Teaching versus Discovery

I was reading Joe Bower the other day (Why Preschool Shouldn't Be Like School). He often includes great quotes to support his perspective. This time he quoted Seymour Papert,

"the scandal of education is every time you teach something you deprive a child of the pleasure and benefit of discovery"

I need to remind myself of this every day when I plan my class activities. Surely I can make school better. Yes, there is the challenge of herding 27 kids all on separate paths and one of me. At least I understand the goal. Not saying I'm there yet. Need to keep trying!

Transformational Math(s)

Check out this fun video making fun of the way we sometimes teach math!

Why You Need an RSS feed or Google Reader

I was talking to a colleague the other day at a PD session and he wanted to get my blog address so that he could see what I have to say about Math. Of course, much of what I do is learn from others and add my experience. I am happy to be able to follow the likes of Dan Meyer, Vi Hart, Dean Shareski, Will Richardson, Alan November, Joe Bower and many others. You may have noticed, these are not all math folks.

His questions reminded me of how absolutely essential it is these days to have an RSS feed,

net vibes or google reader. If you are reading this you probably have one. If you don't have one, you should.

I tried explaining it to him without insulting him, hope I didn't. I'll try again here. Let's say you see someone on a TED Talk and you like what they say and how they say it. Chances are they have a blog where they have a chance to talk more deeply about their ideas. This is how I hooked on to Dan Meyer. I saw Will Richardson, Dean Shareski and Alan November at a conference. If I subscribe to their blog I am most likely to read it regulary. I will likely not if I just visit it when I get the urge.

From my blog reading (which I do happily daily), I have notice that some of the writers I subscribe to don't write much. I may delete them. Most writers have great blog posts some of the time, they do not inspire me with all of their ideas. The example I used with my colleague is that I might write great blog posts that are useful to you 10% of the time. You are not likely to catch that post if you just visit my blog occasionally.

Some writers like Dan Meyer and Will Richardson get my attention in 50% or more of their posts. For the same reasons, subscribe to their blogs so that you catch the great, the mediocre and the uninteresting.

If you want to catch fish, keep your line in the water, don't cast it from time to time. Good fisher persons also listen to others about where the fat fish are.

Find out who stimulates great ideas in you and subscribe.

"How fast would we have to drive to keep up to the sun?"

The other day I wrote a post on crowdsourcing a math test. I was extremely pleased with the results. The basic idea was that students worked in groups on a multiple choice test until everyone in the class had 100% on the test. It took 20 minutes for all of them to succeed. I thought at the time that it was a wonderful strategy for peer learning and maybe it was.

Sadly, I gave a short traditional computation-based test after three days. The result was that half the class failed. It appears that what was happening in the crowdsourcing test was that the students who understood it did most of the work and that very little teaching took place within the groups. I am not done with this strategy as I think it has great merit for collaborative learning and peer coaching.

Why is -3 X +2 such a hard idea to grasp for many students? Is it our failure to teach students to conceptualize math processes, skills and strategies? Is it that we don't try hard enough to make math real-life? Do we fail to allow students to be creative? Do we frame the problem for students and not allow them to frame it themselves? Is it because we emphasize computation in our classrooms at the expense of the other components of mathematics?

Perhaps a personal experience will help me to understand. At Christmas my family was driving to Calgary to see my dad and brother. My 13 year old son took a break from his playstation and asked,

"How fast would we have to be driving to keep up with the sun?" It just so happened that I knew a fact (if light could travel around the earth it would go seven times around the earth in one second) that enabled us to work out the answer to his question without a calculator. We may have made calculation errors, but the process was fun. His mother thought we were nuts.

I thought I'd make a list of the key factors enabling that great "math learning":

1. he asked the question, he was interested, it was relevant to him
2. he had success previously when he asked similar questions
3. interested parents and some skill (education) to talk to
4. he knew it would make me happy if he asked me the question
5. he is still curious
6. time was available to talk about it
7. he was not evaluated
8. the right answer wasn't that important
9. he wasn't worried about looking too interested in front of his peers

It is not that easy to do this in class every day. Commonly, the students you teach will not have parents who support deep thinking in math (they have bad experiences themselves). In order to have this type of situation in our classrooms more often, we will all need to do some deep thinking, sharing and collaboration.

I plan to keep up the battle with the help of my on-line math PLC (mostly twitter) and my school CIT (community of interest team).

Crowd Source Math Test

Today I gave an integers test to students in groups of three. I asked that they make the groups. One person had to describe themselves as loving math, the second, liking math and the third, not so much. I gave them the test of 20 multiple choice questions, although the chart below shows only 9. They were given 20 minutes to complete the test as a group of three.

When they were done they were to send someone to the board and write their answers on a chart like the one below. After everyone was done they were told whether or not all the answers were correct. If their answers were not all correct and in agreement with one another, they were allowed to talk to other groups and to change their answers.

The results were very interesting. After 20 minutes all of the students answers were correct with no help from an adult. I thought this was a very effective way of reviewing for a computation based test and of encouraging peer collaboration and mentoring. The kids thought it was fun and experienced success.

In this instance the test questions were simple computation and that is why the group succeeded in the time given. This crowd sourcing/collaborative method worked very well on this type of task. Not exactly creative, divergent, higher order and critical thinking, but well worth using again as a learning and evaluative tool.

CROWD SOURCED MATH TEST

Results

GROUP	#1	#2	#3	#4	#5	#6	#7	#8	#9
Tanner	A	C	D	A	C	B	B	A	D
McKenzie	A	C	D	A	C	B	B	A	D
Kathleen	A	C	D	A	C	B	B	A	D
Sabrina	A	C	D	A	C	B	B	A	D
Marinko	A	C	D	A	C	B	B	A	D
Cole	A	C	D	A	C	B	B	A	D

Dan Meyer's Bean Counting

Dan Meyer has posted a series of videos (Dan Meyer's bean counting). It was inspired by a word problem that can be read on his blog. This word problem is very similar to problems in most math books I have seen. I love his approach and will use it often.

I now just need to set out to prove that my students test scores will improve when I use this method! Need to start that task soon, our school division's current standardized tests are not set up to measure gains from year to year!

Please visit Dan's blog to see his full list of math videos. You can visit my math wiki for a quick resource and more.

Bean Counting — Problem #1 from Dan Meyer on Vimeo.

Nature Math

William Emeny has posted a wonderful video of math in nature. It is well worth watching and using in class. I have also added the link to my math wiki page.

Born to Learn: from the 21st century learning initiative

Joe Bower has posted a video from the 21st century learning initiative that is worth watching. When I was watching it I was reminded of a speaker who really got my attention years ago. His name was John Abbott. Guess what? This is his organization and this was his message!

Keep up the good work John and Joe.

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.

Wolfram Alpha widget builder

I was playing around with the Wolfram Alpha widget builder. It is quite fun and has potential to get kids interested. Have a look and experiment for your self. I have embedded a rhyming words widget and a country comparison of population density and annual income on my classroom blog.

"No One Cares What You Think"

One of the all time best movies for me is "The Bucket List" with Jack Nicholson and Morgan Freeman. I don't imagine there are many people who have not seen it. One of the great lines in the movie is when Nicholson is being lectured by his assistant and Jack gives him that classic look and says, "no one cares what you think". If you watch the trailer the line is near the end.

I love that line and, of course it is delivered in the way only he could do it.

At times when I write this blog or share ideas with other staff members, it seems to me that they are thinking, "no one cares what you think". I have always been passionate about sharing ideas with colleagues. I know that sometimes I expect too much from people. I expect them to validate my ideas, share my passion, tell me theirs, join me in my project, etc. Sometimes I'm sure they wish I would just go away.

Blogging is perfect for me. I get to write and share to my hearts content. If anyone "doesn't care what I think", they can just hit the X or not subscribe to my blog. It is still the perfect way to get others ideas from a large network of people and to get mine out there to whomever "cares what I think!"

The Bucket List - Trailer
Tags: The Bucket List - Trailer

Purposeful Work: Alan November TED Talk

Watch Alan November's TED Talk from March this year. He is quite a compelling speaker. I always come away with something big.

His main points I will take away are:

1. My class should look different. Kids need to find a problem in their world, figure out a way to solve it and find out what technology they need to solve the problem (not the other way around).
2. Students need to add value to our world because they own the problem. They need to leave a legacy. Too much of our school work is without purpose.
3. I need to direct more kids to fanfiction.net! Students would rather publish for the world than write for their teacher.
4. Social learning is under-stated.
5. Students should go to staff development activities.
6. We all need to reach the tipping point, where we realize that the kids should be working harder than the teachers.

Alan is definitely one of the most influential educators in my network.

Math from Real Teaching Means Real Learning

I just read a blog entitled "Real Teaching Means Real Learning" where the author quotes Schoenfeld's "When Good Teaching Leads to Bad Results". There were many great blog posts about math instruction on this blog and I will visit it often. Schoenfeld concludes that students have four beliefs about math:

1. The processes of formal mathematics (eg. "proof") have little or nothing to do with discovery or invention. Corollary: Students fail to use information from formal mathematics when they are in problem solving mode.

2. Students who understand the subject matter can solve assigned mathematics problems in five minutes or less. Corollary: Students stop working on a problem after just a few minutes since, it they haven't solved it, they didn't understand the material (and therefore will not solve it).

3. Only geniuses are capable of discovering, creating or really understanding mathematics. Corollary: Mathematics is studied passively, with students accepting what is passed down "from above" without the expectation that they can make sense of it themselves.

4. One succeeds in school by performing the tasks, to the letter, as described by the teacher. Corollary: learning is an incidental by-product to "getting the work done".

Not a glowing review of what we do in school for mathematics! Certainly Paul Lockhart, Alfie Kohn, Conrad Wolfram and Dan Meyer have said similar things. Compare the above to Dan Meyer's description of his math students prior to changing the way kids learn in his class.

lack of initiative

lack of perserverance

lack of retention

aversion to word problems

eagerness for formula

See the similarities?

More evidence that we need to change the way our kids learn and view math.

Will Richardson's TED Talk

I am a fan of Will Richardson and enjoyed his TED Talk. At first I thought that Will was going to promote his upcoming book! He goes on to describe the crisis in the U.S. in education. Test scores, firing teachers, common core, waiting for Superman, increased funding, standardized teaching, scripted teaching, teaching to the test, ear bud teaching, schools as test prep, 2 billion teachers, re-envision schools, deep inquiry, collaboration, great teaching, political commitment.

Learners will inherit the earth!

Ethnocide: The purposeful destruction of cultural diversity on the planet

My good friend Jennifer Hingley sent me two TED Talks and they (like her!) are just amazing. I love the learning one can do from your own living room. I have so much to learn.

Are you teaching culture in your classroom? Chances are you are or will. You can't not show this TED Talk. I previously wrote about the plight of Big Bear and his people who wouldn't sign the treaties and the damage/destruction to indigenous culture.

Have you ever thought that what happened in Canada in 1880 had nothing to do with you? Watch this video by Wade Davis and get a picture of what is happening in the world at this moment. I couldn't stop what happened to our First Nations people 150 years ago. What can I, must I do right now to prevent the purposeful destruction of cultural diversity (ethnocide)?

See the other TED Talk on my post called "Owning History".

Owning History: Aaron Huey

What do you know about the world in 1850? Today?

What do you think of Abraham Lincoln?

What do you know about the emancipation proclamation?

Do you teach history, learn history or own history?

How much do you know of the treaties?

Have your ever enjoyed a trip to the Black Hills?

Do you ever wonder why First Nations people don't seem to be thriving?

Who has taken the best meat?

Have you ever been in a POW camp?

Watch the video. Still think this is not your problem?