Friday, December 31, 2010

Grammar Workbooks and Math Tests

Joe Bower has posted on his daughter's experience in school on a fraction unit. He reports:

"I have been teaching 8 years and have struggled under the weight of grades and what they don't mean for true learning. The truth of their effects didn't become crystal clear to me until a recent discussion with my 6th grade daughter's math teacher. After doing very well on homework and in class work, my daughter has "struggled" (i.e., gotten poorer grades) on the unit tests."

The test his daughter did poorly on was a provincial assessment. This is a familiar story to me. Many students in my class struggle with provincial assessments when during class they are learning at their own rate. I am all for the assessments as a measure of their progress and relative standing. It should not be hidden from them that they are behind or ahead of others in their learning. That should not limit their ability to learn at their level and to be taught using the best possible methods.

Early in my career I had a very poor concept of how to teach reading and writing. I adopted a grammar and writing skills workbook for the students to complete every week. I had all of the students do every exercise in the book throughout the year. One particular student struggled, yet he completed the exercises religiously. At the end of the year I gave a comprehensive test on grammar and writing skills taken directly from the workbook. He scored below 30%.

His mother came in to talk to me and wanted to know why he did so poorly. She knew how hard he had slaved at the weekly workbook. I was dumbfounded and was unable to avoid the conclusion that what I had been providing him yielded little in the way of learning grammar and communication skills, for that matter, any meaningful learning at all!

I was so embarrassed and had no excuse to offer. The parent and the student deserved better. Since that time I have learned so much about how kids learn to read and write. Workbooks have been in my bad books for a long time now.

Joe Bower's daughter doing poorly on her math test may be:
  1. a sign that she is not learning the concepts of math in class. It may be taught in the same way that I taught grammar years ago, workbook style, algorhythms, repetition and little meaning.
  2. the assessment was inadequate in measuring the learning that his daughter had achieved in the classroom. I have had great success with teaching math using open ended, "conceptual math" (Dan Meyer et. al.), yet it has become obvious to me that the way I assess learning will have to change along with the more patient, creative approach to learning math concepts. It is my sincere hope that the changes I have made in my math classes will eventually result in my kids out- performing others on provincial assessment or, at the very least, improving their test scores drastically.
Lastly, in our earnest attempts to achieve the best possible learning environments in our classrooms, we have to be careful not to be too judgmental of others' attempts to provide great learning environments for their kids. I am the first to admit that what I provide in my classroom is a work in progress. I am open to sharing and know what I offer is imperfect. I am not the only educator trying to achieve the perfect learning environment, most others are on their own journeys as are the authors of the provincial assessments.

I am not judging Joe Bower's position with respect to his daughter's teacher. On the contrary, I believe he is a wonderful warrior for change that will improve learning for his kids and many others. I love the difficulty and challenge of change. It will keep me interested in learning about teaching for a long time.

What University Might Look Like

Check out the following two videos portraying what university could be like. They are both relatively long yet enlightening. Hope you enjoy them.

Mike Wesch's version of university.

Wednesday, December 29, 2010

Suggestions for the computer lab

I was tweeted Gary Stagers post, "Humble Suggestions for the Computer Lab". He has great advice that we each need to heed as we assess our effectiveness as 21st century teachers. Please refer to his post for his thoughts. I have included his main points (with some modifications) and added comments of my own.

  1. Ask yourself each day, “Was what the kids did with computers today good?" "Did it include higher order thinking and was it a transformative use of technology?"

  2. Remember that quality work takes time. The structure of the classroom and the timetable will need to be changed.

  3. Shun ‘software du jour. Have an all encompassing goal like "students will learn to think".

  4. Stop using computer time for non-computing activities. Use the encyclopedias in the library if you need to.

  5. If a kid is breathing, she has probably surpassed the NETS. Real change occurs when you have one achievable, measureable goal, not a shopping list (much like the curriculum?!).

  6. Commit to the entire writing process for digital products. Great digital products like movies and slide shows are based on great writing.

  7. Stop integrating someone else’s curriculum. Commit to your goal (perhaps to have the kids learn to think) and stick to the course, don't deviate for every holiday theme.

  8. Not with my computers you don’t! Demand that appropriate, engaging and transformative technology use is a requirement in your class and in everybody else's too.

Quick and Easy?

I watched a video on a Joe Bower post on how one school used cash rewards to get kids to achieve, attend, etc. This video reminds me of a conversation I had recently with a teacher colleague who stated that "Alfie Kohn had it all wrong... that all students need some carrot to achieve..." Made me wonder what kind of reward he was talking about. What are the rewards in your classroom that get kids to work, attend, achieve, ... oh yea... and to learn?

Sunday, December 26, 2010

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.


Dean Shareski TEDx

Although I missed going to see Dean Shareski when he was here in Saskatoon, I knew I would see it on-line. Have a look at his TED talk. His most interesting point is that through social networking people are working towards building a sense of community that we once had in the day of unlocked doors, barn raisings and drop ins. An interesting perspective, many would say that the age of computers has a depersonalizing effect on us. What do you think?

Wednesday, December 22, 2010

Great quotes and posters

I was tweeted this flickr link to some great quotes and posters about educational change. Have a look at them and see what you think! (compliments of David Jakes, Dean Shareski and Mike Fisher)

David Jakes on Change 2

Screen shot 2010-11-28 at 1.07.52 PM


Power of Twitter: Add your name to the list please!

Matthew Arend retweeted this google doc . A teacher is using it to prove to their students the power of twitter. Have a look at it and see how many people have added their names. Add yours! I plan on showing my kids this. One of the nice things about a PLN is that sharing allows you to do amazing things like this. (To tell you the truth, I'm not sure who had the original idea! Guess I'm not yet totally twitterate)

I decided I would gather data for a presentation I am doing on higher order thinking in math and writing (or any other subject). I created my own google doc that I hope you look at and add the ways you ask your students to be knowledge producers in your classroom. Help me out with my presentation and pass it on!

Saturday, December 18, 2010

Math Class Needs a Makeover: Dan Meyer Classroom 2.0

I just watched the Classroom 2.0 session with Dan Meyer. This was my first Elluminate session and I was just amazed. Make sure you check this link out. I would suggest you watch the whole interview. It has helped me to know how to create higher order math problems for my students.

(photo taken from Dan Meyer's blog)

Some of his main points are:
  • formulation of problem is more important than solution to problem

  • pseudo context or pseudo problems, insulting to students

  • we are fixated by problems on dead trees

  • images used to convey problem should contain structure, steps and hook

  • the hook should be up front

  • roll of tape question, no one doesn't know how to start

  • have more demanding questions

  • build a culture of curiosity

  • most traditional problem solving is impatient problem solving, banging numbers together to get to one right answer

  • new problems should focus on objects of perplexity that pose questions to the viewer

  • photo from the movie "Holes"- the movie, shovel deep and wide. How much dirt? How long? Let them ask the questions. ( see Dan Meyer's blog)

Friday, December 17, 2010

Will Richardson: Exciting time to be an educator

In case you haven't had the pleasure of seeing Will Richardson in person, here he is at a PD session in Minnesota. The hour is well worth it, compliments of Dean Shareski.

He begins by saying that many of us have it wrong. We are talking about changing schools. What is really happening is that the way everybody is learning is changing. When he was in Saskatoon at the IT Summit he said that if we did nothing else and didn't feel ready to change our classrooms, we needed to begin to be a 21st century learner ourselves.

MSDC Will Richardson Fall 2010 from msdc-mn on Vimeo.

Top Ten Ways to Improve Student Achievement and Create Learners: Pam Lowe

I have just read Pam Lowe's, "Top Ten Ways to Improve Student Achievement and Create Learners". Amazing how many of them are goals of our school and our school division. Nice to know that we are well set up for change and success. For details, follow the link. Here is an outline of her top ten:

1. Share a Vision- our vision is that all students will use technology to be knowledge producers

2. Your School Should Be a Change Agent- our school is a technology school within the division

3. Analyze Data- we are collecting data based on our objective

4. Introduce Students to Their Data- students in my room are aware of our schools objective and the data collected

5. Increase Rigor- we are learning about rigor and the levels of rigor

6. Teach Students the levels of rigor- we are teaching our kids the levels of rigor (Bernajean Porter)

7. Expectations- we try to keep our expectations are high

8. Teach Students How to Learn- there is a lot of talk about meta-cognition and think alouds

9. Teachers as Learners Environment- the PLC's are dedicated to making teachers learners

10. Teach Smarter and Not Harder- it is hard to teach smarter, it is a process of change

As I wrote all of the comments for our school, I realize that I have salted in a heavy dose of optimism. Perhaps I'm too easy on our staff?

How does your school rate on the list?

Wednesday, December 15, 2010

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!

Data management can be amazing!

From time to time, I hear that the university community isn't embracing 21st century tools and skills. This video certainly doesn't support that idea. I love it when he says it is not enough to just present the numbers, he wanted to engage his audience and present some ideas through data. I've definitely got this video on my delicious account for when my class is looking at data management.

Not sure you caught that? As I wrote the last sentence I realized that great math is not isolated topics and isolated lessons. I will plan to use this video to encourage my students to report their data in a creative way for their critical thinking projects. (In case you are wondering, our current class critical question can be found on our water wiki. The critical question can be found at the bottom of the page.)

Saturday, December 11, 2010 Tutorial

Check out this video posted by Dan Meyer on If ever you need to have a list of links from a presentation available for participants, this is your tool! Tutorial from Dan Meyer on Vimeo.

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!

Alan November "meets" Kim Cofino

Kim Cofino took notes from an Alan November keynote presentation in Japan. I saw Alan November present in Saskatoon at the IT Summit three years ago and am using much of what he presented often. He was an integral part of how my class presently operates and my goals for where I would like to be as an educator.

One of the beautiful ideas of 21st century learning is the idea of sharing. How cool is it that Kim attneds a conference in Japan, takes notes and makes them available to me (and everyone!). I plan to use many of the links from her google doc.

This reminds me of a class activity we did the other day. We are developing a list of research and critical questions on the topic of water with our partners in Puerto Vallarta, Mexico. Six pods of students took a half an hour of class time to create a google doc. It was imperfect, a bit disjointed and unformatted. After we were done a student stayed back from recess to format the document and to add more questions to guide our research. I did not ask her to do this, for her it was fun. Felt a lot like wikipedia to me, for that matter, we could have used a wiki.

Thanks a million Kim, I'll do the same for you when I am lucky enough to be at a conference!

Wednesday, December 8, 2010

Mathalicious is delicious! So are Open Educational Resources (OER)

"If you haven’t heard, there is a new movement in education and it’s called OER which stands for Open Educational Resources". This is a statement taken from the Innovative Educator blog which lists many sites rich in resources. One of the great ideas of 21st century learning is sharing and non-proprietary, collaborative resources. I'm not sure why we would ever crack another textbook!

One of the sites on the OER list is mathalicious. Wow! I can't believe this stuff is out there. If you are a classroom teacher this is just too juicy. As Alan November once said to us, "This stuff is low hanging fruit!" These resources "can" fit so well with what Dan Meyer, Paul Lockhart, Conrad Wolfram, Alfie Kohn and many others are saying about learning math. These multi-media activities are truly impressive, engaging, creative and are aimed at middle years to high school students.

Notice I said can fit so well. If you take a look at the activities they are very engaging and well put together. An example is the tunnel digging activity for ratio and proportion. If you take a close look it is really just traditional problem solving questions put in an engaging way. All the information is given, as Dan Meyer says, the way is paved for them to find the answer, no deep thinking is needed about the processes involved. For my taste, the questions give too much information for them to be process oriented, creative problem solving opportunities. For example, the simple question I would ask is "How much dirt would have to be removed to dig the tunnel?" I would not mention volume, I would not give numbers. As Paul Lockhart says, "let them struggle, then give them some technique, but not too much".

They also give links to favorites of mine like HippoCampus and the Khan Academy.

Among the other OER resources listed are:

Carnegie Mellon University (OLI)

· Curriki·

Open CourseWare Consortium·

Flatworld Knowledge·


Digital Library for Earth Science Ed··

Math Archives·


National Science Digital Library·


Blooms Taxonomy and Technology

Way back in my university days I remember Bloom's Taxonomy and I also remember it had no meaning to me. Perhaps it was the uninspiring professors or my inability to comprehend it's significance. Today, for my classroom, Bloom's is big.

Our school's main PD focus is to have our students understand and perform better in math. Everything I read these days is about higher level thinking and creating as integral processes in learning mathematics. My "community of interest" group's goal is for students to understand and use higher order thinking as learners (and to be knowledge producers).

For a long time, I had described this as teaching thinking rather than researching or following directions. Turns out that in 1956, Bloom had this cased for us. This year has been a very rewarding year for my students and I because for the first time ever, it is a clearly stated goal in my classroom to learn how to think in every single thing we do!

I was sent these links by a good friend Judy Byers. She is a very important part of my PLC. Check them out!

Saturday, December 4, 2010

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?

Wednesday, December 1, 2010

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

Create a wiki

Launch a blog

Make videos or podcasts

Comment on blogs and in discussion forums


Create a Facebook Page

Create your own domain

New video for 21st Century Learning

Check out this new video on 21st century learning!

Saturday, November 27, 2010

12 2/3 + 7 3/5 = huh

The other day I was watching my intern teach a math lesson on using the algorhythm method to divide fractions. I was working with a young person who had no real concept of what a fraction was a month prior, indeed she did not understand what multiplication actually represented, much less her multiplication tables. We had been doing conceptual work such as open ended fraction questions (a la Dan Meyer) and manipulatives and diagrams so that she could visualize fractional numbers and problems.

She had made good progress in the weeks prior and now we were teaching the algorhythm method to divide fractions (invert and multiply, divide the top, then the bottom, etc.). As I worked with her, it became more obvious than ever that teaching the algorhythm alone is a tremendous obstacle to real learning in math. With this student, in this instant, I decided that if she could estimate the answer of a dividing fraction question, that would be enough.

On Friday, a few teachers had a discussion in my room as to why kids do not do well in math. I made the statement that much of it is due to the poor teaching methods of teachers. Alfie Kohn has posted a great article on Math instruction! He says:

"...that traditional forms of teaching, and an emphasis on the basics, contributed significantly to the low standing of older American students....instruction in this country still seems – compared to instruction in some other countries – more centered on students as passive absorbers of knowledge rather than as active participants who construct, transform, and integrate knowledge.”

He cites studies from Japan where math instruction may be different:

"...three out of five U.S. teachers said they were chiefly concerned with “skill building.” Only one out of four Japanese teachers responded that way: the overwhelming majority said they wanted their students to understand a particular math concept. That goal led those teachers to include deductive reasoning in their instruction, which played a role in 62 percent of Japanese lessons and 0 percent of U.S. lessons. Japanese teachers also explored the intricacies of specific mathematical concepts with their students rather than just naming those concepts, American style. In Japanese classrooms, fewer math problems were considered in more depth, and students participated actively in suggesting different ways of solving those problems. Also, interestingly, homework was rarely assigned."

Teaching the algorhythm alone seems to me to be the most unproductive way to teach math, or conversely, the most productive way to produce disengaged, confused math students! Much of what I read these days backs this up. In a recent post, Conrad Wolfram claims that we spend 90% of teaching time in math on computation and not enough on the conceptual and real life application. Kohn goes on to say:

"the research conducted on such programs has been concentrated in the primary grades, and it points to a result that can be summarized in six words: better reasoning without sacrificing computational one study, forty first-grade teachers in Wisconsin were given special training in how to make problem solving the organizing focus of teaching arithmetic. When achievement tests taken by their students were later compared to those of traditionally taught children, the results showed a modest, though consistent, edge for the former group. “A focus on problem solving does not necessarily result in a decline in performance in computational skills..."

I love teaching math and the challenges it brings. There are a world of educational opportunities out there for math teachers. 21st century learning applies to math in a big way.

Tackling Myths

People talk about technology affecting children in negative ways. Nick Sauers has just written a post on "1:1 Schools" to help debunk some of these ideas called "Tackling Myths". He gives statistics that do not support the following statements:

  • People are losing their abilities to connect with one another in "real life" because they are living in an online world.

  • Our language is being destroyed because of the language kids use while texting or while in chatrooms.

  • Students won't be safe online!

The New York Times (Virginia Heffernan) has also published an article called "The Attention Span Myth". Heffernan argues that our modern fascination on the importance of attention span is ill founded. As one comedian quipped, "remember when having ADD meant that you had an imagination?!"

On the other hand, CBC television produced a video entitled "Are We Digital Dummies?" This video makes the statement that "no one is happy with the time they are spending with technology". This video is both convincing and one sided and well worth watching for an alternate view.

One of the most interesting things the film says is that over-use of technology causes anything from marital stress to work burnout. Families may talk less and work life is extended beyond the office. One example suggested workers prior to blackberries (32 billion worldwide!) worked 45 hours a week, post blackberry was 70 hours.

The film suggests that we are a nation of distracted technophiles. Brain research says that middle age multi-taskers make more mistakes. They also argued that technology can discourage creativity. This is because as soon as you get an idea you put it out there instead of taking it further with deeper reflection and research.

There is some suggestion that technology is rewiring the brain. This point was not well supported by the authors, yet is something for me to do further reading on.

I do like the concluding point in the film. We need too manage technology in our lives or it will manage us.

8 Videos to Help Teach Innovatively

The Innovative Educator has posted a blog entitled "8 Videos to Stimulate Conversations about Innovative Education". These are great resources for you to use in PD opportunities for your staff and also for your own learning. The videos titles are:

  1. High School 2.0

  2. Progressive Learning Environments

  3. Cells in the Classroom

  4. Internet 2 and High Bandwidth Connectivity

  5. Facebook, Youtube and Other Mainstream Tools

  6. The Impact of Social Media in Schools

  7. Disruptive Innovation

  8. 21st Century Skills

Thursday, November 25, 2010

Real World Math and Computers

Check out this TED talk by Conrad Wolfram on "Real World Math and Computers". Conrad Wolfram is the co-founder of the Wolfram Alpha website and he gives an amazing perspective on the teaching of math. This video is a must see for those with a real desire to change the way math is understood and learned (see Dan Meyer, Alfie Kohn posts).

Wolfram says there are four parts to teaching math. They are:

  1. posing the right question

  2. taking a real world problem and changing it into a math formulation

  3. computation

  4. taking the math formulation and applying it in a real world verification

He says that 90% of what we do in the class is computation which is the least beneficial and the most painstaking. He uses the example of teaching beginning calculus to very young students. it is not that hard for them to get the big ideas of calculus but we don't teach them because we get too involved with the onerous calculations of calculus.

When people like Dan Meyer and Conrad Wolfram talk about the changes needed in the teaching of math, I feel like they have been in my classroom!

Have a look at the video! Read more of Alfie Kohn and Dan Meyer.

"Wikipedia is Bad?!"

The other day a note came home from one of my kids teachers explaining a research project. In it they gave some guidelines for how the students should be conducting on-line research. The note was not in depth, a few short notes about using different search engines such as google or yahoo, not terribly helpful. I assume most of the teaching occurred in the classroom.

One particular statement on the note caught my attention. The statement said, "Wikipedia is bad, anyone can edit." I wrote a note back that said I believed that they did not quite understand the worth and significance of wikipedia as a tool and as a symbol of 21st century learning. I offered to provide them with information to support that statement and refute theirs and to come to their class and to talk to the students about the nature of wikipedia and 21st century learning.

I know of many teachers who routinely dismiss wikipedia as not to be trusted. This drives me crazy as I think so much can be learned from it as outlined in many books on 21st century learning. I decided to do some quick googling and to list the reasons wikipedia is extremely important and successful. Here I go.

  1. collaborative construction of truth

  2. as accurate and reliable as traditional sources (Nature magazine)

  3. more current

  4. people (adults) use wikipedia first

  5. 15 times the word length of Encyclopedia Brittanica

  6. most successful in world

  7. over 10 million articles in over 233 languages (2007)

  8. goal is the sum of all human knowledge

  9. editable

  10. changing, improving

  11. collaborative vs. proprietary

  12. warnings given when article is in dispute or not referenced properly

  13. not editable if vandalised frequently

  14. perused by thousands for accuracy and mechanics

  15. second most visited site after google

  16. represents a new way of learning and business

  17. many contibute to one article instead of a few

There are possible flaws as there are in traditional sources of information.

Potential Problems

  1. errors

  2. vandalism

  3. lies

  4. writing is not always good or consistent

  5. writing too complex for younger readers

I would love to teach my son's class the pros and cons of using wikipedia. Are you in your classroom?

Saturday, November 20, 2010

10 ways to encourage students to take responsibility

I was tweeted Ed Ustanges's posterous post on the 10 ways to encourage students to take responsibility. I have listed his top ten, for more details see Ed's post. Great work Ed! I think I will ask my intern to evaluate me on Ed's list. I hope I pass.

1. Don’t make all the decisions

2. Don’t play guess what’s in my head

3. Talk less

4. Model behaviors and attitudes that promote learning.

5. Ask for feedback

6. Test less

7. Encourage goal setting and reflection.

8. Don’t over plan.

9. Focus on learning, not work.

10. Organise student led conferences

Kim Cofino, Finding the Right Fit: International Schools

I was tweeted a great post by Kim Cofino called "Finding the Right Fit", which is about applying to teach in an international school. Kim's post is very well written and makes me want to apply. I know I will keep her post in mind as I plan for the future. There are a world of opportunities out there. Have a look at her post!

I have included the promo movie for the school she is at, the Yokohama International School(YIS).

An Introduction to YIS from Yokohama International School on Vimeo.

Blooms and 2.0?

I got this schematic from a retweet (). Have a look at it, click on it to enlarge.

While I think it is interesting, why would we think that using voicethread or glogster would involve the higher order thinking and creating of Bloom's taxonomy? I have seen many projects done with those tools which were all about knowledge consumption and lower order thinking rather than knowledge production. What do you think?

Wednesday, November 17, 2010

Public Education?

Joe Bower has posted a video on preparing kids for kindergarten tests. Watch the video and be amazed. Is this some people's dream for what school should be?

It reminded me of a speaker at our convention who talked about the importance of public education in society. His name was John Ralston Saul. I did not know him and did not know what to expect. Turns out the guy had given this topic some thought! His main point was that as people spend their money and resources on private education, less time and money will be available for public education. He warned about the increasing lack of social mobility in the U.S., a country founded on the idea that everyone can succeed and that there were no set social classes. (OK, so that was the theory anyway)

An emphasis on private education and kindergarten testing results in further stratification of society and the creation of ghetto schools. Would you want your children to go through this? Who is responsible for maintaining some balance in society and trying to make sure the poor have a shot?

I will never agree to the practice unveiled in this video. I find it quite alarming and sad. Have a look.

George Couras Top 100 Tech. Tools

George Couras has posted a cool slide show that gives the top 100 tech tools. You simply must follow the link to see his post. The top ten are:

  1. Twitter

  2. Youtube

  3. Googledocs

  4. Delicious

  5. Slideshare

  6. Skype

  7. Google Reader

  8. Word Press

  9. Facebook

  10. Moodle

How many of the 100 are you using? Could you use?

Saturday, November 13, 2010

David Warlick on xtranormal

I got this video on a tweet from David Warlick, educational blogger and creator of classblogmeister. I have been following him for years as he was a keynote in Saskatoon. I also currently use classblogmeister to host my class's blog. I loved it that the person who introduced me to blogging has never used xtranormal, a program that creates cool animations with text to sound.

I point this out because in this 21st century world of education, it is hard to claim expertise on anything in particular. We are all learners and that is liberating and exciting. I can imagine my humble blog posts helping someone who is not as far along as me. If no one is interested in what I create, I still win as I learned in the process of creating something.

I also like the point he makes, that students need to be connected and information has to flow freely for them to learn freely. Our school boards need to hear this message many times over.

I am blogging and skyping with a class in Mexico. They just got a computer lab in the school and they decided to not install internet connections for the kids' computers in the lab. What the heck would they use them for? This kind of protectionism is amazing to me. I don't know how we could even think of stifling young learners curiousity in such a deliberate way, in the name of caring.

Nice job David. Keep having fun.

Twitter for Teachers and Students

I have just recently began using twitter to build my PLN. I love it, it is so fantastic to be connected to smart, motivated people. It is humbling that so many people are willing to share what they know and they find. I am going to introduce the idea to my class and I think it will benefit them immensely. One of our classroom goals is to build a learning network on-line and twitter will be a big part of this.

I found two posts (on twitter, there will be many) that may be helpful to other teachers breaking the same ground as me. One is The Ultimate Twitter Guide for Teachers from the blog Edudemic. It has many links and is an ample resource that you need to bookmark and share.

The other one is "5 Twitter Uses for School Leaders", from the blog Leaders On Line. This post gives five foundations for effective twitter use that is very helpful in guiding educator use and convincing staff to get on board.

Enjoy the resources!

Thursday, November 11, 2010

One Grade 7 Student's 21st Century, or is it?

I found this on the cpchat daily blog. I saved it immediately and showed it to my class the next day. I thought it was a great example of a 21st century kid in a 21st century classroom.

As I watched it again I began to see it differently. It didn't seem to me to include the kind of rigor and heat Bernajean Porter calls for when technology is used. Our goal in our classroom is using higher level thinking, hopefully using technology! Does this video show signs of transformative learning and being a knowledge producer or is it using technology to be a knowledge consumer?

Watch it and let me know what you think!

Wednesday, November 10, 2010

Social Action Sites

I was tweeted the fantastic site "Invisible Children" the other day. It reminds me of how the internet brings great hope to our world. I was just at a presentation on violence prevention in school where we were shown a video comparing the world of the 80's with the world of 2010.

I was skeptical as to the point of the video. It seemed to be saying that the world of the 80's was a better, safer place. To me, the beauty of today's world is how there is something available for anyone, no matter what it is. I also think that anyone wanting to make a real positive difference has a greater chance to do so with instant, global communication and social networking.

I have used three main social action sites in my class, and plan on expanding how the students use them to build a better world. Have you seen or used these sites? How do you use them?

Taking it Global


Me to We

Sunday, November 7, 2010

"Meyer Math"

I am so enthused about the work of Dan Meyer in the area of how math is taught and am using his ideas a lot in my class. I have decided to post my "Meyer Math" problems in this post, in honour of his inspiring TED talk.

Joe Bower has also posted on what Alberta is thinking about the teaching of math. He includes the following video on how math is everywhere. Have a look at the Alberta video and then see what you think of my "Meyer Math Problems"! (my son Marcus took the photos)

At what angle would you have to kick the ball for it to travel 50 m. in the air?

How long would it take for the cheese to be consumed by mold?

How long will it take for the ball to reach the ground?

How high would you have to jump to dunk a basketball?

How many gallons of paint would you need to paint the fence?

How fast are you growing?

How much would you save by turning off the lights?

How far is it to your house?

How much will it cost to fill up your tank?

How long does the furnace run to change the temperature of the room by two degrees?

How many tiles will you need to tile the floor?

Saturday, November 6, 2010

Professional Learning by Ryan Bretag

Ryan Bretag writes a great post in Metanoia entitled "Raise Your Hand". He talks about the imperative to learn and to share as extolled by the likes of Dean Shareski and Will Richardson. The traditional way for teachers to learn were PD days, convention and summer university courses. The opportunities for us to learn now are infinite. The same opportunities exist for our students and parents. The world is changing so fast it is imperative for teachers to adapt quickly to keep up.

When I talk to teachers about the many learning opportunities on-line, they almost always say that they don't have the time. Many say that schools will evolve into 21st century schools given small steps and time. David Warlick recently tweeted, "Small steps!" Do we (our children) really have that much time?"

Bretag writes:

"How would we react to students if they told us they didn’t have time to learn? they didn’t have time to improve upon their skill set? they didn’t need to know that? they didn’t need to try anything new, challenge their current ideas, or push beyond the norm? Would terms like prioritize, organize, time management, etc. be part of our discussion? Many students have so many demands outside of the school day that if we as educators are demanding their learning be 24/7, shouldn’t we be practicing what we preach?"

I love the learning collaborative, social networking sites allow. I can hardly stand it when I am unable to learn in that way for too long. I too get a bit frustrated with staff who appear to not care about changing the way the classroom works. I find it hard to understand why people are reluctant to see the opportunities to learn in amazing ways in an incredible world.

Bretag makes recommendations fo teachers:

1. Dedicate a portion of your day to honing your professional practice both locally and digitally

2. Establish a professional learning network

3. Establish and maintain a virtual professional learning space that fosters shared knowledge and resources

4. Make professional reflection, scholarly work, and learning a priority and make it public.

5. Model professional learning for colleagues, students, and parents

6. Take a risk, rethink your norm, challenge your assumptions, and embrace the idea of being disturbed.

I think it is great advice. The challenge of building PLC's and becoming twenty first century learners and teachers is too important to wait another moment!

12 videos posted by Scott McLeod: Dangerously Irrelevant

I just read a post in Dangerously Irrelevant by Scott McLeod entitled "12 Videos to Spark Educators Thinking". The videos listed on this post are just exceptional for teachers' educational journeys. I would sugggest that you look at each of them and possibly use them for staff PD opportunities! I have included a TED talk by Jeff Jarvis, the author of "What Would Google Do?"
For ease of access, even though I didn't collate the list, I have shown it below:

Sir Ken Robinson, Changing education paradigms (11 minutes)
Sugatra Mitra, The child-driven education (17 minutes)
Clay Shirky, How cognitive surplus will change the world (13 minutes)
Chris Anderson, How web video powers global innovation (19 minutes)
Dean Shareski, Sharing: The moral imperative (25 minutes)
Henry Jenkins, TEDxNYED (18 minutes)
Daniel Pink, Drive: The surprising truth about what motivates us (11 minutes)
Dan Meyer, Math class needs a makeover (12 minutes)
Jeff Jarvis, TEDxNYED (17 minutes)
Lisa Nielsen, Response to principal who bans social media (4 minutes)
New Brunswick Department of Education, 21st century education in New Brunswick (6 minutes)
Charles Leadbeter, On innovation (19 minutes)

Wednesday, November 3, 2010

Higher Order Thinking

In a post by Joe Bower entitled "Poor pedagogy + Technology = Accelerated Malpractice", he responds to comments he received when he criticised a teacher who posted about using google docs to create tests.

The debate is quite lively and Joe really digs deep to defend his point that creating google docs tests is not a twenty first century idea. According to Joe, true-false content tests are just another example of out-dated assessment tactics in a teacher centered classroom (my words).

He tells the story from a Kohn book where a surgeon from a century ago visits a modern operating room and would feel quite confused. A teacher from 1oo years ago visiting a modern classroom would feel right at home. Bower makes the point that it is our job to speak out and to recognize the old and tired from the new. He quotes Kohn:

"all that is necessary for the triumph of damaging educational policies is that good educators keep silent"

And Gerald Bracey:

"There is a growing technology of testing that permits us now to do in nanoseconds things that we shouldn't be doing at all."

At our school, we have just come up with a goal for our technology initiative. We came up with the following:

"students will develop and practise higher order thinking skills (will be knowledge producers)"

We are quite proud of our goal as it is student centered, pedagogically based, as old as Piaget and 21st century as well. Notice that it doesn't even mention technology?!

Creating tests with google docs is a great idea. Does it change the classroom?

How about using microsoft publisher, web 2.0, blogging, web pages, e-books?

What is your school's goal with technology?

Nokia gives it's two cents worth

Alan November appears in this video. I'm going to look for dissenting viewpoints! I'll let you know where to find them!

Introduction to Technology and 21st Century Learning from New Learning Institute on Vimeo.

Tinkering School

Check this out on TED talks. Wouldn't you like to have gone to tinkering school?

University courses on-line and exams using google

I love it that M.I.T. offers all of their courses on-line for free. This is such a great idea that announces loud and clear that sharing is the way of the present and future. The New York Times published a post on M.I.T. and others' open, on-line courses. They offer over 2000 courses that anyone can audit for free. Have a look and enjoy!

In another great example of 21st century learning, Danish students are able to use google when writing exams. This seems incredibly simple to do and very practical if you are interested in assessing higher order thinking and not retention of data.

The BBC article goes on to say:

"The internet is indispensible, including in the exam situation. I'm sure that is would be a matter of very few years when most European countries will be on the same line."

In my class, I am using a math curriculum posted on-line by Dan Meyer for my advanced students and I will use the internet for many exams from now on. It is amazing how many useful innovations are available from people sharing on-line. Hope you find it as fun as I do.

Sunday, October 31, 2010

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?