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Jeff Johnson Talk

Last week, I was fortunate enough to be invited to a small meeting at which Alberta’s Education Minister, the Honourable Jeff Johnson was invited to speak. He left me hopeful. He spoke openly and without seeming like he was reading a canned speech. He seemed intelligent and it was obvious he has been doing his homework in his new portfolio.

Johnson said a few things that really stuck with me. I’m not quoting directly, but paraphrasing from what I wrote down and remember.

  1. We need to blur the line between secondary and post-secondary education.
  2. In a competency-based system, the zero is irrelevant.

He also mentioned the things he believes the public wants more than anything else.

  1. They want to know that kids are earning their way through school. There should be no free passes.
  2. They want to know that there are competent educators in front of their kids.

It sounds to me like the guy has a pretty good handle on what is going on in Alberta right now. I’m encouraged.

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An email came out from Alberta Education yesterday announcing that the -3 math stream in Alberta (equivalent to the Trades and Workplace stream elsewhere in the WNCP) has seen wide acceptance from the trades. I know the fellow working on this at Alberta Education had a huge job. He had to get all 49 (or so) trade boards to set their requirements, one at a time. He has done a great job, though, because if you take a look at this nice, one page summary, you will see that there has been tremendous acceptance of this stream. His diligence and persistence have paid off.

You can see that the minimum requirement for most of them is Math 10-3 or Math 20-3. It also looks like having these courses will mean students don’t have to write the entrance exam. This is fantastic news for our kids.

Four trades still need to make their decisions. Once those decisions have been made, they will be posted here.

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Happy New Year

Resolution: Write shorter blog posts.

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Sketchpad Explorer

Somebody tweeted last week that The Geometer’s Sketchpad was free for iPads until September 1. I have never been a fan of GSP, preferring to use GeoGebra instead, but I installed it mostly because it was free. I tried it out, and it turns out it is pretty darn good.

You can get the free Sketchpad Explorer on the iTunes App Store. I have no idea what it will cost after September 1, but I’d pay for this app. You can’t create GSP applets with it, but you can view and explore already created ones. The app comes built-in with a series of Algebra, Geometry and Elementary applets. The built-in ones are really nice. A slope one is shown below.

I think the real power, though, is in the Sketch Exchange site, where you can download and transfer applets built for the iPad to your device. It is easy to do this through iTunes once you download the applets from the exchange site. This exchange site will only grow and have more and more available applets over time. Two screenshots are shown below.

Recommendation: Get this app.  You can’t beat the price.

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At ISTE 2011, I attended two sessions aimed at showing off as many web tools as possible in 60 minutes. Tammy Worcester showed her Top 20 Favorite Web Tools, giving herself an average of 3 minutes per tool. Brandon Lutz kicked it up a notch, and showed off 60 in 60. He gave us one per minute, for an hour. There was some overlap.  I made a Venn Diagram because I’m a math geek. In the next three posts, I’ll discuss the tools they shared, and what I see as their use for me.

I’m not going to discuss all 74 unique things I saw. Some of them are of no interest to math teachers. If you really want to see them all, you can click on one of the links above.

Overlapping Tools

Because I think it is interesting to see the tools that they both recommended, I’ll start with the overlap.  I will discuss all six tools that they both shared.

Tiny URL – This is a URL shortener. I use bitly, and I know many people are fond of Google’s version.

Plurk – I had never heard of Plurk, but I definitely plan to check it out. According to them, it is like twitter, but has better threading of responses. One thing that drives me nuts in twitter is that if I reply to someone’s comment, I have to seek out other replies, because I only see the replies of the people I follow. Apparently Plurk does this better.

Evernote – My boss and my consulting colleagues have been raving about Evernote for months. I don’t use it because I haven’t needed to. Evernote lets you create, modify and synch documents among all your devices. I do the same thing using the QuickOffice app on my iPhone and iPad, and storing the documents on Dropbox. I annotate PDF’s on my iPad using GoodReader. If I ever encounter something I can’t do with these tools, I’ll give Evernote a try. I know it’s good because people have been bugging me to try it for months.

Dropbox – I was pretty clear about how much I love Dropbox when I wrote my Ode to Dropbox several months ago. They have had a security breach recently, and there is some question as to whether or not files are encrypted on their storage, but I still love it. I don’t keep anything there that is sensitive or could jeopardize my privacy. It’s the best way I have found to store and share my presentations and handouts.

Qwiki – I’m not sure I see use for this for math teachers, but it is pretty neat. I see this having great value for teachers of struggling readers. It is a search engine type site. When you enter a search term, it brings back information on the topic, which it then presents to you. It reads aloud the text that scrolls up, and brings in images and other links. Share this with your colleagues. The best way to explain it to you is to get you to go there and try it out.

Wolfram Alpha – It was interesting for me that both presenters shared Wolfram Alpha, even though neither one was a math teacher. Readers of this blog probably don’t need a description of this one.

In my next post, I’ll look at the other tools that Tammy shared.

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I’ve been thinking a lot lately about experts. More and more, I find myself quoting experts in my sessions. As a teacher, it used to really annoy me when speakers came to us quoting experts. It seemed that the opening line from any speaker we brought in always went something like, “I have been out of the classroom for 15 years, so it’s great to be back in a school. In his book, Change Leader: Learning to Do What Matters Most, Michael Fullan says…”

Three things would come to mind immediately, and I’d begin to lose respect for that presenter.

  1. You’ve been out of the classroom for 15 years, and you’re going to tell me how to teach today?
  2. If you think it’s so great to be back in a school, why don’t you get a job in one?
  3. You’re going to quote somebody else?  Don’t you have any of your own ideas?
Inevitably, I would begin to doubt everything the speaker said. I find myself in a funny position now, after two years in this consulting job. Am I becoming that speaker?

I started thinking about what kind of experts I cite in my sessions. I broke them into three categories.

  1. Me.
  2. Current classroom teachers.
  3. Educators without classrooms.

I wonder which type of expert is preferable to the people who come to my sessions. As I see it, there are benefits and drawbacks to each type of expert.

Me As the Expert

Plus: People like to hear about things that I developed and have tried in my own classroom. I speak about these things passionately, and I can attest to the fact that they work.
Minus: I’m only one guy – and not a particularly creative one. I’m limited in the number of original ideas I have. The longer I stay out of a classroom, the farther removed these things become.

Current Classroom Teachers as the Experts

Plus: They are blogging and tweeting about the things they are doing right now. They reflect on what worked, or why they failed.  It doesn’t get more current.
Minus: Some people in sessions want to hear from experts. We are in a bit of a strange profession, in that not all of us consider out colleagues experts.

Educators Without Classrooms as the Experts

Plus: Most of these people have organizations that support them in their research. Their stuff is polished, thorough, and well marketed.
Minus: It takes a long time to publish a book, so sometimes it’s out of date before it hits the shelves. Some people question researchers who haven’t been in a classroom for a long time.

Imagine yourself in one of my sessions on assessment.  Which of the following three statements is most likely to engage you and motivate you to explore changes to your assessment practices?

  1. When I taught, students were allowed multiple chances to show me they had learned the material.
  2. Shawn Cornally, who teaches in Iowa, uses a system called Standards Based Grading to ensure that he provides an accurate assessment of student mastery of the material.
  3. In his book, Formative Assessment and Standards Based Grading, Robert Marzano presents an assessment system that is supported by his research.
Imagine yourself in one of my sessions on the revised program of studies in math.  Which of the following statements from me would engage you most in an activity?
  1. I’m going to model a problem solving approach that I used when I was in the classroom.  I used this one with my Math 30 Pure classes, and they loved it.
  2. Kate Nowak just shared this lesson with us on her blog.  She used it last week in an Algebra II class, and it went over very well. This activity fits our Math 20-1 curriculum. I’d like you to try it.
  3. In her book, More Good Questions: Great Ways to Differentiate Secondary Mathematics, Marian Small explains the idea of open and parallel tasks.  I’d like to try this open task.

If you’re sitting in one of my sessions, who do you want to hear from?

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Note:  This post is part 5 of 7.  Click here for part: 1 2 3 4 6 7

Recently, I was asked to model learning through problem solving in a school.  I will post about that experience in part 6, but I thought I should provide the teachers there with an outline of a learning through problem solving process prior to my visit to their school.  With credit to Dan Meyer, who gave me many of these ideas, this is what I gave them. What follows is a step-by-step description of the process I use.

Learning Through Problem Solving Process

1. Present the problem.

  • The problem is best presented using a multimedia artifact like an article, video, picture, story, song or any other multimedia artifact.
  • It is best if the question the teacher wants the students to explore is not explicitly stated in the artifact.

2. Have students come up with the question they want to answer.

  • Ask students what perplexes them in the artifact.  What questions do they have?  What do they wonder about?
  • Let this discussion go on long enough for them to come up with the question that you want them to answer.  This is the hook.  They feel like the question came from them, rather than their teacher.

3. Ask them to intuitively answer the question by providing a guess, a lowest reasonable answer, and a highest reasonable answer.

  • This is one of the most important steps, and is easily overlooked.
  • Ask students to make a guess.  No mathematics allowed.  They can use only their intuition.  Allow them to discuss and debate what they think is a reasonable answer.
  • By the end of this discussion, the teacher should have recorded on the board a range of reasonable answers.
  • Students could be asked to attach their names to guesses within that range of reasonable answers. I like to have them put their name somewhere on a continuum between the two answers.
  • This process makes it safe for students to be wrong, and allows them to recognize wrong answers later on if the answer they come up with doesn’t fit in the range.

4. Provide them with clarification and any information they think they require in advance of beginning to work on the problem.

  • Ask the students if they need any clarification on the question before they get to work.
  • Ask them what further information they require (if applicable)

5. Students work on the problem.

  • The teacher’s role here is to circulate and make sure that the groups (or pairs, or individuals) are on task.
  • Some groups will require help to get started.  Don’t let them opt out.
  • Some groups will finish quickly and ask if they are right.  If they are wrong, ask them a question to steer them in the right direction.  If they have the right answer, don’t tell them because as soon as they know they are right, their thinking will stop. Instead, give them an extension.  Extensions are challenging to create.  They can’t be the same question with different numbers, because that’s just more of the same work.  Instead, extensions must truly extend the student’s thinking.

6. Share student solutions.

  • The amount of time required to finish will vary based on the problem.  Some will take only a few minutes, and others might take a whole period.
  • Do not interrupt the group until they have all gotten an answer. Nothing is more frustrating than being truly engaged in a problem, and having your thinking stopped.
  • The teacher should not give the solution or the answer.  Have students present their solutions in one of the following ways:
  • Use a document camera for students to share with the entire class. (stressful for some)
  • Have groups share with another group. (safer)
  •  Some teachers have students working on boards around the classroom.  In this situation, the class can sit down and look at all the solutions simultaneously.

7. Teacher summarizes the learning.

  • The teacher should spend a few minutes summarizing what mathematics was learned.
  • This is not time for the teacher to show his own method of solving the problem.  It is simply time to consolidate the learning.

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LTPS Is Not…

Note: This post is part 2 of 7.  Click here for part: 1 3 4 5 6 7

In the last post, I attempted to define what I believe learning through problem solving is.  This brief post will explain what it is not.

Word problems assigned at the end of a lesson are not learning through problem solving.

I was going to stop there, but I’ll elaborate. The word problems given at the end of the exercise section in textbooks are just further practice.  I am not criticizing textbook publishers.  They spend a great deal of time and money writing decent contextual problems (and the occasional blatant and painful Pseudocontext).  What they do wrong, however, is place them at the end of a lesson and after a bunch of rote practice questions.  Many of the well thought out problems they create would be much better used if they were placed first in the lesson.  By giving them first in a lesson, we can let the students struggle with them for a while, and see what they learn. At best, it’s a compelling hook for the lesson.  At worst, it shows the students that they need you to teach them something. Either way, it’s better than having them assigned at the end of the lesson.

The learning through problem solving process can include word problems if used properly. But word problems are not the only way we should be presenting problems to our students.  We must also let them come up with their own problems after hearing stories, reading articles, watching a video, looking at a picture, listening to a song, and wherever else we see math around us. Sometimes it can be as simple as asking a straight forward math question, but doing it before you teach them how to do it.

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Speeding Teenager Answer

A possible solution to the teenager problem.

1980 feet in 30 seconds happens to work out to precisely 45 miles an hour.  Some kids may stop there and say he wasn’t speeding.  Ask them if it’s reasonable to assume that the red light turned green the second the first ping went out, and that Shaun was instantly traveling at 45 mph from that moment on.

Then they can explore further.

According to Car Specifications Directory, a 2000 Toyota Celica GT-S takes 10.6 seconds to go from 0 to 60 mph. My math is going to get weak here, but let’s assume it then takes about 8 seconds to go from 0 to 45 mph, and that Shaun’s acceleration was constant.  He would travel 264 feet in that 8 seconds, leaving 1716 feet to travel in the next 22 seconds. That would require an average speed of just over 53 mph.  Since we know he was going 45 mph at the end of 30 seconds, there will also be a period of deceleration.  Since it’s a big assumption that he started moving the instant that first ping went out, it is probably safe to conclude that he was speeding at some point in that 30 second interval. Exactly what top speed he may have reached is a calculation that is beyond me.

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My Edublog Nominations

I’m excited to do this for the first time.  I’m new to the blogging world, so things like “Best New Blog” don’t mean much to me, because they are all new to me.  I also have to admit that I don’t think I understand the difference between “Best Individual Blog” and “Best Teacher Blog”, which is fortunate, because I could fit two of the best into my nominations based on their rules.  Here are my 2010 Edublog Nominations.

Best individual blog

Dan Meyer’s dy/dan has been a great source of ideas for me as I learn to support teachers in my role as a High School Math Consultant.  His ideas around student engagement and problem solving are timely and relevant to my current work.

Best individual tweeter

@k8nowak Kate has a large network, throws out good questions and challenges, and posts tweets that prompt discussion and learning.

Best resource sharing blog

Sam Shah’s Continuous Everywhere but Differentiable Nowhere is a wonderful source of teaching ideas.  His compilation of favorite blog posts, his collection of classroom ideas, and his brutally honest reflection on his own practice are valuable sources of ideas for math teachers.

Best teacher blog

Shawn Cornally’s Think Thank Thunk has provided so much detailed explanation around Standards Based Grading that it must be considered here.  His work has prompted a large network of teachers to incorporate SBG into their practice this year.  On sheer influence alone, this is one of the most important education blogs out there. This guy is a superstar on the rise.

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