Musings on technology in the Maths classroom

circletheorem diagram

circle theorems for the iPad

Over the last couple of weeks I have had the benefit of visiting two different Maths departments in secondary schools. I was lucky to have the chance to talk to about 14 different maths teachers across the two schools.  It was fascinating to see what an amazing job teachers do and what a complex situation they are dealing with. Many levels of differentiation, behaviour issues, a challenging curriculum and the sheer level of organization required to create an effective learning space all make to create issues.

As ever I was fascinated to observe how technology can add or take away from this situation. It was very clear that without good robust infrastructure the technology can definitely be destructive and basically ends up with people not using it. Electronic whiteboards certainly have their problems – often lighting interferes or just placement of students in the room can mean they can’t see it. Most teachers used both a whiteboard and an electronic board.

Whiteboard lesson planning tools can be valuable for teachers as they can build up resources over time. I was shown lots of interactive calculators, interactive worksheets and tricks that teachers used to keep things interesting. For instance one teacher used a random generator to pick the student that they asked a question from. Other teachers used video clips. Teachers also used physical props, scissors and glue, physical text books and worksheets too. Each have their place and  contribute to a varied experience.

It was interesting to see that most teachers did get a fairly dedicated classroom which means they can configure it how they wish (in terms of seating and technology). That opens the door for lots of experimenting which is valuable.

Lots of questions came up for me as a novice observer of this environment notably:

  • Different curriculum models and how they work with technology.
  • Motivating students and Behavioural Issues.
  • Constraints of the Classroom
  • Differentiating

Circular versus Mastery curriculums

In the UK we have a circular maths curriculum… the hope is that if the same things come up year after year getting progressively more complex in the end the student will development their understanding of the whole curriculum. I wonder how we assess if this holds true?

On the plus side the circular nature does give the teacher a sense of security that if they don’t get it this year they will get it next. It also allows for the kids developing at different levels who just aren’t ready for a concept yet.

On the negative side isn’t maths all about building blocks? Sometimes you can’t move forward if you don’t have the basics. Maybe this distinction is build into the curriculum i.e. the concepts that are more basic are taught more solidly. However this wasn’t explicit to me as an observer.

What was obvious is that where you have good IT infrastructure teachers can use the technology to build up good teaching resources. The circular curriculum means that there is potential for lots of re-use (especially because multiple year groups do the same bits of the curriculum at the same parts of the year). The challenge as in any classroom is pitching the material to the class. So there is some scope here for test based tools to provide clues for what should be in a class.

In the States there seems more of an emphasis on Mastery. The Khan academy knowledge map is built on this principle (http://www.khanacademy.org) … you move down the tree once you have mastered earlier concepts (measured via small focused tests). The Gates foundation talks about a non-technology method to do this here.

Technology can be designed to perfectly support this mastery. You can build simple tests (formative assessments) to identify weaknesses and then focus the curriculum to individuals. I can see that a differentiated learning model could be implemented very well. Of course such a model requires a more flexible teaching environment. Again in the US they have been doing this by using something called flipping the classroom. Teachers video there classes and students watch the video’s at home. They then spend the whole of their class time doing problems in differentiated groups. In these classes the teachers role becomes one of a coach. Students who are stuck can review the video live in class and pause it where necessary. These classes tend to be very technology rich with tablets and software that most schools in the UK can only dream about. However certainly the videos showed a very engaging environment.

I wonder whether such a flipped method could be put in place to work with the UK national curriculum? Certainly it would require adequate infrastructure. I wonder a watered down version of flipping could be put in place. I love the idea of student being able to review the original lecture at will. To be honest most of the classes I observed were focused on problem solving for much of the lesson. But this might not be the case at higher GCSE and A-level lessons (unfortunately most of the these lessons I saw at this time of year are based around going through exam questions so were not very representative of the average lesson).

Motivating Students and Behavioural issues

One of the issues that came up when talking to all the teachers was the negative attitude towards maths in the general population. Getting over that has to be one of the key hurdles. Technology can an should be useful in several ways:

a) It should be able to allow you to play with a problem e.g. interactive visualisations of geometry. These can really trigger understanding.

b) Introducing competition by pitting groups against each other. Mathletics and tutpup both do this in the mental maths arena – allowing students to compete with people across the network on simple maths problems.

c) allowing you to escape the classroom and take maths to a different environment e.g. go out and take photos of a item … now find its volume.

d) Maths games – for me perhaps these should be offered as a incentive for groups who have scored highly or even made an improvement on a formative assessment.

e) Give students the tools to go over the information at their own pace. Mymath fills this gap – as well as the numerous videos online. Sophia has hundreds of videos from individual maths teachers. Probably videos created by the students own teacher are the ideal here.

f) Motivational systems that allocate awards, stars etc. I have seen these work extremely sucessfully in the primary sector both teaching typing and in Mathletics.

g) Systems that allow you to record behaviour and rewards/punishments simply.

I was talking to an top stream maths year 8 student yesterday and who said to me “but maths isn’t useful for anything”. This is the age old problem of teaching for understanding or teaching by method. Certainly in the UK curriculum the focus for the lower set students is on method. But are we doing the students a dis-service by not allowing them develop generalisable knowledge?  I liked this video by Dan Meyer which discusses reformulating text book questions to take out a lot of the information and force students to develop understanding.

Constraints of the Classroom

Some of the students I observed clearly found it hard to focus or spent a lot of time fidgeting on chairs. I felt like sending them for a quick jog around the playing field! My sense here was that you needed to get them moving and take them on from one thing to the next.

The classroom really constrains things in some ways. Some teachers did have classes working around tables … but many were in straight lines. Teachers did move students around from week to week. A good technology system did make resetting the seating plan a lot easier.

However I can see that it might be even better if you could change groups more flexibly within a lesson (particularly a longer one). If the technology were to enable you to work in a a hall e.g. with tablets and and a whiteboard – I imagine the class having a different feeling.  Certainly might be fun to make a change from the lecture/problem solving/answers format.

Differentiating 

Differentiating has to be an area that technology can help you because if a students answers are recorded then it should give you clues as to problems. The key here is to keep it as simple as possible. Providing focused material for differentiated groups did seem to be an area which could be supported by technology and perhaps is not at present. This is a great example in early years.

I did not see any explicit mentoring although perhaps that is purpose behind some of the frequent seating plan changes. Some of the best classes I observed definitely had a hum of focused discussion around the problems which was interesting to see.

Conclusions

Technology is being used in the secondary maths classroom to help the teaching process. There are many ways this could be extended in the future.

I am particularly interested to see how the advent of very cheap tablets might change the way maths is delivered in the classroom. I can see there are many ways that this could be done to support learning and the teacher. What seemed very clear is that perhaps the answer is not huge complex systems because teachers need to adapt everything all the time to cater for the complexity of the real life situation.

An app type model might work although it would be great if these could deliver data to a central tool … so that the teacher can get an overview of where the students need to focus more learning.

The other issue is the reliability of the system. In many ways standalone technology should be the aim (i.e. not reliant on the internet or wifi). This would make the system much more robust and also give teachers the freedom to get out of the classroom and take the technology with them.

The important thing to focus on is that the technology must add to the learning experience rather than detract from it. To do this it has to be robust and it has to be extremely simple. Of course there are overheads learning to using anything new but this is different from technology that add complexity to the live situation once learnt. Such technology is not going to be used!

A huge thank you to all the teachers who let me observe in their classroom. Clearly these are the musings of a Secondary Education Novice. I would love to hear comments or reflections from others. Especially on area’s where I may be being naive!

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