ToonDoo's and Don'ts

I’ve covered a lot of information about mathematical concepts over the last few weeks but today we’re going to cover some great tools and websites that students can use to get help when they need it!

The first tool is ToonDoo’s.  This is a great tool for creating cartoons. .

I really like the transformation cartoon.  I’ve discussed vocabulary as a very difficult aspect of geometry and other math concepts.  I think having many ways to present that information keeps it interesting and also helps with different learning styles.  More visual learners will benefit from the drawings and other visual aspects of the cartoons.

Another great resource for students is IXL.  The district I hope to teach in uses this site and it is incredible.  It aligns with each state academic standard and provides a great way for students to get the practice that is needed when dealing with technical subjects like math.  There are objectives to complete and when all are mastered the students get a gold medal for that subject.  There are also more in depth explanations for each problem and students can practice as much as they want.  The students in the fourth grade class my mentor teaches in loved the medals.

A great educational tool that has math questions (as well as other subjects) is freerice.com.  It’s basically a quiz site and for every correct answer the UN donates 10 grains of rice to needy people around the world.  I was skeptical initially but a professor from a previous class said it was a legitimate site.  The bowl of rice on the screen fills up as you answer questions and students really seem to respond to that.

All of the information in the world is great but not very helpful if it isn’t presented in a variety of ways; hopefully these sites come in handy!

Detail is not just a river in Egypt

Ok, so it's all coming back to me now.  I know I've talked about how I didn't do well in Geometry in High School, but this week reminded me why.  I am not a details person, that's why I prefer cooking to baking.  When you are cooking you can throw a little of this and a little of that in and taste it and keep going.  In backing, the more precise the measurements, the more likely your product will turn out the way it should.  There is also an "order of operations" in baking.  You can't add the Crisco after the flower is mixed in, you have to mix it with the sugar and then mix in the flour.  That's geometry, it's baking with numbers.  What exactly am I talking about?  Take a look at this.

Now you could argue that all math is "baking with numbers", but I disagree.  There are often times in mathematics where you can use different methods to get the same result.  I could multiply by 1/3, or divide by three.  I could subtract 7 or add -7.  With geometry though, unless you're some sort of genius, you better just take the formulas for volume as they are and punch the numbers in.   On the plus side though, Geometry does let you use Algebra a lot, and everyone knows Algebra is fun! 

So back to the details, what do I have the most issue with?  The steps, it's all about missing a step and getting the totally wrong answer.  That made me think "if I actually want to learn this stuff and have trouble, what about students that don't like math?"  I'm trying and not doing great, how can I make this accessible to all students, not just the ones that think math is fun.  Then it came to me, I can't!  Well, that's not a good attitude, how about I can, with some help from the internet!

 

Ok, so the video is pretty cheesy, but it's accurate and catchy enough that students may actually remember some formulas.

Let's get back to reality for a minute.  There is really only one way to become proficient with solving problems like volume, and that's practice.  There are many steps and the only way to really learn it is by doing it, over and over again.  It's just like anything, learning an instrument, a new dance move or a poem.  You have to put the time in to get the benefit out.  As teachers, we just need to make it as painless as possible.

Geometry Part II: The Sequel That's Better Than The Original

This week was all about delving deeper in to the different aspects of geometry.  While last week was mostly about becoming familiar with the different terms, this week we learned about transformations and got our hands dirty calculating angles of different polygons.  This week also introduced some new vocabulary as well.  My favorite new word:  Tessellate.  Here's a joke, Why was the number six afraid of tessellate?  Because tessellate nine!

Actually the definition of tessellation according to wikipedia is a "tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps."  That's fancy talk for the tiles you see in your bathroom or the designs in driveways or patios.  Of course it's more complicated then that and there are also different types of tessellations.  Regular tessellations are made up of congruent regular polygons of one type, all meeting edge to edge and vertex to vertex.

There are also semi-regular tessellations. These are formed by two or more regular polygons with the arrangement of the shapes the same at every vertices

Last but not least are the curved tessellations.  These are basically patterns of shapes that fit together to fill the given plane without leaving spaces.  The drawing below is from MC Escher called "Day and Night"

Tessellation is a great way to introduce the idea of thinking in patterns, which is an important factor in understanding mathematics.  Something that I always try to keep in mind when learning new aspects of mathematics is that I'm not just learning a new concept, but also a new way to think.  I think out of everything I've learned so far about mathematics is that the problem you're working on is second to the process.  Most people (including myself) forget the formulas and names of mathematicians, but it's hard to forget a thought process that is a part of every math lesson.  It becomes a way of life!

My favorite kind of plant? A geometry!

I knew it was just a matter of time before we started to tackle geometry.  This was my Achilles' heal in high school.  I was never sure why until I went through the geometry section of our book.  The vocabulary is what gets me the most mixed up.  Polygon, perpendicular, transversal, the list goes on.  I posted in my other blog how important vocabulary was and I really think if the vocabulary around geometry would have been emphasized as much as the measurement of angles and types of triangles my experience would have been much different. The good news is that I have the opportunity to take what I've learned from my own mistakes and emphasize those more in a classroom.

Something I've always found interesting is that when I ask people what they did well in math class the answer is almost always algebra or geometry.  Very rarely do I hear anyone say they were really good at both or that they really liked both.  I liked algebra, that made sense to me and I picked it up very easily.  I've now come to make the connection that geometry is really an extension of algebra.  Algebra is used as a means to an end in geometry as a way to calculate unknown angles and dimensions.  I think weaving the different types of math's together can get people who like geometry to like algebra and vice versa.

The above video is a great example of algebraic formulas for geometry.  I think video is such a powerful tool for math.  It can be difficult to get one on one attention from teachers because of growing class sizes in all grade levels.  Videos allow students to experience one on one lessons regardless of the time of day or how busy a teacher may be.  The videos we are using in 1510 and 1512 have been a huge help in understanding how different algorithms work in a simple, graphically reach way.

Statistically speaking, 90% of the time someone says "statistically speaking" what they're saying is made up

Wow! What a crazy week.  At one point or another I've covered every aspect of probability at some point in K-12, but I've never done them all at once in one week.  This week I was introduced to a few concepts I hadn't seen before, the first was the idea of the "fair game".  This concept basically looks at games of chance and compares the cost of playing the game to the payoff of each game.  If the payoff is equal to the buy-in the game is considered fair.  I wish I would have known this about 15 years ago when I turned 18 and went to a casino for the first time.  Those games would not be considered "fair" by a long shot.

A concept I struggled with this week was the idea of permutation versus combination.  It's actually a pretty simple concept, permutation is a data set in which the order of the elements is specific, whereas combination is the same idea except the order doesn't matter.  For some reason I really struggled figuring out when to use the correct algorithm to solve each type of problem.  The question I missed on last weeks test was about home builders with 6 lots to build but 12 model's to choose from that they could build.  I solved it as a permutation, but of course it was a simple combination.  My answer was only off by about 650,000 but I still got it wrong, talk about nitpicking.  Check out this great video on permutations!

I really like statistics, one of the first online classes I ever took was a statistics class back in 2002.  As a computer programmer I use different algorithms and formulas for creating passwords for security issues.  As an Analyst I compile user data and use that data to understand usage patterns and look for areas where there can be improvements.  I still struggle with what I consider are abstract ideas of probability, the calculation of dependent events when there gets to be three or more events still doesn't make a whole lot of sense to me, but I'm getting there.

There's laws in them thar standards!

I thought the frequently asked question this week that covered the standards for Minnesota was a great way to get some background info on why we have standards and benchmarks and how they affect the classroom. There was actually a time last year when I was speaking with a middle school math teacher who said all eighth graders must take algebra, whether they're ready for it or not.  I thought it was counter-productive, and it didn't seem to make much sense to introduce students to a subject they weren't prepared for.  The state legislature actually passed a law that says all students must have an algebra I credit by the end of eighth grade.  I understand the necessity to keep students moving forward and challenging them, but it seems those decisions should be made by educators and researchers, not lawmakers.  I would like to see a progressive increase in skill required, rather then such a simple answer to a complex question.

I think the requirements for math in high school are a good thing, but dictating what math courses students take (like algebra in eighth grade) treats students like commodities and tries to fit what may be square peg in a round hole.  I, unfortunately, opted not to take math my senior year, because it wasn't required, and I paid for it later when I had to take remedial math classes in college.  I had completely forgotten any advanced math concepts I had learned in high school.  I would like to see the legislature require math for all four years of high school rather then just three.  Even students who enjoy math, like myself, the temptation to skate through their senior year of high school might be too great to pass up.

Another reason the requirement for grade eight algebra seems odd is that the standards and benchmarks for grades 9-11 are combined.  If the legislatures goal by passing the law to require eighth grade algebra I was to push students and teachers to meet a certain goal at a certain time, it would make sense for them to legislate what appears in the other grades as well, especially subsequent grades.  It makes me wonder if the state just wants to make sure students complete algebra I, and if they need to they have their entire high school career to do so, or if the decision was simply based on the idea that most students take algebra in eighth grade anyways.  Regardless, I think there are inconsistencies that need to be remedied in the standards that have been handed to students and teachers.