Selling study strategies (Math studying strategies pt. 1)

My school is very big on teaching kids strategies to help them succeed. This makes me happy because I feel that there are a lot of strategies for learning and test taking particularly in math that may have been obvious to me, but aren't obvious to many kids.  With my 9th and 10th graders, I focus mostly on how to effectively learn in class from your teacher and review strategies for test taking.  In 12th grade, I like to specifically take a decent chunk of time to model, explain and discuss how to learn and study from a math book.  I believe this is an essential skill as it is inevitable that at some point in college students are going to need to learn directly from the book.  This may be due to the fact that they didn’t understand the lesson, they misunderstood a portion of the lesson, or they missed a class entirely.  Surprisingly, many kids don't understand how to read from a math book or even how to study for math at all.  I feel certain that we have all had the experience of hearing a student say, "Well you can't really *study* for math..." or "I just look over my notes to study for a math test."

So, in my senior classes I take a chapter from one of our tests, and exclusively read through it together with the students.  We focus on figuring out what the book is saying, and how to organize and study the concepts in preparation for college courses.  I started this process today in class; and to be honest, we covered very little math material.  Nonetheless, I really believe that today was infinitely more important for them than any single math topic could ever be.

I'll talk about my specific process and strategies in upcoming posts, but I want to intentionally stop after I make my next point because it's very important:  I think many teachers go about teaching study skills in the wrong way.  There are a lot of great teachers out there providing countless useful studying strategies, and I'm not saying those strategies aren't equal to or more awesome than mine.  It's essentially the introduction that in my experience (as a student) needs improvement.

My selling of study strategies goes like this:

"Studying strategies are for people that don't want to study a lot! I promise you that at some point you're going to want to learn a lot about something in life whether you just have a strong interest in a topic, want to learn a specific skill, or just want to get a better grade in a college course.  I never liked studying. I wanted to spend my time going out with friends, playing video games, enjoying a nice sunny day, but definitely not studying! However, I still wanted to do well in my classes. What I realized is that if I used effective study strategies, then I really didn't have to study nearly as much in order to understand the material and be successful.  So again, good studying strategies are used because you don't want to spend that much of your time studying!"

At this point, I have their attention.  To really drive the point home, I give an example from my own experience.

"My first year in college I was in the First Year Science and Engineering dorm.  My floormates had mostly gotten 4.0's in high school, and there were a decent number of valedictorians.  With my mere 3.5, I was feeling a little intimidated.  Throughout the first semester I was always trying to get my friends to go out and do fun things, but was frequently met with "I've gotta study, you should try doing it sometime, Sweeney." This happened especially in the weeks leading up to exams. As the semester came to a close, a number of my friends were convinced I was going to fail.  What happened?  I was one of three people on my floor to make Deans list. (There was a dinner for us, so I knew).  I ended up doing better than a lot of intelligent classmates who had studied much more than I did.  Why?  I'm not a genius, and (as all of my students know at this point) I have a terrible memory!  The reason for my success was that I used effective study strategies and knew my strengths and weaknesses as a student when I did study."

I had pretty high hopes when I first decided to share this concept with my students a few years ago, and I wasn't disappointed.  They can't argue with the logic that good studying = less studying.  Many students just don't study. To me, it seems like if students feel they have to study a lot only to still maybe not do well, they're just going to choose to not study.  When I suddenly present this third option of studying not that much, but doing it really well it's effective enough to give me their attention and eager discussion of strategies for a few periods.  I can't be sure how much of the strategies we go over will stay with them, but at least I know for certain they're getting in there.

Sick of security camera problems...

I cover a couple units in my Intro to Calc class that cover some topics from trig.  Sick of security camera examples with sum and difference identities, I came up with this goofball problem to change it up a bit. I guess it's a little gruesome, but come on... We all know the evil professor will step out of the room and our hero will escape!

Slope, slope, slope, slope, slope, slope, slope, slope

First, I have to say I can't take credit for this myself.  The mysterious "Andrew" left a comment on this post

and it was too awesome to ignore.  It didn't seem like he had a blog, so I figured I'd post this because it worked really well.

Second, I swear that my classes aren't all songs and dances.  I just wanted to post this now because I know teachers will have just done slope or are starting it soon, and it went really well.

Andrew's suggestion was to use the tune to Flo Rida's "Low" but with the following words:

The difference of the y and the difference of the x

Also known as rise over run

Divide the two

And then reduce

Then you got slope, slope, slope, slope

I added the following verse in between chorus' to add a little excitement:

"When I'm sittin' in math and I'm tryin' to find

How to get the the slope, the slope of a line

I think about the rise, and the run all the time

Then I think of this song, and I'm gonna be fine

1/2 slope come on

1 slope come on

2 slope come on

now that's three slopes

You think I'm a dope?

I'd gotta say nope

I am gonna find that slope!"

So, I easily found an instrumental version of the song by searching google and played it in the background.  I had a student from another class help out the first time to introduce it.  This is how it went(the 3rd time through):

I cracked myself up today

I was looking through my lesson on slope from last year, and there were a bunch of frames with this skateboarding guy to help show how to think about slope.

So I'm flipping through the frames and I come to one where I was trying to explain how the slope of a vertical line is undefined, which I completely had forgotten about...

 

I laughed pretty hard.  Chalk up a positive for having a terrible memory.

(Now with 100% less titlefail!)

Being Less Helpful

A few weeks ago, Dan Meyer (http://blog.mrmeyer.com/ like you didn't know...) gave an online talk about being less helpful and his WCYDWT. (http://www.oreillynet.com/pub/e/1450) I decided to immediately try to incorporate some of those ideas in an algebra class the very next day where we were going over word problems with formulas.

What I came up with was two questions, one given explicitly and one implied in a picture.  The first one was "How fast does Mr. Sweeney drive to work?"  Granted there was no piece of media attached to this, but it was an accessible question that every kid had an opinion on, and every kid wanted to know the answer to.
"Mr. Sweeney is young, I bet he drives really fast!"
"Is there traffic?"
"He must take the highway, I bet it's like 65!"
"The highway doesn't right from his house to school, so it must be lower"  etc.

I wrote down each student's individual guess and told them there would be a piece of candy for the closest (I'm not above bribes).  My goal was to "Be less helpful" so I was determined to only tell them where I live. They figured out they needed to use D=RT and know how long it takes and how far it is.  They kept asking questions trying to get me to do work for them, and I resisted answering. Eventually, they realized I wasn't going to budge and someone suggested to go to google maps.(Which gave both time and distance) We came to the answer, and then I told them how long it actually takes me(there's *always* traffic on the expressway!) and we solved again and I was happy.

Next, I showed them these pictures:

All I told them (When they asked) was that I am exactly 6 feet tall.  The question we decided on was "How far across the wall can I paint?"  ("How many cans of paint would it take?" was the first question, but I insisted there was only one can in the picture so we saved that for afterwards) To answer the question, they:
Enlarged the picture on the smartboard so they could see how much the can holds.
Figured out they'd need the formula for area of a rectangle solved for width.
Copied and pasted the picture putting my feet on my head to figure out the height of the wall.
Went to Behr.com to find out the range of areas you can paint a gallon of interior-semi gloss paint.
Converted from gallons to quarts.
Solved for the minimum and maximum distance across the wall that the paint would cover.
Measured the back wall and found how many cans of paint they would need.

They also came up with a lot of other ideas that we could've done if we had other tools or information ("Let's measure the height of the wall" "Alright, who has measuring tape?")  It was a lot of fun, and they really got into the lesson.  The best part was that a number of kids who don't usually participate at all were brimming with excitement and ideas.  It was so successful that I decided to call an audible on my second class and do the same activity with them too.

What kind of things like this have you done in your classroom?

The Dance Steps to Solving and Equation- The Lesson

I generally do this lesson after I've taught solving equations entirely. At that point there are at least a few students that get really overwhelmed by the process, and I've found that this helps them to break it down into steps (and to actually remember what those steps are) and it's just a heck of a lot of fun for everyone.

The day before the lesson I tell students that their homework is to remember to NOT bring their bookbags to class the next day. (Otherwise we wouldn't have room).  At the beginning of the period, I race to get all the desks stacked on the sides of my room to clear a nice dance area for everyone.  Then, I give them this speech:

"Today is a math fun day.  I *absolutely* guarantee that if you don't act "too cool" for this lesson that you'll have fun.  In fact, this will most likely be the most fun you ever have in math class!"  Cutting the too cool kids off at the pass right up front has always worked for me, and was my biggest fear before ever doing this lesson. (I also tell them participation is mandatory)  I then stick my arms out and swing them back and forth and tell them that they need to be able to do that without hitting anyone so they have space.  I start the beat, and sing the intro, then put the lyrics on the board with the smart screenshade hiding the moves we haven't done yet.

From there, the lesson goes pretty much like this:

After they are able to do the dance with some proficiency, I speed it up 10% and keep speeding it up each successive time until it all ultimately falls apart.  Then, I have them grab a desk and go get their backpacks and work on a sheet of difficult equations to solve, telling them to think about the song as the go along.  When they ask questions, I pretty much just prompt them with song lyrics.

Here are some important tips:

• You should definitely try this lesson if at all reasonable.  I'm fairly certain you could throw this lesson inside 179 other days of teaching like Ben Stein in Ferris Bueller's Day off and kids would still think your class was fun.
• The video is only 3:49, but the dance part of the lesson actually takes me 15 minutes (and an extra few moving desks out and back in).  So, if you are to use the video above to teach the lesson I would highly suggest pausing and going back a lot to give kids time to really learn it.
• I'd suggest writing the lyrics on a side board even though they are in the video so that it's easier for the kids to follow.
  
• If you use the instructional video, I would still highly suggest doing the dance along with them.  If you are too cool to dance, they probably will be too.
• Call them out as a group if some kids aren't singing along, I think sometimes they honestly get so wrapped up in the dance they think they are singing along when they aren't.
• Have some sweet moves prepared for the check portion.(I like the lawnmower or the shopping cart)

Video files (right click to download):
Dance Steps instructional video (High Quality, 110 megs)
Dance Steps instructional video (Low Quality, 30 megs)

Audio Files (right click to download):
The beat (play it in a continuous loop)
Audio of the full song
Faster full song
Even faster full song
Fastest full song

The Dance Steps to Solving an Equation - The Story

This lesson is by far my most well known lesson at my school.  I'll post how the actual lesson goes soon, but I wanted to share the story of its creation because it was integral in forming the teacher that I am today.  Feel free to skip to the bottom for video and lyrics.

A few years ago, I was looking for something to help the kids understand that even if an equation seems really long and difficult, there are solid steps that can be done to get through it.  I'd taught multistep equations, distributing, combining, how to deal with variables on both sides and printed out colored sheets explaining each step.  There were, however, a few students that got totally lost when we tried to put it all together.  I was racking my brain on the ride to work thinking of some way I could get the steps to stick, and hopefully make it a little more interesting for them after we'd been working on solving for so long.

"The steps to solving an equation... The steps to solving an equation... The... DANCE STEPS to solving an equation!!!!"

As with all of my ideas, I knew I had to act on it right away or risk never doing it.  I got through the school day and started to work.  By 10 that night I was finished and ready to do the lesson the next day.

Morning came and I nervously told the head of the upper school before assembly that he should probably check out my algebra 1 class.  After the words left my mouth, I started to panic.   I started seriously thinking that I was about to do something wrong. After all, I was going way off the normal formula that was every math class I had ever known.  Shouldn't I be lecturing? Is this a big waste of class time? Luckily, it was too late to do anything about it. I didn't have a back up plan, and I had already told my boss something interesting was going to happen.

I cleared the desks and chairs to the sides of the room.  Class started, and I ensured my students it would be the most fun math class they ever had.  Full of nerves, I started into my carefully planned dance lesson. The kids were all smiles.  They loved it, and before I knew it there was a crowd forming at the door.  Twenty minutes later the kids had mastered the dance, and knew the words by heart.  We brought the desks back in, and started on a difficult equations solving worksheet.  Students were stuck much less, and when they did ask questions they had a much stronger base to work with.  "Well, what's the first thing you should look for? And then what and then what?"

Later that day, the head of our school came up to me and said he had already heard about my lesson, that he wished he would've known about it and that he most definitely wanted to be in attendance next year. (and he was)  By the end of the week, my 10th and 11th graders were demanding that they get to do the dance ("Hey, we solve equations in algebra 2 too!"), and our 8th grade algebra teacher was asking me to guest teach it to her group.

I really grew as a teacher that day.  I didn't fear taking risks in teaching anymore. When I've had legitimate reasons to do something a little crazy or different to shake things up and get kids learning I stopped questioning it so much. I learned that my school fosters a creative learning environment for not only the students but the teachers, and because of that I am able to thrive.

Okay, enough typing.  Below you'll find the lyrics and video.  The video of me doing it alone doesn't really do the lesson justice. The kids add electricity like you wouldn't believe. More to come soon with audio files and the flow of the lesson.

The Dance Steps to Solving an Equation
 
First you simplify
put your hands up in the sky

so you distribute
then you do a little scoot

Still need to simplify
Put your hands up in the sky

So you combine like terms
and do the squirm

Add and subtract, x terms alone on one side
So take a step back and do a big slide

Multiply and divide, the answer you will learn
when you jump to the left and do a full turn

Now check check check ch-check check check

f(a bag of skittles)

Today, I realized mid-class my students desperately needed a review of working with functions to get through the limit definition of derivatives.  The picture below is what spontaneously occurred.  I wrote the left half and then had them tell me should be on the right.  They seemed to really enjoy it, and understood what was going on much better when we tried to apply it to the definition of derivatives.

f(x) = 5x + 1

Systems of Equations Project - Sparking Interest

I started this project last year, and I was amazed at the results. I modified a project I had done in previous years to allow students some room to use math to explore something that they were interested in. (Believe it or not, analyzing the amount of homework they got didn't do much to get them excited!) The vast majority of my students got really into it, especially ones that otherwise were not very motivated.

For this project, students find data online that they are interested in comparing.  (Sales of video games v sales of movies, Wins of their favorite sports team v wins of their friend's favorite sports team, Women's race times v Men's race times, Success of movie with many sequels v another, Sales of Abercrombie v sales of American Eagle, etc)  They graph and find best fit lines for each set of data, then answer some thought provoking questions about the results.

The most time consuming part of this project was having students find good data.  Anything sports related is easy, finding movie sales is easy, but other things got pretty difficult to find.  When things got difficult, students often wanted to take the easy way out and pick something they didn't really care much about, but could find easy data for. I discouraged that heavily because the key to this project is bringing in their specific interests and showing them how math is involved.  When students worked hard, but couldn't come up with data, I did my best to point them in the right direction. (Try this search or website)

I used 3 40 minute classes for this, but that's because I only expected students to do work at home if they were getting behind. You could significantly cut the in class time down by giving most of it as homework.  If you decide to do this or a similar project  with your class, I would highly suggest making your students check their data with you before they continue onto the rest of the project.

See the project description here.

One of the coolest things about this project was that I stuck excellent projects on my back wall and a number of times saw students from other classes thumbing through and actually reading the results on their own!

Any suggestions for more conclusion questions?  What kinds of things do you do to get your students working with what they are interested in?  Let me know.

Graphing Stories Remix

As you might have heard on Dan Meyer's blog I've started making some of my own Graphing Stories videos.  Dan Greene (other Dan) on twitter suggested I make one that shows a system of equations. I filmed one of me in a no holds barred footrace versus myself. (Don't worry, I won)  Here's how it came out:

Once I'm finished I'm going to make a bigger post about all of the videos for this, and by then I will hopefully have found a way to provide them in better quality than Youtube. In the meantime, I'm looking for some input...

I'm not sure how well it translates at this angle.  What do you think?  Do you think what's going on in this one will be discernible to students?

Also, I'm looking to make some more of these (it's really easy now that I have a template).  Anyone have any more good ideas?    Let me know in the comments.