As many of you know from my blog posts, math is a very important passion of mine. I have in a way devoted my educational career to learning about math education and how it can help transform student learning. This has gone on for me for the last 9 years of my teaching career and five years before volunteering at an amazing school in Peel. Over the course of these 14 years the arguments in the above articles have always been happening; so I think it is funny that when Ms Wente mentions that this is a “new faddish fuzzy notion.” Since mathematics was first introduced into the curriculum in the fifteenth century it has always been a debate over skill versus conceptual understanding. This debate will always be there all I can give you is fact from experience and from the classroom (which I will say many who write articles in the Newspaper or make policy cannot).

Let me first start of with my own evolution. Like many of you I was taught with very traditional methods. My father drilled in me from a young age that fact recall was the most important thing. I still remember practising for hours on hours flash cards and being randomly asked multiplication questions to see if I knew these facts. I also remember that my Math class was all in a work book and my teacher sat at the front of the room and wrote many things on the board and then we did questions to practise and show what we learned. This continued all the way through school and as I got into the high school and eventually University this is what I remember of my Math class. Did it help? No, I don’t think it did. Don’t get me wrong, I did learn math. In fact Math has never been a hard subject for me (except problem solving). I was able to work through and memorize what was needed and then when the test came I was able to retell those facts and get an A. My problems never came until University Calculus. Here I because I didn’t have a good foundation in Calculus I struggled, in fact I failed.

Sorry I digress here. This method of teaching stuck with me, more so because this was all I knew. During University I changed majors and decided to become a teacher. I was able to volunteer at an Amazing school in Peel and soon learned Reform Mathematics (what discovery math was called at that time). I was also fortunate enough to have an Amazing principal who let me question her and learn what reform mathematics was all about. At first I said the same things that many of these article, and our parents say when they see problem based learning. You have probably heard these before (I know they are in the article):

1) What is wrong with Rote, it worked for me?

2) What about facts? There not learning them like I did?

3) I memorized and got good grades?

4) They can’t possible learn this on their own?

5) What do you mean discovery? What is your job then?

6) You’re the teacher so teach?

7) This look chaotic, there is no order, how can they learn?

8) What about the language, seems like more reading than math?

I can go on but they start to sound the same. During this process I was able to see students truly excel and showcase their learning. In fact, looking at scores (which is not the end all to be all), the school went from 42% to 93% in that first year in mathematics. I was also able to reflect on my own learning and how I learn. This started the ball rolling and has helped me to ask questions back. Here are a few to think about:

1) How do you truly learn as an adult learner?

2) Do you memorize things and then succeed? Or did you have to make mistakes, go back and relearn or have someone help you through it?

3) When you are learning do you like to ask questions? Or just sit and receive information?

4) **(my favourite one) **As a successful adult how did you become successful? What traits do you like in your employers?

Here are my thoughts to these questions:

I personal learn by doing, struggling, asking questions and then going back to relearn it. True mastery comes from doing something over and over and over again. Yes I can see how this backs learning facts, and I am not saying facts are not important, but my learning is in context to the concept not in isolation. Memorization only works with some things but I still make mistakes no matter what I am doing and then I learn from them. As for success to me I value students who are free thinkers, creative, adaptable and able to see past just simple direction. This has been the case even when I was managing people in the private sector in my University jobs. I don’t think the world can evolve from people who can only follow direction and not think beyond what is on the paper.

With this in mind I began my teaching career. Here I too continued to question but now I also had to field questions from the general population about my style of teaching. Here are my responses.

Q: Why is this better than traditional learning?

A: I hope that I may have answered this above but most students, and adults do not learn through traditional learning. There are a very few who do and we also have to consider that style but many don’t. Learning is developmental. It doesn’t happen in a linear fashion and PBL allows for this to happen. Learning in PBL also doesn’t happen in isolation from the world, or other subjects. It is always connected to a context, which helps all students to hold on to something and work with it. Furthermore, all learners can access PBL, whether gifted or with a learning disability all students can do the problem. Also, personally, it makes the day go by a lot faster, I enjoy it and so do my students. Check out this video: http://curriculum.org/secretariat/justice/insights.html for student reflection on what context can do.

Q: You know my kids don’t know facts, why aren’t you teaching them?

A: First and foremost, I want this to be said, “FACTS ARE IMPORTANT!” they must be taught and learned; however, how are we learning them. Let’s go back to my question back to you. Can you recall something where pure fact learning has help you be successful? If yes, no think was it just fact memorization or was it in a context? Fact knowledge is important and needs to be done. I prefer to do this through games and mini-lessons. This allows me to talk about a strategy and have students discuss the pros and cons of the strategies. The talk focuses the learning. Check on my previous blog post on it.

Q: “Teachers and Students are learning together” Great so now we have the blind leading the blind!

A: This is the one that bothers me the most. It bothers me because PBL actually takes more understanding, more planning and a lot more patience then traditionally teaching. I have almost completed my thesis, in where I researched the impact of my questions on students learning of fractions. It was interesting to see where I had moments of direct teaching that my students stopped talking. In fact, they just sat there. Which is exactly what traditional teaching does, students sit and listen then do. PBL takes planning. In another of my posts I talk about five practises that teachers should be following for PBL implementation (http://mrsoclassroom.blogspot.ca/2013/11/blog-post.html ). Teachers actually need to learn the mathematics and it is through critically placed questions that the learning is brought out. Students develop at a faster rate through this proper questioning style and can achieve a higher level of understanding. I have grade twos right now who are learning about equivalent fractions, ratios, division and adding three digit numbers in their head. It is truly amazing to see what they can do. But this takes planning on my part. It takes understanding of learning trajectories and understanding what students are doing (so you can redirect or push beyond) and understanding the math to be effective in PBL.

Q: Test scores are falling?

A: this might be so but I would caution you on this. First of all tests are a snap shot of learning at a particular moment in time. They have a place in assessment. In my personal opinion a very far place but a place nonetheless. There are many factors to low test scores: 1) poverty, parents education, home life, social problems that day, being sick, stress, reading level, context, etc. The list is endless. When we put all emphasis on test we are taking away so many other factors of learning. I know more about a student from a problem that they solve then by what they can retell me on a test, just a matter of fact.

I am going to stop here for now as I think I have written more than I ever have in a blog. This topic is very dear to me and I have heard a lot of the questions in this “Math War.” It will not go away but please don’t take this as a discouragement to stop PBL or even start. To me PBL is the best way for ALL students to learn. It gives the teacher the most time for true assessment and understanding of their students needs and next steps. It allows you to meet all levels of students and be able to get to all of them. I have and will continue to only teach through PBL (problem based learning). Love to hear your personal stories, questions or answers to this lovely debate.

Jonathan, this post is brilliant! I think that you should send it in as a Letter to the Editor in response to the other articles. You have completely captured the reasons for discovery math, while also ensuring that students have strong foundational skills. I was in awe of what you do in your math program (along with in other programs), and you've helped me reconsider some of my own math teaching. As always, I think it goes with really knowing your curriculum, really knowing your content, and really knowing how to differentiate to meet the needs of all students. You know this! Thanks for sharing so much for your “knowing” with the rest of us!

Aviva

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Thanks for the comment. These “math Wars” can really be hard on people, as I know they have been on me. I'll think about the editor part. I am all for a debate but we'll see how my writing stands up. Thanks again for the compliments. I love watching your class and have learned so much from you too.

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I also teach math. Just like you said I also believe in struggling and learning from our mistakes. Thanks for sharing your ideas.

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