Category Archives: Pedagogy

To de-track or not to de-track; that is NOT the question*

Although the debate over ability tracking (placing students in classes by mathematical level) in the mathematics classroom has been alive and well for some time, the heat has exponentially increased recently after California looks to adopt a new framework where students of all levels of mathematics will be mixed in together. This framework aims to address academic, social, and racial disparities in the mathematics classroom. The new framework has been heavily influenced and co-authored by Professor of Education and fellow Brit: Dr. Jo Boaler (who I had the pleasure of interviewing for the MathEd Out Podcast) of Stanford University. She argues that “tracking looks horrible when you look at the racial inequities, and we have to ask, ‘What do we want for this country? Do we want a country that has these racial divides in achievement?’ If we don’t, we need to work on a different model,”

Reaction has been emotional, political, swift, and strong, especially from those who associate the initiative with a leftist agenda. I have often heard the argument that this will water down the curriculum and hold back ‘more advanced students’ and will not help those in need of support. There are even studies that seem to back up both sides of the argument. A 2014 Fordham Institute paper argues that tracking helps disadvantaged students be more successful when it comes to preparing for AP math classes. On the other hand, Boaler has published multiple peer-reviewed papers on the negative consequences of tracking both academically and culturally.

However, de-tracking vs. tracking is a simplistic question which ignores a large and crucial part of the conversation that needs to be simultaneously considered if not reflected upon first: What is the nature of the mathematics that we are teaching and learning in our schools? One question simply cannot be considered without the other. When taken at face value, with the narrow and linear curriculum that students go through in many schools, it makes complete sense to track in ability groupings. Students need to be able to learn how to find the square root of a number before they can solve a quadratic equation. They need to know how to simplify fractions before they study before they can consider rates, ratio, and proportion. The way the curriculum is structured is why we track in mathematics and not in History or Science, for example, which are more multi-dimensional and complex. If a major aim of mathematics is preparing students for AP level math, then I can see the benefit of working with students at different levels, at least for more advanced students. My question is: Is that it?! Is that why we teach math? To prepare students to succeed in AP? If that is it, this is nothing short of a travesty.

Beyond mere preparation for AP level mathematics, there is a big problem with this model. For students who are struggling, placing them in a lower ability group can cement the fallacy that they are not capable of accessing even basic mathematical principles and skills. And, it can be challenging to move upward once students are set on a particular path. As the new framework puts it: “the subject and community of mathematics has a history of exclusion and filtering, rather than inclusion and welcoming. This is a much bigger issue to consider when compared with whether advanced students can understands imaginary numbers or not and this conversation should take up proportionally more time in our curriculum reviews.

Tracking even advanced students with current curricula is not without its drawbacks. I have had multiple parents of 6th-grade students in my conferences who are deeply concerned that their daughter/son is on track to get into good colleges or into a certain profession. Is this really what we want our 11-year-olds to be worrying about?

I enjoyed math at school, working through a linear narrow curriculum that I found straightforward, and I was able to demonstrate mastery in assessments. I also went to a school where there was an admissions exam so I should have been surrounded by similar minded peers. However, I was still in the minority in terms of those that enjoyed mathematics. Today, I tell friends that I teach math and I often see the shudder as they reply “oh I was never great at math”. I believe this to be a cultural legacy after decades of students working their way through a linear and monochromatic curriculum. This also makes me sad.

I only began to love math after I started to learn to teach and was blessed to be inspired to teach and learn great math by a phenomenal professor. He showed us that mathematics was so much richer and complex, so much more useful, so much more interesting than was often found in textbooks. After for teaching for over a decade, I have seen how such ‘Low-Floor-High-Ceiling’ activities can provide noticeably more engagement and a deeper level of learning. If we don’t start with the consideration of the nature of the mathematics we are teaching in our classrooms, there is no point in asking whether we should track or de-track. Thankfully, organizations such as YouCubed, Desmos, and Nrich are leading the charge to bring in a new kind of mathematics learning where de-tracking makes a lot more sense.

It is an uphill battle. Progressives are up against divisive politics and decades of established narrow curricula. This is much is for sure, however: Rather than simply just preparing students for AP level mathematics we should be asking:

  • Why do we teach mathematics?
  • How can we design a curriculum and learning space that is rich, engaging, and useful at every level?
  • How can we help students see how different parts of the curriculum are deeply connected?
  • How can we help students of every ability, culture and socio-economic background get excited about learning mathematics and their own capabilities to solve problems?

Math is so much richer, so much more useful and crucial than many curricula portray. In the real world, there is no neat and narrow linear progression of skills, there is are complex problems to be solved in whatever scrappy way possible. Let us at a minimum give every student, irrespective of academic prowess or culture, the chance to access the confidence to say ‘I can do this’.

*Opinions are my own and not associated with any school or organization with which I am associated

The Great Wall of Questions

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Any strategy that raises the level and status of questioning in my room is useful. I found that there were times when a student asked a great question but that it was just no the time to go into that topic too deeply. I have also found that there are times when I have a 5-10 minutes gap in my lesson where these topics would fit into nicely.

The Great Wall of Questions is my attempt to solve these two problems at once. If a student asks a great question, then I proclaim ‘get it on the board!’ to the delight of the person that asked. They know that if it goes on there I think it is an important question, one that is worth thinking about for a longer period of time. When there is a good moment I will take a question and try to get students thinking about some answers or at least ways to find the answers (I am going to avoid just answering the questions as much as I can). Here are the rules:

  • A question only goes on the board if it has come out of genuine curiosity (rather than an attempt to get their name on the board)
  • Their name goes with the question and the color of the stickie determines which class it came from
  • When the question has been addressed (different from answered), a small dot goes on there so we can see what needs to be looked at in the future.

I only have four questions on there so far this semester (after 8 school days). I am hoping that by the end of the semester the board will be full. Here goes….

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Summer Reading 2014

Summer is rapidly approaching. A great time to reflect and decide what I want the next 12 months to look like. Time is precious and I want to read books that will not just improve my philosophy but that will help on a day to day basis. I am currently looking forward to devouring these two books:

I’ve been thinking a lot this year about how to teach my students how to learn, how to think for themselves and direct their own learning. I’ve skim read ‘Making Thinking Visible’ before but I’ve been looking forward to going through this with a fine toothed comb and extracting every word of worth from its pages. The philosophy statements in the first couple of chapters is worth a read all on its own. It seems clear that students who can name and show their thinking processes do a lot better than those that just go with the flow. I would like my classroom to foster the former. Thoughts to be blogged/tweeted as I go along.

This is the other book I’m really looking forward to going through. It has come highly recommended and anything that is going to help me become better at asking questions and promoting debate and discussion is worth a look. I haven’t even opened this yet so watch this space for highlights online and in my classroom.

Because LeCarre is amazing.

What will you be reading this summer? Any recommendations?


I’d completely forgotten about feedback

This summer I was all excited about reflecting on what strategies I would use to enrich each part of the learning process. I made the following list in my teaching journal:

Inspiration –> Creation –> Education –> Preparation –> Performance

This post from Daniel Schneider reminds me that I have missed out one of the most important components of the process: Feedback. Without this, students will not know how they are performing and get a good sense of what is expected from them. This is now added to my list and ‘the wall of champions’ is a great place to start!

I also have to remember that just as with formative assessment, I will need to think about feedback at every part of the process. So in the end the process looks a little more like this:

Learning Process

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: