What's in a Grade?

"How many pages does it have to be?"

"Is this going to count?"

"How many points is it worth?"

"What can I do to bring my grade up?"

"Can I do extra credit?"

You've all heard these before, right?  I have said for a long time that the worst part of teaching is grading.  It's a tough situation because somehow we have to put a number on it.  If we don't grade, then "kids won't do it."  But because of grades, we often get students who are looking for the least amount of work for the maximum grade. I hate that about this job.  I want to ask questions that lead them to ask questions and have class end up with a giant group hug where we all walk away realizing that we may not know the answers, but man, we sure questioned the heck out of it. 

We have done a lot of work on our campus to try to get kids to go beyond the curriculum.  We just became the first middle school in our county to reach 800 in API.  Yeah, hold the applause.  It's based on a standardized test which we all know don't mean nuthin' when it comes to having kids actually think.  But truth be known, this means that principals from our area will come calling asking, "what are you guys doing?"  They may be disappointed when they come to see the dog and pony show but end up seeing a staff that is doing their darndest to get kids to question and speak/write complete thoughts.  You see, these principals are asking the wrong question.  It isn't about what we are doing.  It's about what the kids are doing. 

Apparently our students are doing something right, though.  They are developing a reputation in high school for being "Sequoia kids" who sit in the front row, ask questions and, at times, challenge an occasional teacher to step up their game.  Fantastic!  But how do you grade that?  How do you grade a kid who has learned how to learn?  Last I checked, that isn't in my state framework.  There's no standard for that.  Which brings me back to grades.

How do you quantify learning? Why is 90% average the accepted norm for a kid who really gets it?  90% of what? Is this student truly advanced, or did she take a bunch of tests full of a bunch of basic questions and get 90% of them correct? 

So tell me, what does a kid have to do to earn an A in your class? What are you doing to ensure that the grade actually means something and isn't just verification that a student jumped through all the right hoops?

I'm Telling Ya, Lesson Plans are Overrated.

This year, I have kind of introduced equation solving to my 7th graders very informally.   One way I have done this is by giving  them a few balance equations like this:

It seems like it takes the edge off when the variable isn't there.  But today one of our warmup problems was: 5x + 1 = 2x + 7.

I have been amazed at how many of my students have been willing to attack equation solving by using a guess and check table.  I've never taught it that way, but some kids have just taken to it.  After today, I may start to encourage it.  One kid noticed that when you let x=1, the right side is greater than the left side.  But if you let x=10, the left side is greater.  When the balance of power shifts, you know that the answer is between your last two guesses.  Of course, typical guess and check strategy.  But the thing I like about it when dealing with these linear equations is that they are beginning to think in terms of linear systems and how the point of intersection acts as a dividing point between which equation has greater value.  They're teaching me something. 

But Brandon took the cake.  He says, "Mr. Cox, you can tell the left side is going to be 6 because 5+1=6 and the right side is going to be 9 because 2+7=9."

"What does x have to be for that to be true?"

"X=1.  But as we make changes to x, the other one is growing faster."

"How fast is it growing?"

"The left side is growing by 5 and the right side is growing by 2.  So eventually, we know that the left side is going to be greater than the right side."

"Yeah.  So when are the 1 and the 7 important?"

"Only at the beginning."

It took all the self control I could muster to keep from talking about initial condition or rate of change at this point.  I'm glad I didn't because I think I would have ruined an authentic learning moment for this kid.  The thing I wanted to encourage the most in him was the fact that he looked for patterns and then asked questions to help make sense of those patterns. 

One warmup which I expected to spend 5 minutes on turns into 20 minutes of slope, y-intercept, linear systems and problem solving strategies all because a few students took an approach I've never taught. 

Another example of the kids re-writing the lesson plan.

SHOW YOUR WORK!

I've been getting real tired of having to sift through my students chicken scratch to find the few nuggets of information they have hidden in their "work."  It kind of came to a head the other night as I was grading our most recent geometry test.  It became clear that many of these students really have not been taught what it means to show work in a clear and organized manner.  I have modeled it many times, pointing out how one should line up the equal signs, how arithemetic isn't necessarily showing work, etc.  However, I think that when I've tried to explain this, all they hear is Charlie Brown's teacher. "Wha wha wha...wha wha whaa."

I decided to give them a taste of their own medicine. I took the warm up I had planned and dumped it into Wordle (I figured Wordle must be good for something). Yesterday's warm up:

 

 "But Mr. Cox, what are we supposed to do?"

"The directions are all there.  It's worth 100 pts. you know, so ya better make it snappy."

"It's hard to understand."

"Ok, you don't like this one; how about this?"

 

"That's no better."

"No?"

They're on to me by now. 

"Yeah, of course I'm proving a point; but what is it?"

 The conversation went something like this:

"You think this is confusing?  Well that's what you do to me whenever you show your work.  Why is it that in your Language Arts classes you all understand that we start writing in the top left, we work left to right and top down, but in your math class, you seem to think that starting right in the center of your workspace and then going any which way is a good idea?  How in the world am I supposed to understand what you're telling me?"

So I threw up some examples of what to do...

 and what not to do...



 and we discussed what made one student's work acceptable and the other's unacceptable.  We also discussed the difference between "showing your work" or "showing your steps" and that which belongs on scratch paper.

Oh, we also agreed that starting in the upper left hand corner of the workspace is acceptable in a math class as well.

Monologue to Dialogue

"When you add a positive integer with a negative integer, how do you know if your answer is positive or negative?"

 "Well if the negative number is bigger, then the answer is going to negative.  If the positive number is bigger, then the answer is positive."

"Aren't all positive numbers bigger than negative numbers?"

"Well, yeah.  But if you take the sign off the negative and it's bigger than the positive, then the answer will be negative."

"Why are  you taking the sign off the negative number?  What rule allows you to do that?"

"Uhh..."

"I know that I can give you 20 addition problems and you will probably get all 20 right, but I want you to explain to me why this works the way it does.  Come talk to me when you think you have an answer."

*10 minutes goes by*

"Alright, I think I've got it.  If the negative number is farther down the number line than the positive number, then the answer is going to be negative."

"Farther down the number line?"

"Yeah, it's more negative than the positive number is positive."

"How do you know that?"

"It's farther from zero?"

"Oh, what do we call that when a number is farther from zero than another number?"

"Uhh..."

*5 minutes later*

"ABSOLUTE VALUE!.  If  the negative number has a greater absolute value, then the answer is negative.  If the positive number has the greater absolute value, then the answer is positive."

"That is correct young grasshopper.  You have done well.  You may now enter into the realm of proficiency."

I have had this conversation about 10 times over the last few days.  Our current system has students take a common formative assessment (CFA)which is very closely aligned to our state's standards.  It's a multiple choice test that has questions that look an awful lot like the same questions they'll be seeing in April when we take the CST test.  Based on their score, they have a set of activities to do before they can re-assess.  Re-assessment may look like the conversation above.  I think I am really going to like this system because it allows for dialogue between teacher and student.  I have the opportunity to ask them about the why and actually tie it to their grade.  The benefit to this is that students have choice in how they demonstrate their proficiency the second time.  The first time, it's a multiple choice test.  However, the second time may be written, oral or heck, they may even draw a picture. One of the best things about this is that the students are taking more ownership of their learning because they have to direct some of the activities.  They actually have choice.  And that's empowering.  They aren't waiting for me to give them another hoop to jump through. 

The parents are coming along slowly.  Many of them didn't understand how their student could score 100% on the CFA and yet the score in the grade book shows up as 80%.  Last night was Back to School Night and I got the chance to explain that each standards' assessment is two parts.  The first part is multiple choice and the second part depends on the student.  Once they realized that their child's grade quits improving when they quit trying, I think they got it. 

It'd be nice if we could focus less on the grade and more on learning, but...

...baby steps.

I'm Lovin' This!

A couple of weeks ago, I posted a question regarding how I should handle my advanced 8th grade class.  I got a bunch of great responses which cemented my opinion that these PLN's are no joke.  In a matter of hours, I got a responses from Kate Nowak (telling me to pull my head out and quit encouraging this "jump through hoops" mentality), Darren Kuropatwa (detailing some great extension lessons as well as some online resources), a tweet from Jackie Ballarini (suggesting that I go with an analytical approach to geometry) and an email from Alison Blank(offering a problem based analytical geometry curriculum).  By the end of the weekend, I was in conversation with Alison and Jim Wysocki regarding the geometry curriculum. 

This problem based geometry is good stuff.  It is rigorous, but the skills the kids need are all review.  We may only get through 10-12 problems every day or two, but they are really causing them to think.  That's good, right?

Anyway, this allows me to try to implement something I have been working on for a while.  Chris Lehmann called it "inverting the classroom."  I like the idea because it allows me to have kids work on the skills review outside of class while we spend the class time discussing the meaty stuff; the problems that make our heads explode only to find out that if I would have just stepped back and taken a different look at the problem, there is a simple yet elegant way to solve it.   

I can see two camps evolving in the class.  Those who embrace the problem solving and those who feel like they can't do it.  I'll keep you posted on how it goes.  But, so far, so good. 

Thanks again.

What's the point?

One of my favorite activities is to have students draw a point on a paper and see how many distinct lines they can draw through the point.  I usually set it up as a competition to see who can get the most lines inside of 15 seconds or so.  On your mark, get set, GO! Pencils start flying.

Then to bring the lesson home, I say, "Alright, flip the paper over and put two points on the page.  Now we're gonna see who can get the most lines through both points." 

Ready, set, GO!

They get the first line fast.  Then they panic as they move the ruler and pencil searching for that elusive second line.  Most of 'em end up looking something like this:

I tease them a bit and we all get a good chuck out of it. I know, I know.  It's not nice to take advantage of these trusting impressionable children.  But I don't care who you are, that thar's funny!

 

And, they never forget it.