Math video from Dan Meyer and NatScivideos: Pendulum Motion

Check out these two great videos to use in science and math class. The first is from Dan Meyer, the second from NatScivideos.



Height v. Time from Dan Meyer on Vimeo.

Vi Hart, add to google reader!!

Someone sent me a video of Vi Hart doing math doodles one day and I have used it in class quite a bit. It is fun and she obviously is a smart person who thinks creatively about math. Months later I got another tweet about her blog. I thought I would alert you to her blog and embed one of her always "interesting" videos.

I have subscribed to her posts and put a link on my math wiki page.

I hope you enjoy her as much as I do.

More great math video from Dan Meyer

Dan Meyer has posted a series of fun and very usable videos on melting cheese and surface area. Here is one of them for you to look at to get the general idea.

[WCYDWT] Cheese Blocks — Cheese Cubes from Dan Meyer on Vimeo.

If you are a follower of Dan, you can see his blog archive for more great stuff. You can also access a lot of great math resources for framing and conceptualizing real life math challenges on my math wiki.

Can We figure Out Math: according to Joseph Ganem

I found an article by Joseph Ganem in the Daily Riff entitled, "Can America Figure Out Math?" His dilemma is two-fold. The first is that so many college students drop courses requiring math because they score poorly on the math entrance exams and lack the basic skills to do university math (in particular, calculus). The second is that middle school kids are taught math at a college level. He points out the disconnect between the two. He asks:

"How can students who have studied college level math for years need remedial math when they finally arrive at college?"

He gives three answers.

1. Confusing difficulty with rigor.

He claims we are "pushing students to do ever more difficult problems at a younger age. Attempting difficult problems without the proper foundation is actually an impediment to developing rigor. Students need to be challenged but in such a way that they learn independent thinking. Pushing problems that are always beyond their ability to comprehend teaches dependence-the opposite of what is needed to develop rigor".

2. Mistaking process for understanding.

He says "just because a student can perform a technique that solves a difficult problem doesn't mean that he or she understands the problem...learning techniques without understanding them does no good in preparing students for college... at the college level emphasis is on understanding, not memorization and computational prowess".

3. Teaching concepts that are developmentally inappropriate.

He says "teaching advanced algebra in middle school pushes concepts on students that are beyond normal development at that age.... because math involves knowledge and understanding of symbolic representations for abstract concepts it is extremely difficult to short cut development."

He adds that:

"all three of these problems are the result of the adult obsession with testing and the need to show year-to-year improvement in test scores. Age-appropriate development and understanding of mathematical concepts does not advance at a rate fast enough to please test-obsessed lawmakers. But adults using test scores to reward or punish other adults are doing a disservice to the children they claim to be helping."

He goes on to say that:

"It does not matter the exact age that you learned to walk. What matters is that you learned to walk at a developmentally appropriate time"

I love how this fits with what Dan Meyer and others are saying about learning math. For years I have thought that learning an algorhythm and doing endless calculations does not produce math thinkers and problem solvers. Many of my students still do not know their "math facts". I'm guessing that math has had no meaning to them. I am enjoying the challenge of changing our classroom with these ideas in mind.

Thanks for sharing Mr. Ganem.

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Meyer gas tank/grocery store

Dan Meyer has posted more pictures on his blog regarding "math needs a makeover". The first post is about measuring the level of a cylindrical gas tank with a dip stick. It is quite fun and easy. Read his post here.

His second post is about comparing items in the grocery store. He provides many photos which will create great opportunities for your kids to do higher order thinking in your math class.

If you are new to his ideas, you can read more on my posts about math and/or Dan's work. Basically, his idea is that in math problem solving we pave the road to the answer and don't allow deep, divergent thinking about the process of problem solving. From my experience, even when teachers try to provide more open ended questions, students ask them for more information and the teacher can't resist and begins to pave the road again by giving hints or teaching convergent techniques.

As Conrad Wolfram says, let them struggle, hear about their process and give them a little technique (not too much). I would highly encourage you to look into the work of Dan Meyer, Conrad Wolfram, Alfie Kohn and Paul Lockhart. I have blog posts on all of them and links to their work.

Enjoy continuing the math-makeover!

Why We Need Pi by Wesley Fryer

Check out this video by Wesley Fryer (someone I follow on twitter). He shows how he used google earth in his math class to teach circumference. As is often the case when someone shares, I think I have a better way to do this for my class.



I plan on having my kids find sports stadia/arenas on google earth and then describing how big they are. I will tell them they have to describe their size in three diferent ways. I may teach them how to use the ruler tool on google earth.



I may follow through with further study of how the building was constructed or to compare it to other sports arenas. I would use higher order thinking questions such as "which building ws the hardest to build?" or "which building has the most impact on it's community?"



It's going to be a blast!

Toaster Questions: more ways to teach Math

Toaster Question from David Cox on Vimeo.

In another great blog post by Dan Meyer, I found this video by David Cox. Watch it and see if you don't wonder what you should do with it.

In a previous post on Dan's TED talk, I learned that the way we pose math problems to kids can be limiting and convergent. Since viewing his TED talk I have tried to use his strategy in my everday math classes. It has been fun to have such a powerful strategy. I have not created videos for these lessons, I have just been making up examples that are open ended and missing enough information that the kids have to assist in creating the problem.

One simple example of my earliest attempts is this question:

John wants to have a bath and fills the tub partially (a fraction) full with hot water. He soaks for a short time and then decides the water is not hot enough. While he has been soaking his sister has had a long shower and drained most of the hot water. He adds another fraction of a full tub with colder water. How much of a full tub does he have and what is the temperature of the water after the second fill?

Some of the variables the students mentioned and asigned a value were:

• first fractional fill
  
• second fractional fill


• temperature of the water, first fill, second fill


• volume of John's body


• temperature of the room


• volume of the tub

This is really fun for me and the students look forward to the divergent thinking and creating of the problem.

Back to the toaster problem, it took me a moment to think how this could be used in my class, but it has great potential. How would you use this in your math class?

Dan Meyer TED Talks: Math

Dan Meyer talks about how exciting it is to teach math in today's world. I was so taken with the power of his message that I have subscribed to his blog and will begin to change the way I teach math on Monday! I can hardly wait! You really have to check him out.

He begins by listing his students roadblocks to learning math:

1. lack of initiative
2. lack perserverence
3. lack of retention
4. aversion to word problems
5. eagerness for formula

The way most of us teach math now (textbooks and cookie cutter problems) does not lead to mathematical thinking and problem solving. We teach "impatience with irresolution". We (and textbooks) present a compelling question with one answer and congratulate them when they get to the one correct solution.

He quotes Einstein who said, "The formulation of a problem is often more essential than it's solution, which may be merely a matter of mathematical or experimental skill."

He gives great video examples of the following techniques in the 21st century math classroom:

1. Use multi-media
2. encourage student intuition
3. ask the shortest question you can
4. let students build the problem
5. be less helpful

Join me in following Dan to have great math minds in our classrooms and share what you learn and create in an on-line community!