It turns out I wasn’t done. There is one more thing I need to look at regarding the PISA results in Alberta, because now our curriculum is being blamed by some Alberta parents and Manitoba mathematicians.

First of all, it needs to be pointed out that the students in Alberta who wrote PISA in 2012 came all the way through elementary school on the old math curriculum. Their curriculum included all the “back to the basics” stuff that some parents and some mathematicians want us to emphasize. The Alberta students who wrote PISA in 2012 had timed multiplication facts on their grade 3 PAT. If their PISA results are because of poor foundational skills, those skills were learned (or not learned) under our old program of studies.

Note: I used this implementation table, and counted back to grade 1 for students who were 15 in 2012.

Based on that same table, the 2021 writing of PISA will be the first time that Alberta students who have been on the revised curriculum since kindergarten will be assessed internationally.

I just don’t think that the curriculum is a problem. I don’t believe that if we reverted to curricula from the 1980’s that all students would suddenly thrive in math. Alberta classrooms are evolving, complicated environments. Since the beginning of my time in education (1975 – Joseph Welsh Elementary School), I have seen that many students struggle with math in grade school. I have seen many students who did well in grade school math struggle with University math. These are not new phenomena.

Further, it is important that Alberta parents (and Manitoba mathematicians) realize that Alberta stepped out of the WNCP curriculum in a number of key places.

This document highlights some of the key changes Alberta made to the K-9 curriculum that make it different from the curriculum elsewhere in the WNCP. A couple that I’d like to highlight for the “back to the basics” movement are below.

- Alberta added this statement, which clearly indicates that recall of number facts (ie. ability to multiply without a calculator) is important. “Mastery of number facts is expected to be attained by students as they develop their number sense. This mastery allows for facility with more complex computations but should not be attained at the expense of an understanding of number.”
- In grade 5, Alberta changed the phrase, “determine answers for basic multiplication facts” to this phrase, which clearly indicates that recall must be efficient, “determine, with fluency, answers for basic multiplication facts.”

I spent some time on the Singapore Ministry of Education site. Singapore is being held up as a country that is doing a better job than us. This quote from their own curriculum says essentially the same thing that Alberta’s curriculum does in the bullets above. In fact, their entire curriculum is strikingly similar to ours.

The development of skill proficiencies in students is essential in the learning and application of mathematics. Although students should become competent in the various mathematical skills, over-emphasising procedural skills without understanding the underlying mathematical principles should be avoided.

In my high school world, Alberta significantly modified the -2 stream (Foundations of Mathematics elsewhere in the WNCP). In Alberta, this stream contains much more Algebra. The intent was to get wider acceptance for that stream to programs in University that do not require calculus. It seems to have worked.

The problem with blaming a curriculum is that it is an ideological debate that is hard to prove definitively one way or another. Compound that with the fact that curriculum implementation is a long, slow process, and reacting too quickly to one measure (PISA results) can lead to some rash decisions being made. We face way bigger challenges in educating Alberta’s future than how we teach division algorithms.

on December 20, 2013 at 5:09 pm |A. StokkeI am delighted to read that you like the Singapore curriculum. I guess we’re not so far apart after all. I happen to be very familiar with that curriculum and with the Singapore Primary Math series, which I have actually used with kids. In fact, several of my colleagues and I gave a presentation to the Ministry two years ago where we compared the Singapore curriculum with the WNCP curriculum (you can find that comparison on the WISE Math site). We have been advocating for a curriculum that looks like the Singapore curriculum. Perhaps you’d like to do the same. We could throw out the WNCP curriculum right now and adopt the Singapore curriculum. We could even put the Singapore Primary Math series on the recommended resource list in the WNCP provinces.

on December 20, 2013 at 5:52 pm |John ScammellI need to work on my writing skills, apparently. My thesis was that whatever curriculum we use doesn’t really matter. A supporting detail was that our curriculum is similar to Singapore’s, and lots of people seem to like their PISA results.

on December 20, 2013 at 8:57 pm |A. StokkeYes, I understood that. I think you have great writing skills. If the curriculum doesn’t matter and ours is indeed similar to Singapore’s, let’s adopt Singapore’s curriculum, word for word, with outcomes placed exactly where they are in the Singapore curriculum. I would support that wholeheartedly.

on December 20, 2013 at 11:48 pm |R. Craigen (co-founder of WISE Math)Hi John. As the “Manitoba mathematician” you cite perhaps I should elaborate a bit here (warning: mini-essay!), to clarify my intentions (I’ll start with a word of thanks for helping raise the profile of my piece, it is something that should be brought to the attention of your readers who don’t get the WFP). Perhaps I also need to work on my writing skills, because I thought I was quite clear that I regard the curriculum as only part of the story.

For brevity in that piece I refer to an amorphous complex of curriculum, classroom resources, methods, and ideology under the rubric of “fuzzy math” and speak in loose terms about a “consultant class” driving the change. Such terms are unavoidably imprecise. Limited to 750 words, there’s an awful lot of condensation needed to cover this ground, so everything you read is massively compressed. My words there can, and will, be misunderstood.

To be clear, curriculum is only a formal expression of part of the fuzzy math agenda, which involves educational ideology, some academic theories about how children learn, and political dogmas about what the objectives of teaching small children should be. It rolls up into one big snowball of “math education” that is imperfectly but concretely expressed in curricula, and perhaps a bit more explicitly in resources associated with these approaches. You could fix the absurdities in the curriculum today but if we still had an army of consultants pressuring teachers into fuzzy methodology and ideology in the classroom outcomes would not change by very much.

One needn’t regard that statement as mere conjecture. What I describe is, after all, precisely what happened in California a little more than a decade ago — they adopted what may have been the best-structured curriculum in North America, but the education schools and consultant class merely doubled down on the fuzzy agenda, pushing various forms of minimal-guidance instruction (“…not a sage on the stage — a guide by the side…”), assorted types of unstructured learning (“Rich tasks!”), disparaging any tools that involve practice for mastery (“Drill and kill! Drill and kill!”), eschewing individual work and paper-and-pencil skills, making these subordinate to social and verbal domain skills, preempting conventional methodology with “strategies”, using poorly scaffolded materials based on the idea that if students struggle to make sense of mathematics (as opposed to seeing further by standing on the shoulders of giants) then they will “understand” it so much better than if it is presented to them well-sequenced with proper precursors in place. Nevertheless some minor gains were seen in California results after the introduction of the improved placement of outcomes. it is an open question how much more of an improvement they would have seen had the consultant class not decided that it was worth making the classroom into an ideological battleground.

I am not saying that curriculum should not be fixed — I enthusiastically second Anna’s recommendation about adopting the placement of Singapore outcomes. However, those doing preservice and inservice training of teachers need to be weaned of trendy but unwise methodologies and get back to helping teachers structure a learning environment in which all children can succeed.

According to the timetable you reference (the same one I have used) the 2012 PISA cohort in alberta would have had 4 years of instruction under the “new” WNCP curriculum. As you and I appear to agree, the curriculum itself is not as significant an influence as associated classroom methodology that may be pressed upon teachers by the consultant class.

I cannot speak for Alberta but I can say that here in Manitoba we experienced something of a “full court press” in advance of adoption of the current WNCP as there was a determination amongst consultants to “bring teachers onside” — it was felt that they must be prepared to use appropriate “reform” methodology for a curriculum that was designed under this assumption, and that progress toward that end was not successful with the first WNCP curriculum in the 1990s. So this methodology was coming “online” prior to the official implementation deadline.

A second consideration is that full “system-wide implementation” generally happens after a couple of years of voluntary adoption. You can see this stated explicitly in the Manitoba timeline here:

http://www.edu.gov.mb.ca/k12/cur/math/timelines.html

Now, since Alberta is the lead province in setting WNCP math, it seems likely to me that there were pilot districts there even before Manitoba began implementation, and perhaps you know the specifics, but the timeline is not specific about this, and I make no such assumption here.

But what does seem clear is that full Alberta system-wide implementation lagged the other WNCP jurisdictions by perhaps a couple of years. (Yet note that even in Manitoba, full implementation to grade 10 was only beginning in 2009.) This is an important thing to note when reading provincial PISA data. For you see that in PISA and PCAP, the other WNCP provinces’s scores had already dropped dramatically by 2009 and 2010, though they were only in early stages of implementation by then, and the consultant class was only partway finished their reprogramming of teachers. At the time, Alberta’s score remained quite high. But three years later, we see Alberta’s sudden fall as they have reached a comparable level of system-wide implementation with the rest — overall since 2003 the second-largest decline in scores among Canadian provinces.

… and “the rest” … continue to fall from where they were in 2009. In my view, 4 years of fuzzy methodology in Alberta were enough to do measurable harm to student outcomes. If you like what you see so far, you’ll love what you get in 2015 when your PISA cohort will have had 7 years of it.

You seem unaware that ALL the WNCP provinces implement their own version, with variations, of the basic framework document. Manitoba also differed in numerous ways, retaining the underlying philosophy, like Alberta. Ours also spoke about the importance of “number facts”. The problem was that both the document and the training teachers were receiving made clear that what was meant was that students knew how to CALCULATE “with mental math” small number outcomes quickly. For example, a friend of mine had a son in a Grade 4 class in which a consultant was demonstrating how to teach the “new curriculum” for the teachers at their school. He asked the class to work out 8+6. The boy immediately put up his hand an said “14”. “Good” said the consultant ” — now tell us what was your strategy?” The boy said, “I just know the answer. We do number facts at home.” The consultant showed annoyance at this and made it clear that it was expected that he must be able to describe a STRATEGY to get there. When I discuss these things with our local consultants they tell me that merely ONE such strategy is insufficient — students must be able to articulate three different ways (I’m not sure why 3 is such a magical number here, but it seems the consensus in that group).

The problem with this approach is what I call “cluttering”. It is imperative that students are taught, in their early years, efficient mental habits that maximize their capacity as they go further into more complex and demanding tasks later in their education. If working memory is cluttered with procedures in places where automatic recall ought to happen, students will be too encumbered to easily learn advanced tasks. I see this every day in my classes now that the WNCP kids are amongst us. One class went into panic when I told them (no calculators allowed, as in most university courses!) that I expected numerical answers of 3 digits or less to be fully resolved on the exam. A few years ago this would have been a nonissue for most of them. I have had to tutor some of my students in long division. Some tell me they have NEVER seen this algorithm, which is critical for the understanding of many key concepts as one proceeds into the math required in many professions. It is worse in some college classes, which admit students taking the “consumer” pathway in grade 12. A friend teaches accounting at a local college and he was shocked at the sudden drop in arithmetic skills the year the “full” WNCP cohort showed up. He polled one class and found 50% of the students had never seen long division and had no idea how to handle division of more than 2 digit numbers or anything with a decimal. We have several courses here that enroll over 1000 students per term (such courses are required by most professional programs). One of them just saw a drop in average performance by about 20%. I believe that training teaching students to “clutter up” their thinking, as is visible throughout the WNCP K-8 curriculum, inculcates inefficient mental habits that may be the most significant factor contributing to these sudden deficiencies.

When the new wording was brought in to the Manitoba curriculum we insisted that it be clear that “recall of math facts” — meaning the results of +, -, X when applied to single-digit numbers, must be made AUTOMATIC, and that the term “automatic” necessarily means that students arrive at the answer immediately without intermediate steps. Consider, for example, the paper of Ansari et al here on the educational consequences of the two types of “recall of math facts”:

http://communications.uwo.ca/media/singledigitmath/

I would be happy to hear that the Alberta curriculum makes this distinction. But I doubt it.

You find Singapore’s curriculum “strikingly similar” to Alberta’s. Hmm. Let’s see … they’re both in English. They both talk about math education. They’re both written on paper and available in PDF form online. I suppose those qualify as similarities. But you cite only the inconsequential preamble, which uniformly in curricula I’ve seen is amorphous fine-sounding mush into which you can read almost anything you like. Look at the grade-level outcomes. Look at the pedagogical directives throughout the Alberta curriculum. The preamble is not the “curriculum”. The subject matter to be covered … what is to happen in the classroom … is. You’re comparing the wrong things.

One more thing: You may know that PISA is designed with “process standards” in mind. It is ideologically matched to the philosophy of WNCP math and what the consultants are pushing with it, examining markers for the kind of learning this approach claims to emphasize. This is what I call “testing to the teach”. You would expect students learning under WNCP and similar systems should have an advantage and do better than those learning conventional math, as in most of Asia. But they don’t. This will surprise nobody who is familiar with the results of the largest educational study in history, Project Follow Through, from the 1970s. You may know of the TIMSS assessment, which tests both process outcomes and conventional “basics” skills, parsing them rather neatly with rather clever methods. Alberta also participates in TIMSS, and the results therein are even more revealing.

Surely you are aware that fluency with division and fractions is the current best known predictors, at grade 8 level, for later success in mathematics. With that in mind, check out this graphic I constructed for a piece I recently was asked to write for the Globe & Mail:

http://www.theglobeandmail.com/incoming/article15763259.ece/BINARY/PDF%3A+How+Canadian+students+fared+on+two+problems%3F+Not+much+better+than+guessing

Note that Alberta results are barely distinguishable from random guessing on the fraction “basic skill” question, and (insignificantly) worse than random guessing on the pure test of “understanding” concerning multiplication of non-integer positive numbers. The latter is precisely what the framers of the WNCP curriculum pretend to emphasize. But whenever procedural skill is de-emphasized, purportedly in favour of “understanding”, both skills outcomes and understanding are harmed. The framers, apparently, were unfamiliar with the lesson of Project Follow Through.

on December 21, 2013 at 8:37 am |John Scammell“those doing preservice and inservice training of teachers need to be weaned of trendy but unwise methodologies and get back to helping teachers structure a learning environment in which all children can succeed.”

This is what really bothers me about our correspondences, Robert. I have a 3000 word condescending email from you in which you go on and on about the merits of your personal mathematical abilities. I get that you are better at math than me. It’s what you do. Being good at math and knowing how to get ALL children to succeed in math are two different things. Have you considered that what worked for you in grade school might have worked because you were so smart? Did it work for every single kid in your grade school classes?

I wish you’d be willing to consider that I might actually be good at what I do. I teach hungry kids. I teach angry kids. I teach kids who speak no English. I teach kids who show up twice a week. I teach kids with learning disabilities. I teach kids who are afraid to go home. I teach kids who have never set foot in a school with walls before. I teach kids who genuinely struggle with math. I teach kids who genuinely excel at math.

You teach a small subset of the kids I teach (the best, brightest, and fed) and by your own admission, only about 50% of the best, brightest and fed get through your class. I know you think it’s our fault (lack of basics, and all), but you also tell me that the 50% pass rate in University Calculus has been around for two decades. It’s not a new thing with a new curriculum.

Which one of us truly has more experience dealing with ALL children?

In Alberta, we have mathematicians who collaborate with mathematics educators. We have an environment of mutual respect. It’s a nice place to be.

on December 21, 2013 at 10:18 amA. StokkeHi John,

Please don’t be offended by the 3000 words. I have many email messages from Rob and they are usually that long. This is his writing style and he is simply trying to be informative.

I want to address part of your comment:

“I teach hungry kids. I teach angry kids. I teach kids who speak no English. I teach kids who show up twice a week. I teach kids with learning disabilities. I teach kids who are afraid to go home. I teach kids who have never set foot in a school with walls before. I teach kids who genuinely struggle with math. I teach kids who genuinely excel at math.”

I agree that you deal with a wider range of abilities than we do at the university level. However, does discovery-based learning and the multiple strategy approach really work best for most learners? That’s where I have to disagree. You have more experience with kids than I do, but my husband and I do run a weekly after-school program for 107 kids (as volunteers). We also ran a math camp in inner-city Winnipeg last summer. In my experience, these approaches hurt the struggling kids the most. They find the multiple strategy approach very confusing and they quickly become demoralized because they’re not sure what to do since there are so many strategies being taught.

Also, I want to tell you that I became an advocate precisely because of those kids “who speak no english, show up twice a week, have learning disabilities, are afraid to go home, etc”. I see that there is a problem with the way math is being taught and that too many kids are being left behind. I can and do teach my own kids myself. I could afford tutoring or private school, etc. if I wanted to go that route for my kids. I could just sit back and watch this happen and look out for my own kids. In fact, I believe this is precisely what is happening: those parents who can afford it or have the academic abilities to do so are self-insuring while those who do not have those opportunities are being left to fend for themselves. Ineffective math instruction in schools simply widens the gap.

In any case, I am sorry that we have offended you. I want to wish you a happy and relaxing holiday with your family.

Anna

on December 21, 2013 at 9:46 amR. Craigen (co-founder of WISE Math)Hi John. The 3000 words was to provide you with a more complete version of my positions to work with. I am discursive, and I like to finish my thoughts. Space-restrictive p-eds are good places for neither of these.

“…in which you go on about the merits of your personal mathematical abilities”? I had to re-read my comment in case I missed something. What the are you talking about? Which “admission” in my comment had to do with the proportion of students who “get through” my class or the pass rate in university calculus? I realise 3000 words is a pretty big swallow but … did you even skim my comment? If you must construct straw men … at least be a bit subtle.

With regard to your last comment, When I requested, from the provincial team leader Christine Henzel in 2011 that she provide me with contact information for any mathematicians who — like me in Manitoba — had been involved in cooperating with the ministry on the provincial curriculum steering committee that implemented WNCP Math or in the earlier design of it, she provided me ONLY with the names of Math Education professors with no actual advanced background in math (i.e., no mathematicians). I’m not saying that no mathematicians were involved, but if you have some names to share with me, I’m all ears.

Yes, we math professors see only a minority of the students in your high school class. However, we see — and teach — close to 100% of those among them who are headed into professions other than teaching, most of which require Calculus I or Linear Algebra I.

on December 21, 2013 at 6:23 am |mrdardyA. Stokke – It seems that you have a predetermined answer to this question and that you are not actually ‘listening’ to John here at all.

on December 21, 2013 at 8:13 am |A. StokkeJohn seems to like the Singapore curriculum and so do I. In fact, it is claimed that the Singapore curriculum is “strikingly similar to ours”. If this is indeed true, why don’t we simply adopt the Singapore curriculum? I agree with the quote taken from the Singapore curriculum above. However, there is much more to the Singapore curriculum and I propose that we adopt it in its entirety. It seems that that would please us both.

on December 21, 2013 at 10:28 amJohn ScammellAnnaAnna, you’re growing on me. Next time you’re in town, I’d love to have a coffee and chat math education. We are all in this together. We all love math. We all love kids.

on December 21, 2013 at 10:23 am |John ScammellRobertRobert, re-read my reply. The 3000 words refers to an email you sent me two years ago (almost to the day). It seems we do this every two years around about Christmas time. Maybe we should add each other to our Christmas card mailing list. Trust me. I read all 3000 words carefully. You pointed out your work in combinatorics and your Kirkman medal, and addressed first-year calculus failure rates.

Your post here was1964 words, all of which I read carefully.

I will not provide names of the mathematicians I correspond with, or the ones I know were involved in the writing of our curriculum. Two such folks helped me run a session for secondary math teachers earlier this year. I had lunch with a lovely fellow last week. We talked math, solved problems, and shared iPhone apps. He showed me this one. It’s a lot of fun: https://itunes.apple.com/en/app/akinator-the-genie/id484090401?mt=8

I can’t have you jeopardizing my relationships with these fine people. Some of them are among the 6 people who read my blog. Maybe they’ll engage you on their own.

on December 21, 2013 at 11:05 am |R. Craigen (co-founder of WISE Math)It was not clear that “email” referred to earlier correspondence. It seemed to me that you were (and in this forum ought to be) addressing my comments in this thread. I vaguely remember our earlier correspondence, which covered a lot of territory. Oddly, you don’t seem particularly eager to deal with the subject at hand, and … you know … words of mine your other readers here can actually read.

I have no interest in “jeopardizing” your relationship to the fine mathematicians you work with. I am, in fact, the public schools liaison person in my department. I am the director of the Manitoba provincial mathematical competition. I am an executive member of the Manitoba Association of Mathematics Teachers. I attend local teachers conferences. I visit high schools to do enrichment with their students and speak with their teachers. In the past couple of years I have participated in, and spoken at, several meetings sponsored by the Ministry of Education for our provincial public school “math leaders”. For years I was director of our provincial problem solving workshop, which would draw upwards of 100 students from schools across the province. Since my WFP article the other day I have received numerous supportive emails from local teachers, and a few phone calls from teachers and principals, none at all disparaging, and most thanking us for the changes we have helped bring into our curriculum this year. I am all about engagement between mathematicians and math teachers in the public schools. I wonder what it is you imagine I would do that might jeopardize your relationship to your mathematician friends?

However, I also have repeated experiences with those in the educational establishment (my correspondense with Ms. Henzel being only one instance) in which they claim having had engagement with “mathematicians” but when pressed for details the best they can produce (if anything) is the names of folks in education faculties, with no mathematical credentials to speak of.

I am aware, by the way, of a few Alberta mathematicians who are involved in such ways the public schools, at least one of whom I consider a very good colleague, and I often correspond with him. But I am interested not in whom I can identify as active, but rather those mathematicians whom educators adduce to validate fuzzy policy in math education. Tracking down these elusive phantoms is a bit of a sasquatch hunt for me, and thus far I’ve been unsuccessful.

on December 21, 2013 at 10:33 am |John ScammellAnnaThis is something I’d be really interested in hearing about if you take me up on an offer of coffee. I’ve seen the opposite and I’d love to share war stories. In my experience, the strong students are less willing to muck around with the math, and just want to be told how to do it. They’re good at that model.

It seems to be the weaker students who like to explore and play and learn that way. Now, I have never once suggested we leave them hanging without algorithms. All I want is for them to have the chance to explore a little first, and let the algorithm come second.

At any rate, if I don’t get off this blog and into family Christmas, I risk divorce.

on December 21, 2013 at 10:53 am |A. StokkeHi John,

I would be happy to meet with you for coffee and talk about this. I work with a professor at U of A and may be visiting Edmonton at some point next term. I would also recommend that you watch the Ansari video that Rob links to in his first message.

Anna

on December 28, 2013 at 1:58 am |Running Away Isn’t Always Wrong | SoshiTech[…] Curriculum and PISA (thescamdog.wordpress.com) […]