Learning geometry with the help of Minecraft

As a teacher teaching in an International school my students come from all over the world. It is so rewarding for all the many reasons  - I know all of you know (if you don't know what I'm taking about - take the plunge and teach in an International School). On the other hand, it can be challenging as students come to the maths class with very diverse mathematics backgrounds. Being an IB school, we do not 'stream' students as you found find in other school across the UK, so it is essential for me to make sure that each of my students are being challenged in creative ways every time they enter my classroom, but particularly so at the start of a new unit.

So... the plan is?
At the start of this geometry unit, it was essential for me that students had a common understanding of vocabulary as we progressed through the unit. I created a wordlist (without definitions) of geometry terminology that I shared with the students in class.

I then asked them to represent their math terminology in Minecraft. They created a few worlds and decided amongst themselves what terms of the list they will build. I just made sure in the end that all the terminology was covered. As they were building and came across something they didn't know, they had to find out (from anybody or anything - Internet, etc. except for me), but they could use me to confirm their understanding. As they were building, I would prompt them with certain questions pertaining to what they were building at that moment in time. In the back of their minds, students had to keep the definition in mind, because the end product would be a Minecraft representation of the term and it had to be accompanied by a definition. Students then had to put these together then define in the accompanying video that they made on iMovie. This then acts a 'glossary' or wordlist for the unit.

What happened in reality?
As we know about students, what we plan for almost always has a twist to it and that is what I love about teaching! The students did what was expected of them (of course), but then they stretched themselves so much further. For example, as students were constructing pyramids, I was asking them what the differences were between triangular based and square based pyramids. They thought about it and build it. As I came round to them again - they were taking inspiration from ancient pyramids and comparing it - the Mayan step pyramids and the Egyptian pyramids. They added so much depth to their own understanding! 

The final product(please note that I did not edit anything, so there are some errors, but I think it is so great, it's worth sharing!) of one of my classes.

The verdict: My initial list given to students were too long and if you are going to do this, I would suggest you stay within a particular group of shapes at a time: such as polygons or quadrilaterals and add it in the end to the movie together. My mixed up wordlist created a lot of confusion for weaker students. 

It's a bird, it's a plane... No it's an AstroPi!

There are some professional development course you attend that inspires you. You go back into your classroom and you think... Oh, wait! This is too expensive, not enough space... and the story goes on and the training had no real impact on your classroom practice. 

If however, you happen to go on a RaspberryPi training, or PiCademy for short, not only will you come back to school buzzing, you'll come back knowing where to start and what to do. 

I recently returned from Cambridge, HQ of all things Pi and met some amazing people that didn't frown upon this math teacher wanting to learn how to code (and knowing very little) and apply it in my classroom. If fact, I was encouraged and inspired! 

My Pi journey started when I was introduced to all things Pi by my lovely friend and colleague, Lenny Dutton (@missedutton) that attended the very first PiCademy (Read all about her experience in her blog). We attended a RaspberryJam soon after that and I was blown away (and slightly overwhelmed). Lenny encouraged me to apply to a PiCademy. The process was straightforward and at the end you need to upload a video explaining your reason for wanting to attend.

My PiCademy application video below:

I was of course thrilled to be accepted and very quickly connected with other people over Twitter that was going to be attending the same time. If you consider attending, I would suggest this as it was great turning up already 'knowing' people.

The new and improved Pi2

PiCademy started on the Monday and we were all thrilled upon arrival to find our very own goodie bag with a Pi and some more Raspberry swag!
 We received all the essentials to get us going and from the start it was all hands on deck.

Babbage was present to cheer us on!

My day started with an introduction to SonicPi and how fortunate to have the workshop run by the man that created it, Sam (@samaaron)! The code is so simple and straightforward, you have your own piece of music in a few minutes. 

For example:

Play 85

Will mean that the 85th note on the piano will be played, you can add drums and any other instrument you want to. Sam also introduced us to live loops meaning you can change the code in real time. 

Here is an example of him performing at a nightclub in Berlin using live loops - music on the go! 

Apologies for the bad quality photo!

Then Clive (@clivebeale) run as session with us using GPIO (general purpose input output) and we used scratch to control the pins on our Pi's that was controlling a traffic light system on the pins. This was my first time using scratch for any sort of programming and my-oh-my do I see the appeal! This is dead simple to use with kids to introduce them to coding. By dragging a few blocks and changing the parameters you have code!

The session after that Ben (@ben_nuttall) showed us all things PiCam and of course with that a selfie! This photo on the screen is a photo taken by the PiCamera and the phone you see is taken by my phone....

PiCam in action

The afternoon was spend showing us how to build robotics code by Les (@biglesp) and my ultimate favourite (because my students love it so much) MineCraft! The last session was run by Martin O'Hanlon (@martinohanlon), one of the co-authors of the Adventures of RaspberryPi in MineCraft. It started off really easy by first coding the message you would like to see on the screen instead of writing it.

Above: Image of Minecraft with my message 

I loved making Steve do all kinds of stuff, such as making a multi-coloured bridge appear under Steve's feet so that he is no longer flying.

Above: Steve on his multicoloured bridge

And the code for it is just a few lines!

Above: Code making this possible

One of the last things we were introduced to by Dave (@dave_spice) was the AstroPi that completely grabbed my imagination! This made me super excited as a Science teacher as the options here are endless! The AstroPi has so many cool features such as a magnetometer, gyrometer and accelerometer along with an ... Oh LED screen! 

Above: you can see part of the message "One small step for Pi" scrolling the screen.

Day 1 concluded with a lovely meal in a restaurant on the river Cam. 

Day 2 was a day of going away and doing everything yourself. We were asked to think about what grabbed our attention on the first day and to create something. There were such interesting projects creating, such as this one by Mark(@mvnorwood) and Grace(@MissTurner101) where you press Babbage's tummy and he gives you and inspirational quote. 

Above: Babbage providing a quote when you push his tummy.

Then there were also a good project by Alex(@alexyoung25) and Steve(@mrbEDU) that was perfectly suitable to primary school students, where they incorporated SonicPi in Minecraft where you get a different sound every time Steve (from Minecraft) steps on a different material/surface it creates a different sound. Really lovely to see it in action!

 Of course my own bias comes in when I say the last project I'm going to mentioned rocked!!! David(@DesignSaunders) and I hacked an AstroPi and created our very own... MagniPi. The purpose being that if AstroPi can go to space - it can also be used to safe lives. Our idea is that you will place the Pi on the ground and every time there is movement in the ground (more than just vibrations from moving cars, kids playing etc.), of course the theoretical aspects still needs to be sorted, then by using our code, as soon as the Pi moves (more than 10 degrees in either direction), if will tweet a message to you saying: "Get out of here!"

Hacking the AstroPi to turn it in a MagniPi

 After presenting our group projects, we received our certificates:

 And finally we had the opportunity to add our twitter accounts the RCE (RaspberryPi Certified Educators) wall of fame:

And finally I can now say that I am an RCE and this is going to be the start of many amazing all things RaspberryPi to come!

Word of thanks to all the amazing people that organised PiCademy such as Carrie Ann (@MissPhilbin) and James (@jrobinson_uk) that was always on hand to help and a special thanks Lenny (@missedutton) that encouraged me to apply.

How to get involved: Visit the RaspberryPi website and click on this link to apply for an upcoming PiCademy, so that you can join this photo and be part of the next cohort of RCE's and meet amazing people along the way!

Cohort no.8 graduates with a superhero pose!

Superheroes on a coordinate plane

As a way of introducing my grade 6’s to coordinate geometry, I opted for a something different this time - superhero’s. Who doesn’t love it, whether it is DC or Marvel comics and superhero’s have captured our imagination and especially at this age.

I did the basic introduction of x- and y-axis and the origin and how the label - x before y, etc. We plotted a few points together to ensure everybody knew what to do and then gave students the following task sheet containing a list of instructions and coordinate points. 

Above: Instructions given to students

Taking inspiration from connect the dots, I asked students to connect the coordinate points as they are plotting it.

                                            Above: An example of work in progress

Above and right - examples of work in progress

The final product:

The verdict: Students loved this quick activity and you can easily differentiate it by connecting the coordinates to more complex superheroes - other than just a batman logo.

Suggestion: A sunny day works best to hold an image of the logo/superhero in the window and place grid paper over it with an axis already drawn on. If you are finding it difficult to 'plot the dots' plot some dots or your original superhero, it makes it a lot easier.

Gaming in the maths classroom

On Saturday, I presented at the Education Show in Birmingham on gaming in the maths classroom and thought I would share some of my ideas with you.






















Above: Some photos of me before the show. The photo on the right-hand side was taken before the presentation (note the nervous smile!)


As teachers, we need to be convinced of the positive impact something would have before adopting it as part of our educational practice. Initially, we I started out with this project and research I was unsure of (1) why gaming works and (2) how to make it meaningful so it is not just perceived as a reward. However, now I am convinced that gaming is the way forward for mathematics education (within given parameters of course), but gaming is definitely changing students' mindsets and engagement in mathematics.

How the brain works:
If we start with what we know about the brain (at least at this moment in time), stressors for teenagers include many factors and one of those is repeated failure. When students are confronted with these stressors, the amygdala (also known as the switching station) is not allowing information through to the prefrontal cortex. In most mammals we see this as the 3F's - fight, flight and freeze. However, in a teenager in a maths classroom we see it manifest in one of two ways:
1) Acting out
2) Zoning out

It is essential that information arrives at the prefrontal cortex, as it is the prefrontal cortex that allows for critical thinking, reasoning and application of what we are learning in mathematics. However, for the majority of students, mathematics is associated with repeated failure and as a result, the amygdala is not allowing information to the pre-frontal cortex where the need to process and apply the information.

Above: Image of the brain from MyBrainNotes.com edited by Sarah-Neena Koch

This is where the games come in:
If you have ever observed someone playing a video game, you will have noticed that repeated failure doesn't seem to deter them from playing - and you would be correct. When playing games, the amygdala doesn't associated repeated failure with the switching that in other mammals is so important for the preservation of the species, in continues to allow information through to be processed by the prefrontal cortex.

Gaming in my classroom:
It is important to understand the differences between gamification and game based learning. This video I created will explain more:

Gamification:
If you are new to gaming, gamification is the best way to start off. Get comfortable with the various ways you can game in the classroom. I would suggest Kahoot, as teachers you can get it at: getkahoot.com and students access the games you've created at kahoot.it.  You can use kahoot to create polls of just using the online gaming tool. I also use kahoot for formative assessment or as a lesson starter.

Above: Engaging the audience at the show with a kahoot we played together.

I have also used Lego to gamify what students are learning/doing in mathematics.

Game based learning:
There are several games that I have used for game based learning in my classroom, using dragonbox and MineCraft This video will explain more:

I hope you have found this useful. Please get in touch if you are using games in your math classroom so that we can create a community where we share ideas and resources.

Investigating quadrilaterals

Following on for the investigation into triangles last week with my grade 6 MYP class, I had students inquire into the interior angles of quadrilaterals today. They firstly had them identify the different types of quadrilateral and find a ways of organising and identifying when you have what type of quadrilateral.

Afterwards, they had different types of quadrilaterals and cut out the angles from these quadrilateral add them, by means of glueing it to find the rule: interior angles of quadrilaterals add up to 360 degrees.

The verdict: Another fun and easy way for students to investigate the angle rules in quadrilateral. I had them complete a traditional determining angles exercise afterwards and they found it really easy to determine based on previous knowledge. Recommended! 

Investigating triangles

During today's inquiry into triangles with my grade 6 MYP class, we reached for old-fashioned technology - and with great results! Students were really engaged throughout this activity.

I started by giving students an example of triangles with their identities written inside, and they had to label these. For example, acute and isosceles, students had to identify the acute angles within that triangle and then had to indicate the two sides that are of equal length in order to make it an isosceles triangle.

Here is a great example of two of the pieces of work the students produced:

I then asked them to use the exact same triangles (I made two copies of the same triangles), and to cut out the angles (HINT: if you are getting the students to do this activity, get the to cut it round, otherwise it becomes difficult to see where the original angle was). 

After cutting out these angles, students were asked to glue together these angles to find the pattern in the angles. 

After repeating it several times, students realised that it demonstrate that the interior angles of a triangle will always add up to 180 degrees.

The verdict: Great use of time, quick activity, but students find it so easy to remember that interior angles add up to 180 degree. Give it a go, it's so worth it!

Math class without numbers?

You are joking right? Surely that is not possible in a high school?

In an attempt to re-engage my students with sequences and series, I invited them to create a sequence using only paper and scissors. I explicitly told them that they are not allowed to write any numbers, but can model and explain their sequence using words in everyday language.

After a few moments of staring at the pieces of paper in front of them, ideas started to emerge and the previously disengaged class was not only engaged and the most surprising, the students that I struggle with most in terms of engaging, was the most engaged! Not only were they ‘hands-busy’, cutting away, they were ‘heads-busy’, as I would often hear conversations about whether this particular piece was indeed a sequence or not. 

Here is some of the work they’ve created: 

Each time the paper is folded open, it produces the sequence 1, 2, 4, so as this student commented, that if it was a infinite piece of paper, this would have produced a geometric sequence.

Considering you are starting (with the man in the middle) each additional layer, would provide a +1, so therefore this student created an arithmetic sequence.

We had discussions that ranged from what makes a pattern a sequences, and when it is a ‘normal’ arithmetic sequence and when it is a recursive arithmetic sequence. They could correct themselves on the terminology we so easily get tripped up on, one student started “this is a series of circles, oh no! I’m not adding, the pattern repeats. This is a sequence of circles…”.  (As seen below). 

One of the students referred to different terminology - she explained “this is my pattern of triangles, but when I fold my paper and bend it down, I introduce a line of symmetry”. 

Another student, produced smaller cut-outs that they arranged and re-arranged every time to create various different sequences (both arithmetic and geometric).

The verdict: This is a fun way to either introduce or reflect on sequences in mathematics. It is not very time consuming, but involves great amounts of fun! Fantastic to get students talking about what they created without feeling the 'pressure'. Highly recommended! 

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!