Archive for the 'pedagogy' Category

Personal Responsibility vs. Learning?

Yesterday I had a few students absent and we did a lot of examples involving multiplying binomials, factoring and solving quadratics by completing the square. It was one of those lessons that “just happened.” I had one idea I wanted to nail down and it kinda morphed into a bunch of examples. I made up most of the examples on the fly because I was just gauging their reaction and taking what they gave me. So believe me when I say, “they wasn’t the pertiest lookin’ notes ya ever did see.”

Apparently, they were effective, though. The countenance of the class went from chin-on-hand-it’s-Friday-I’m-tired-here-we-are-now-entertain-us to thank-you-sir-may-we-try-another-cuz-this-is-some-cool-stuff-and-I’m-gettin’-it.

Its tough to reproduce lessons like that so I exported the notes to .pdf and emailed them to the absent students.

I just received this email from one of the recipients:

“Thanks for the notes! They will really help. I do have one question though; did you have to take time specifically out of the lesson to take the pictures or some other program that did them for you? I’m asking this because I think that if you did this every time we learned something new and posted it on your website[s], it would be a good resource.”

So I told him I slaved over my computer all of 30 seconds to export and email as an attachment. Which leads me to my question:

I have always taken a “students gotta take responsibility for their notes and review them regularly” kind of approach which has prevented my from exporting and posting the chicken-scratch covered slides from class. But if posting them is going to help them learn, should I care about the personal responsibility they take on (or don’t take on) in regards to their own note taking?

Whatdaya think?

Note: if you’re interested in what a spur-of-the-moment-ugly-as-heck-yet-equally-effective lesson in my class looks like on static slides, hit me up in the comments and I’ll update the post with a link. I’m posting this from my phone and won’t have access to the notes until Monday.

The Easter Egg

Gotta thank Kate for introducing me to the Row Game.  I also like the idea of using as a way for teachers to upload and share them.  But, me being me, I couldn’t leave well enough alone.  I like the fact that these activities are self checking and that if students find that they have different answers, then there is a mistake.  The problem with that is if I create two sets of 10 problems, I would like my students to work as many of them as possible. 

So I introduced the “Easter Egg.”  I have used this concept in the past when doing test review.  Basically, I hide wrong answers so students need are a little more alert when looking at the solution to a problem. 

How does this work for row games?  Well, in the row game, if the partners have different answers, then someone messed up.  This opens the door for discussion.  But what if they never disagree?  Then there was no real need to discuss anything.  With the Easter Egg, I will make a couple of the problems diverge, that way agreement doesn’t necessarily equal correctness.  Now they have to talk even if they get the same answer. 

Today I rolled out this row game on slope with my 7th graders.  Once they got used to the concept, the did pretty well.  I look forward to doing more of these. 

I don’t know, maybe this defeats the purpose of the row game.  Maybe not.  What say you?

Speaking Mathanese

Kids butcher the Mathanese language.  I’m just sayin’.  We have all these kids who speak text just fine.  It seems to me that Mathanese should be right up their alley.  All we are doing is taking a bunch of words and converting it to symbols.  Should be easy, right?  Not so much. 

I find that kids have a tough time translating algebraic expressions to English and vice versa.  Am I alone? 

Yeah, didn’t think so. 

One of the things that I have been trying to focus on this year is to convey to students the universality of the things they are learning.  For example, cause/effect in language arts becomes input/output in math.  Conflict resolution is the same as problem solving.  Language arts has expressions and sentences, so does math.  Scientific method can compare to making a conjecture in geometry, testing it out and then using inductive logic to arrive at a conclusion (read: rule). 

So what happens when you tell them to translate: the product of 3 and the sum of x and 2?

You get: 3x+2, right? 

Not quite. 

Well I figured we needed to develop a mashup of English and Mathanese; Mathglish, if you will.  Here is what we came up with:

English to Mathanese:

This should read: The product of 2 and the sum of the product of 4 and x and 3.

Mathanese to English:

The key this time was to allow the mashup.  I live in a rural area where the Spanish speaking population is very large.  Many of my kids speak and understand Spanglish.  I have never done it this way before and the kids nailed it. 

How do you do it?

Update:  Just did a quick check for understanding 2nd period and  26/28 kids circled the bases.

Intro To Problem Solving

A while back, Justin Tolentino had a post asking how others might go about teaching problem solving strategies.  Great question.  I have started and scrapped a couple of responses to his post as well as a posts of my own on this topic.  I think the easiest way for me to describe it is in the question I gave my 7th graders this morning.

A man lives on the 10th floor of a building.  Each time he leaves his building, he will take the elevator from the 10th floor to the 1st floor.  However, when he returns, he will take the elevator to the 7th floor and walk the remaining three flights to his apartment.  Why does he do this?

I am sure that many of you have heard this lateral thinking puzzle before and may wonder how it belongs in a math class.  I realize that this problem has nothing to do with math, but in my opinion, neither does problem solving.  We use math as a vehicle to teach students how to take information they are given and then discern that which they can use and that which they must refuse.  From there they can ask questions to gain any new information they need in order to solve the problem. 

The only requirements I give students the first time I ask them one of these puzzles is that they ask “yes or no” questions.  I also tell them that my answer to their questions will either be “yes, no or irrelevant.”  Then I turn them loose. 

They start firing random questions like crazy. 

“Is he afraid of heights?”

“Does the elevator work?”

“Does he need the exercise?”

These questions come in all shapes and sizes and many of them are very specific.  After about 10 questions, I tell them I’m only going to give them 21 questions and I make a mark on  the board after each question.  At first, it doesn’t deter them.  They keep at it, often times repeating a question that was already asked.  Then they get to about 15 and someone suggests that they slow down a bit and start thinking about what to ask next.  Today, we got to 21 with no resolution and I was about to walk away from it when one of the kids who knew the answer asked if he could ask a question.


“Does he have to walk the remaining three flights?”

“Yes he does. And if you guys would have asked this question in the beginning, it would have kept you from having to waste some of your other questions.”

This brings us to a great discussion on how we can look at a problem and ask general questions that eliminate the need to ask other more specific questions.  As we carve out large chunks of potential questions, we begin to narrow our focus and become more specific.

I really like what I see when I present these puzzles to my students.  Kids who won’t normally offer much in a class discussion, will often times ask really good thoughtful questions.  They feel safe to do so because the given information is so limited, there is no way to feel “stupid” for not knowing the answer.  In fact, the entire process assumes that no one knows the answer. 

This leads me to ask: How can we get students comfortable with what they don’tknow? How do we convince them that being educated isn’t about knowing all the answers; it’s about asking the right questions?

What Are You Looking At?

Today I gave my classes a survey as a way to gain some feedback on how the first quarter has gone.  One of the questions was “What would make you more comfortable asking questions in class?”

Here is the response that really pushed back:

Well, this may seem silly and childish, but you want the truth, right?
Well, when a student asks a question, you seem to direct your answer to the person who asked it, which makes me feel uncomfortabe. I mean, if other people don’t understand, then why only talk to one person, instead of the whole class? It makes me feel weird, like I’m the only one who doesn’t understand, and the teacher looking at one single student seems to cause everyone to look, making the student even MORE uncomfortable. As I read over this, I feel I want to delete it, because it seems so silly and unnecessary of mentioning. I won’t delete it, I guess, because I suppose you want to know this, no matter how silly it (mine) is.

WOW! I had never really thought of that.  Yeah, I guess if I am burning a whole through a kid with my gaze while I am answering a question, it may just make them think twice about asking another one.  I don’t think I do that, but perception is reality to these kids.  So if she says I do it, I guess I do.  Need to keep a watch out for that one. 

Where do you look when you are answering a question from a student?

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:

Balance diagram 2

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.