Continuing a flipped classroom

In continuing with my exploration and implementation of a flipped classroom a new question arose. "Well, what do I do now?" I use homework time as an avenue for initial instruction via short lectures (Its hard keeping these short!) and now use my classroom for deeper level conversations. Not only does a flipped classroom change the way students are learning but I am seeing a slight change in the dynamics of the class as well. Just the simple fact that students have a greater opportunity to communicate and collaborate has helped all students who are at various levels of understanding. I am learning at #edcampCNY about more uses and resources for Fliiping a classroom. Having a great time!

Flipping a math classroom

I have been following the evolution of a flipped classroom over the past few months on blogs and twitter. At first I was totally turned off but the idea has grown on me. So, I am trying it in one of my math classes. I am very intrigued to see the results. One blogger wrote that he is going back to the traditional classroom after trying the flipped classroom for a couple of years just to see the results after flipping. I though that was quite interesting. So I am SLOWLY transforming my Geometry class to a flipped room. I am very anxious to see how this takes off. As I read more and more about the flipped classroom the more interested I get. Anyway, thanks for reading and here are some feeds/blogs that I find interesting for implementing a flipped classroom.

http://flipped-learning.com/
http://www.flippedclassroom.com/
http://trc.virginia.edu/Flipping%20the%20Classroom.pdf
http://www.brianbennett.org/
#flipped classroom
#flipclass

Fire!

Hey, how about an interesting topic! What is the difference between the log and the pieces of kindling?

Well I am glad you asked! One is easier to start a fire. And the answer is not the cat's tail. Well, from my observation, I would say the pile of kindling. Why is it that the kindling is easier to start? Just give you a hint, the answer has to do with two geometry principles and one science principle. I thought about writing a vague long winded description but the little voice inside my head said, 'no'. Why? Because I want some of your feedback. Can you give me an explanation as to why the kindling would start a fire easier as opposed to the log. Thanks, and happy thinking!

More bicycling....

On a ride today I came up with an interesting idea. For example, I completed a ride that was 20 miles and my average was 13 mph. I decide to complete the ride again a couple of days later and my average increases. Well, I get to thinking that when I do this ride again what will happen to my average. So I attempt the ride again, trying to keep the variables somewhat consistent. After doing this a number of times I graphed my results. Guess what? It wasn't what I was thinking. I thought it might be a negative quadratic. Not really. Just a line of best fit.

Just a plug. Yes it Desmos.

Here's a table with the graph.

I just think it is cool that math can evolve from just a thought.

                        

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?"