I’ve been blogging about my experience at the Alberta Mathematics Dialogue last week, in which a group of university mathematics professors offered a critique of the K-12 math program in Alberta. My colleague, Pat, attended as well. Pat has more than 30 years experience as a teacher and consultant in Alberta. She has a BSc (math major), BEd and MEd. As a high school teacher, I can’t pretend to know a whole lot about how young children learn mathematics. Pat, however, is truly an expert in this area. I asked her if she would be willing to share a few words here, and she agreed. What follows are her words.

I’ve been an elementary teacher since 1979. It’s a designation I’ve always been proud of, even though it seems the complexity of the work is poorly understood and not always respected. For most of the past 4 years I’ve been out of my classroom, supporting Alberta teachers in the areas of mathematics and assessment. I attended the 2014 Alberta Mathematics Dialogue in Camrose on May 1.

In addition to attending the presentations examining the Alberta K-12 mathematics curriculum, I was able to join a round-table discussion at the end of the day. The presenters from the earlier sessions were there, along with other interested participants. The discussion focused again on the math curriculum – past, present and future – and its impact on mathematics learning in Alberta classrooms.

There was overwhelming agreement among the post-secondary faculty in attendance that the math skills of their students have significantly declined over past 10 or more years. This is not an area I have expertise in, but I’m willing to work under the assumption that they know what they’re talking about, and are not guilty of looking to the past with rose coloured glasses. However, almost no one in the room seemed prepared to question the causes of this perceived decline. It seemed accepted as a truth that changes to the Alberta curriculum caused the problem, and that reversing those changes would fix it.

Alberta teachers (as well as teachers in many jurisdictions around the world) have been asked to teach math through more of an inquiry approach – teaching math *through* problem-solving rather than *for* problem-solving, if you will. Teachers present problems for students to explore, and then help them use this exploration to develop an understanding of math concepts and strategies they need to move their learning forward. Personal strategies for operations are part of the equation, and a mastery of basic facts is still critical. (Even as I try to explain this in a nutshell, I sense the eye-rolling of the masses of critics who see this approach as so much hogwash. Please accept for a moment that I have some serious experience to back up my opinions.)

In my classes I have mathematically talented students who need to be challenged, as well as students whose past experiences have made them fragile, uncooperative, discouraged and hard to motivate. I need to find a way to interest all my students, sometimes almost against their will, in the problems I’m asking them to explore so they can begin to grapple with the ideas that might be useful to solve them. Once students have worked to solve a problem, sometimes unsuccessfully, they are far more likely to be interested in thinking about an approach (mine or another student’s) that might do the trick. I try to give them a need for the math I want them to learn. A hard lesson I’ve learned after many years of teaching math to elementary students: as much as I’d like to, I can’t do the understanding for my students. All I can do is my best to engage them in thinking about what I need them to think about. I have to rely on them to do the hard work of making sense of it.

It is unbelievably complex work, but an inquiry approach in my math classroom helped me and my diverse students function as a mathematics community. Without a doubt, I was a better and more successful math teacher using the current math curriculum, as well as the one before it, than I was using the 1975 mathematics curriculum (which, according to Anna Stokke of the University of Manitoba, was the last excellent math curriculum in Alberta). My students thrived under an inquiry approach.

I’m pretty sure I don’t need to lecture the mathematicians in the crowd about the difference between “correlation” and “cause and effect.” The perceived decline in math abilities is correlated with an enormous number of changes and challenges that have impacted students and teachers in Alberta schools in the past years, and the curriculum is just one of them. I find it fascinating and disturbing that critics, particularly in the media, seem so unwilling to consider the possibility that the task of improving math achievement is far more complex than it might seem at first glance (and, in my opinion, impossible to measure using a single standardized test). An easy fix like making the curriculum more rigorous or traditional or focused on basics almost certainly does not exist.

Recently, when I polled a roomful of university educated adults about their opinion of math as students, about a third of them admitted to having hated it. I fail to see this as evidence of the great success we had back in the “good old days.” Instead of blindly charging back in that direction, why don’t we take a deep breath, set aside the destructive, combative nature of the current debate, and support the work of our teachers and curriculum developers (who, believe it or not, bring essential skills and expertise to the table) in whatever way we can. The challenges we face are more than failure to memorize times tables. The world we live in is changing at a dizzying rate. Preparing our students to navigate it successfully is the most important work I can imagine.

on May 11, 2014 at 6:53 pm |kylepearcePat (and John),

Great post! I couldn’t agree with you more regarding the importance of guided inquiry/discovery and the misconception that a lack of multiplication table memorization is killing math.

I recently posted something that discussed some of the same points here:

http://tapintoteenminds.com/2014/04/13/memorizing-multiplication-tables-hurt-help/

Have a great week!

on May 11, 2014 at 8:03 pm |suevanhattumJohn, thanks for all the great posts on this. And Pat, thanks for your thoughts here.

on May 11, 2014 at 8:33 pm |A. StokkeHi Pat,

Thanks for taking the time to share your thoughts and experience.

I’d like to make a clarification. I didn’t say that the 1975 curriculum was the last excellent curriculum in Alberta. I said that the curriculum used in Manitoba from 1975 – 1995 was an excellent curriculum (actually it was written in 1978 but I do remember saying 1975 at the meeting). I haven’t seen the curriculum that was used in Alberta before 1995 and I’d be unlikely to get my hands on it because I had to go to some trouble to get the Manitoba curriculum that was used before 1995 and I’m a Manitoba resident. I have no idea when the curriculum used in AB prior to 1995 was written or what it looks like.

In 1995, the Western provinces and territories (under WNCP) adopted a common math curriculum. Prior to that the provinces each had their own curriculum, as far as I know. I was suggesting to my Alberta colleagues that they look at the curriculum that was used in Alberta prior to 1995. What I noticed, from looking at the MB curriculum that was used prior to 1995, was that many outcomes were moved to later grades. As one example, in the 1978-1995 Manitoba curriculum, fraction addition and subtraction was covered in Grades 4/5 and in the 1995 curriculum it was moved to Grades 7/8.

Anna

on May 12, 2014 at 7:12 am |PatThanks for the clarification, Anna. The comment (as I heard it) was made as an aside to another point you were making, and may not have represented your thoughts accurately. You were pointing out that the Alberta curriculum before the current one was already heading down the wrong road, and that the one from 1975 was our last excellent one.

on May 12, 2014 at 11:17 am |A. StokkePart of this is correct. I was pointing out that the AB curriculum before the current one was already heading down the wrong road (that’s the one that was written in 1995, which was common with Manitoba’s curriculum). However, the better curriculum I was talking about was not a “1975 Alberta curriculum”. Again, I have not seen the Alberta curriculum that was written before 1995. I have only seen the Manitoba curriculum that was written before 1995 and that’s the curriculum to which I was referring.

on May 12, 2014 at 12:28 pmPatGot it. Thanks, Anna.

on May 12, 2014 at 7:49 am |Nathalie HuntHi Pat,

Thank you for this write up. While I agree with you in theory of how an ideal discovery/inquiry program should work, it will only work if it is handled as you outlined above. The teacher needs to oversee the whole process and guide the road to understanding to the correct/appropriate outcome. Unfortunately, this isn’t the case of what is actually happening in classrooms. Now I can’t speak to all classroom, but only the ones that my own 2 children (currently grades 6 and 3 in the Calgary Public System). Too many times a questions is given without any previous lead up about a principle and then the kids are asked to figure it out. For example, 6 years ago when my daughter was in grade 1, the teacher put the question on the white board to be solved during student led conferences: “If I had 2 snacks a day for the month of March, how many snacks would I have?”. The kids had not been introduced to the idea of multiples/multiplication in grade 1. In fact, most were still adding single digits on their fingers, but were expected to go 2+2+2+2+2 etc 31 times. I helped my daughter by guiding here into thinking about it in terms of multiples ex. what do I have if I have 1 snack a day, now what did the question actually ask for. She figured out the correct answer in about 5 minutes. A friend of ours, just let their child discover on their own the answer (as the teacher was expecting to happen) and after 30 minutes of marks all up, down and around the page, an answer wasn’t reached, a frustrated child and parent left the student led conference. This is just one specific example. Unfortunately, there are many more instances where the children aren’t being guided at all but just left to flounder on their own, and not given any feedback as to whether they were right or wrong. Also, as a last point, I agree with Ms. Stokke that the curriculum has deteriorated in Alberta. Delaying outcomes until later grades is not serving kids well. I have taken over teaching math at home. Given my kids the correct guidance that isn’t happening in our school. I am also making sure that they actually do math on a daily basis which also isn’t happening at our school. My grade 6 student and grade 3 student haven’t once brought home any math sheets or math questions of any kind to do. No mastery or understanding of any concept will be met with only 2 to 3 hours of work a week on it. My kids are bored to tears in class right now because they actually know and understand the math that is happening. That wouldn’t happen without my interference however, as evidenced by the floundering of their classmates, taking an hour to answer 3 questions.

on May 12, 2014 at 5:39 pm |PatHi, Natalie –

Thanks for your comments. I agree that the teacher’s role is critical, and teachers need support to make the transition successfully from a traditional to an inquiry-based approach. A typical elementary teacher is expected to be teach all core subjects as well as extras, often to two grades at once. We need training, time to collaborate and plan together, coaching and a chance to observe others teach if we’re going to do our job effectively. Our education system doesn’t necessarily make that easy.

I can’t really speak to the specific concerns you raise without more context. I liked to give my students problems now and then for which they had no obvious solution strategy. That might have been in the mind of the Grade 1 teacher when she sent home the problem you mentioned. I can imagine Grade 1 students at all levels having many possible entry points to this problem, and there might be a very interesting class discussion the next day. Students certainly don’t need to have studied multiplication or multiples to explore the problem. Sometimes I find that parents are more concerned than students about doing it “the right way”! I remember sending a problem home with my Grade 5s that was solved quite quickly by many using a “guess and check” strategy. One student, though, brought back a full page of algebraic formulae and a note from her dad suggesting it wasn’t a suitable question for Grade 5. I begged to differ.

Last year I read a piece in the National Post (I think) that questioned why on earth anyone would need 4 years of university to teach Grade 2. Really, the right question is, “How on earth can you begin to know everything you need to know in just 4 years?” You can’t – I’ve discovered that even 30 years of on-the-job training isn’t enough time to get it all right. Instead of calling for curriculum changes or the firing of teachers who are experiencing difficulty, maybe we should be calling for more resources for teacher professional development and support, and more time for principals to act as instructional resources, rather than evaluators, for their staff. Please forgive the political aside.

Thanks again for taking the time to comment –

Pat

PS – While I did give my students a “Problem of the Week” assignment in math, I rarely gave other homework unless it was to finish a class activity or collect information for an upcoming investigation. Parents were always welcome to practice math facts, of course :)

on May 12, 2014 at 9:52 am |Ted LewisWhen I read about the advice that university math profs (and I’m one of them) give to elementary teachers I am reminded of an incident from several years ago. My son-in-law is a graphic designer, and I had to contact him about a sign he was creating for our department. I suggested how he could make it better, and he replied “That sounds like a great idea, Ted! Why don’t you come over here and design the sign and I will go over there and teach your Calculus class.”

Thanks Pat for a great article.

Ted Lewis

on May 12, 2014 at 5:42 pm |PatThanks, Ted. I brought my students to the U of A a number of times for the math events you organized (when I was quick enough to get us registered!) We always had a great time, and it was exciting to see my students so pumped about math activities!

on May 13, 2014 at 10:24 am |chrisExcellent insight. I wonder what the probability that similar instructional strategies applied by non-math majors or math-phobes will yield similar results? In terms of large scale implementation, the next question seems to be what percentage of of each group can a large scale educational complex likely field or grow?

on September 16, 2014 at 2:28 pm |thinking101canadaReblogged this on thinking101canada and commented:

Thanks, Pat, Very nicely written.

I would ask what areas of mathematics the participants involved in this dialogue are associated with as my years of experience with mathematicians, scientists, computer scientists and engineers from a wide range of Universities around the world convinces me that we too often only hear from one side in this debate about what math professors see, hear and want from students. I have a colleague who every Fall would call me and complain that despite the A’s on their transcripts the students he is getting in for his PhD program cannot think, problem solve or create… what is wrong with the math programs they are in….? So where does he fit at this roundtable discussion?