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Book List

I haven’t read this book, but I intend to, based solely on the quote below. I’m intrigued.

There are some kids growing up with way too much adversity in their lives and what they need more than anything is protection from that adversity. And then we have other kids, especially kids who grow up in affluence, who just don’t have enough adversity in their lives. I think that is a hard message for parents to hear… In trying to protect them from adversity, we can sometimes be doing more harm than good.

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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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Common Ground with WISE

My post yesterday has generated much discussion. I’m trying hard to understand where WISE is coming from, so I sought out more information. One of the people behind WISE is Dr. Robert Craigen.

Dr. Craigen appeared on QR77 with Rob Breakenridge this week to talk about their movement. The full conversation between Breakenridge and Craigen can be found here. It’s about 16 minutes long, so let me summarize some of what I heard.

First of all, I should say that Rob Breakenridge impressed me. He seemed aware of what the revised program of studies is about, and he asked good questions to facilitate the conversation without making apparent any of his own biases. It was a good interview.

Secondly, Dr. Craigen did a good job explaining the WISE position. In fact, he presented his position in a much better way than it is presented on their website. I disagree with much of what is written on their site, but if Dr. Craigen truly believes what he said on the radio, then we have some common ground.

Dr. Craigen states that it is important for young kids to have algorithms to perform calculation because those algorithms will help them in later courses. I agree. I suspect we disagree on how these algorithms should be developed. I suspect Dr. Craigen wants teachers to show the students the algorithm that he thinks is best. I want teachers to help students develop their own (correct) algorithms so that the students understand the algorithms better. Students who can’t develop their own (correct) algorithms need to be steered to one. We are not leaving kids completely on their own. I have never suggested to teachers that we send kids home with no algorithms at all.

Dr. Craigen states that there is a false dichotomy between skills and understanding. He says that both skills and understanding are important. I agree with this statement. The struggle we face, though, is that when we teach in a more traditional way, for most of our students, all we get at are the skills. Dr. Craigen states that some students get the understanding in spite of this method. For years, I taught kids to factor polynomials. They could do it, and I could prove it because they could do it on tests. I’m not as confident they understood factoring. The revised curriculum and its more constructivist approach helps get at this understanding. I believe that kids can demonstrate math skills without understanding. I don’t think the converse is true. I don’t think they can demonstrate understanding without the skills. I agree that both are important, and we need to teach so that both happen.

I have less common ground with Dr. Craigen’s beliefs about automatization. He states that repetition and exercises are important so that students no longer need to think about the math. He wants students to be able to do the basic calculations and practice them so they become automatic. I would argue that too much automatization leads to imitation without understanding, particularly in the higher grades. If students can be made to truly understand their division algorithm, they don’t need to practice it 100 times. Some practice is important. Excessive practice is not worth it. The problem we face with asking kids to practice in K-12 education, that Dr. Craigen may not experience in his setting, is that students who would really benefit from practice don’t do it. Students who don’t need the practice faithfully do every single exercise we assign.

I love Dr. Craigen’s observation that in the old curriculum, there was a great deal of teaching without understanding going on. This comment is certainly true. Even with this new curriculum, it is still true in a lot of places. It’s true in nearly every University mathematics course I took. It isn’t a new problem. I fail to see how going back to more of that kind of teaching, as Dr. Craigen advocates, will alleviate this problem.

Dr. Craigen and I both want our students to come out with all the skills, understanding, and problem solving abilities that will benefit them in future studies and in life. He admits that a discovery and exploratory approach is good, and should be maintained, but this approach should be balanced with some direct instruction. I agree with this statement entirely. I see a typical math lesson following a patter that goes like: Exploratory activity, students share what they learned, teacher fills in gaps, students practice what they learned. I’m starting to wonder if teachers are leaving out the important third step. Are they sending students home without filling in the gaps? Are they sending students home with no understanding or skills? If so, then they have misinterpreted the intent and philosophy of the revised curriculum.

What Dr. Craigen doesn’t address is a passion and love for mathematics. I have it. He has it. The students he teaches mostly have it. The students I teach mostly don’t have it. A discovery and problem solving approach can show these kids that mathematics can be interesting, relevant, and fun.

A stand and deliver approach whereby proofs and algorithms are explicitly presented works well for him, me, and about half of the students he teaches. It works for far fewer of the students I teach. I’m not convinced that from his world of academia, Dr. Craigen understands my world. The bottom line is that in my world, I need to be a better teacher than the one he suggests I should be.

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Improving Math Education

Yesterday I came across these guys. The Western Initiative for Strengthening Education in Math (WISE) is a movement organized by some University Mathematics Professors. On their front page, they state:

We began this initiative because we are experts in mathematics and we care deeply about the education of Canadian children. Children who do not receive the strong education in math that they deserve may ultimately be excluded from many careers in trades, technology, science, engineering, business, and economics, to name a few. Our ultimate goal is to ensure that all children have the opportunity to achieve their potential in math so that they may enjoy lives free of innumeracy, may experience the beauty in math, and so that they may have a wide range of career opportunities.

It seems like a noble goal. Digging deeper into their site, I discovered that they believe the following things will improve mathematics instruction in Western Canada.

  • Only “math specialists” should be permitted to teach math, at all levels from K-12.
  • Math curriculum should be written by “professional mathematicians.” They should decide on both content and pedagogy. Only those who use and teach math at such a high level are qualified to make decisions about math curriculum.
  • Standard algorithms must be taught.
  • Students must be given lots of practice.
  • Calculator use should be minimized.
  • “Mathematicians” should review all resources including texts, teacher guides, and all other tools.

Their site asks people to sign a petition to lobby governments to make sure these things are addressed. Many parents have responded indicating support for this initiative, mostly because their kids can’t make change. Regular readers of this blog (both of you) will probably know where I stand on this one. For any new readers who happen across this post, let me tell you how angry this made me.

The sheer pompousness of this group of mathematicians, who seem to think that everybody should learn mathematics the way that worked for them, astounds me. I guarantee that this group of professors has absolutely no idea how to deal with a range of struggling learners. Their classes are full of only the best math students, and those who love math. They deal with students who had over 80% in high school math, and yet I suspect they still can’t (or won’t) differentiate adequately to help students who struggle in University math. Despite their ignorance of what math looks like in the trenches, they assume that their methods would work for all the diverse learners we have in K-12. Rigour is the answer. Algorithms are the answer. Real mathematicians in front of kids is the answer. Give me a break. Not one of them would last more than a week in a K-12 math classroom. And even if they did survive, only the best and brightest students would have learned anything. The rest would have been shuffled out to a shop class.

Despite my anger, I wrote a comment that respectfully disagreed with them, and tried to post it on their blog. They claim to encourage debate on this issue. My comment was rejected, so I’ll share it here. I’d love to hear from some Math Education Professors. They must deal with this kind of thing from their colleagues in the Math department. How do they handle it?

My comment to the folks behind WISE (?):

You guys are attributing an old phenomena to a new curriculum. It’s misguided and actually ironic in a lot of ways.

  1. Parents who hated math in school are supporting this movement and effectively asking us to teach their kids in the same manner that didn’t work for them.
  2. This site was set up by some University Math professors. Twenty years ago, when I took first year calculus, it was these same people who told us on the first day to look left and right at the people beside us. They told us only 1 in 3 would pass. They expected a 66% failure rate. They wore that failure rate proudly, like a badge. This happened in a time when we had the kind of curriculum this site advocates. That kind of curriculum didn’t produce good thinkers who are successful in University math. It produced good imitators. Now those same professors want us to keep producing imitators rather than thinkers?
  3. University math professors were, in fact, involved in the writing of this new WNCP curriculum. The ones I talk to are excited about the prospect of getting University math students who are deeper thinkers. I encourage this site’s group of Math professors to talk to the ones who were involved in the writing of the new curriculum. Or do they think they know better than their own colleagues?
  4. Not one student has graduated from the new WNCP math curriculum yet. The first set of graduates come out next year. Any perceived deficiencies in students’ mathematical abilities right now is based on the outgoing curriculum, which was the kind of curriculum this site is advocating. You folks seem to want to go back to the very system you have suggested was broken.

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I’m in the Middle

I have recently had interactions with two people who are passionate about math education. A few weeks ago I exchanged emails with Michael Zwaagstra. I wrote a whole post about that interaction. Last week, I met Joe Bower in person for the first time. I’ve been thinking a great deal about my conversations with them. Both Michael and Joe have strong beliefs about the state of math education in Western Canada. They are, however, at completely opposite ends of the spectrum.

Michael argues in favor of traditional teaching methods, tougher standards, and more standardized testing. Joe is opposed to all things standard, and advocates for more constructivist teaching methods.

After reflection, I can only conclude that I am solidly in the middle on this one.

Standards

Joe made me feel badly for admitting that I like our curriculum. Michael made me feel badly for admitting that I like our curriculum. Joe thinks it is too rigid and full of external standards. Michael thinks it advocates too much constructivism, and not enough rote learning. I think what both of these people are forgetting is that the WNCP curriculum is written by teachers. It is not a top-down process led by government employees who have no connection to education. Teachers are involved in its creation at every step. It is a good curriculum. I shouldn’t have to apologize for thinking that.

Assessment

Joe made me feel badly for thinking it was OK to use exams to assess students. Michael made me feel badly for thinking it was OK to use more open tasks to assess students. I think any solid assessment program should include a mix and some student choice in terms of assessment types. To say testing is wrong or that performance based assessment is wrong is narrow-minded. To accurately assess our students against the curricular standards, we need a diverse set of assessments. I suspect that both people would argue that the standards are the problem, but Joe would say they are too rigid and Michael would say that they need more rigour.

Standardized Tests

I’ve been reflecting on how I feel about the provincial exams. I’m sure Joe would eliminate all of them, and Michael would introduce more of them. Once again, I find myself in the middle. Alberta students write province-wide exams in core subjects in Grades 3, 6, 9 and 12. I believe that these exams cause undue stress and fear to students in Grades 3 and 6. I suspect they do not necessarily assess what we think they do. I’m not sure how I feel about the grade 9 ones, but I believe that a grade 12 exit exam is not a bad thing. Perhaps 50% weighting is a bit excessive, but the notion of such an exam does not offend me.

Just like our curriculum is written by teachers, so too are our provincial exams. They are not written by a giant testing company in Toronto. They are the best exams that can be created, given our current parameters. I lament the loss of written response questions in a curriculum that emphasizes things like communication and deep understanding. I hope our government can find a way to get written response questions back on the exam. I don’t, however, believe we should scrap them at the grade 12 level.

Pedagogy

Joe argues in favor of a constructivist approach, and Michael argues in favor of direct instruction. Both are solid teaching practices, which is why they should both appear in any differentiated classroom. There is a time for each of them, and neither of them should be used all the time. As educators, we have a responsibility to meet student needs in a variety of ways and using a variety of practices.

Fence Sitting

All I can conclude is that I am right in the middle of the beliefs of these two people. Our system isn’t broken. If Alberta was a country, we’d rank right up there with the Finlands and Koreas of the world. We’re doing a pretty good job. To swing too far one way or the other would be foolish.

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Last week, a fellow named Michael Zwaagstra from Manitoba published an article for an organization called the “Frontier Center for Public Policy“.  I have no idea what the Frontier Center does, or what their agenda is. I suspect I wouldn’t like it.

Michael’s bio in the article lists him as an M.Ed. currently teaching Social Studies. He tells me he has experience teaching math. Michael has published a book called What’s Wrong With Our Schools And How We Can Fix Them. The chapters have titles like, “Tests are good for students” and “Direct instruction is good teaching”. His blog, which fortunately hasn’t been updated for more than a year calls for punitive grading, more tests, and eliminating technology.

With that brief background, guess what I thought of his article? Feel free to read it here and form your own opinion before looking at mine.

I honestly find the whole thing ridiculous. Any article that questions the work of John Van de Walle and Cathy Fosnot probably isn’t worth my time. There are so many things in the article I’d like to refute, but I’m just going to tackle his assertion that we are poorly preparing students for university.

It’s not entirely clear to me after reading the article whether Michael is aware that we are in the middle of implementing a revised curriculum. We have yet to see how students from this revised curriculum will perform when they reach university since it will be two more years until graduates of this curriculum get there. For the first three years after that, these students will only have had three years of the revised curriculum. It will take many more years before we can judge how students who had 13 years of the revised curriculum will adapt to university. Michael’s arguments about university preparedness, then, should be based on our outgoing curriculum rather than the new one. He neglects to clarify this in his report.

In the article, Michael states,

University professors who are responsible for instructing first-year students work on the front lines with high school graduates. There is a strong consensus among math professors that the math skills of these students are much weaker than they were two or three decades ago.

Michael cites two sources as evidence to back up this claim. They both interview some University professors. They are not exhaustive or extensive surveys. Plain and simple, they are anecdotal.

Since Michael’s evidence is anecdotal, I’d like to respond with three anecdotes.

I took first year Calculus in University two or three decades ago. On day 1, the professor asked us to look at the person on our left, then at the person on our right. He then told us that only one of those people would pass the course. He was basically telling us, up front, that he expected a huge failure rate. I can honestly say he underestimated the failure rate. He lost more than two-thirds of the class. It wasn’t a problem with basic skills of my classmates. The guy couldn’t teach. Moral of anecdote #1: High school graduates having trouble with University Calculus is not a new phenomenon.

At another point in his article, Michael mentions  that,

First-year post-secondary students are increasingly unprepared for university-level mathematics, and this has led to a proliferation os remedial math courses at universities across Canada.

No evidence is cited for this claim, but I suspect it is true because I know it began happening at least eight years ago, as this anecdote will show. Eight years ago, I had a math professor from the University of Alberta come to talk to my AP Calculus class. He was an award-winning professor, who cared deeply about his students’ success. I found myself wishing he had taught me first year Calculus when I went to U of A. He was there to talk about a program they were setting up to support students in first year university. Their goal was to improve the completion rates of students in first year Calculus. They wanted to do away with the ridiculous failure rates that I discussed above. Moral of anecdote #2: Universities were offering supports and remedial courses long before this revised program of studies even began, and certainly well before it hit high school.

When I first saw the revised program of studies about five years ago, my first reaction was concern over material being removed, so that we’d have more time to cover topics in greater depth. I was worried that students wouldn’t be as prepared for first year calculus if we took material out of the curriculum. I found myself having a conversation with another professor from the University of Alberta. This fellow had been involved with Alberta Education and the WNCP in the writing of the revised program of studies. I asked him if he was concerned that students would arrive at university knowing less material than they currently knew. His reply was that he felt exactly the opposite. He was excited about getting students who knew how to problem solve, explore, and think mathematically. He said that the material wouldn’t be a problem for students who thought like that.  Moral of anecdote #3: University math professors want students who think deeper about math.

My biggest fear in reading Michael’s report is that some teachers may try to use it as an excuse to ignore the front matter of our revised program of studies. I think it is irresponsible of an educator in the WNCP to suggest that we should teach math differently than our curriculum tells us. I fear that this article could set us back in the good work we have been doing in implementing a curriculum that allows students to get deeper understanding through meaningful exploration.

I’ve lectured in class. I’ve let kids construct their own meaning in class. The kids who I let construct their own meaning knew the material cold and retained it longer. That’s all the evidence I need.

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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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