moment, but since I don't often tell them outside of the classroom, I forget.

Make it short and dumb, they'll be captured, even if they complain.  Then, back to the lesson.

And with all of these, you just jump right into the attention getting performance, you can do it mid-sentence if you please.

The second method is with a quick story about something interesting.  It can be that you wanted some cereal for breakfast and there was only a splash of milk left in the fridge!  So you couldn't even have dry cereal, just slightly less than soggy junk -- How FRUSTRATING!?!?!  Get some feedback and jump right back in.

The last method I use is direct.  I simply tell them they're distracted and that they need to do their best to focus.  I'll sell why (perhaps the material is dry but will be very important and interesting in context later, or some other reason).  I'll share that I feel the same way, burned out and tired, but explain that we all have a job to do.  "Let's just get through these next few parts and we're done for the day, if we do them well.  If not, we'll have to revisit this again in the near future."

Whatever methods you use, mix it up.  If you become too predictable with these they'll fail to gather attention.  So, "Stay frosty," like the line in Aliens suggests.

Anyhow, I hope these are helpful tips.  Just remember, no how great your lesson is, engagement is still the most important part of the lesson.  Without it, they'll not learn anything!

The Problem with PEMDAS

The problem with PEMDAS

This problem has really stirred a lot of interest and created a buzz on the internet. I can see why, it’s an easy one to miss.  And yet, PEMDAS is such an easy thing to remember, the mnemonic devices offered make for a strong memory.  So people passionately defend their answers.

6 ÷ 2(2 + 1)

I am going to tell you the answer in just a moment, but before I do, please listen to why I think this is a worthy problem to explore.

There are two fundamental misconceptions with math that make math into a monster for so many people, and this problem touches on both.  In a sense, neither has anything to do with the order of operations specifically.

The first issue is understanding that spatial arrangements in math mean something.  The way we write the numbers and symbols has a meaning, very specific at that.  In this video by Mind Your Decisions, https://youtu.be/URcUvFIUIhQ, he shares where there was a moment in time when we used different conventions to write math.

And while math may or may not be a human invention, the symbols and arrangements and their meanings certainly are.  Just like the letter A is only a letter and with a specific sound because we all agree.  Just like a red light means stop, a green light means go and a yellow light means HURRY HURRY HURRY!

The second, and more over-arching issue here, is the misconception that addition and subtraction are different.  They are fundamentally the same thing.  Subtraction is really addition of opposite numbers.  Perhaps to shore this misconception negative numbers should be introduced instead of subtraction.

Now you might argue and say, Wait, addition has properties that subtraction lacks, like the commutative property.

You’re correct, 5 + 3 = 3 + 5, while 5 – 3 does not equal 3 – 5.  However, 5 – 3 is really five plus the opposite of three, like written below.

5 + - 3

And that is the same as this expression below.

-3 + 5

So the AS at the end of PEMDAS is really just A, or S, whichever leads to the better nursey rhyme type device to improve recall.

Since we believe that addition and subtraction are different, we also come away with the belief that multiplication and division are different.  Sorry, they’re not.  Division is multiplication of the reciprocal.  Remember that whole phrase from your school days? (How was that for a mnemonic device?)

And while division does not have the commutative property, that again is a consequence of the way we write math.  If we only wrote division as multiplication of the reciprocal, we would see that multiplication and division are in fact the same.

So, back to the problem.  The most common wrong answer is 1.  The correct answer is 9.  Here’s a great video on the order of operations, super catchy and articulates the importance of left to right as written for multiplication and addition.

Last thing:  Now, in creative writing the intent of the author must be considered, should it also be considered here?

Let me know what about this you like, dislike or disagree with.  Let me know what is helpful.  I really want to promote success through making math transparent.  It’s my mission.  You can help support my mission by just sharing and liking this.  Subscribe to my blog if you’re a teacher as I will be populating it with lots of teacher advice, not all math related.

Thank you again for reading.

Wrongful Punishment was the Best Thing

When I was in 1st grade I suffered punished from a wrongful accusation, well, kind of.  And the punishment would land people in jail today.  In front of the entire 1st grade class I was spanked, but not spontaneously.  I was paraded to the front of the room and quite a spectacle was made of the ordeal.  Then I was sent to the principal’s office where I suffered a similar fate.  And at home, once again.

And while it is true, I did knock all of the lunch boxes off of the stand where they were stored, and they did spill open and they did make a big mess, it was an honest accident, no intent involved.  And I was very willing to clean all of it up, all of it!  The opportunity was not provided.  Instead, I bent over, knees straight, palms placed flat on a chair at the front of the room while the teacher drew back her arm, equipped with a wooden paddle, and brought it forward squarely on my six-year-old hind end, with all of my peers in audience.  Thrice over it happened.

It was spring and I had been spanked at school so frequently that my parents made a bargain for me, a bribe really.  If I could manage to not get spanked for an entire week then I could go out for ice cream on Friday.  And, being that it was spring, the local ice cream shop had my favorite ice cream in the whole world … peppermint ice cream!

Somehow I mustered the will-power to keep the tornado of energy that sprung forth from my body under wraps.  I sat properly, as instructed by the teacher.  And the teacher’s name, Mrs. Fortenberry, was pronounced clearly and accurately, all week.  I raised my hand at appropriate times, passed papers forward neatly and returned from recess with punctuality.  There was no cutting in line at lunch, no teasing other kids during class and the shenanigans that transpired when the teacher would turn around ceased to occur.

The staying power of six-year-olds is questionable, but I held this superb behavior through all of Monday, Tuesday, Wednesday, Thursday, and half of Friday.  Upon returning from lunch on Friday I went to place my lunch box on the stand and it slipped.  I had not been goofing off, running around, just an honest accident.  But it was as if I threw a basketball at them, they toppled like dominos … to this day I marvel at the physics involved in knocking over all of those lunch boxes in such a fashion.  Entropy is sometimes spontaneous in the presence of six year old boys!

My protests of innocence might as well have been mute.

That evening my family went out for ice cream.  I’m sure there was plenty of the delicious peppermint ice cream eaten.  I wouldn’t know, though, because I was left home by myself.

And while this may sound tragic, I realized something from this experience. I had my first epiphany.  I realized that nobody believed me with just cause.  They should not have believed me, my reputation was well earned.

From this unjust punishment I realized the power of reputation.  I realized that if I wanted to be believed in uncertain circumstances, when light spilled over me in a questionable fashion, that I needed to have a reputation of being honest.  The only way to establish such a reputation was through being honest.

My behavior did improve after this.  Perhaps not getting the ice cream was the best thing that ever happened to me.

Sometimes the best lessons are hard earned.