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!