A Sick Teacher’s Morning/ Newton’s Law of Cooling Application

If you are uninterested in my  battle and detective work against e. coli and only want to talk Newton’s Law of Cooling, skip down to paragraph 6. I understand Newton’s law of cooling is way more interesting.

Starting at 2 am today, I woke up with a horrible stomach ache. I believe my morning from 2 am-6 am was a result from an evil army of microscopic, hairy Mic n’ Nikes- I looked up what e. coli looks like. I constantly forget about and do not give enough respect to our microscopic world that can overtake so easily.

I have two suspect sources:  I sprouted some alfalfa sprouts in my magic sprouter. I am now afraid of my beautiful cup full of alfalfa, and sadly I think I may just compost them. Or, I also tried eating dandelion leaves for my first time, which I first washed in the rain collector barrel we have. Either I am allergic to dandelion leaves, which I think is like being allergic to lettuce- so unlikely. Or, the NPR program over how rain barrels are e. coli collectors is sadly true.

Anyway, I think e. coli ruined my morning pretty horribly. Never fear though; my students had lessons today yet. I hunched over my computer on the bathroom floor putting together lesson plans. It was sad because there are three weeks of school left, so the crunch time is upon me to get all that I want done. I prepared so well on Saturday night and had today laid out perfectly, only to hand it all over in dry-heaved, butchered form.

Anyway, I slept in hard and woke up feeling a lot better (:, but still not wanting to move around a lot. So, of course the mind starts to nag at you about all of the things I could do. Three things nagged the most: 1.) Writing a month overdue thank you- check. 2.) Writing a blog since it has been months- doing it, check! And 3.) correcting some papers- oh yes, always those; never check. Never L.

I figured I would take the time to share a recent lesson. It is in progress, so it is rough. I love having my students make websites. I love it. So, for our final project to close up our Calculus course, I am having them review an application of integration we went over through a fudge making project. They will be making a nerdy website by bringing in calculus calculations to calculating the time at which the fudge needs to cool.

I only have 7 more days with them. Two of which go to taking a test, so five. The first outline for this project is down below:

Newton's Law Project

Task 1: My students at first had no idea what I meant by task one. Which to be honest I was peeved about. Was my objective not clear? Did they not know they should research about fudge making in order to do the task “CREATE THE INSTRUCTIONS FOR MAKING THE BEST FUDGE!” I got over myself though. I realize my instructions are vague. I had to prompt them, with too sarcastic of questions like “So you guys know all it takes to write instructions on MAKING THE BEST FUDGE.” I had the questions from the like “Are recipes good enough for task 1?” My response was “No. They need to find some tips and secrets." Then one students found a great resource (the first link I provided)  in the links down below. In a nutshell, they say the key to smooth fudge is in the COOLING and the WHIPPING. These were the resources I hoped they would come across:

1.) http://main.kitchendaily.com/2010/03/03/secrets-to-smooth-fudge/
2.) http://www.exploratorium.edu/cooking/candy/fudge-story.html
3.) http://www.kincaidbooks.com/Candy/PerfectFudge.htm

Task 2:  We tested over Newton’s Law of cooling as an application to integration a couple months back, so I handed back there old test, and we discussed and journalled. Then we did the referenced problem which is as follows.

“46.)  When an object is removed from a furnace and placed in an environment with a constant temperature of 80^o F, its core temperature is 1500^o F. An hour later after it is removed, the core temperature is 1120^o F. Find the core temperature 5 hours after the object is removed from the furnace.”

Task 3: I think the essential questions are the hardest part. We so far just discussed the two that I did as examples. We decided we are going to do a few batches to see how the rate at which it cools varies depending on the type of fudge it is. The types of fudge they listed: Cookies N’ Cream; Peanut butter; and regular. We are going to go with a standard room temperature. We also said we could do it on another day where the room is warmer (we do not have air conditioning at our school).

I will let you know how the rest of our discussion goes.

I see us taking two days to come up with more questions and write the protocol for the experiment.

We will take three to actually do the fudge making and website making. The roles for the website making can be the instructions for the fudge, the recipe writing, and the typing out of the protocol. Together, while the fudge is cooling and while we are eating, the calculations and the reflections can be pounded out and put up.

Stay tuned!

Project Based Learning VS. Project

I am deepening my search for projects and working towards Problem Based Learning. I have been content in developing and stealing project ideas that are meant to be an end-of-the-unit assessment to see students collaborate and make connections and applications for the skills they are learning. For example, in the last blog, we did the radio project.  I was happy with the type or problem-solving and collaborative spirits that came out of my students for the project.

I recently did another project where students were to transfer their skills of vectors to a challenge problem, which I will call a project. First of all, I learned the pretenses of calling a problem a challenge problem. The mere connotation of the word “challenge” made some students assume impossible/too hard to do without the teacher. AHHH!!! We had to talk about how life poses challenges all the time. I expressed my hope for them to be the ones to persevere and fight through challenges that came up.

After taking notes on vectors and vector operations and completing a vector operation assignment, I thought they could tackle the challenge problems worksheet. It turned out to be a real mess. We spent extra time trying to straighten things out. The motivation of the students was pretty low too. I had a target marked on Geogebra (which I love now!) where they would give me the direction and the time in the air, I would enter the date, add the wind, and viola!, we would all see if the direction they took along with the wind would end up hitting the target. One group out of the 20 students managed to do it. I am very frustrated with how it went.

6.3 Vector Intro by msbakermath

I had a handout for the vector vocab and notes- just because there was so much vocabulary

After doing an assignment on the component forms of vectors, operations, and working with direction and magnitude, students faced the following challenge problems.

6.3 Vector Operation Activity

I have to mention: I also have a student teacher right now. I have gotten a lot of time to be reflecting about the atmosphere of the classroom. I have felt a little overwhelmed with the question of "how do I get them to think for themselves?" Are my students really facing the everyday challenges and transfering their knowledge to face the unknowns. The process and fight of problem-solving is the real fuel to my fire, or real passion of my teaching. How do I get that fire going in my classrooms? 

I felt I had to recenter my goals, so I do not get overwhelmed with all I have been taking in and observing from my classes. Observing as a person in the back can really shine some light on things to work on in the classrooms.

Goal 1: Design a unit that is truly PBL and not just a project at the end of the unit. I need that students to question and push hard to create understanding for themselves, so they are ready to face the end-all CHALLENGE at the end. I have read and article that is helping me see the difference between a project and  a true PBL set-up http://teachbytes.com/2013/03/17/whats-the-difference-between-doing-projects-and-project-based-learning/. I will be working towards that.

Goal 2: Work on my own “Three-Act Task” like Dan Myer’s which I believe falls in line with my goal 1. https://docs.google.com/spreadsheet/pub?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE&output=html

Goal 3: Work on a project with the English department and the Ag department at my school about sustainability of rural communities that will build on the BIG IDEA: Students will research their community, investigate population changes, and economic impact and decline. Students will learn how to address issues that affect the sustainability of a small rural community, create 

Foxhole Radios

I am having a few regrets about a project that I started. It is a constant effort for me to try to find activities that students will find interest in, so they can apply some of the math skills we go over to real life scenarios and situations. I have come up with some great activities, and then of course some not so great activities. Recently, I launched a radio project where students were to apply their knowledge of sine and cosine waves to sound. One of the focuses I thought I would direct their attention to as an application was the sound we hear from radios. I thought it would be neat to have the students build fox hole radios, and then have them make a website about how amplitude, frequency, period, and key points of these sinusoids apply to radios. Here is my radio project guide:

Radio Project Objective Sheet and Rubric by

The problem with this project is the students are more interested in getting their radios to work. I keep having to remind them that the radio is not the biggest portion of the task. The creation of an informative website about sinusoids- how to graph them and the applications of them- is the major part of the project... It has been a learning experience. I am just still not sure if what they are learning is what I want them to learn.  I want ask out, and see if anyone will help with what is going wrong with our radios. No one, including myself have gotten the radio to work yet.

Here is a picture:

Can anyone tell me what is wrong? The left blue cable is the connection to the antenna which is out the window and hanging over our school building. The other is plugged into the wall to be grounded.

The following links are to my students' websites in progress:

http://pink-panthers-radio.blogspot.com

http://purplepenguinsradios.blogspot.com

http://prairiedogradios.blogspot.com

http://itsourradio.blogspot.com

http://trigfunctionsnradios.blogspot.com

http://radi-what.blogspot.com

Student Videos

I fell behind again. Blogger initiation came and went… my self-discipline really shows.

My ill-excuse, robot club. Yeah. I have been with kids building robots.

We went to a FTC Qualifier Event on Saturday, Dec. 8^th in Ankeny. We scored 17 out of 18. Not the best I know, but my kids were awesome. We met challenge after challenge with things going wrong, ordered parts never showing up, things not being legal on the robot, not being able to find things… We set our school alarm off because we stayed at the school working so late the night before we left. My students rose to every challenge. We will be competing again in February, and I know we will do a whole lot better.

Though I may have been busy, aren’t we all? I read f(t)’s recent blog http://function-of-time.blogspot.com/2012/11/day-in-life-dulce-edition.html  and found it amusing as usual. Again, it is comforting to know there are others who understand how active and involved a teachers’ day is. My husband asked why I was so tired one day. I wanted to lop him one. I sometimes envision my brain is like a car engine that if I put too many miles on it now, I will not have anything functioning when I am older. Then I remember my brain is a muscle. I get serious brain DOMS- a term a learned from my brother-in-law about stretching muscles. But, hopefully the constant activity I am giving my brain will only make it stronger for the future, right? Is that how it works?

Anyway, I thought I would try to resume some self-discipline and get my blog on again. Below is a Calculus “quiz” I am giving my flipped calculus students. The typical me teaching through videos is going to be put in their hands, for they are going to be the ones making videos. This quiz is a bit out of the ordinary, because it is somewhat of a group quiz. Ideally, you would have groups with three students to a group. In each group, each of the three students will be assigned the f-, g-, or h- functions. They are to complete the two problems they are assigned and complete a video on the two problems. Then, the next day I post up all of the videos, and they can watch each other’s to help complete the remaining problems on the quiz. I will post up the videos from one group. I have recently been on a kick to bring out students who are able to explain and articulate their understanding and assess this understanding appropriately. I believe this assignment does that.

chapter 5 Quiz.docx

Here are some videos created by one of the groups:

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...