Sunday, May 6, 2012

Lessons Learned

Over the years, there have been many people who have helped me in my journey into Mathematics, but one has been there all they way through providing me with guidance, wisdom and humour about mathematics and the study of it.  That person is Dr. Brian Mortimer. PhD., but I call him Dad.  The reason I chose to start my blog with a post about him is quite simple, I cannot think, talk let alone teach math without one of his lessons, jokes or insights coming to mind.  So I thought I would share a few with you,

Math and related lessons learned from my Dad...

Lesson #1: "There is a difference between mathematics and arithmetic."
"What you are doing in elementary school is arithmetic not math.  Arithmetic is a part of math, but is its own entity."  I am not sure if my elementary school teachers appreciated being corrected when I shared this knowledge in class, but I certainly felt special knowing the difference.  To this day I am aware of the distinction and although the distinction may not come up that frequently, I did learn that it is important to use the correct terms while discussing subjects and that teaching students proper math terms can give them confidence.

Lesson #2:  The answer lies in the questions.
I do not think my Dad ever told me how to solve a Math problem, although it might have happened one or twice. What I do remember are his questions.  He strongly believes that each learner has the ability to find the answer, and that his job is to facilitate this learning with carefully positioned questions.  Now, as a teacher I strive every day use good questions.  Questions that are challenging yet accessible.  Questions that are simple and profound, and questions that allow the learners to find their answers themselves. 

Lesson #3: It is not just about getting the correct answer.  
It is knowing how you got it when you do and figuring out why you didn't when you don't.  Learning takes place in the thinking about the problem and the many different paths one can take to find an answer.  Getting the answer is great, but knowing how you got it means you can do it again in another context.  If you have written down your thinking then it is possible to see how and why it worked.  Conversely if you do not get the right answer then an examination of thinking can show that you knew a lot of the right steps, but got off track at point d or miscalculated 6x3.  Recognizing the bigger picture can help students shift from "I don't know anything, because I got it wrong" to " I got a lot of it right and next time I will double check my multiplication.  It is not just about getting the right answer.

Lesson #4:  Never underestimate the power of humour.
"When you go down to the mathematical swamp beware of algegators and calcudials." One of the many jokes used on the top of assignments in Prof. Mortimer's classes.  He would often start his worksheets or test with a joke.  I relate this practice to an icebreaker in the classroom, something to break the tension, or stress and get folks focusing on what the task is at hand.  The jokes also helped students to realize you can take something seriously while still having fun.  In class, I find myself using humour quite often to make a point, change the tone of the class or just to add laughter.  Sometimes only a couple of students get it, but those who do smile so it is worth it.

Lesson #5: "Don't let the turkeys get you down."
This lesson is not Math specific, but certainly helps in teaching. 

My Dad is still teaching math and arithmetic, and is now working on online video instruction.  I keep learning lessons from him through our time together and am grateful that he keeps asking me questions.

Thanks for reading!



  1. Wow, Lucy! What an insightful first's going to be hard to follow that. It's great that you've had such an inspiration in your life. I think that's important not only in education but specifically for math (as we are all taking this course). Those are some great lessons and I think they have definitely benefited you in your teaching career.

    Unfortunately though, there are also those teachers who do not inspire students. I loved math in elementary school, but when it came to grade 9 I had an awful teacher so became less enthused about the subject. Of course, when it came to grade 10, I had a great teacher - but I can still remember that one teacher who made it difficult for me by only teaching through the textbook and not realizing that some students don't just "get it" but need to experience it and figure it out.

    Anyway, that was a bit of a tangent! But now to focus on one of your lessons that I liked the best. Lesson #3 - it's not just about getting the correct answer. Even in just the past few days, interacting with the Kahn Academy, and working on skills that I haven't done in many years I have come to realize this lesson on my own. Also, something that was definitely discussed at large in my BEd year was the concept of letting students figure out the steps on their own. Long division isn't long division anymore, there is more than just one way to get the answer - and students may know many more than you as the teacher do. They see things differently then you do up at the front. Definitely something to remember when you're teaching!

    Thanks for the lessons Lucy!

  2. Wow Lucy, what a coincidence because I was thinking to start with a lesson that my dad taught me during my elementary school years and it's exactly lesson 2 on your post. He was a Math teacher,too (now retired). He tells a story when he was a student himself in the university and wanted to ask questions to math professors. They would ignore him most of the time until one day one of them said "oh enough, put your hand down becuase you have your own theory":) So, every time when I used to come from school he would ask me "did you ask any good questions today?" instead of asking how my day was.
    Therefore, I think not only us as teachers should try and come out with good questions but also we should inspire the students to think and create their own questions in math. My dad lives in Albania (East Europe)so we don't talk about math very often now...he wants to know about his nephews (my kids) since he lives that far:)
    Thank you for sharing the lessons Lucy.

  3. Sharing personal stories is a common type of blog post. Good job on this one as it is both personal and helpful.

  4. Don't forget to tag your posts.

  5. I really liked your blog lucy. I liked all the lessons but I think Dad's lesson #4 especially resonates with me. I try to do this all the time, not just in math class. When students come into a class that they might have had a bad experience with in the past (which often occurs with math) they are nervous and scared. It is much easier to break the ice and then get them to trust/like you. Once you can achieve this it is much easier for them to learn whatever you are trying to teach them.