'Technology and rich mathematical tasks'

This page is a brief description of a 6 hr course being run offered at this years TSM conference in Keele, UK, July 8 - 10 2014. The long running conference is organised by Douglas Butler and friends and will, this year, host guest speaker Simon Singh.

Eventually, this page will be used as the hub of the course for participants.

Rich, engaging tasks that promote mathematical thinking are, for me, the holy grail of maths teaching. I have often made the mistake of assuming that technology that got me excited will get my students excited and been disappointed to find that it did the opposite. We can’t assume that technology alone will be engaging and need to give as much thought to mathematical task design when using technology as when not.
This course will offer numerous examples of technology based tasks that promote mathematical thinking and are rich in possibility. Tasks will cover a range of software including Autograph, Geogebra, Excel and a number of web based virtual manipulatives.

• Participants will do mathematics and we will examine the merits of the tasks offered and suggest alternatives.
• Participants will receive tuition in the skills required to design and perform the tasks offered.
• We will consider how we turn a versatile manipulative in to a rich task.
• We will look at how technology can breathe new life in to old problems.
• We will look at how and when technology and paper based tasks blend together.
• Having considered the elements of rich mathematical tasks, some time will be devoted to creating new ones.

At the end of the course, participants will hopefully have seen how great tasks are often made out of simple bits of technology that depend more on task design that technological skills. People will go away with a host of resources they can use in their classrooms but also, perhaps more importantly, the confidence and skills to continue creating their own.

Resources

For those taking part in this course, you will need access to some files along the way. They will be shared with you at the start, but are also available through this link  Technology and Rich Tasks at TSM on Google Drive

The sessions are roughly split in to the three categories below, but there are other things that can creep in here and there and more resources to go with them in the folder. Also everything remains flexible, depending on how things go.

Guiding Questions

The sessions principle aim is to focus on the notion that technology itself is not necessarily engaging. Often something is technologically very cool, but not necessarily a mathematical task. Our job as teachers is to make that conversion. To take that technology and see what role it can play in helping students to do, explore  and think about mathematics.

To that end the tasks that are being presented are by nature 'incomplete'. The exercise is part to demonstrate some ways in which the above can be acheived, but more significantly to play with those ideas to develop new ways.

It is also important to balance some perspectives here by considering both our own reactions to tasks as well as those of our students.

The following is a summary of the things I would like us to be thinking about during the sessions. The

• What is the maths involved?
• What role is technology playing? Could it play?
• What is technology adding? Taking away?
• What other questions could we ask?
• What other ways could we present the task for what other benefits?
• What other directions could the task take?
• What other ideas are you having?

A number of key works might be worth referencing here as inspiration for the sessions.

 A Mathematicians Lament - Agree or disagree, it is a great read and deeply thought provoking. 'The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such.'  So many terrific quotes it was just easier to go with the beginning!

 Maths is not linear - A bot shorter than the above but similarly thought provoking. 'Should we be teaching students walk before they can run or giving them something to run towards?'

 Desigining and using Mathematical tasks - This and other works from John Mason have been deeply influential for me. I cant recommend them highly enough and indeed we will be using some of his tasks.

 Mindstorms - My current read from Seymour Papert on the impact that Logo could have on teaching and learning mathematics, written in 1980 with principles holding very much still true.

 The Mathematical Experience - Blantly abusing the opportunity to put myself in such illustrious company, here are some of my assimilated thoughts on the topic of task design!

and finally......

 Is technology a natural medium for mathematics I love this question!

Share your thoughts and ideas

I really like the idea of a back channel for thoughts and suggestions as we go. It always depends on the audience, but it would be great if people would have a go. At the same time you get to try out a useful tool for your classroom. Follow the link  https://todaysmeet.com/TSM2014 By all means, think about answering the questions above on this link.

For now and or later, if you are not already members of this facebook group  Mathematics Teacher Exchange, then please consider joining and sharing. There are currently 492 mathematics teachers from all around the world in this group.

If you are in to twitter then please lets follow each other, I am @teachmaths

Tuesday - Geometry 14h - 16h

In this session we will be looking at some old and new problems with geometry. We will make use of some of the files linked above and some of the activities can be seen in more detail at the links below.

 Congruent Halves,  Dr Who,  Kaleidoscopes  The Voderberg Spiral  How round is your circle?

The main software used for this session will be Autograph  and Geogebra - you will need to make sure you have the software loaded and ready to go.

Wednesday - Functions 9h - 11h

In this session we will be looking at some old and new problems with functions and modelling. We will make use of some of the files linked above and some of the activities can be seen in more detail at the links below. 

 Dancing Quadratics,  Modelling population growth,  Dynamic Scattergraphs,

Manipulatives for scattergraphs Illuminations   Scatterplot    

The main software used for this session will be Autograph - you will need to make sure you have the software loaded and ready to go.

Thursday - Spreadsheets 9h - 11h

In this session we will be looking at some tasks designed to be done using a spreadsheet. Again, files needed are available through the google drive and on the memory stick.

The main software we will sue in this session is Excel.

 Divisibility