There has been a lot of discussion in the media around so-called “Discovery Learning” in math and a petition was presented to the Minister of Education in Alberta asking to have Alberta go “Back to Basics” around student learning. Quoting from the petition, math basics seem to be algorithms, timetables, automatic recalls, and vertical additions.

The question is not about just “memorizing basic facts” or “discovering math.” There is a whole world in between and we need to look at this in a better way than as “new math” or “old math,” but as what is best for our students and designing and implementing mathematical learning that works for each and every one of our students.

**We have never left the basics, we have just made them more purposeful…**

Let’s actually make ourselves start to think on what mathematics means. Is it beneficial to know basic facts? Absolutely! Is it important to be able to think within math? Absolutely! I worked with my grade 5 and 6 students to easily be able to mentally multiply numbers like 40 x 60 (2400, if you were not sure). They could do that. But, I also have a calculator and am a total spreadsheet geek to do and check operations as they become more complex. There is nothing better than using formulas in a spreadsheet…

Unfortunately, spreadsheets and calculators do not tell me if I am using the right formulas in the correct manners to figure out what I need, or if my answer is the “right” one. I have to be able to understand the output and decide if it makes sense or not. I do not need the headaches that would come from an accountant who cannot understand my bottom line and puts a decimal in the wrong place… Oh my!

**3 Analogies to Guide Us…**

**1. Science** – Imagine if we use the same thinking in the sciences. Students should only learn the skills… Science is meant to be experimental and allow students to think. They are meant to think about outcomes, create hypotheses, and come up with ways to be able to test those hypotheses. When I teach science, there are times that experiments don’t work out perfectly. Students had to figure out if it was something in the process, in the materials, or just a fluke. In other words, they had to think as well as the able to use scientific skills and reasoning.

**2. “Practices” and “Games”** – My son loves soccer and hockey, and he is currently 7 years old. He has a ton of skills that he needs to work on, but if it was only the skills that he practiced, he would get bored really fast and his love for soccer would be lost. Instead, we help students of the game of soccer to do both, they practice skills but they also get to test out the skills in a game situation. We don’t want kids only playing the games, but neither do we want them only practicing. Imagine if we said to a soccer player that they could not play a game until they were 16 years old…

**3. Lego** – In many ways, learning is a lot like Lego. When they get a new Lego set, most kids will build the set using the step-by-step instructions and will create a perfect replica of the photo on the box. Afterwards though, my son cannot help taking the set apart and rebuilding it into crazy castles with moving arms and laser guns and hidden doors and what ever else is imagination can create. One is not better than the other, but LEGO is supposed to be reimagined and utilized in other ways. Otherwise we would not be able to take it apart and use it and much more imaginative ways that the Lego designers could have ever imagined themselves…

**So, to those who say that we need to go “back to the basics,” I argue the “basics” are in the Alberta Program of Studies already (honest, take a look!). It is just that teachers are no longer using only a textbook or a useless worksheet to help students learn the “basics” in isolation.**

Rather, I hope that students would be learning math in a fashion that creates high levels of engagement, authenticity, energy, focus, and, most importantly, THINKING!

When I am budgeting, I use a spreadsheet with 870 lines and 11 tabs, and there is no “correct” answer where I get a nice checkmark from the “teacher” if I did it correctly… There are tons of options and different approaches, and it is definitely an art! I used to be able to copy my teacher very well in school, and so was “good” at math. I did not have to actually think, I just had to be able to recreate what the teacher did on the blackboard, and I knew my basic facts, but I did not understand it. Math is not a nice, cut and dried “find the correct answer” kind of discipline.

After all, Einstein would never have gotten anywhere if he had only worked on mastering one method and only knew algorithms, timetables, automatic recalls, and vertical additions! Math is changing and growing, and we need to become better at enabling students in how to use and understand math, as mathematics is so much more than just memorizing basic facts…

**The whole question of “old math” or “new math” is moot, as we need to set up mathematical learning that works for each and every student.**

Change happens because we have learned and grown, and that we want to make something better. We have learned and grown in understanding of how we learn math, so let’s continue to make it better.

Just having the tools does not make you a carpenter! But if you don’t have the tools, you can’t be a carpenter… (And I am sure any carpenter would tell you there is a ton of thinking and math in their work!)

Click here to go to the Make It Memorable: Learning is More Than Memorization petition

Yours in great mathematical learning,

D

[…] For all the opinions and all the rants from both sides, I think the perspective that locked it into place for me came from a principal’s blog called Unraveling New Frontiers, and specifically a post titled: Going “Back to the Basics” or “Discovery Learning” in Mathematics? The Wrong Question to Ask… […]