In the Geometric Zone

This week in math we revisited Vygotsky's zone of  proximal development. The idea of finding the precise zone of a students development is a complicated and difficult task for teachers. The goal is for teachers to find the zone for their students so that the math is not to hard and not to easy. People traditionally like to learn and they like to be challenged and at the heart of this work is the work of caring. If teachers care about the work their students do and care about engaging the and scaffolding their learning so as to create a classroom environment that makes students feel like they can succeed yet be challenged then they will be engaged and excited about the learning they are doing in the classroom.

Later we went to the computer lab and experienced software called geometers sketch pad. First we were asked to draw a square. This proved to be very challenging and required some thought as to what really constitutes a square. I had to thing about the four sides and how they have to be the same length and about the corners and how they all have to be right angles. I realized it is not that easy to really draw a square even though we think we do it all the time.

Next we were asked to use several shapes such as a square, a rhombus, a kite,etc. This game proved to be very challenging and frustrating. Especially when you were trying to put a shape on top of another shape that didn't allow for that shapes properties.

I wonder about the future of education and how technology will be used in the classroom and I worry about the allocation of resources will all students have access to the technology and software, Will the new technology available in the classroom for some widen the gap between the haves and the have-nots even more than they are today?

Zero!!! What a crazy number!

So I had the opportunity to observe a teacher with many years of experience this week. I was shocked by a few things I saw #1 The lack of enthusiasm for learning and teaching was all around the room. Throughout the morning I only saw direct instruction and I did not see this teacher go out of her way to tap into any of her students ideas or thoughts even thought they were doing a work sheet from like a kids time magazine or something. Granted this is a grade that is younger than I have normally been involved with but I still think they might have had an opinion about Egypt and what is going on there. Plus I believe with some more information delivered in a story form the kids might have had a better understanding about what was going on.

The next thing the teacher did that morning was math. Boring! Un-Instructional! & a colossal waste of time and resources! The teacher had her students create multiplication flashcards on note cards. (72 of them) I feel this is a waste of time today we have creative ways of teaching math facts and if the teacher really believes her students are going to study these flash cards she is dreaming. But that wasn't the my biggest problem my biggest problem was when the teacher wrote the problem 1divided by zero =1 I questioned her about this and she thought about it and then said yeah that's right. Well I am not the most confident person when it comes to math and I definitely would have trouble going head to head with a veteran teacher about this but it kept eating at me all day I was sure that could not be right. So I ran the problem by two college professors that teach math and yeah I was right you cannot divided by zero! This is another example of something I will never do in my classroom.

You gotta give all students even students that are not good at math an opportunity to feel success!

Today in math class we were challenged to create a giraffe using tangrams. Now you can call me crazy but I have never seen or used a tangram before. I found it very challenging to create the giraffe using the tangrams. I was the first one at my table to almost create the giraffe I almost had it with a little more manipulation I got it. My table group then created the giraffe twice its size. Once we created the first giraffe doubling the size of the second one was still challenging and took some thought.

This was an excellent opportunity to see how working with shapes to create something was challenging for some and easy for others and is a great way to explore the individual strengths of ones peers.

We also talked about backwards design and the idea that it was teaching to the test we decided backwards design is not teaching to the test it is away for the teacher to focus on what she wants to learn from the students and what she wants the to learn. If the math is not beneficial then it should not be on the test. You have to find out whats important to you.

Math journals are and excellent way to  provide a possible entry point for students to work through their understanding and provide a deeper reflection on what they comprehend about the concepts and ideas they are learning. Math journals provide learners with a place to put math into words and give all students the opportunity to be successful at math.  There are numerous way a teacher can use a math journal they can be created as an online document that allows a teacher to touch base and discover a students understanding almost instantly and away of checking in with students who are struggling or might have misconceptions as they are trying to explain something.. Especially if the math journal is an open ended assignment that is not necessarily graded can provide an access point for multi-ability learners.

Combining math with literacy is an excellent way to combine math with other subjects. mathmatizing literacy is an excellent way to get here and another great way of incorporating group work. Allowing a student that claims I am not a math person but I am a creative person to thrive in math especially if this is a group assignment. When students struggle and flounder as a group they are more likely to discover each others strengths and a lot of learning can come out of that.

Line Graphs and the story

Today in math class I was using a program available on the coputer called gapminder. I thought this was the greatest program and coolest way to see graphs brought to life! I really like the idea of graphing information and telling the story behind the graph. I think this is a good way for kids to understand how the graph, the data, and the story are realted and what a graph is really reresenting.

I also had an oppportunity to observe a 6th grade science teacher work wirth her students about how to create a line graph. I thought it was an excrutiating experience. The teacher was eeexcited and engaged but the students were bored to tears they were litetrally pulling there eye lids off. I was thinking to myself man this is so boring does she really have to teach the kids to make a line graph like this. I just watched a video with a teacher that taught 6th graders to make a line graph and the students in his class did not seem to be bored. He allowed his students to create their own data and gave them paper and the kids had to create their own line graph. They had to decide what kinds of measurements they would and how they would set up their graph so that it made sense of the data.

I was also reminded of the teacher at Liberty Bell Elementary that used the man eating sugar video then had her students do graph work on gapminder. This teacher claims you cannot be to creative when teaching math. This teacher found a creative way to teach her students how to use, create, and interpret line graphs. Along with the graphing skills she taught or reinforced literacy skills. If you can interpret the graph then you are using literacy skills. Therefore when you ask students to collect, graph, and interpret data you are hitting every single standard: creating, reading, justifying, problem solving, this exercise hits all important literacy skills. Reading and interpreting data is going to be a very important skill for the 20th century.

Algebra Tiles & Manipulatives

Algebra tiles are a fabulouse tool and I wonder if I had seen them when I was a freshman in high school if I would have passed algebra. I took algebra from Mr. Dawkins in 1978 he was fast and furious with his explanantions of x and y and how to solve fgor them. Actually I dont remember knowing that was what I was supposed to be doing! I was lost on day 1. I can still see him with his chalk and that chalk board. I remember thinking I have never seen anyone write on a chalk board so fast! He would throw a problem up on that board and fly through it chalk dust just a flying. I got left behind very early on in this class and finally in 2006 I learned an x was a symbol for an un know interger!

I think it  is so cool we are already teaching our 5th graders algebra concepts right now. We are not calling it that but we are teaching it.  my fifth grade students are learning to write and solve equations and they are learning to use x for unknow integers in their equations. I think this will make algebra much easier as they move through school. Having some experience with this and seeing it before they have all the pressure of highschool.

I never would have thought of using red and white beans as a manipulative what a cheap cool easy way to provide counters for kids! Poker chips that's perfect! Some kids learn better when they touch things. Today we have so many ways to provide manipulative's to our students and to tell you the truth only after suing fraction bars and learning how to draw that fraction table thingy did I really understand how fractions work. I love love love manipulative's I am totally one of those people that needs  to touch the math and work out the math and having manipulative's to do it with is very beneficial for me.

Virtual Manipulative's are great and can be an excellent tool for students to practice the concepts and ideas they are learning about in the class room. I can see how it would be important to allow time for each kid on a computer to drive. I know when I am a passenger tend daydream or sleep.

My biggest question about manipulative's is how long do you let students work with manipulative's before you move them to the traditional algorithm?

Group Work and Cooperative Learning!

 For teachers group work is both difficult and not. The the hard part of group work  is getting it planned and set up. The roles have to be set up everyone has to have a role and teachers have to make sure students are clear about their roles.  Students need to know that it is expected by the teacher and the rest of the class that each person maintains their role. Once all that is done the learning more or less takes care of itself. Students share their ideas and learn from each other. Sharing ones thoughts and ideas with peers and having the opportunity to discuss new ideas and complicated concepts is one of the best ways to get new concepts worked out and clarify understanding. I know sometimes if I have been given the opportunity to discuss a problem and think it through even if I am only talking the problem out to myself I can make sense of the problem.

 

Grownups Say The Darndest Things

I have heard caring adults that were very invested in their children's education say, "well she is more of a literacy person" or "Oh little Suzie John she is more of an artist." These are the same adults that are on their kids to read every night and monitor there TV watching and do all those things "good parents" do. Yet when they are asked to practice math with their students they say "Eh I'm no good at math either." Their kids get the message you have to read thirty minutes every night and you should read in the car or when your bored...they don't say the same thing about math.

Why do we as a society believe that people that can do math are inherently born to do it? Like your either a path person or your not. Kinda like the ides that you were born to teach you don't have to learn how to teach. The idea that kids can learn to do math and that we as teachers can teach math in away that is relevant to our students lives and serves a meaningful purpose seems to be a far fetched concept. How many times have you heard children and adults alike say: "I hate math! I have the worst math teacher they don't make any sense why do I have to know algebra I will never use it?" We hear statements like that is all the time and our kids hear us say them.

The big question is how can we change this concept? I am not certain about how to  answer to this question but I hope if enough teachers begin to change their attitudes about math then society will begin to change with them. I can only hope so.

I did not learn to do math until I returned to college a good 25 years after I had graduated from high school. The funny thing about that is that I never believed I could do math until I had a math teacher that told me I could. She told me everyone could do math. Once I realized I could do math I actually did it. That is what we have to get through to our students as teachers and we have to teach the math in away that empowers and engages kids so that they can make real life connections with the math and their real world.