Differentiation without discrimination*

Each and every one of us have faced and taught one of ‘those’ classes - ‘those’ classes that challenge each and every bit of your being, classes that you are frustrated by and that equally challenges you. They frustrate me, because their learning needs and understanding of mathematics is so diverse, yet they challenge me, like no other class as I am constantly thinking of different ways to engage them all in class and to provide for each and every students according to his and her needs. Don’t get me wrong they are a great class and wouldn’t want it any other way, but it doesn’t mean it is easy. Things that I would normally do and be able to do in a mixed ability classroom is not so possible with this class, as they require such different work in order for them to be simulated.

Differentiation can sometimes be a sticky subject - please don’t think I’m against it, hear me out! When you differentiate, you provide different opportunities for students to reach the end goal, but it requires them standing out. If you provide students with something else, piece of paper, different set of instructions, etc., they stand out. High school is awkward enough, standing out as being different is worse! How can I help my students without making them feel awkward, but still challenge them in a way that is personally appropriate?

This is one of the many advantages of being in a 1:1 iPad (technology) environment, is the opportunity for anonymity. You will never know what someone is working on/doing without explicitly looking. I used this anonymity to provide an opportunity for greater differentiation.

I would create/simulate a flipped classroom environment where I record videos of me teaching/explaining a specific concept. I used the app ExplainEverything to record these videos ranging from 1 - 5 minutes per video. I am very careful and make sure that none of the videos introduces more than one concept at a time, it might cover and use concepts previously studied but a new concepts is introduced per video. My students are provided with these concept check/explanation videos, and questions to be working on. These are all posted on their iTunes U course, where they can assess it and work on it as and when they want to.

Above: Screenshot from my iTunes U course

Students can then work through these concepts and questions at their own pace and I assist when they are struggling. My classroom has now become a place where students work at the pace their are comfortable at and I facilitate their learning. Some students would be watching videos in a lesson while others might be engaged in discussing a problem and others are working one-to-one with me. This model is not perfect, but it has allowed me to differentiate without discrimination. Of course, some students are more intrinsically motivated and this gives them the opportunity to ‘have’ me at home when they want to work through more concepts, giving them the opportunity to continuously challenge themselves to reach higher. Equally, students struggling have me to help them in class on the bits they are finding difficult, without the pressure of peers judging them.

As technology continues to improve, we need to find new and interesting ways to engage and differentiate for the different learning needs that exist within the classroom.

*For this post, I refer to discrimination, as defined by dictionary.com as the "treatment or consideration of, or making a distinction in favour of or against, a person ... based on the group, class, or category to which that person ... belongs rather than on individual merit".

Using google docs for collaborative learning in mathematics

During today's lesson with my Grade 6 class, we were looking at finding factors and multiples of specific numbers. As we were looking at finding factors, one of my students posed the question: Would an even number always have an equal number of factors? Equally: Would an odd number have an odd amount of factors?

What a brilliant question and exactly the example of how we would like MYP students to inquire into mathematics. My response was - Great!!! Let's look at what you are asking as a class together. 

We quickly made a google doc and started looking at factors. Here is an image of the work in progress:

After finding the first eighteen factors, we looked to see if it holds true, and we highlighted the outliers (as seen below). Factors of 4 was the first exception (highlighted in orange) and we suggested that maybe it is the exception to the rule. We looked further at the factors, and found that it was true for all the other factors, except for 15 and 16 as seen below: 

Thus, as a class today, through a great inquiry a student posed, we learned so much - it was a quick visual for me to see who understood the concept of factors (as they were doing it live on my screen); students inquired into a fellow classmate's question and students discussed prime factors (having only 1 and the number itself as factors) and it was a wonderful collaborative learning opportunity where we could investigate and find that there was not a pattern holding true for all factors. 

My students reminded me again today that they have so much creativity and if I give them the opportunity to inquire and explore, they develop as confident mathematicians!

Using lego and minecraft to model square and cubic numbers

When introducing exponents such as square and cubic numbers to grade 6 students, they are often unsure/unclear what these exponents represent. I started my unit by giving students an investigation into square and cubic numbers, and here is the outcome... 

I asked students to start the task by constructing a 1cm square (on 1cm square paper given to them). Together we counted the squares inside the square - 1. Then students had to construct a 2cm square, count the squares inside - 4, the 3cm square - 9 squares and so on. I asked to them construct squares up to 10cm and to count the squares inside. Immediately, some students realised that there was a faster and more efficient way to determine the number of squares, exactly what I wanted them to find. They derived for themselves that for example is 4cm square is 4cm x 4cm = 16cm2. I had to guide them to ensure that they were squaring the units as well. As soon as they discovered their "formula", I asked them to look over all the squares they constructed to make sure that it holds true for all of it. 

If you are planning on doing this, I would advice that you make sure that students understand and get the pattern before moving on to the next part. If they did not find that pattern, get them to construct more squares and guide them through the process. 

I then asked them to construct a cube from paper, this was to realise the 3D nature of addition and additional dimension. By drawing the lines and folding the cubes, some students got quickly bored (and this is what you want), so that they think of ways to be representing and finding the practical application of cubes. Students had different outcomes for this second part of the task, some students were most comfortable to stick to paper, as this was the initial medium they were working on, but most students want to challenge to be building/constructing cubes in a different way. This is where I opened the task and told them I want them to be using their creativity - they can construct these cubes any way they want to. 

Below is some of the outcomes, the first image is the squares and cubes made by using paper, in the second image the cubes were made from plasticine and the students made a lovely comparison with the squares. 

Some of the students chose to use Lego's to represent their cubes. 

While other students used Minecraft to represent their squares and cubes:

Your doubt might be the same mine was - how do I know if they are playing or doing work? I was very honest in telling my students that I'm unsure whether they are working or playing, so we agreed that I will give them the benefit of the doubt and after completing 2 cubes, they had to 'check-in' with me and talk through their thought process. I was super surprised! We had an extensive discussion about the 2D nature of squares and why they had to blow away the ground and inlay the squares so that it remains 2D when looking at it from above, despite not being 2D anymore. Equally enlightening was the cube discussion!

The verdict: Even though this was a relatively time consuming activity - it is really worth it and is something that I would highly recommend. Students constructed the knowledge for themselves. Don't be afraid to let your students challenge you - I was hesitant about Minecraft, but my students demonstrated both their maturity and new ideas in my classroom. It's ok if your unsure, but negotiate your uncertainty with your student and I'm sure you'll be surprised!

Special thanks to: My two 6th grade classes at Halcyon London International School for allowing me to share their work. My colleague, Lenny Dutton  for encouraging me to start blogging!

Welcome!

My first post - yeah! I'm finally happing to start blogging... it's been a long time in the making.

Watch this space!