Experimentation

New plan.

Functions are out, variables are in.  Multiplying variables v. adding variables.  I could not get a satisfactory model for functions.  My ideas all ended up being lighted multiple choice questions where students determine if an equation is a function or not. I decided to switch to a simpler idea that was more specific, and my students have consistently had trouble with the difference between the exponent rules when adding variables v. multiplying them. After I switched ideas, the prototype was done in an hour.  A good sign.

The day the refreshers came to give feedback I was nervous, though I know from experience that I always benefit from allowing others to see my work. Also, I wasn’t sure that exponents could be demonstrated using circuits or that it was even a decent idea, but I was sure that my students have trouble with them, and this seemed like a simple idea to start with.

My feedback group liked my clearly defined goal: to have students understand the difference the product rule of exponents by contrasting it with the principle of combining like terms.  In a nutshell:

x+x+x=3x       and      xxx=x³

The idea is that students create one circuit that represents 3x and a second circuit that represents x³. The prototypes follow.

For  x³(notice 3 lights in one circuit, one battery required):

For 3x (3 lights in 3 circuits, 3 batteries required):

    

I am so happy with my idea, and my group asked me some excellent questions, focused mostly around implementation.  How am I going to work the lesson logistically? How do I tell the students what I want them to do?  How am I going to introduce circuits?  If I model my version, won’t they all just mimik mine?

They also presented ideas:  What if each student made one circuit and had to find their “partner”, so 4x would have to find x4? What if the battery has an x on it to represent the base? What if they do one circuit individually, then do a second one in groups, or maybe just do this in groups to begin with?

This feedback I recieved got me thinking about the logistics of how to implement this into my classroom, like the knitty gritty, what-do-I-do-next, logistics. I teach in a very traditional method with lots of direct instruction, so introducing a project like this is new to me and my students. Furthermore, my students are mostly poor. Last year I read the book A Framework for Understanding Poverty by Ruby Payne.  One of her ideas is that students with a poverty mindset need clearly laid out instructions because they have never been taught how to learn. A project like this could overwhelm someone who doesn’t know how to go about figuring something new out.

With this in mind, I considered how I do something new:

1. I get an idea that inspires me.
2. I get excited about it.
3. I go the the internet to figure out what tools I need to do the project.
4. I stop reading instructions about ⅓ of the way through (due to boredom or something more interesting walking by or a new post on Facebook)
5. I start trying to make my project.
6. I get frustrated.
7. I try harder.
8. I get angry and frustrated.
9. I give up for a time.
10. If I am really dedicated, I will then go back and read the instructions or finish watching the video.
11. I return to the task and successfully complete my project.

Making my prototypes was like this. I dumped the contents on my desk, I started cutting copper wire and sticking it on the paper, pulling it up and trying to make it stick in a new location.  I went through about 3 pieces of paper and even tried drawing the circuits on the paper at one point.  Long story short, there was a big mess, little strips of paper all over my desk and evidence of where adhesive had been removed from my paper.

I would really like to be able to set out a bunch of supplies and a computer for my students, tell them what I’d like their product to be, say “go”, and watch them eagerly figure out how to make paper circuits that represent monomials.

These are not the students I teach. My students give up, don’t try, and are not interested in learning new things.  One reason is that they don’t know how to learn.  These types of students need clear cut, accurate instructions with correct vocabulary used.  I think I will make my “how to” about how to teach paper circuits to students who have no idea how to go about learning something so far outside of their comfort zone.

Here is the draft of the steps I have so far as a play-by-play guide for students to learn how to create a paper circuit:

1. Read the Paper Circuit instructions (link to PDF) all the way through before beginning.
2. Watch a video (here’s one) to see someone in action and get an idea of what it will look like.
3. Have 3 pieces of string, an LED bulb and a battery out.  Arrange them in a basic series circuit, using the PDF above as a guide.
4. When it look like it’s supposed to, cut copper wire the length of the string, but DO NOT TAKE OFF THE ADHESIVE!!  The circuit will work without being attached to the paper.  It’s a bit awkward, but it will work. If it just won’t stay still, you can use a small piece of tape over a small section of the copper wire to hold it in place.
5. When the circuit lights up (it is VERY important to keep checking to make sure your bulb lights up- this is the point, after all!), and the circuit is arranged the way you’d like it, NOW, peel off the adhesive and attach your circuit to the paper.
6. Test again, and if it’s still working, decorate all you want!
7. Follow the same process for a parallel circuit, including watching the video again with an eye to these specifically.
8. Once the basic system is mastered, it will get easier to make variations, more complicated decorations, etc.

Right now my lesson plan will go something like this:

Day 1:

• warm up- review exponent rules, 6 problems
• introduce paper circuits- make a fun one for practice

Day 2:

• Warm Up – 4 problems on exponent rules
• Introduce the task of representing 2 monomials with paper circuits
• Make the 2 paper circuits in partners (everyone makes 2 circuits)
• Clean up
• Formative assessment: give warm up from Day 1 again to see any improvement

Day 3:

• Present circuits to the class
• Write explanation of both circuits to be published on class web page

 

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References:

Payne, R. K. (2001). A framework for understanding poverty. Highlands, Tex: Aha! Process.

 

Epiphany!

Ideation was the focus of the Maker Project on Wednesday, and we brainstormed our “How might I…” questions in groups.  I have to say that this part of the process did not feel very useful.  Perhaps it is because I usually work by myself; perhaps it is because I tend to think I know best what to do, or that I had no confidence that a solution to my “what-can-I-make-for-my-project” dilemma exists.  It could be because we were lying on the floor!  Whatever the reason, I pulled myself together and focused on brainstorming my group members’ questions.  I must say, I found it quite comforting to see that other people had struggled with a question.  Maybe the process was more helpful that I originally gave it credit for!  If so, I didn’t notice that day.  My poster is still folded up and quietly resting on the desk in my room.

What the…?

Today’s Maker Project task was mind-mapping (thinking visually) to help us get to a central question on which we can focus, in the form of, “How might I…”  At first I was, not surprisingly, resistant.  But I pushed through and started.  I began with what I knew about the Maker Movement, which was about 3 popplets!  Next I mapped my concerns (of which there seemed an abundance) which was super helpful because it forced me to get to the specific issues I have.  Then I got stuck, so I made another bubble system, independent of the first, with Teaching Questions at the center.  My goal was to articulate things I find difficult in the classroom and see if the two main ideas, the maker movement and my teaching concerns, would overlap.  I trusted the process, hoping for a breakthrough, and I got it!

The items that emerged from “Teaching Questions” started very broad: students’ inability to remember (i.e. know) processes like how to solve equations; tackling student apathy; and  differentiation of instruction.  I began to draw lines connecting my two main ideas.  Differentiating instruction and the collaboration inherent in the maker movement could go together–I drew a line connecting them.  Slowly I realized that a well-implemented “maker project” has the power to address all of these things at once–that that, in fact, is the whole idea!  The rest was easy as I began to envision ways that “making” could be used to address topics in the curriculum.  The “how” still eludes me, but I was told to “trust the process”.  We do not have to have an answer to the question yet, I kept telling myself.  My anxiety lessened.

The questions I was asking began to be more specific as I understood that students could actually learn the skills I was trying to teach them through the vehicle of making.  This made it easy–I wrote several “How might I…” questions on topics that I historically have trouble teaching, and thus was a beginning made.

 

Confrontation: Me v. Me

Over the weekend I watched the TedTalk by Dale Dougherty, the founder of MAKE Magazine and the world’s first Maker Faire.  I had never heard of the Maker Movement before, and, quite frankly, my linear mind did not find this video helpful.  I was hoping for a bullet list of the characteristics of the maker movement.  I was disappointed.

Today, however, we experimented and tinkered with maker tools.  I got to experience a little bit of what it would be like to be a student in a makerspace.  I really enjoyed playing with the sticky circuit, the Little Bits kit, and the coding website.  The wall I keep approaching in my mind is how this will translate into the math classroom.  Even as I write that I hear the contradiction–making is, by definition, cross-curricular.

I have been excited and engrossed in every topic we have covered in class, until we got to the maker movement.  It was like standing in front of a brick wall that reaches up higher than I can see.  After we tinkered with the kits in class today, however, I found my resistance lessening.  Then, when we got into our SIG groups (mine is the maker movement) I started talking to my group about it (which was really me talking and them listening, but it worked),  and I began to understand what’s going on with me when it comes to the maker movement.

One: the other stuff is more interesting to me than the maker movement.  But that isn’t everything.

Two: In my mind’s eye I don’t see a bridge from where I currently am in my teaching, which is mostly direct instruction of subject matter on End of Course tests, to making things as a device for learning mathematics.  I am really struggling with how students will learn skills like solving systems of equations if they are making robots.  I understand that the ideas of solving systems is inherent in such tasks as building electronics and designing mechanized objects, but I still have this picture in my head of my students not doing well on the EOC because I didn’t teach them the actually process of solving systems of equations.

Three:  There is an entire mindset shift that must take place in me if I am going to be able to incorporate this into my classroom.  I tend to get caught  in “all or nothing” thinking, so there is a good chance that I am skipping steps.  In my imagination, suddenly my entire classroom is about making things without any conventional learning going on.  (Oh, and it was supposed to happen yesterday!)  As I am writing this, it occurs to me that I don’t have to change everything all at once (and, in fact, most change doesn’t happen that way at all!), but rather I could start small–maybe a project in class.

Four:  I am afraid that I do not have the scientific and mathematical knowledge to pull this off.  Don’t I have to know more than my students?  Don’t I have to know the answers before I ask the questions?  Don’t I have to know how to make the stuff before I ask them to make it?

Five:  I will proceed with a deliberately open mind.