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.