Hi Darren,

I wish I had more time to reply to your comment but I am very busy preparing for classes which start tomorrow. However, I'd like to point out that you did write the following:

"What I've read in the comments on John's blog and on Anna's blog seems to hold K-12 teachers in a disdainful light."

This is not true and we all think very highly of teachers (my mother and my sister were/are both teachers in the public school system). Again, we advocate for an improved curriculum and improved K-8 teacher preparation. How does this hold teachers in a disdainful light?

I can, incidentally, give quite a few examples of schools and math educators who are under the impression that standard algorithms are banned and discourage kids from using them. I will not do this in this public forum, though.

I also completely agree with Rob's statement about learning math: "Sometimes skills naturally come first, sometimes understanding comes first. Many times they are learned simultaneously -- and this is the ideal."

Did you learn all of the intricacies of real analysis at the same time you learned introductory calculus? Should you have? Should one start by building the real numbers from the rationals using Dedekind cuts?

Why are you surprised that Anna and Rob advocate for a balanced approach? Read point 3. of the WISE Math Mission Statement:

"... Math curricula must support the development of understanding of math concepts AND the learning of basic skills and concepts through incremental practice. The two are NOT mutually exclusive. There must be a healthy balance between understanding and practice, to allow students to grow in both senses."

You hear them arguing for what's missing - this does not mean that they are opposed to a balanced approach. The key word here is balanced.

You wrote that you're in favour of mathematicians being included in curriculum design "given they're also well versed in modern approaches to pedagogy".

Perhaps, by a similar argument, those on curriculum committees should also be well-versed in higher level mathematics which is taught at the post-secondary level. In fact, one might advocate that they should have taught higher level math courses themselves so that they understand what they are preparing K-12 students for. (I'm not saying that I'm advocating for this but it is as extreme as your view.)

Furthermore, simply because someone doesn't agree with what's currently in vogue within the math education community, doesn't mean that they're not well-versed in pedagogy.

Again, given that the vast majority of students who wish to obtain a degree in science, engineering, pharmacy, economics (et cetera, et cetera) are required to take a course in introductory calculus, does it not make sense that you should welcome input from the individuals who teach math content courses at universities?

I hesitated adding this comment because most of the comments are about math pedagogy not so much about our results but in conversations with people this might be being missed

I was reading the PCAP website and found this

"Some of the key findings about the performance of our students include
the following:

Over 90 per cent of Canadian students in Grade 8 are achieving at or above their expected level of performance in mathematics, that is to
say, at level 2 or above. Almost half are achieving above their expected level.
In math, there was no significant difference in the performance of girls and boys at the national level. However, more boys than girls were able to demonstrate high-level math knowledge and skill
proficiency.
For Canada as a whole, girls performed better than boys in both science and reading. More variation was seen at the provincial and territorial level.
In most provinces and territories, students attending
minority-language school systems outperformed students in
majority-language systems in mathematics. This was reversed, however, for reading, where students in majority-language school systems
outperformed students attending minority-language systems. There was no significant difference by language in science performance."

I don't want to get into a statistical analysis war with mathematicians but this summary makes me think that as Canadians, and Manitobans, we're doing well.

As a retired teacher ,I agree that it is ao important that students learn what they are doing as they learn new concepts.It is not enough to just memorize material but to understand the concepts and what the concepts mean.

Hello,
Teaching the curriculum is important, but I do feel that what is more important is they way we teach students. The strategies, the volume, and the presentation is key to teaching students of all ages. Adults and children need to have the opportunity to learn in a multitude of ways. Educators need to be open to new ways to teach so that the pedagogy of each educator continues to bloom.

Interesting post Darren, as an educator I do want my students to understand the concepts and applications of it. So, they can know how to apply it when the need arises. And that is the true purpose of learning.

Interesting post. In nursing education a great deal of emphasis is being placed on understanding the concept and not just memorization. Once an individual fully understands the concept it becomes easy to apply it in different and real world situations.

I have to agree here. I have seen in other countries how children learn by rote-- repeating after the teacher-- and I don't understand how they can call that "learning." I believe that when learning, the individual has to be able to understand the concept being taught and be able to apple it. Memorization means nothing if you don't know how to use what is being taught.