Function Machines

A couple months ago I posted about teaching functions and using the function machine analogy.  I'm working on the same thing again now with a different class and am taking the function analogy and running with it.

First they worked on some practice and did fantastic with it.  I kept the pictures of the machines on there which actually seemed to help I think.

On this too we spent some time talking about how -x doesn't mean negative, it means the opposite of x. We discussed that the f(x) machine switches the sign of the number and then adds 5.

So today I had something else planned but got inspired all of a sudden and changed up everything that I was doing because I thought the new idea was way better.

About a year ago the Math Midway was at the Liberty Science Center and I really wanted to go check it out.  In particular, I was extremely excited to see the Organ Function Grinder in action.  Unfortunately though, it was gone when I finally got to the Liberty Science Center for teacher appreciation day.  I was really sad to have missed the function machine.

Today it occurred to me that I should try to make something similar.  I did some searching and came across the activity guide for the function machine and it gave me all the information that I needed to run with the idea.

I made this to use with the activity:

Now what I really want is something cooler that actually spins.  But for throwing it all together in about 20 minutes, this is as far as I've gotten.  I'm still considering it a work in progress though. (update on this here)

I gave the kids the activity sheet right from the activity guide.  To introduce the idea, I had the kids work on the first part which only uses one of the dials.  So one operation only.

As for the inputs, they had numbers to choose from.  I just took the numbers from the answer sheet included and gave them out.  I decided to separate them into the ones that they would need for each part, but I think in the future I would just hand out one list of inputs to use for the entire activity.

This is a completed one:

I enjoyed this a lot for a few reasons.  For one, it wasn't just problems where they plugged in numbers and got an answer.  They had to think more and use some common sense and reasoning which is always fun.  Also I really liked that some of them got the same answer different ways and they realized that both of their answers were correct.

I liked this too:

Technically my directions were to use only one operation, but that actually made me enjoy seeing this way more.  This kid didn't do two operations because the directions said to, he did it because it was what he needed to do to get 8 as his output.  I plan to use this as a perfect tie in to tomorrow's part of the activity where we use two and then three operations which I expect to be much more challenging.

Now as if that wasn't enough fun, I also made this:

I plan to have it as an ongoing activity, perhaps for extra credit I think.  On the side I will have different inputs on the index cards...negatives, fractions, decimals..whatever.  Kids will pull a given input, evaluate it for the given function and toss the card into the slot on the top of the box.  I will regularly change the function on the front.  I plan to differentiate this using the inputs.  I am going to let the kids pick their card, but for kids who are struggling either I can pick the card for them or I will make them one with a number of my choosing.  I'm not planning this for an actual class activity, but just to sit in my room and have the kids work on it when they have a free minute.  It'll be for extra credit points so I hope that should be enough motivation to get them over there.  We'll see how it goes.

Extra Help

I have known about Livebinders for a while now but never saw them as something that I really needed (until now).  Honestly most of the ones that I had seen seemed messy to me and just a ton of links all thrown together.  I don't like messy, it stresses me out.

As I mentioned here, I was feeling that I could be doing a better job of offering extra help.  I try to stress that practice on their own isn't all that valuable without checking their answers.  Then one day as I was teaching I overheard a girl say to her friends that she wished that she could record my teaching so that when they got confused later at home they could watch me explain how to do an example.

Uh, yes..I absolutely should be doing that.  So that comment inspired me to go home and find as much good supplemental materials as I could.

Originally I posted the links right on the class website page, but soon realized that things were going to get messy soon.  Also I didn't want to delete the links because I didn't want to have to remake the page again next year.

Livebinder, however, was exactly what I was looking for.  I wanted a way to compile a whole bunch of links in an organized fashion.

I went with the layout that has the tabs on the side.  I think it's more organized and less cluttered looking.

I set up one tab per unit and then labeled each subtab to match the skill that it addresses.  I also post the SBG skill list for each unit.  For each skill, I have mostly similar stuff:

• A kuta worksheet with the answers.  This is not fancy, it's just a ton of good practice with the answers included.  The problems also get more difficult as the worksheet goes on (which my kids know) so I tell them to choose problems accordingly.  If they are having tons of trouble they focus on the easier ones until they are getting them correct.  If they are finding them simple, they can skip further ahead.  Some kids that know they're pretty good with a skill will skip right to the end of the worksheet and work on the most difficult ones.
• A Khan academy video of the skill.  Now I know that most people hate on Khan academy, but I don't think it's all bad.  I do not think that it can ever replace my class, but I think that in an extra help capacity, reiterating what I already taught, it's good.  Most of the videos are short and I can find ones that focus on exactly the skill I've taught.
• Khan academy practice.  Now this, I really love.  In my opinion, it is wonderful guided practice.  It gives kids a problem and they type in their answer and check it.  The part that I'm loving is the I'd like a hint button.  It gives kids small hints to guide them in the right direction without actually giving them the answer until the very end.  Depending on how much help a kid needs, they can keep pressing the hint button until they know what to do.  Take a look at this one and look how the first couple hints are just nudges in the right direction.

For now these three have been my "formula" for setting up online skill practice.  I'm sure I could find hundreds of websites that provide practice problems but at a certain point it's just overload.  I think this is actually really important.  If you give kids too much, it can get overwhelming.  Instead I think it's better to focus and handpick exactly what you think is the best.

I like using the Livebinder format because it can be an extra help work in progress.  In a year from now I will have posted all the chapters and can just continue to tweak things from there, instead of recreating it all every year.

One thing worth mentioning is that posting all this stuff is useless if the kids aren't going to use it.  You need to get them to want the help and see it as valuable.  I think that the standards based grading helped with that immensely.  They are motivated to get help because they know that it will help their grade.  They want the 5's.  After the first unit, they are starting to realize that they aren't improving by just retaking quizzes.

Also just saying, "I put some stuff online, go look at it" isn't enough if you want them to use it.  Because they just won't.  I took the time during class to put it up on the projector and walk them through each link and what to do.  One girl that is strong in all the skills said that even though she doesn't need help, she wanted to go on to play with the Khan practice because it looks fun.  So yeah, that's awesome.

A couple days ago a student that has been struggling and reluctant to ask for help came to me with about 4 pages of practice she had done.  She said she watched the videos from the livebinder and that they really helped her to understand what was going on.  Then on the next test she did better on substitution than she ever had before.  So it really is working.  Even if she's the only one, it's worth it.

This is a copy of the binder I'm using with my kids.  I'd share the actual one, but I like using the view counter to get an idea of how many kids are actually using it.  So this one will not update, but you can check it out to get an idea.

Post-It Printing

I saw the idea on pinterest about a year ago to print directly onto post-it notes and thought it was so cool but never ended up trying it out until couple days ago.  

I had kids do a short activity to extend something they had done in their ISN and wanted to give them some feedback on it but not write on their papers since they are getting hung up.  I was going to give them 10 points on it and rather than an arbitrary 8/10 it occurred to me that printing up a quick rubric onto the post-its would be way better and less that I'd have to actually write out for each of them. 

Love it.  So easy.  I'm not sure why but for some reason I imagined the post-its jamming and getting all stuck in the printer (I'm paranoid) but it all worked perfectly.  FYI I used a laser printer...not sure if this makes a difference.  For the template click here.

Only thing that I didn't think about (which is my fault for not really reading the directions) was forgetting to erase the borders when I went to print onto the post-its.  So the first batch wound up with some extra lines around the edges.

I think that printing post-it coordinate planes to stick into ISNs would also be cool and useful so that may be next.

On an unrelated note- and a bit of a rant- I'm tired of giving kids any less than 100%.  I graded these and many of the kids left parts off.  Some didn't define variables, some didn't list possible solutions, some didn't graph correctly.  So the way I see it there were two options:

• Option 1: Put the grades into the computer and complain that I can't believe these kids didn't follow directions after I made it so clear.  Call them lazy because I gave them a detailed example.  Tell them that they got grades they deserved. Be angry that they don't know what they're doing.
  
• Option 2: Don't put the grades in.  Pass back papers with feedback and let kids make corrections.  Let them see what they forgot and where they were missing points.  Have them look at examples of correctly done ones.  Recollect them, enter 100%'s for everyone because they now deserve them and be happy that now they understand what they're doing and what I wanted from them.

I went with option 2.  That is all.

Standards Love

source

After reading about standards started off fairly small with it, and even now I know I'm not implementing it as fully as many other people are.  I expect though that like anything else, it will continue to develop the longer I stick with it.  Baby steps.
based grading since summer I finally drank the kool-aid in January and got hooked.

So although it hasn't been all that long, I have noticed some changes already.  I've also noticed some things that I was doing that needed to be changed.

For starters, assessments have become WAY less stressful.  I don't think it's that kids are taking them less seriously, it's just that they know I'm not trying to "get them."  If they mess up or just need some extra time to learn something, it's ok.  Scores are flexible...more of a work in progress instead of concrete.

A couple times I've had kids absent a day or two before a quiz and typically I'd let them wait to take the quiz until they were ready.  Instead now I tell them to try the quiz to see where they're at and we'll go from there.  So far none of them have objected in the slightest.  Often students are actually asking me for more topics on their quizzes sometimes when they feel like they've improved on something.  Last week I had planned to do a quiz on only two topics, but ended up including two older ones as well because they asked for it.

My favorite thing by far is that slowly but surely, my kids are learning the importance of practice.  A couple weeks ago I gave a homework assignment that was to do 6 out of 13 problems on a worksheet.  It was a puzzle type one that I like because it's kinda self-checking without actually giving them an answer key.  If they get an answer that isn't one of the possibilities they know something went wrong.  So I hand it out (on a Friday) and tell them they only have to do 6 problems.  Upon handing it out I heard comments like:

• Can we just do all of them?
• I'm just going to do them all because I really need to practice this a lot
• I'm gonna do them all because I need to know what the joke is

It was awesome.  Some of them were voluntarily choosing to do additional "homework"...on a Friday no less.  And I say "homework" because at that point it wasn't really homework per-se, they were opting to do more work because they knew it could help them to improve.  I told them that they were only required to do the original 6, but if they personally felt they needed more then of course they were welcome to.

I've also given a couple of homework assignments that are for them to do whatever they want.  Anything at all, but the stipulations are that they need to choose problems (usually from the review sections in our book) where they can check their own answers.  All I check is that they have something done.  They are to use their SBG skill list to help them choose where to focus their efforts.

Along those lines, I've realized that I haven't been doing nearly enough to help them out.  Yes I am always willing to help them before or after school, but often it just isn't all that feasible.  It really got me to thinking and led to a revamped website and a class Livebinder (more on that later).

My goal is to create a resource that is crazy helpful and jam packed full of good and helpful stuff.  I showed it to my kids today and they were pretty excited about some of the stuff.  As I was showing them one girl said that she didn't really need to practice what we're doing right now, but she wanted to go on just to play with some of the stuff that looks fun.

All year I've been struggling with this class and and a seeming lack of motivation so I'm thrilled to find something that seems to be working.