Monthly Archives: May 2013

Summer 2013

The summer is an amazing opportunity to step back and reflect on the teaching and learning that takes place in my classroom. For this I have two strategies:

  1. Take part in the free Stanford Online Course: EDUC115N. If you are involved with Math Education, you should definitely consider going through this with your department.
  2. Reflect on what I see as each part of the learning process in the classroom: Inspiration (Why Math?), Creation (How Math?) and Preparation (Which Math?).

Here are some questions I will trying to answer:


  • What activities are going to create the need for the math in each unit/lesson?
  • Where can I incorporate Dan Meyer’s 3acts style lessons into the curriculum?


  • How can I develop student questioning and facilitating their finding out the answers rather than just disseminating independent skills that they need to regurgitate?
  • How can I stretch my most gifted students?


  • How am I going to prepare my students well for standardized testing?
  • How can I make this part of the lesson a lot more fun?

I think I would be happy next year if I could improve on these things.

What about your teaching will you be reflecting on this summer?

Everything that happens in the classroom is in my control

Recently I read this thought provoking article, from the Washington Post, on things that contribute to student achievement. This has to be the biggest ongoing discussion in education today and of all time.

Yes it is true that there are many factors that go into student achievement including social and economic background as well as the culture of the school as a whole. However, I do believe it is right for teachers to focus on their responsibility in the classroom, hence whether the title phrase of this post is true or not, when I am standing in front of my class I cannot afford to think otherwise. Policy makers and administrators will need to consider other factors a lot more, but when I am teaching, I cannot afford to give myself the excuse that what is going on is not down to what I have planned to happen.

This morning in our weekly professional development meeting our Assistant Dean of Faculty expertly put it like this (I paraphrase):

‘When your students enter your space, you have the opportunity to create a world for them that will trump any social and economic situation the have come from at home, that will trump anything they may be going through, that will trump any difficulties they may be facing in mind, in body and in spirit.’

This is what I have to believe. I must do my part with what I can control and have a lot of hope for the rest.

Escape the Worksheet: Sidewalk Chalk

Mathematics students need to practice mathematical skills. That much is certain. What I am trying to do in my classroom is to get away from the here-are-20-questions-go activity that puts shivers down the spine of many students. So how do I still help them to practice but in a less monotonous way?

A simple idea, now that the weather has improved, is for the students to do the same problems but using sidewalk chalk to decorate the school’s pathways with beautiful math. There is something in this that appeals to the 3-year-old in all of us.

The lesson objective was clear: To prepare for the quiz on 1) Solving triangles and 2) Using the unit circle to find trig ratios. We wandered outside and went for it.


How it went:

  • Most students enjoyed the lesson with a handful opting to carry on with a paper worksheet. At the end, students fed back that they enjoyed working outside.
  • I loved the instant assessment. It took very little time to see what was going on in the students minds. It also kept the accountability high. It is difficult to a student to fake writing their work on a sidewalk and check out.
  • It would have been useful to have a little more structure to the activity than just going through the worksheet but on the sidewalk. Perhaps assigning roles, for example, scribe, coordinator, calculator.
  • The sun was hot meaning that students became lethargic towards the end of the lesson. Choose a shaded spot if possible.

What motivates my students to learn?

I used Google Forms to survey 56 of my students (I know, it sounds like a statistics textbook question already!). I wanted to know what motivated them in my classroom. The survey was anonymous and I encouraged them to be as honest as possible.

The question: What motivates you to learn in the mathematics classroom?

The response: 1 – No motivation, 4 – Highly motivating


Any other comments? (here is a sample):

  • I would like to work in groups of my choice
  • Competition only puts stress on me
  • I find the mathematics interesting, but I feel immense pressure to get a good grade and get into college
  • I like working on my own with music playing
  • I need one on one help and lots of time to practice

My initial thoughts:

  • Clear patterns here are motivations of getting to college and getting a good job. I wish it was the same for ‘the mathematics covered’
  • Also clear is that students want lesson activities to be fun
  • Not so clear is the motivation of groupwork, individual work and working on practice problems. This just highlights the diverse nature of how my students learn and how to get the best results I need to cater for different learning styles. This is an art form, for sure.
  • Also interesting is that not all students appreciate competition. Even more interesting is how this graph changed with different classes. For example, for the first class that took this survey, there was an intense dislike of competition. This leveled out as the day progressed.


  • College and career is more of a motivator than the math. I would like this to level out somewhat; for the math to be its own motivator. I’m still working on this point.
  • My students are very different in terms of how they learn and what motivates them. Some appreciate individual work, some appreciate group work. In a math ed world where the group-work-is-the-only-way team is by far the loudest, I have to remember that this is not always the biggest learning engine for all of my students.

This process reminded me of the following TED talk on ‘The Power of Introverts’. An important idea to think about if we want to tailor education to the individual student:

Spaghetti Trigonometry – Extension

This is a direction I found myself going when some students had finished this activity.

– What would the graph of y = sin (2x) look like?
– y = 2 sin (x)?
– y = sin (x+2)
– y = sin (x) + 2?


What does this tell you about?
– f(ax)
– a.f(x)
– f(x+a)
– f(x) + a


Next lesson we are going to bring together everything we know about linear, polynomial and trigonometric functions and make some amazing graphical patterns using I hope to post the best ones here.

Spaghetti Trigonometry

This lesson was adapted from the NCTM website.

The aim: For students to understand the origin and characteristics of the graphs of sin(x) and cos(x).

Student comments during the lesson:

  • This was the best lesson of the year!
  • Where did time go?
  • Can we have more lessons like this?


Students will need:

  • Blank unit circle and trig. graph 
  • Glue stick
  • Protractor
  • A small pile of spaghetti noodles.

The student steps are simple:

  • Label the unit circle axis (-1 and 1’s) and the trig graph x-axis (0degs to 360degs). Do not yet label the y-axis.
  • Use a piece of spaghetti to mark a the unit distance from the origin at 15degs to the x-axis. Stick it down and label the angle.
  • Take another piece of spaghetti and measure the y-coordinate (sin(x)) of the point on the circle. Transfer this piece to lie on the trig graph vertically above the 15deg mark.
  • Repeat at 15 degree intervals all the way around the shape.
  • When you have finished, draw a line going over the top of all your spaghetti sticks to show the graph.
  • Finished all the way to 360degs? Try the same again but this time measure the x-coordinate (cos(x)) of each point on the unit circle (you will need a blank trig axis).

What I learned from teaching this lesson:

  • For general buy-in, it is really good for students to make predictions about how they think the graph will continue past 15 degrees, at the start of the lesson.
  • I certainly needed to demonstrate the first couple of noodles for students to get the idea, but they loved it.
  • I need to make more of the last 15 minutes of the lesson to really cement the learning, but this has given me license to talk about the graphs of sin(x) and cos(x) for some lessons to come.

It was very satisfying to show the animations found here in order to discuss the shapes of the curves.

Why We Teach Math

Last week ‘The Atlantic’ website published an article on how little, mathematics is used at work.  First of all an admission. Yes, there are not going to be many students who end up using complex numbers in their place of work. There will not be many who have to use trigonometry. However I believe this article completely misses the point of what mathematics education is all about. It just highlights the view of math that we see much of society holding, today. Why do colleges and employers still look out for those with at least some mathematical competency? What do they see that this article is missing?

Many would say that Math is about problem solving. I agree, that is involved. I think it goes far deeper than this, however. Mathematics is about the ability to see a pattern in the world (often between two or more changing variables) and to take it into the abstract to communicate this pattern and to be able to predict what may happen into the future. This principle is used in pretty much any job you could think of.

Demand –> Prices

Water purity –> Disease

Store layout –> Sales

Speed –> Fatalities

Practice –> Test scores

Time –> GDP

When everything stops changing, perhaps then we can shelve math education and just look at what is. I don’t think this will happen any time soon, though.