Students reflecting

Well, it's been a long time since I have written anything. The beginning of the school year really takes a toll sometimes. Especially when my teaching assignment has changed some and my girls are starting kindergarten. Anyway, I have something really extraordinary to share with you. As aforementioned my teaching assignment has changed, I think, for the better. I now have a really small math class that is a mix of 7th and 8th graders. This new class has presented itself with a really neat perspective on teaching for me. I started the 7th grade curriculum in a much different fashion. I am using something called an "Interactive Math Journal" (http://www.rundesroom.com/).

It is strictly notebook fashion with the students having the opportunity to give me one proof of their understanding and to write a reflection. I have seen some amazing stuff! One student in particular has done some really detailed and well thought out drawings. In one example she has ever so delicately drawn a dot. I know, I know, you are probably thinking how creative and intricate can you get with a dot and a statement about the size using scientific notation. A gut feeling came over that helped me realize how much we are missing in education when we are driven to make us look good or schools look good by test scores. Shouldn't we provide an avenue so the students themselves look good. And feel good about their "own" education.

Sorry I haven't posted in so long, I have been caught up with these amazing math journals.
AAAAAAAAAAAAAAAAAAAAAAHH!!!!!!!!!!!!!!

A Ten Year Reunion (Math Blogger Initiation Week 2)

At a ten year reunion a class looks back on their high schools and reminisces about the teachers they once had. Many come to mind but one in particular stood out; Mr. Snaith. 

One person piped up and said how he always got excited about what he was teaching and how he loved math so much he wanted to marry it. What was up with that!? Another responded and said that she was so enthralled by his devotion to teaching such an intricate course that she studied to be a teacher. She said that he brought out the best in students and always showed respect. Mr. Snaith also helped students realize that math was not just some course where calculation after calculation was made but rather a course where questions could be ansewered with questions which provoked thinking. it was a time in the day where students didn't have to worry about who was the best or who was the worst in math. It didn't matter. Everyone was treated equal. 

During the period there was a 99% chance that Mr. Snaith encouraged silence and thinking to such extent that when the time came comments and answers sparked great new thinking and the class usually realized they had surprisingly answered Mr. Snaith's question. Smiles would be exchanged between students and the typical, "I know right, I didn't even realize it either" quotes would be shot around the room which gave the impression that a bunch of friends were sitting around a campfire.

Another "student" added that they always felt that he made them think harder than any other teacher without them realizing. But in fact it wasn't that they "thought harder" but more so they felt comfortable to share ideas and thoughts in his classroom. They always felt trusted, respected, and worthwhile in Mr. Snaith's class.

The conversation slowly turned to the content that Mr. Snaith covered and he presented it with such inquiry. He always described math as a thinking course where calculations came second and inquiry came first.

After much conversation that consumed most of the evening the classmates decided that Mr. Snaith's jokes were above the worst but why did students always laugh at them.

Why are students "good" at math?

Why are students good at math? I have had this idea for along time that any person that can visualize text is able to process the content better. What do I mean by this? Simple. I am sure you have talked to someone and realize that you have read the same book. Usually this strikes a conversation about the book. You may converse about pieces of the plot or character development. Anyway, as you read you develop an image of what something looks like. Some images are really clear and other images are not as clear. So let's look at an example of what I mean. Say you are at a really good part in a book. One scene that comes to my mind in a Grisham book is when the main character and, I think their cohort and suspect, are searching for a body. They are walking from the road into the woods to where the supposed body is. Grisham's words become so clear in my mind that I can actaully hear the leaves and branches breaking under the character's feet. I think you get the picture.
So let me take this idea and parallel it with mathematics. First, let's look at a real simple concept like one-to-one correspondence. When I say the number "two" what comes to your mind? For me, two bananas comes to mind. 'I really like bananas.' You may picture something completely different. Moving towards something more complex try to answer this question, "how many steps does it take to walk to your mailbox?" If you don't have a mailbox think of something else that you could walk to that is outside. Now, as you are imagining your lovely stroll with a hot morning drink try to picture yourself taking steps towards the mailbox. This imagining is a simple skill that many of us take for granted. I would assume a great number of us could visualize ourselves walking. Maybe some can't. However, let's throw into the equation trying to figure out the number of steps.
Here's another assumption. Some people may get stuck here and others would naturally ask more questions. Such as, "I can't quite comprehend the amount of steps to the mailbox but I could assume there are _____ steps to the tree, and if there are _____ steps to the tree and I and I am halfway there then I'll just double the amount to the tree." Simple, right. Wrong.
Attending to detail here we could analyze the breakdown of skills involved here but we would stray off topic.
So, back to my initial idea of the movie playing in our mind. From my experience talking to students about their inadequacies which impede these skills we take for granted I strongly believe that if students or anyone for that matter are able to play a movie in their head of the math concept at hand then that person will have success at deciphering tougher math problems.
In a way, isn't this what we ask student all the time, "can you visualize the blah blah and then see how the blah blah changes?"

A Bike Ride... not really

Well, the other day I took a bike around our block. I usually have a speedometer with me but since I know the block and I roughly know my average I didn't bring it. Except this time I took my wife's gps with me. I have been using the gps on some morning walks. I have been taking it because I am really interested to see my path on the computer after I downloaded the info from the gps. So, after a couple of miles I got to thinking which would give me the most accurate distance, my wife's gps or my bike computer. What an interesting thought, I am sure you all are thrilled to read this. After some mental disagreements I realized that after my ride I could also drive my car on the route and then average all three distances and then go on Google maps to see which would be most accurate, one of the three measured distances or the average of all three. Heck I don't know what you are thinking but that is a lot of work just for accuracy. Then I got to contemplating "does accuracy really matter to me?" I decided the heck with it. I won't drive the car and I'll just have a good stinkin' ride, right? Two months later.... Back to writing this blog. To further complicat things I recently purchased a Garmin Edge 500 (a really expensive piece of plastic that tells you where you are). I guess I telling you this because I do believe that we all have some interest in math and we may not know we are performing "math". So until next time, try to discern if you are doing " math" when you are contemplating wonderful daily thoughts.

So... "What Does Math Mean?"

So... you are probably wondering if I am going to answer the question "What Does Math Mean?". Well, that is a good question. Math is in our daily life whether we realize it or not. You may be doing math right by wondering if you have enough time to read the rest of this post. Or sitting there thinking, "geez, my posture is really bad. I know my back isn't perpendicular to the ground".
Or, you may be like me and as you are mowing your lawn you wonder at what distance will my vision be a 30 degree angle to the ground!

I know, its truly an amazing depiction of me.

More importantly, how do you know you are "doing math"! Simple, when you are about to walk up a set of steps starting with your left foot, and you ask yourself, "will I take my last step with my right or left foot?" Along with this, I might ask, "what number of steps will always make me start with the left and end with the left?" So the next time you find yourself asking questions like these you can also ask, "is this what math means?"

Fun with mathematics

I have fun with mathematics. I get a sense of satisfaction when I am engrossed in math. The thinking that I referred to in my previous post truly gives me joy. Aside from my family and keeping up a household, I spend some of my free time watching math videos and searching for cool math things on the internet. When I tell students this they really question my sanity. I hear things like, "wow Mr. Snaith, not only are you losing your hair you are losing your mind".

In reality, some of my students in my class throughout the years have actually followed in my footsteps. There has been a handful of times in my teaching career when students have come to me and said, "Mr. Snaith, I found this really cool video on '????' on the internet, you should check it out". In addition to "thinking" about math, watching others truly get excited about math topics also gives me joy.

SO... math is fun!
http://www.wimp.com/fibonaccisequence

Thinking

The word, THINK, is really quite an extraordinary word. In my classroom, whether it be Algebra, Geometry, or  a third credit math course, "thinking" is one of the first "math" concepts I teach to my students. I stress to the students that thinking is a skill. In order to master the skill a person needs to practice. In our classroom, we practice "thinking". There are two situations where I see "thinking" taking place. The 1st, during classroom discussion. Discussion, in general invokes "thinking".  I explain to the students that discussion is very valuable and through discussion many great ideas are formed. In addition, an insignificant answer (are there any insignificant answers????) may spark provocative thought. A 2nd situation when "thinking" is beneficial is during quiet time. For my classroom, I have stressed that quiet time can be truly amazing. I explain that quiet time allows a learner to reflect on the class period.
Anyway, I want to thank you for reading my first blogpost.