Mathematician's Lament

Yesterday Will Richardson tweeted the Mathematician's Lament by Paul Lockhart. It is, hands down, the best read I have ever had pertaining to mathematics education. Where was this kind of direction when I was being trained as a teacher? How long has this been available to me and why have I not been exposed to it?

If you can't read the whole thing (25 pages) I would suggest you move to his conclusion where he gives a scathing description of math education as it is in most schools.

His main idea is that math education is broken and not worth fixing. The patient is dead. Math needs to be recreated, not revived. He says students claim "..math class is stupid and boring...they are right...". Math is taught as a paint by number method void of imagination, creativity and discovery. Students are never allowed to create or think. Traditional math is about following directions, not creating directions. His main claim is that none of us recognize math as an art.

Math reformers claim for testing and/or higher standards will fix the problem. Lockhart says they are all wrong. He gives solutions:

1. thinking rather than following directions
2. math need not relate to real life, sometimes it's beauty is in it's complete irrelevance to real life
3. give them a problem and let them struggle with it, don't show them how to solve it
4. give them some technique to solve the problem, but not too much
5. play games, teach them chess and go, hex and backgammon, sprouts and nim, whatever, make up a game. Do puzzles.
6. expose them to situations where deductive reasoning is necessary.
7. don't worry about notation and technique.
8. help them to become active and creative mathematical thinkers
9. don't get caught up in the vocabulary (ie. quadrilateral)
10. story that matters, not the ending

I have been in love with teaching math for my entire career. I feel like I have many things right. Thanks to him I have a more accurate road map for the learning of math in my class. I can hardly wait to get back into the classroom and to share this with my colleagues.

Thinking Classrooms, Visible Thinking

• Deeper understanding of content


• Greater motivation for learning


• Development of learners' thinking and learning abilities


• Development of learners' attitudes toward thinking and learning and their alertness to opportunities for thinking and learning (the "dispositional" side of thinking)


• A shift in classroom culture toward a community of enthusiastically engaged thinkers and learners

These are the stated goals of the blog "Visible Thinking".

On their blog there is an assessment tool for thinking classrooms. The criteria from the tool are below (see the assessment tool for complete viewing).

1. In this class, the work students are doing is connected to big or important ideas in the subject area.
2. In this class, the work is focused on developing well articulated understandings. It is relatively evident what understandings are to be developed as a result of doing the work.
3. In this class, a few topics are explored in depth rather than attempting to cover or touch on many.
4. In this class, the work is purposeful and has meaning for students. It is not just work for work’s sake.
5. In this class, students find the work engaging and worthwhile. Engagement is intellectual as well as social and/or physical.
6. In this class, there is a level of meaningful choice embedded in the work that allows students to have real ownership of the work or helps to personalize it.
7. In this class, the work challenges students in some way, by pushing their thinking in new directions or asking them to reexamine ideas or beliefs.
8. In this class, the work asks students to generate original ideas, explanations, solutions, responses, or findings.
9. In this class, the work has depth and regularly goes beyond the level of knowledge/skill building.
10. In this class, students’ thinking is made visible through the work/discussion/ reflections they do so it can be discussed, shared, examined or reflected upon.
11. In this class, patterns of thinking/habits of mind are on display. It is possible to identify the types thinking that students are engaged in and must do to be successful with the work
12. In this class, there is adequate time for thinking, to prepare responses, and express ideas.

I apologize for copying and pasting another's work. I think this is an amazing assessment piece which I am going to have my students fill out on our classroom. I also have an intern (not exactly and independent source) and I will ask him to assess our class as well.

Look forward to the results in a future post!!

Dan Meyer's follow up on Toaster Math

Dan Meyer writes about how to solve the toaster math problem he posted and I wrote about. This couldn't be more timely as I just used his toaster math question to get my class thinking about ratio and proportion. I did three lessons of "Meyer Math questions", culminating in the toaster math question before I even mentioned that the topic of this month's unit would be ration and proportion.

Meyer — Toaster Regression from Dan Meyer on Vimeo.

I had a volunteer in my classroom and he was busy in the back of the room trying to solve the toaster quesstion. Notably, I did not even speak during or after the toaster math video. Part of the appeal of such questions is that the kids have to figure out the question themselves. Check out the first link for the toaster math video and the second for possible solutions. Keep in mind that one of the big ideas is that there can be many solutions (divergent thinking).


One particular student, who has a real mental block about math, exclaimed, "we should do math this way every day!" after we finished the first three activities. I look forward to many challenging lessons addressing the conceptual foundations of math instead of the computational barrage typical in our classrooms.

Watching TV vs. Blogging

At home I often settle in to watch a movie with my family and soon find it to be not catching my interest. On many occasions I end up reading my feeds, on twitter, blogging or catching up on my e-mail (somehow, I have not joined the texting generation yet). I am leery of the effect this has on family relationships, but I find it an interesting phenomena.


I think that I choose to be connected and creating, a producer rather than a consumer. My theory is that kids in my class are very similar, that is if they are guided towards areas of interest (choice!). My oldest son is a very good athlete yet never liked organized sports with a top-down structure (ie. a coach). He skateboarded and snowboarded for hours each day (and still does) alone and with his buddies. They would jump, somersault, spin and crash, often filming it and posting it to youtube. In a small way, I believe this is the new generation's way of creating instead of consuming.


Back to my theory, people who blog, twitter and build learning communities on-line watch TV less. TV is passive, TV is for consumers, TV is asocial. Creating and collaboration is more rewarding, and more fun. What do you think?

Failure by Ted Sizer and Alfie Kohn

Joe Bower has included a quote by Ted Sizer. He says:

"....good schools promote displays of incompetence (strange as that may sound) in order to help students find their way to competence".

Alfie Kohn is also quoted by Joe. He says:

"teachers who want to encourage intellectual growth give students time to be confused and create a climate where it's perfectly acceptable to fall on your face".

These quotes make me feel really good about my classroom. Every single day I talk about the cool things we try and every single day I admit that I am failing to some degree. I love to toss around the big ideas in my head and try like crazy to incorporate them into my classroom. Some days it matches what is in my head and some days doesn't.

As I reflect on the importance of failing for teachers and for students, I am happy to say that my classroom looks very different from what it looked like five years ago. I need just a little more time....

Create a Digital Identity

I just read a great post on "Controlling Your Digital Identity" on the Innovative Innovator. There is a reason that Deven Black was nominated by Edublogs for the best individual blog of 2009. Please do not read on if you want the definitive post on "controlling your digital identity"! He says it all if you ask me. I love the learning available on-line and I plan to take Deven's advice on each of the following! I suggest you do too.

Google yourself

Spezify who you are

Check out your online Persona

Use Google Alerts to monitor what others are saying about you

Create your Google profile

Connect with Flavors.me

Create a wiki

Launch a blog

Make videos or podcasts

Comment on blogs and in discussion forums

Tweet

Create a Facebook Page

Create your own domain

New video for 21st Century Learning

Check out this new video on 21st century learning!