Knockoff Project: The Aftermath

The first project that we did in Applied math was called the Knockoff Project. This was a brand new project meant to utilize the 21st century classroom and the Project Based Learning initiative that this class is now based on. The drive behind the project was to design a “knockoff” phone that improved on the design of their current phone.

They had to do the following:

  • make measurements with a caliper in metric and english (and choose one to use for the rest of the project)
  • design a virtual model in 3d software (Google Sketchup)
  • design a real-life model in clay (with much help to our awesome art teacher, Mrs. Palmer)
  • take 2 individual quizzes on the math that was used. One on measurement, one on volume & surface area.
  • create a spreadsheet, recording the rough amount of material present in their phone and the cost of those materials
  • present their results to the class

Some results from some of the groups:

This is an iPhone that has a slide out keyboard:

This is their clay model:

The presentations went pretty good for the first time of the year. Lots of places for improvement, but they are at a good place at the start.

Changes for next time.

  • Be more specific for giving them my expectations for each part. Because this was the first time I have done a project like this, I barely knew what I wanted, and so they had no clue. I have to think more about the relationship about what I want them to learn compared to what they are being measured on.
  • Don’t let them choose groups. It’s a bit pathetic for me to say, in my 7th year of teaching, that I’m still making rookie mistakes. But we had started so early in the year that I barely even knew their names, let alone their personalities. No excuses. Next time the groups will be assigned semi-randomly. Spent waaaaaaay too much time with classroom management due to the combination of being with their friends and having the “freedom” of time management that a project gives them.
  • Be clear about a timeline for handing parts in. I don’t remember as a student handing in parts of the project in until the very end, but that doesn’t work nicely for a project that spans 4 weeks. Now I have a boat load of order cialis with paypal different parts to grade, and they have lost the feedback that could have been present throughout the entire project. Plus they might have been motivated to improve their effort if they had been specifically aware of their poor efforts.
  • Be more rigorous about the math content. This is math class. I am a math teacher. I need to be more careful about how they calculate and present their calculations. I got lost in the minutia of running the timeline, and some of the math fell by the side.

I’ll think of more as time goes by.

Resources:

Knockoff Project Outline.

Individual skill quiz 1. (measurement)

Individual skill quiz 2. (surface area & volume)

Grading rubric.

Edit : 10/21/10

Student Responses from feedback form:

Timing

So timing sounds good.

Difficulty

Despite most people choose the middle choice in any survey, the balance on both sides indicates the difficulty level is good.

What did you like?

  • I liked being able to see the phone in 3d
  • i think the fact that we made phones out of clay was cool
  • I liked the project as a whole mostly. I didn’t like the clay models, but I did like the 3D models even though they were a huge pain.
  • the idea of creating somthing somewhat original through math
  • i liked how you gave us both option of using technology and artistic approaches.. you gave everyone a chance to excel

What could be changed for next time?

  • More hands on, less on the computer
  • be taught the material a little more in depth so we understand (ed. note: Absolutely)
  • you should give the prices for the materials, too hard to find what we’re looking for online.
  • No clay models. And I think you should add two peer assessments throughout the project to see how the students are working and how much effort they’re putting in.
  • longer time spent on measurements and longer time working on 3d model
  • i think maybe we should paint the actual phones as an option
  • hmm….i think we should take two days on making the clay phone models.

Anything you want to get off your chest?

  • i should have worked more.and talked during the presentation
  • Nothing that I hadn’t talked to you about prior. It upsets me that I did 99% of the project on my own, but it isn’t too big of a deal. It happens.

Any ideas for future projects?

  • Making something else with the clay
  • Something to do with sports.
  • Working with numbers on a piece of paper, not anything with computers and cell phones.
  • more hands on projects instead of computer based projects
  • astronomy interests me, but i don’t think you can relate astronomy to math. (ed. note: haha, going to go show this to their earth science teacher)

So?

Responses were a bit everywhere, but I got good feedback. Happy with the results. But I now know what needs to improve for next time.

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Spot the error.

He is a birthday present from my sister in law.  Awesome gift, I’m going to put it over the clock in my room (there would be rioting, but the kids can’t read an analogue clock anyway).

But can you spot the error?

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Data Density

Following question driven by seeing a box of floppy discs in tech room.

Question: How large would the floppy disk have to be to hold a hard drive of content?

Facts:

  • A floppy disk holds 1.44 MB
  • The largest consumer hard drive is 2 TB

Size of a desk? room? building? field? town?

Extension 1: What about a CD or a DVD?

Extension 2: How small could the hard drive be if it only held a floppy disk of material?

any more?

Revision: 10/1/10 (or 22 to CS geeks)

Answer!  Highlight the text below to find the answer to the first question.

The floppy disk with a size of 2 TB would have a radius of about 47 meters.

Here’s a picture showing how large it would be: http://twitpic.com/2tpar3/full

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Cake:Frosting (A look into a proper ratio of real math:cool tech)

With all the new technology in the classroom (see this post), I’ve been interested in trying out the new toys. One of those toys is the 25 laptops (dell inspiron 11z, small and cheap) which are loaded up with some great software.

For the Intro to Geometry unit, we go through the definitions, symbols, and nomenclature for how to represent objects in Geometry. They all know what it means “to cut an angle in half” from middle school, but our concept of an angle bisector is more detailed and nuanced. I used to do this lesson with pencil and paper in a very traditional way, but to change it up we did the entire set of notes in Geometer’s Sketchpad (not Geogebra because I haven’t had time to learn efficient use of it). A page of notes looked like the following:

Why?

As I can see it, there are two benefits of doing the notes this way:

  1. The dynamic nature of sketchpad is nice for the students building an intuition of how geometry works. Does the angle bisector always stay inside the angle? Do midpoints move if the segment changes? Etc. Obvious answers to math teachers, but these concepts are not hard-wired into the average 10th grader.
  2. It’s an excellent intro to how to use sketchpad. They practice just about all the skills necessary to quickly research a topic with this software. I could now have them create a triangle and see if the centroid is always inside the triangle. I could ask them to find the sum of all the exterior angles in a pentagon. I hope that they have gained a knowledge of how to construct and measure with sketchpad.

Disadvantages:

  1. It was a battle between going fast enough to keep the quickest students engaged, and not losing the slower process students. I ended up going at a good pace, and buy prednisolone eye drops telling the students to just keep up with me, even if you can’t type everything in yourself. Some of the students still can’t touch type (!), so that was a disability for them. At the end I passed out a printed packet of the finished product, so they had a full set of notes. This also stunk because I think it would be cool for them to just print theirs out, but that would have required 3x the amount of paper and 100x the amount of hassle.

Overall I am still battling myself to find a proper mix of and old-school thought of “Get the Math done!” to the new-school techie thought of “Gee-Whiz that’s cool”.

Have any of you tried such a technique? Where have you done this differently?

p.s. As usual, in education, the problem is tremendously difficult, there is no easy way of measurement, and no clear solution. I like this job.

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Big Bad Wolf (a SBG tale)

I am the Big Bad Wolf.

http://en.wikipedia.org/wiki/File:Zeke_midas_wolf.jpg

The students are some mix of the three little pigs. http://en.wikipedia.org/wiki/File:Threelittlepigs1.jpg

They don’t know yet that I am the Big Bad Wolf, and they are building away at their houses. However this story is a bit different because I’m going to tell them which set of houses that I’m going to attempt to demolish. If they are Fifer pig (going with Disney version FYI) and they have built their houses from straw, uh oh. If they are Fiddler pig and built their houses from sticks, uh oh. But if they are Practical pig and they spent their time and made the house out of brick while the others were out at play, then they will rejoice.

Say what?

I’ve been pondering the whole “grades can go down thing” with Standards Based Grading for a while now (try #1, and try #2). I want them to retain the knowledge they’ve previously gained, but I don’t want to have them thrash about thinking that there is no point in remediation. Why build a nice sand castle next to the ocean if the next wave knocks it down?

So after a couple weeks of my brain (yes it is a separate entity to myself) chewing the cud; I’ve come up with a game plan. Nearer to the end of the term I will tell them a set of standards that will be under attack in a “criterion standards quiz”. These criterion grades will replace any old grades for that standard. It won’t be a large list of standards under attack, but I would be smart to choose the standards that will be useful for the next quarter. If they choose to, they can seek remediation for any of those standards that went down and they can build them back up again.

The warning of the list of standards is important because I feel that many of them may have pride in their knowledge of standards, but they may not have an appropriate amount of faith in the knowledge retained.

In the end, I’m looking for the students to build brick houses, and not straw or sticks like I get the feeling some of them are getting by with. I want buy prednisone in the UK the students to feel the need to really get a standard before they move on. Most importantly, I want the students to know when they’ve build shoddy houses, but may have gotten a good grade anyway. They need to be able to know the difference between mastery and luck.

I will let you know how this Big Bad Wolf ends up with his experiment, and I hope the pigs are taking their time to build brick houses. I’m also looking for feedback on the validity of this endeavor, give me your opinions people!

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SMART Response (Clickers)

These worked great.  They integrate with the SMART notebook software, so they require a bit of tweaking when entering an assessment.  SMART notebook, even with math tools, requires entering any equations again… even if they were imported from Word or a google Document.

<plea> Please, please will all this software get on board for equations.  Everyone go to LaTeX (or something else open) with a visual editor.  I want these equations to work in Word, Google Docs, SMART notebook, etc, and I do NOT want to have to type the following:

f(x) = sqrt{1+x} quad (x ge  -1)
f(x) = sqrt{1+x}, quad x ge -1
f(x) sim x^2 quad (xtoinfty)
f(x) sim x^2, quad xtoinfty

I will hurt someone if that is how we have to enter equations in 2010. </plea>

Anywho, after entering the class information in the Teacher Tools, the kids were all able to login and get started in under 3 minutes.  FIRST TIME FOR ALL OF US.  3 MINUTES!  Amazing.  Going through the questions afterward was nice too, a nice pie graph shows up and lets you know if you should skip or stay on that questions.  No longer will the army of quiet kids who get stuff wrong go forgotten!

Here’s an action photo:

Overall I liked the clickers and how the assessment turned out.  It was a quick review assessment, and it did well for me to see what needed to be covered and what didn’t.

p.s.  I’m pleased that 75% of the students got the most important question of the assessment correct.

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Blah blah blah blah blah

Facts:

·         Humans average 2 words per second when speaking.

·         Humans average 60 minutes per day speaking.

How many words will you speak in your (average) life of 75 years?

(hint: break it down to smaller questions)

This is the question that the Applied Math guys worked on yesterday. (I got the question from Number Freaking, an excellent book.  Go buy it!)

Some good comments/questions from the students: “I talk a lot more than 60 minutes a day, and probably faster than 2 words per second”, “I wasn’t talking for the first two years of my life, so do I have to add that in?”, and “What about leap years?”.  I didn’t directly answer any of their questions, and I only showed my calculations after they had all committed to a result and put it on the whiteboard.

Nice activity for a throwaway 20 minutes at the end of class.

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Track(ing) the tips

For the past two summers, I’ve worked at the oldest horsetrack in the country, Saratoga Racetrack. I work as a mutuel teller and my job has me selling and cashing bets. It’s an okay job, the pay is not high, but it’s quite flexible and it’s totally different from teaching and so the break is nice. Plus all kids of interesting characters are present:
5'6" Hulk Hogan
A bonus to working the betting windows is that you can get tipped if you are considered “lucky”. I am not a bubbly female, and since most of the tips come from males, I don’t bring in as much as others around me (sorry to the fairer sex, but ladies don’t tip anywhere near as much).
As a geek, I have been looking for a pattern for when I get better tips. Some days are full of newbie bettors who show up for the free t-shirt giveaways and make “$2 show” bets all day long. Others are filled with relative high rollers who routinely bet upwards of $100 a race and can cash in for more than $1000 if they hit. I was curious if tips were correlated to one of the following stats:

  • Number of bets printed
  • Average bet printed
  • Number of bets payed
  • Average bet payed

So I kept track of the information all summer with the summary slips that I printed at the end of each day. Sidenote: google spreadsheet worked pretty well for this task because I could update the info from my phone. But the charts were not as customizable or as nice to use as excel.

The full dataset is here.

Simple scatter-plots follow:

What does it all mean?

I don’t know. Originally at the beginning of the summer I would have bet that the correlation between average ticket cashed and tips would have been the strongest because when you cash out a large winner you often get a tip. So more large winners brings the tips up and brings the average ticket cashed up. But can I buy prednisone online in UK visually it looks like the strongest evidence lies with the number of tickets printed. Busier days yield better tips makes sense, but I would have guessed that the other variables would be, um, more refined. I’m no stats geek (statistics is the red-headed stepchild of math IMNSHO), but it looks like these data have a good amount of variation.

This self-run project encouraged me to keep statistics about other parts of my life, and I ended up ripping off Dan Meyer’s Feltron Project. My Applied Math class will be recording their information for their Feltron project for the next month and you will certainly hear more from this in the future. Good news: most of the kids seemed into the project. We’ll see how they are in a week or two, but they were engaged.

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My New Classroom

So I’ve talked about it before, but I was selected to be a guinea pig for a new 21st century classroom.  I’ll be teaching two classes in this classroom: Geometry Regents, and Applied Math (second half of year is called Consumer Math).  The Applied/Consumer math will consist of mostly PBL (project based learning), while Geometry will have a project or two (don’t foresee it to be fitting perfectly).

Here is an update about what the classroom currently looks like, 2 days before school starts:

What is it all?

  • ~25 Laptops, slightly more powerful than a netbook
  • A new medium-sized smartboard (the large one is 2 years old)
  • Ideapaint in the corner of the room (a large whiteboard)
  • Smart Response clickers (personal response system)
  • 2 computers at waist height for impromptu computing
  • Clip-on microphone and speakers in the ceiling

What does it all mean?

I don’t know.  I’ve used a smartboard for 2 years, and laptops for 4.   Otherwise everything else is new, and I’m not sure how/if it will affect my instruction.  I’m most excited at the constant ability to access computers at my whim, and I’m a little terrified at the idea of the microphone (how can I swear under my breath now???!??).

The classroom, my instruction, my grading system, and my results are a work-in-progress. I’ll let you know how it goes 🙂

p.s. The hardest part of this whole process was essentially kicking out the person who had this room before. I had shared the room with him for the past 4 years, and it was his classroom.  They sadly had to paint over some great sayings he had painted on the walls, and he had to find a new room.

It wasn’t my choice, and having him booted just plain sucked.

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SBG – Question #1

In mentally preparing for this upcoming year, my brain (clearly a separate entity from myself, ala pilkington) keeps returning to a couple of sticking points regarding a transition to Standards Based Grading.

Grades Go Down?

Two issues: should they be able to go down? and how do you put that into practice without riot gear on?

For the first issue, it makes sense to me that they should have the potential to go down.  Say one of my standards from the first week of school is “Conditional and Biconditional Statements” and the student gets a 5/5 on this standard, by hook or by crook.  Then if the standard comes up 10 weeks later (before the end of the term, as I won’t/can’t have grades ride over), the student has no idea what a conditional statement is, it seems the right thing to boot them back down to a 1/5 on that standard.  That makes logical sense to me, but does it have the potential to cause student apathy towards reassessment?

For the second issue, how can I create a potential grade lowering assessment? Should I call it something else, say a “criterion assessment” where a selection of old standards get assessed again, and grades can drop?  Should the kids be warned about what standards will be reassessed “for keeps”?  Will a student’s “conditional” standard grade go like the following?

2/5 – original assessment  –> stays after gets help

5/5 – 3rd assessment in –> got there after a week worth of help

… 6 weeks later a criterion assessment

3/5  and so they’ll have to do more work to get it back up to a 5/5

Does this lead the students to a rational conclusion that all reassessments should happen at the end of the quarter or else it might be viewed as a waste of valuable after-school video game time?

Please let me know what you think!  Thanks.

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