Wolframalpha said what?

What did I learn today?  The real question is what DIDN'T I learn today.......actually no, let's stick with the original question.

1)  Do you ever feel like you want your grade school students to organize data for you and then organize it again....and then present it for you?  Well you are in luck because there is something called Tinker Plots that allows students to take data sets from almost everything in the world (We studied size, weight, color, etc, of cats).  You can plot it out on graphs in any way you see fit.  Classroom wise this provides a visual for organizing data on a graph.  Pros:  It is awesome.  Cons:  It costs $$.   Booooooo!

2)  Geometry riddles.  Our teacher simply handed us a piece of paper and said go.  It reminded me of a time when I was in 4th grade and our teacher handed out a sheet with 20 items on it with the instructions "Please read through all of them before you begin".  Of course I didn't read through them all because some of the items on the list were pretty fun...like jump up and down while you say the alphabet, or create a collage out of 5 magazine pics.  It felt like a really creative use of time.  Then I got to #20 which said "This was a test to see if you read all 20 before you began.  Please sit quietly and watch the show".  Let's just say it left a mark in my memory.
     Anyhoo, this geometry piece of paper listed out about 7 characteristics of a shape.  Our job was to go through each one of them and figure out what shape it was referring to.  In the time before technology this was a method of getting the kids to understand how to work with information about different shapes.
      It brought up the question of whether a teacher would drop something like this on the students BEFORE or AFTER he/she taught the lesson.  I would push for before as the activity would give you a great idea about what the kids already know about geometry AND it would get them thinking about it.  As long as the teacher followed it up immediately with the answers to the riddle the engaged student would be ready and waiting for the main idea behind the riddle.  The disengaged student usually becomes engaged when the answers are being given.

3)  Wolframalpha.com!!  I'm amazed I hadn't heard of this thing before as it is like wikipedia for math.  You type in a math equation and it spits out algorithms, graphs, formulas, and more helping you understand what math lies behind the problem.  Chemistry?  Heck yes.  Type in H20 and you get all the information you ever wanted to know.  Cool site....and it is free!!

4)  An article we read brought up the question of what "personality of math" do we want our students to have.  It broke the groups into three parts, creative, obedient, and social.  I was intrigued at the claim that "obedient" math personalities (ones who see math as a set of rules that must be followed at all times) tend to understand math but rarely pursue further education in math.  It makes sense as they see no further to go once they understand all the rules.  I really enjoyed the social personality because it hinged on one of my core believes that students learn best when they are teaching the subject themselves.  If they have to talk through a topic with others then they are learning it.  By the nature of being social, they have to be creative in how they get their message across.  Therefore a combination of a socially creative math personality is where I think I would push my students to go once I fit myself into a classroom!

5)  Constant rate of change:  No matter what you use to measure one item.  The proportion will always be the same.  You are measuring the same thing so whether you use fingernails, spoons, or chipmunks to measure an item, the rate of change (slope of the line) will always measure up to be the same.

Cheerio

The Royal Tangrams

Our professor hit us with these awesome puzzle manipulatives today called "tangrams".  There are seven pieces to each one and they fit together to make a myriad of shapes.  They are great if you were blessed with spatial awareness.  If not, they will cause migraines.  We were asked to make a picture of a giraffe using the seven pieces and most of us eventually figured it out.  Then she threw this awesome nugget of information at us by saying "now make it twice as large".  The math behind it says if you double the height and width of an object you are squaring its area.  Therefore for every one piece of tangram used to make the original giraffe you would need FOUR pieces to match the identical area of the double sized giraffe.  It was a wicked game, in fact that should be the soundtrack for the rest of this blog.

What else did I learn today you ask? 

A Fathom:  Not just a unit of measurement equal to 6 feet, or 1.83 meters.....or the lead track to the Little Mermaid Soundtrack, it is the name of software used to graph data in the math world!!  It is expensive as heck, but if you want to teach data in an organized and thoughtful fashion then please check it out:

http://www.chartwellyorke.com/fathom.html

The Data and Story Library:  http://lib.stat.cmu.edu/DASL/

This place has a plethora of statistical data for you and yours. We were showed a chart that showed the amount of calories in approx 100 hot dogs tested.  Next to this info was a list of how much sodium was in that same hotdog.  Once again, I have given up hot dogs, but I have gained some new respect for those people we honor by giving them jobs finding out how much sodium and calories are in hot dogs.

How this will help me elucidate my students in the classroom?

With Gapminder, the Tangrams, DASL, and fathom, my students will have statistical data pouring out of their ears.  They will be able to read data, decipher data, and come to conclusions about data.  That is what all of this leads to, and I love it.

Questions?

Why is it all the good things in life cost a lot of money?

I'll have more thoughts on this as I put it into use over the next couple of weeks.

Good stuff today.

Taking a bath in math

Math Thoughts Week 5

What did I learn (this week)?
From my placement classroom I learned that multiplying decimals is harder to understand these days.  I remember the moment in 5th grade when my teacher told me, "Student, if I give you a tenth of a tenth of a piece of Little Caesar's pizza...would you want it?"  "Heck yeah" I said.  Then he gave me a bit the size of my thumb and the class laughed.  I looked the teacher directly in the eye and said "Now you listen here.  You WILL divide this piece by .01 and you WILL give me 1 WHOLE piece of pizza!!"  He smiled back at me, took the piece from off my desk and ate it himself.  To this day I'm waiting for my piece of pizza....but I remember the math!!
My point?  I taught this lesson last week to my class and they had a LOT of trouble with it.  This doesn't sit well with me because I'm not sure if it is the way I'm teaching it or if it is just something that takes some time.  Half the class has it, the other half is confused even more than when I started.  The good news is they are all asking questions, and THAT is something I can work with!

What questions do I have?
We are creating a lesson plan involving probability that will be interlaced with science.  What's wrong with me?  (At this point I really don't have any pending questions).

Implications for the classroom?
For me if I can find a way to mix this interdisciplinary lesson together and make it a success, the implication will be a huge confidence boost for my abilities in the classroom.  My nerves fray thinking about mixing an English/Art class.....yikes.  But Math and Science I think I can get a handle on.

Mira Mira on the Wall...

...what is the data you can recall?  It seems that writing a blog for fun is easier said than done as school projects and thoughts are becoming the norm these days.  The good news is my math class is really starting to blow my mind with some of the things in which we are being introduced. 

Thing #1:  www.gapminder.org   NOTE .ORG not .COM

This website allows you to graph out a rather random amount of data collected over the past 10 - 100 years.  Want to know the correlation between number of cups of coffee drunk per person vs. the economic output for any country?  This is the place.  Want to know if the number of licks it takes to get to the center of a lollipop changes depending on the country you are in?  This might not be the place, but you never know with Gapminder!!  With the amount of data collected and organized on this website one has to wonder what the relevance of the data means.  The data sets lead to multiple questions, which lead to multiple hypotheses, which lead to more cups of coffee.  Bottom line - it is a start to getting information in front of students. 

Thing #2:  The old fashioned mira!!

If you are like me, you LOVE beach volleyball, AND you had never heard of a mira before.  Our professor dropped one of these in front of me in class last week and I felt like I was at the police station again looking through a two way mirror (the good side).  It was a red tinted flat piece of plastic that resembled one of the flat winged fighter planes from Starwars.  The wings held up the body of the tinted plastic and allowed for a reflection back and line of sight through.  Meaning if you had a circle on a piece of paper you could line up the reflection back with the circle still seen through the plastic and you would have yourself the line of symmetry.  It was awesome!  I immediately went and bought myself one so I could go home and show my wife my face is symmetrical, just like her favorite actor Denzel Washington!

So how can I use these in the classroom? 
Fair question.  Gapminder has so many possibilities of data that I would introduce the site to my class and ask them to come up with data and some thoughts about what the numbers mean.  It would lead to some great class dialogue and then maybe even further to a small research project.  As for the mira, any lesson on congruency would be horribly hampered without one. 

Since it has been a while since we've had a funny for the day, here you go:

How is duck tape like the force?

It has a dark side, a light side, and it binds the universe together!

MOG #2...Seahawk Style

The Oregon Ducks just lost the National Championship game.....clearly they didn't read the book about winning by the aforementioned Seahawks!!! Some local artists transformed a current rap song into a sweet melody all about...you guessed it, our beloved team from Seattle!! Unfortunately I can't figure out how to upload the audio file to this here blog so in the mean time, click the video below to hear a song from a previous Seahawk team that rode the Blue Wave deep into the playoffs back in 1985! Ladies and gentleman...let's math Blog!!

 

Today our class learned some strategies to help middle schoolers learn some basic math functions. Two in particular stuck out. One is that there is no such thing as subtraction, as all you are really doing is adding the opposite of a number. 5 - 6? Clearly you are just adding a negative 6! Kind of like when you see the $114 check show up in front of you while at the local Buca de Beppos, you can now look up at all the free loaders in your family and say calmly, "Well, we're adding the opposite of money from our future dearest family. Now who wants to go get a job?" The other thing was that the famous pedagogical teaching method of FOIL is waaaaaaay too overrated by the educational community. Technically it makes sense, and gives kids a precise process for working out the distributive property of multiplication, so why don't we just teach the distributive property of multiplication? Ask 100 students what the distributive property is and you might get 2 that can tell you. Ask the same 100 kids what FOIL is and there is a good chance 100 will say "It's that thing you do to numbers in math!" Simply teaching ideas that make sense.

1) Teach subtraction is actually addition

2) FOIL is for campers stew, The Distributive Property of Multiplication is for math stars!!

It is tough to go through a 4 hour class without having any questions but today's class was quite solid in how clear the information was conveyed. So my mind shifts to what more can be done in the classroom. We ran through a quick exercises that helped explain that a number such as 325 is actually 3 100's , 2 10's and 5 ones. For the math geeks out there, we explained the number system of base 10. It seems this is a great way of beginning to explain the base 10 system, and how other systems use different bases (such as computer programming in base 2). If someone understands base 10, they'll understand base 5, and so forth. This understanding would help sooooooooo much in allowing the brain to figure out simple algebraic equations. What would be some reasons we don't add this to the curriculum of our elementary schools?


How would I use this in the classroom you ask? Heck if I know...but it would be cool if my students understood the importance of 10 in our number system in that it makes quick calculations much easier. I mean hugely easier. Like $100 level Who Wants to Be a Millionaire easy!!


MOG #2 out.....with a funny for the day, Chicago Bears Style!

Did you hear the new penalty for speeding in Illinois?

On the first offense they give you Bears tickets, and on the second offense, they make you use them.

OR

Mommy Bear and Daddy Bear were in divorce court. The judge looked down and asked the Baby Bear, “So Baby Bear, do you want to live with Daddy Bear?” “Oh, no,” Baby Bear replied, “I don’t want to live with Daddy Bear. He beat me.” “Well then, you should live with Mommy Bear,” answered the judge. “On, no, I don’t want to live with Mommy Bear. She beat me.” “Well then, Baby Bear, who do you want to live with?” Baby Bear said, “I want to live with the Chicago Bears. They don’t beat anybody!”

Cheerio

Math is Back Baby!!

To all my loyal reader out there, the blog you are about to read will take you on a path down a road lined with numbers.  My math class this quarter is all about best practices in teach students mathematics.  So consider yourselves forewarned if you are looking for quick wit, dry humor, and maybe a little curl at the corners of your mouth....you just might find some here!!  Let's math blog:

Three questions will be the core of each and every "math blog" I write (hence forth knows as the "MOG")

1)  What did I learn (in class)?

2)  What do I have questions about?

3)  What are the implications for classroom practice?

So let's start with #2.  Our class was given multiple math problems that required us to come up with algebraic functions to act as "rules" to help find answers.  Stuff like "you have x number of adults and x number of kids on one side of a river and we need to find out y, how many trips it will take to get all the people across the river under m set of parameters."  My question is simple....are we suppose to know this stuff ourselves if we are going to be teaching it to kids?  If not...shouldn't we?

Back to Question 1:  I learned in class that a collaborative group working on the same problem can offer you several different ways of getting to the same destination.  I pretty much gave up on the river problem when one of the people in my group said "what about if you do this....."  Oh yeah I said, and the ball started rolling.  Unfortunately the ball didn't stop rolling until 5 hours and 12 pieces of scratch paper later when I finally came up with the function.  I could also state that I relearned several math concepts that clearly I had forgotten.  (x-2)^2 needs to use old Mr. FOIL...not Mr. Simplemath like I tried. 

Implications for classroom practice:  Well the answer is in the question....practice!!  Make sure you know the answers from all directions, or at least feel confident that you will be able to see everything the kids will see.  Putting my student hat on I realize we are being taught ways to teach this material, not ways to do it.  So one major implication this lesson has for classroom practice would be to think about how we as teachers can get the students to think about these problems in different ways.  How can we offer up hints that keep them intrigued without allowing them to feel overwhelmed to the point they want to give up. 

I will say I called several friends and threw myself a party when I came up with the answer to the problem.  It was a success that I hadn't felt since the old college days when I would put days into figuring out a math problem.  I notice that most of my math problems the past so many years have begun to all start with "How are we going to pay for x with y in the bank and z yelling gimme gimme gimme?"

MOG #1 Out