TSM 2013

A couple of weeks ago I was lucky enough to attend the TSM Conference at Keele University, hosted by the wonderful Douglas Butler and the Autograph team. The conference is a 3 day residential course, where the focus is on using technology in the classroom to aid in the teaching of mathematics. This is done through two 6 hour workshops, each focussing on different things. The two workshops that I chose were "Laptops and Mobiles" and "Autograph in the Classroom".

Nothing can compare with actually going to this conference, and the number of ideas I picked up was amazing. In this post, I am going to run through some of the ideas that jumped out to me the most.

The Other Parts
I opted in for the optional session on becoming an Autograph Trainer, which included lots of little tips on how to use Autograph to its best, and also how to run a training session. For a two hour session, there were so many ideas that it certainly got me thinking straight away. Some of the most useful buttons (some of which I didn't know about before, and others that I hadn't realised the full potential of) are shown below:

1. the Default Scale button will adjust the scale to fit the graph as best as possible.
2. the Whiteboard Mode setting, which makes all the lines a little thicker, and allows you to select multiple items by just clicking on them one at a time.
3. the onscreen Keyboard which pops up and allows you to not only enter equations from the board, but also has symbols for many common mathematical symbols which can be used in any program. This can also be opened independently of Autograph from the Start menu.
4. the Slow Plot function, that can be used to plot a graph slowly, starting from negative x values.
5. the Constant Controller which allows you to adjust constants in equations to see what happens.
6. the Scribble pen which allows you to write all over the Autograph screen, and easily mark predictions.

The full Autograph Keyboard has many common mathematical symbols that can be easily input to any document.

There are a lot of Autograph resources and links for those who want to learn more, including a huge amount of video tutorials, available at the TSM website.

Although the conference was mainly focussed on the two workshops we did, there were other smaller talks that were fantastic.

We had a fantastic talk from Colleen Young (of Mathematics, Learning and Web 2.0) on blogging as a maths teacher, and she gave a really good insight to why she blogs, and what she gets out of it, as well as some of the highlights of her blog. She of course beat me to it with her own blog post on the conference as well.

There was also a session called the Delegate's Forum, where we got a chance to talk about some technology we have used. Highlights from this included: the fantastic Wolfram Alpha which can answer pretty much any mathematical problem (check out Mr Barton's Widgets); the flipped classroom (see Episode 7 of the TES Maths Podcast); a site full of STEP solutions and other high ability resources.

Laptops and iPads: Putting them to Work for Mathematics!
Session 1
With the introductions over, we were thrown into the first 2 hour session for our chosen workshop. Before we had even started, our tutor (David McGee) had asked us to make sure we were signed up to several services: wix.com; dropbox; google drive; Edmodo. These would prove to be hugely beneficial in our sessions for sharing things we had done easily and quickly. Throughout the sessions we used dropbox and Edmodo to get at files that David had made available in these two areas, and it certainly saved times from emailing it everybody.

We started the session using a Vernier Go! Motion sensor, which records displacement, velocity and acceleration of an object. This data can then be exported as a CSV file, and opened up in MSExcel. We did this for a swinging pendulum (shown below), which gave us a large amount of data.

Vernier Go! Motion recording data for a swinging ball.

A sample of the data recorded from the swinging pendulum.

With this data, we can plot the displacement-time graph in Autograph by copying the two columns of data (Time and Position), and using the Enter XY Data Set.. button in Autograph, pasting the data in the table that appears.

The plotted data of the swinging pendulum.

Since this looks something like a sine graph, we can now approximate it with the graph of y = asin(bx+c)+d and then use the Constant Controller to adjust the values of a, b, c and d to get it to fit over the data.

This could be extended with the velocity-time or even acceleration-time graphs in the same way, and could be used to look at: transformations of graphs; the relationship between displacement, velocity and acceleration; simple harmonic motion.

We also used the Go! Motion to record the displacement of an individual, and got them to walk backwards and forwards in order to plot different graphs. These included y = x, y = x - 1, y = sin(x), y = ln(x) and so on. This could be used to really get students thinking about the shapes of graphs, and how they relate to real world situations, and I really love this idea, as it can be used throughout the whole secondary age range to engage.

Along the idea of fitting curves to graphs, we also had a go at fitting a quadratic to a volcanic eruption, and there are lots of good examples of images that you can import to Autograph on the TSM website.

Using Autograph to fit a quadratic to an image of a human canonball.

In this session, we also talked about using wix.com to set up a simple website (although I personally prefer Weebly, which is how I create this site) to share things with pupils easily. We also discussed and indeed used Edmodo to set up a class to which we could all post documents and ideas to share. This has great potential in my mind, as you can set up a class, add all the students, and then make available to them to download any materials you use in class, post any homework tasks, allow them to ask you questions, and many more things. Edmodo is definitely something I shall be trying out with one of my classes next year.

Session 2
In the second session we looked using wireless tablets (or an iPad) to control what was happening on the screen. An excellent addition (or alternative) to an interactive whiteboard, you can carry a wireless tablet around the room, and even stand at the back of the room whilst writing on the board. You can also then pass it around the room for students to annotate what is on the board. Of course, sometimes you want to get them out of their seats and writing at the actual board, but to have the ability to have them show their solution on the board whilst still sitting at their desk is excellent. The best tablet to buy is the Wacom Bamboo Pen and Touch, with the additional wireless kit. There are apps for the iPad as well, and these were discussed more in Session 3.

We also talked about GeoGebra as an alternative graphing package to Autograph, and the different stengths it has. As with Autograph, there is an excellent "Export to Webpage..." option, which allows users to create an activity and upload it to their own site for students to play around with. The benefit of doing this is that students don't always need to spend ages setting up the activity in the first place, and this way, they can always quickly get back to the starting position. There are many activities for both Autograph (AGG) and Geogebra (GGB) on my site.

One of the major benefits in using Geogebra is that you can have the graph displayed at the same time as the Algebra, and also if you want you can include a spreadsheet. These elements are all related to each other, and changing one changes the others too. This allows for students to really see the connections between graphs, algebra and data. GeoGebra also benefits from the fact that it is freely available to use online, and also, for those that want to, it can be programmed using some javascript or geoscript.

The final thing we covered in this session was using iBooksAuthor to create interactive books for use on iPads, which include descriptions, interactive GeoGebra files, videos and other information. Although a very time-consuming process, the end result that we were shown was very cool, and provided an excellent introduction to differential calculus. Something I might have a play around with at some point in the future.

Session 3
In the third session we focussed on two completely different aspects, both of which intrigued me.

We started by looking at some interesting and useful apps for the iPad (at David's school they have rolled out a one-to-one programme, so every student has an iPad). The uses of iPads broke into 3 distinct types:

1. Controlling the whiteboard and what is shown;
2. Allowing students to connect and work collaboratively in the classroom;
3. Mathematical Apps that are engaging or useful in some way.
   

For the first of these, although there are many alternatives, we were shown Doceri. It was easy to set up with a computer, and intuitive to use. It basically serves as an alternative to the tablets I mentioned above, but with the distinct advantage that you can see what you are interacting with on the iPad screen itself. You can then hand the iPad to students who can write their solutions easily on the iPad to appear on the board. Or why not use the iPad camera to take a photo of their work to show, so they don't need to write it out again. Even better, the whole process is automatically recorded, so any edits you make are recorded. If a pupil is missing from the lesson, you can send them the link to the original lesson, and they will see everything you did in class.

For the second type of app, we saw several different ones, with slightly different approaches. SyncSpace is an infinitely large whiteboard that multiple users can edit at the same time. Assign each student or group an area of the whiteboard to work in, but they can all review what the others are doing at any point. BaiBoard similarly allows multiple users to edit a document, whilst also seeing what others are doing. The difference here is that you can have multiple pages, so can assign a page to each group. You can then easily flick to any page to see what each group is doing. InfuseLearning allows you to pose a question to the whole class, and have their results dynamically displayed as they come in. You can then review their response, and send it back to them with a comment, or bring particularly good examples up on the board, or examples that demonstrate specific misconceptions.

The third aspect of apps we looked at included some of the big hitters in actual mathematical content. The TI-Nspire is a fantastically powerful handheld calculator, with massive computing power and a brilliant CAS system. Unfortunately, the device is very expensive, and the CAS version is not allowed in exams. However, the TI-NSpire app is a fifth the price (at £20.99), and has the full CAS capabilities. The Minds of Math app is a free download and has an extensive amount of information on the history of the subject, with lots to explore. Think 3D Free is an excellent and intuitive app for looking at plans and elevations of 3D shapes.

An image of the TI-Nspire app.

The second part of this final session was on Google Docs, and their uses in teaching mathematics. The ability to share documents easily is becoming more and more important in the world, and Google has provided a fantastic set of applications that can be used online. There is a word editor and a spreadsheet application, that are very good, and rival Microsoft Word and Excel in their usefulness (though they do not yet have the full functionality of these more established products). You can easily create a document, and invite people to collaborate on it in realtime. So you could have the information on the screen, and as pupils input their information it appears. This could be fantastic for the Average Student project I have blogged about previously.

The real power (in my mind) is with Google Forms. Within the same constraints as the other Docs, you can make a form to collect any information you want: it could be ten quick questions on a topic; collecting data for analysis; or any number of other uses. It provides templates, so all you have to do is select the type of question (text answer, multiple choice, on a scale, etc), and type the question. You can then send this out to your students, and their responses are automatically stored in a new Google Sheets document for you to look at. I will be blogging again soon about some of the other cool things I have since found you can do with the Forms.

Overall this workshop was jam packed with loads of different ideas. In fact there are more than I could possibly try, but there were enough exciting ones to keep me interested and looking further in to them. The ones I will certainly be taking further are: Edmodo; some form of tablet to interact with the board; Google Docs. These are the ones that I can see myself making the most out of. I would also be interested in the Go! Motion device, but need to save up a bit more first!

Autograph 3.3 in the Classroom
The second workshop I attended was using Autograph in the classroom, with the fantastic Mr Barton. These sessions were all run in a similar way, where we were shown some ideas, and then given plenty of time to think about and play with Autograph around the main theme of the session. They were split into themes for the sessions: geometry and shape; statistics and data handling; number and algebra. However, although we were introduced to lots of amazing things you can do with Autograph, I am going to focus on the pedagogical points that came up, as well as some types of activities that Craig showed us.

Pedagogy and Autograph
There are two main ways to use Autograph in the classroom. It can be used to demonstrate or it can be used to investigate. The former of these is a passive activity for the students, whilst the latter is much more active. So the question is, how can we make the demonstrations more engaging, and actively involve the students in them. Here are the main pointers:

1. Always get the students to predict what they think will happen. This is probably the single most important aspect of using Autograph (or any other software). This gets the students to think about what will happen, rather than just blindly look and accept. Never forget this.
2. Get students to write their answers down. This could be on a mini-whiteboard, the back of their books, or a scrap of paper, but it gets them to formalize what they want to say, and use mathematical notation.
3. Get students to justify their thoughts and explain their reasoning to each other. You should not only ask for justifications from the ones who get it right, but also those who get it wrong.
4. Use the "wiggle test" by grabbing a particular point and moving it a little bit to show what happens in the image (particularly useful for transformations).
5. Use the software to follow the natural progressions that students follow. If looking at something in 2D, why not extend this to 3D.
6. When using the Constant Controller, start by using concrete numbers (eg y=x, y=2x) then change to the constant (y=ax). However, before clicking OK, go to "Edit Constants" and change the constant to the value it currently has (in this case 2). When you then click OK, nothing will change, and you can ask for predictions when you change the constant.
7. Make use of the Slow Plot and Scribble functions on Autograph.
8. Give students a chance to change their mind. This allows them to feel like they are in a safe environment, where they can make mistakes, but learn from them. It is so important that students feel safe, and allowing them to correct themselves will give them confidence to try.

If you are using Autograph to investigate properties, then think about creating the file before the lesson, rather than wasting time with students creating it themselves. You can then export this as an Autograph Activity and upload it to your own site, or find a collection of premade activities on this site, or from Mr Barton.

Diagnostic Questions
A new project that Craig told us about early on in the sessions is a website he is setting up that will be full of Diagnostic Questions. He described these as multiple choice, closed questions, where each of the three possible incorrect answers reveals a misconception. The theory behind these is that as a teacher you can very quickly identify not only who got it wrong, but why they got it wrong. This also allows you as a teacher to target the students who need the most help, as their misconceptions are the worst.

An example of a diagnostic question. An answer of A shows they have not halved the diameter. An answer of C shows they haven't converted the 2m to 200cm. An answer of D shows they have just multiplied the numbers by pi. So an answer of C is less worrying than an answer of D.

The idea is that Craig is collating a huge selection of these questions, which he will make available in a searchable site, by topic. He currently has around 1200 questions, and he asked us to help by making any more questions for him to add. If you have any excellent diagnostic questions, then I am sure he would gratefully receive them.

Collective Memory
One of Craig's favourite tasks is a collective memory. The idea is that each team has to recreate an image they are shown for only a limited amount of time (and he explains how to run one in more detail on his site). The important aspects for the learning is that you go through any talking points before revealing the image to the class for them to check. He also suggested printing out a copy of the complete poster for each student, which they can annotate with notes and stick in their books. However, the real power of the examples that he showed use was that they all came from an original Autograph file. So once the activity is done, you can open up the file, and use it to further investigate the properties (remembering to get students to predict outcomes).

Data Collection
Mr Barton loves data handling and statistics, and he does not hide this fact. He talked about many ways to collect interesting data to analyse, with one important underlying message: it must be relevant to the students!

One simple way to do this is to show a slide with a number of dots on it for a second, and ask students to estimate how many there are. This is best done if they write their answers down (perhaps on a form using Google Forms), so they are not changing their mind as they see others answers. With all this data, you can then put it into Autograph as Raw Data, and create any number of statistical diagrams, such as a Box and Whisker Plot. Now you can discuss the features of the plot. After this, get them to have another guess at the total (without showing them again), and again collect the data. Ask them to predict how the Box and Whisker Plot will look with the new data, and then input the data, and check their predictions.

Some other ways to collect data that is relevent to the students is: get them to play some online games for homework, and record their best score; use Census at School data, and collect the same data from them (using a Google Form); get them to do an experiment.

One final thing to mention under data handling is the Guardian Data Blog. This takes news stories and creates some fantastic visual data representations which can be used to start lessons, and get students thinking about what the images and charts mean (some of the best examples are below). Even better, most of the stories come with the data available to download, so you can analyse the data using standard methods too.

Overall the TSM Conference was the best course I have ever been on. There were so many amazing ideas shared by everyone, and a real atmosphere of people wanting to find out more. Everyone there was interested in using technology more, and being better teachers. It is an experience I would recommend to every Maths teacher: you will not find any better CPD!