Math Cartoons for Inverse Functions

The evolution of my lesson planning over the past three years goes something like this (By the way, instead of using evolution at first I used evolvement, which is not a word. Spell check suggested the word enslavement... ):

Year 1: The challenge was the unmerciful pace of time as I searched each night for the perfect way to teach a concept I was to teach the next day. Being frustrated  not finding it, I would organize a lesson or create some sort of activity to teach the concept, finish the lesson just in  time, execute the lesson in class, and would think either "Wow- not bad" or "Wow- that did not go at all like I envisioned".

Year 2: The challenge was looking over the lessons and asking "How can I better explain this?" and trying to improve my explanations to make the objectives of the lessons more achievable for my students.

Year 3: The challenge is realizing the way I have taught needs a major make-over. My goals to be the perfect explainer and presenter of information have been flawed. Understanding by Design has been the focus of our professional development, and this year I struggle to change the way I teach so students have joy in discovering and truly understanding concepts. (I just read a great blog at http://bowmandickson.com/2012/09/29/let-them-figure-out-the-power-rule/ concerning this.)

With that rant out of the way, I would like to say I have seen success with some of my units throughout the years. 

I am teaching logarithms at the moment. It has become one of my favorite units to teach. I start the unit with compositions and inverse functions. I find my students really have always enjoyed this lesson. The cause of the enjoyment- a cartoon. I know, I know a happy go-lucky cartoon is not the answer of true understanding, but it helps. I thought I would share it:

The one big observation I get EVERY YEAR from this cartoon is some students points out or shouts out "Where is the robots head?" referring to the third image along slide one. Again the thought through my head is "Wow. That did not go at all like I envisioned." 

However, this really helps with the understanding of why the inverse functions have x and y values and roles that swap. Everything our original machine/function does onto an input is undone by the inverse function. The output of the original function is the inverse's input because the inverse swoops in and takes it. The output of the inverse is what the original had started out with and worked to hard on to change.

Whatever it takes to make it stick, right? 

I have attached the PowerPoint I have for this lesson in the "Lesson's on the Loose" page of my blog. I also will be adding my exponential and logarithm lessons because this lesson on inverses launches that unit. 

Week 4: Thanks Blogger Community

I am going to be honest, and say I have done a good deal of stealing... OF LESSONS! Don't worry; I am strictly in the line of lesson thieving and nothing else. I do give due credit as well. My blogging experience has developed quite a bit over this last summer.  Before, I always searched blogs just on a prowl to find the perfect math lessons. Then I started to see the bouncing of ideas and sharing of experience. I always saw the real benefit of taking, but I learned the true benefit of reading, relating, learning, and also giving back hopefully as much as others have given me. 

Things have been busy for these first weeks of school, but one of week 4's blogger initiation prompts led me to taking the time to read and enjoy some blog posts. One of the many I came across was mathemagicalmolly's blog about "forgetting how to teach" at http://bit.ly/TQjEv9. Mathemagical is now a part of my vocabulary.

She brought up sleep. Oh, how sleep changes during the school year. I really do not find myself doing a whole lot of dreaming while in school. I think at night my brain has to all out die in order to recoup for the next day. I have found throughout many stages in my life, my work life takes over my dreams. When I worked at Target in high school, I woke up to trying to pull my cat across as "scanner" because in my dream I was trying to ring up a costumer at check out. When I waitressed, I always dreamt these dreams where the restaurant was really busy and I just could not keep anything straight. Now, I have dreams about what I need to do for the classroom.

The purpose of this weeks blog. Nothing really. Just a simple thanks to the blogger initiation, and all the committee has done. And thanks to all those strangers I am reading, learning from, and just enjoying relating to. 

Trying to Get Students to Understand Why Math is Important

                I have an Algebra Extended class where algebra is taught over the course of two years rather than one. It makes for a slower pace math class for the students who may need a slower pace type of math atmosphere. The student that normally takes this particular course, let’s just say tends to ask the question “Why do I need to know this?” Not in the nice-polite way, more in the I am asking because I am certain I don't need to know this way.

                I am trying to show my students that you never know when math will help you prove a point or help you make a decision. I have a theme going on in all of my classes this year: “Is it sustainable?” The use of ethanol, the decision to go with one phone plan vs. another, the consumption of energy the school goes through- is it sustainable socially, economically, ecologically?

 I make it clear that they will be responsible for making real decisions and I will be giving them room to form opinions around all of the information I will be bringing into the course. I want them in turn to see the importance of having factual evidence behind what they say.  When they make arguments, math can often times be the tool that serves as fact. If they make financial decisions, doing some calculations can justify their final choice of action. I am trying to establish this theme of thinking critically and not just saying things when really they do not have the knowledge to back up what they say.

                To try to win them over that math can play an essential role in winning arguments, we start the year off with a debate. It is a bit abnormal. On the first day of school, I have students brainstorm some strong beliefs they have or controversial issues they can think of.  Here are a list of some of the things they came up with:

                The war in Iraq                                   Year-round schooling    

                The healthy kids’ act                           Raising corn-prices (This one turned out great!)

                The health care act                              Which car is better Dodge or GMC

         
             I assign random partners. These partners decide on a topic. They then become enemies, for one person in this pair will be FOR "Year-round schooling" and the other partner will be AGAINST "Year-round schooling."
             The actual assignment is quite simple. I have done this for the last two years, and what I see is some students really fly with it, and other students really just do not take it seriously. I think it is well worth seeing the students who make a great learning opportunity out of it. They learn not just about a topic they are interested in, but they also see the force of using math to form facts and backbone to an argument. The outcome of the debates do portray to the students, that good research and factual information does clearly win. I can continually refer to this project throughout the year to make the point that math can really come in handy to justify decisions and hopefully help prove an answer to the theme of "Is it sustainable?"

                All students are to do is come up with a strong argument sentence. I tell them this can be opinion. But, they are to find 4 statistical or numerical facts. I have the “Outline” worksheet with an example paper I made for an argument and the rubric down below.

Outline for Argument Papers

                 For some reason, Excel is not opening for me at the moment. I will be posting the rubric I grade them on. The presentations are in the form of a low key debate where they two conflicting arguments stand up together and read their arguments. I have the pro side go, and then the con side. I fill out the rubric as they present. (I will post this rubric as soon as I figure out what is up with Excel...)

Students in the audience fill out the following evaluation forms as the debates occur.

Peer Debate Eval

                Tomorrow I hear the last of the presentations. Then, we shall see if I made an impact with them...

Proud to Share Algebra Boot Camp for Calculus

Each year in Calculus, I seem to make it a little farther with my students. I have been able to improve the course a little each year to the point where I feel my students were able to not only reach farther, but also get themselves deeper in the understanding of the concepts of calculus.

I am feeling even better about this year. I have a few things in store to make sure my students are able to focus on the key calculus concepts and that they are able to draw connections that will solidify their new learning even better. 

Change 1: Algebra Boot Camp

We have had just two days of school so far, and I am proud to share the first week's work of Calculus material. With the inspiration of samjshah's post "Algebra Bootcamp in Calculus" http://samjshah.com/2012/06/01/algebra-bootcamp-in-calculus/  I too made a bootcamp. I also have found those darn algebra skills causing so much grief.

Algebra could potentially take away from the calculus. Students getting held up on algebra tends to cause frustration. They triumph over defeating the algebra, but in this triumph over struggle, lost track of the new Calculus skill they were actually trying to do.

Then, there are just those algebra common errors.  Students doing things like this= AAHHHHH!!!!

I gave boot camp 1 on the first day of school and boot camp 2 on the second day of school to my calculus class. Here are those handouts:

Algebra Bootcamp Part 1

Boot Camp 2

I feel this was a great start of the year. In my calculus videos/lessons, I can refer to these boot camp skills. They have the worksheets in the binders/notes, so they can refer back to their findings and review. Plus, it was kind of fun to see them resurface these skills. I stepped back, and told them to use their resources and each other. I was pleasently surprised to see they remembered most of these! They worked in groups of 4 and bounced ideas off of each other very well to complete the worksheets. We had great follow-up discussion about answers following the completion.

Change 2: A huge collaborative concept map to link the concepts and skills of calculus. 

Now this one is not one I have done yet, so hopefully I will proudly be able to share this later as I go along. One project I plan on doing is having them make a concept map throughout the course of the year. After each unit, they will collaborate as a group to come up with key skills and concepts they have learned throughout the sections of the unit. They will be putting these skills and concepts into though bubbles (made out of construction paper maybe) and sticking them to the wall. It will be an ever-changing concept map where they can edit connections as we progress. I want to just do it on the wall using construction paper, but I was also thinking about having them do on on a Prezi. 

Yay for Blogger Initiation: A Goal for the First Week of School

Yay for blogger initiation! I think there was a time when I just did not get blogging. I did not think it was a worthy priority to dedicate time to. The thing was, I had not invested time into it to see the greatness that could come out. I said to myself I did not have time for it. Oh but how you can make time when something becomes such a clear benefit for you. The ideas I have already received, the resources, the insight, the communication, and the personal, professional growth make me so excited to become a part of the community.

This will be the start of my third year teaching, and I still exercise the dream I had for my first two years about setting the stage just right for my classes of Pre-Algebra, Algebra, Precalculus, and Calculus. My goal is to have things run smoothly for the first week of school and to get my students pumped and prepared to learn. Big goal of many little goals, I know.  Vague, I know. My first week tends to be a frenzy for me. I am not prepared to give any genius insight on it because I just do not have it down yet.

What I really want to talk about is a shiny, brand new goal for this year that goes beyond the typical first week goals and first week list of things to do. 

I am hoping to raise an interest in at least 5 students and create a team at my school to participate in the FIRST Challenge robotics building program. There is more information about this challenge at http://bit.ly/PEQYVG.   

Newby teams in Iowa are being supported by the company Rockwell Collins. The kits to build the robots are about $1,000, but there is a grant Iowa teams can apply for through Rockwell Collins to cover these costs. (There is options for other states, but I am not keen on them. Sorry other states.) The application is at http://bit.ly/ME6ZKw .

The requirements for this funding include:

1.        Teams will consist of 5-10 members between the ages of 14 and 18.

2.        The team will meet at least weekly throughout the season.

3.        Coaches will participate in a training session for coaches.

4.        The teams will participate in a tournament, which may be a regional or championship event.

5.        The coach will be responsible for managing the team and participating in a post-season evaluation.

I am fully ready to cover and get my group of creators and innovators through requirements 2-5. I just need a team of students who are excited to jump into robot building.

Now, I know a little about computer programming (a very little, little), but I am excited to jump into a project like this though I know I do it kind of blindly. Through this robotics club, I am hoping to create an outlet for students who may not have had that moment/opportunity in school yet to let out some of the creative and exploratory minds. I am excited to see what they can come up with and the beasts we can create. To at least gain a little more knowledge and be a somewhat knowledgeable coach, I want to tell you about my next awesome discovery.

On the radio, I listened to how elite colleges are offering FREE online courses. I went to Stanford’s offerings at http://www.stanford.edu/online/courses. And wouldn’t you know, there is a robotics course! It is a 7 week course, and takes the structure like any online course. You do not exactly get credit, but you get the knowledge and a certificate of course completion. I will most happily flaunt that Stanford certificate in a scrapbook, that I will probably never make, and I will gladly take that wealth of knowledge. There are other courses and colleges participating. For now, with the little goals and things that need to be done at the start of school, I have just signed up for the one course. But this year, I hope to be collecting the certificates of completion and gaining that wealth of knowledge.

What I Got: DIY Wind Turbine

The motor I ended up with is nothing like what I researched about. I got carried away with the research (I am finding this to be a theme in this project). When you are working with limited resources and budget, you cannot be a picky person. I ended up with 17.2 amp, 7099 RPM, 2.5 HP, and 130 VDC (volt) motor.  Nothing like the 3 amp motor I thought I wanted. Also, I did not get the Volts to RPM ratio I wanted. In research, I found that a .035 ratio was ideal. I ended up with a .0183. Again, not quite ideal, but it will do.… When you travel  an hour and a half to pick up a free treadmill posted on Craig’s List, and you take it apart to find a 17.2 amp motor, that is kind of what you are stuck with. That, and a lot of treadmill parts to dispose of.

What does this mean? Well, the scale of my project just got bigger, significantly bigger. I kind of feel like I was just trying to hammer a nail into the wall and I accidently knocked down the entire thing. I actually got myself really worried about the whole project as I stood in Menards trying to figure out what I needed. Things will just need to be bigger. Hey, more power to me though right. Really, I know right.

Here is what I ended up with:

Here is a picture of my husband trying to help me out and taking apart an old broken down hand belt sander. It turned out to have an AC motor… oops.

Soon, I will be posting about the blades. If you are interested in making 1 meter blades, I found an already thought through blade design for using PVC piping at  http://www.youtube.com/watch?v=BawUfbDDvtA . He gives you tables which basically gives you an arc length to cut given how far along the length of the blade you are. I am going to research a little more on them before I decide what to do. I know research, smeesearch. It has not done a lot of good so far, but I am sure this time it will. 

By the way, we do give thanks for the treadmill and the belt sander that was sacrificed in this process. For anyone who is concerned we will hoard the parts and make good use of them one day, or else we will take in the scrap metal to salvage their worth. Hats off to you treadmill and belt sander. May your parts become great contributors to science and making this world a better place.

What is this feeling I am feeling inside?? Excitement?

I am just going to be frank here. I have taught two years, and I have never been truly “excited” for school to start. Of course, this is contrary to what I have said when people asked me, “Are you excited for school to start?” I always gave a big, fat “Yes”. Sorry.

The first year, I was just nervous out of control to be truly excited. The second year, I had kind of a big thing going on (I got married), and when school came rolling around again, I felt completely unready. What have I learned? I learned the feeling of being ready is a rare feeling in teaching for me.  The feeling of being 100% ready is a never. I can spend hours upon hours trying to establish the ins and outs of the lesson, the demands I am making of my students, the anticipated problems and questions the students will encounter, the connections to be made … You need to jump in with the best preparation job you can muster.

This year, I can say honestly- I am excited and ready to just jump in. Here are some reasons why:

1.)    I am blogging this year. During the summer I have started to follow several awesome blogs. Today, I just read at  http://samjshah.com/ about a BLOG INITIATION where I hope to extend my stealing and sharing web even more. I cannot speak more highly of samjshah and how he has impacted my teaching. Good bye to teaching in isolation and regular nights of labor to birth ideas and projects (graphic I know, but it can be ugly). Hello huge network of teachers to exchange ideas. I already have two great new project ideas that I took from other  blogs.

2.)    I just finished my STEM Externship experience, and we had a last get together yesterday in Des Moines. From this conference I have learned about Iowa’s FIRST Tech Challenge where students work with designing programs and building a functional robot. There is more information at http://iowastem.gov/imsep/businesses/inventory/first-tech-challenge-program. If you are in Iowa, Rockwell Collins, an aerospace, communications technology, and defense company, is providing support for newby companies. There is the applications and information at http://www.rockwellcollins.com/Our_Company/Corporate_Responsibility/Community_Overview/FIRST/FIRST_Grants.aspx.  At the beginning of the year I am going to get kids on board as soon as possible, and if there is interest I will be applying for the Rockwell Collins FIRST robotics grant. My students will learn to be producers of technology. I do not think there can be anything not exciting about robots.

3.)    I get a $150 stipend for my classroom this year, a generous gift from the STEM Externship program I participated in this summer. I am thinking about using that money to purchase items for building mini wind turbines in the classroom. I was directed to Kindwind http://learn.kidwind.org/. I will start looking into this. I find the idea of my students doing the work with me to figure out wind turbines a very exciting prospect.

My goals are starting to seem a bit overwhelming. I have the initiative, however, and am mentally preparing for the follow through. Gah! I have so much to do!! I definitely don’t miss this feeling. Again, there is no true feeling of “I feel ready and completely prepared,” so that only leaves excitement now.

Before I start anything, I will finish up my summer goals that ends with me creating 10 new calculus videos for my flipped classroom. This week I will focus on nothing else. Success will be mine.