GeoGebra

GeoGebra is astonishingly powerful and seems to keep just getting better. It works brilliantly on my phone and my tablet as well as on a desktop. I will be using it a great deal more in future with all the students I teach.

Time for some new pages on GeoGebra, this collection will grow, but I wanted to bookmark the tutorials and note also how to very simply use the Data Analysis tools. Sophisticated analysis is possible of course but in moments one can copy data from a spreadsheet application to GeoGebra’s spreadsheet view and see some charts.

These Tutorials are an excellent place to start learning how to use GeoGebra. GeoGebra works not only on desktops but on phones and tablets as well.

The Manual is comprehensive and note the Quick Start tutorials which are very clear. You will also find manuals and much helpful documentation on the same page. The great thing about GeoGebra is that so much has already been written you can probably find what you need already online!

You can also use GeoGebra’s YouTube channel to watch demonstrations.

GeoGeoGebra is not just for Geometry, as mentioned above note how good it is for Statistics too, copy in those large data sets and get analysing! (GeoGebra Data Analysis as a pdf file or  PowerPoint: GeoGebra Data Analysis.)

The slides show the Classic application first which perhaps experienced users are most familiar with, followed by the newer Maths Calculators interface. If you are new to GeoGebra I would recommend using the Calculators which of course have the same functionality and more and will give consistency across the various platforms.

So much is already written for GeoGebra you can use material already written. For example thinking try MEI’s very helpful advice on the Use of Technology, also on Integrating Technology into schemes of work for older students (UK A Level  age16-18). Note that tasks are also given by type of software including GeoGebra.

Another source where you will find GeoGebra used to help students understand and explore Mathematics is Underground Maths where many tasks have associated GeoGebra resources. An Underground Mathematics search on GeoGebra reveals the extent to which it has been made use of!

Note also some excellent examples from the ATM Conference 2017.

See also Use of Technology and Statistics in the A Level series of pages.

I would like to thank MEI for an inspirational (and free) conference recently. So many good sessions including the use of GeoGebra for statistical analysis.  A highlight had to be looking at the GeoGebra 3D graphics view with our 3D glasses!

Functions – an update

I have updated a post on functions with the excellent PhET simulation, Function Builder

The post includes several excellent resources for teaching functions. See also this further post aimed at older students.

PhET Simulations look excellent, I will be exploring more of these. I have used the Projectiles Simulation with Mechanics A Level students and have posted on this for students on Mathematics for Students. There are numerous PhET simulations covering Physics, Biology, Chemistry, Earth Science and Mathematics. Note the growing collection of HTML5 versions which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

PhET Balancing Act working nicely on my phone!

For Valentine’s Day…Make Linked Möbius Hearts

The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  We even have 9 Maths skills you need to win the Great British Bake Off!

For Valentine’s Day, have a look at this post from Maths Careers with instructions on how to make this wonderful pair of linked Möbius hearts.

If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked  as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….

Note the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper. See Valentine’s Day for the Desmos details.

To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white spce at the end – the picture here has been made using strips 10 cells long.

Valentine’s Day …

It’s that time of year again – save your money and send your loved ones (or anybody!) a math-o-gram!

Click on the image and move that slider!

Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!

Valentine’s Day seems an appropriate time to express love for Desmos!
Geeky people you could even use the Desmos API …

Remining with the loving theme you can also express your feelings for WolframAlpha!

Valentine Relay – Chris Smith

For some Valentine class activities, try the Valentine Relay from Chris Smith and note all the other relays in this excellent set of resources. You can find more excellent resources from Chris on TES and follow him on Twitter here.

and here’s a Valentine logic starter from Transum.

Top Tools for Learning 2016

Jane Hart is the Founder of the Centre for Learning & Performance Technologies and 2016 marks the 10th year of her annual Top 100 Tools for Learning list. Jane has put together all the presentation slidesets as well as an alphabetical list of ALL the tools which have appeared on any of the lists.

The 2016 slideset is shown here.

Note from Jane’s overview she has done a finer analysis for 2016 including the Top 100 Tools For Education (for use in primary and secondary (K12) schools, colleges, universities and adult education.)

Back in April, I wroye about my own choices for 2016 and I am always interested to see where my own choices are in Jane’s list.

 CY 2016 votes Education Personal Learning & Productivity Place in Top 200 2016 Place in Top 100 Tools for Education 2016 Evernote x x 17 27 WordPress x x 9 13 Google (search) x x 2 4 Twitter x x 3 5 Slideshare x 18 21 PowerPoint x 4 3 Excel x x 46 45 Moodle x 27 11 WolframAlpha x 198 – Desmos x – –

Those were my own 2016 choices as top tools for learning because these are tools I use all the time in my job, both in my teaching and in my role as a senior leader. Note that we are not discussing subject specialist resource sites here, but tools for education generally; I think it is very useful to remind ourselves of Jane Hart’s own definition:

“Any software or online tool or service that can be used for your own personal learning or for teaching or training”.

Two more very useful views that Jane has compiled is this Quick View showing the place in the top 200 list, compared to against the Top 100 Tools lists for Personal & Professional Learning (PPL100) for Workplace Learning  (WPL100) and Education (EDU100) and the Movers and Shakers.

Looking at the Movers and Shakers, I see WolframAlpha has crept in at 198 on the Top Tools list, so I wasn’t the only one who voted for it! Quite rightly Google Forms is another new entry; I think my own vote for Google (search) was actually also a vote for Google Docs / Google Apps for Education / Google Calendar! Google forms is such a good way to collect feedback. See for example slides 63-83 for Student Feedback on Low Stakes Testing. where I used this form.

Noted in the Movers and Shakers list are tools which have jumped up more than 15 places. Trello is indeed good for organising information and is easy to use for collaboration. With my interest in retrieval practice I want to revisit Quizlet. Also on my list is One Note, though not to replace Evernote but complement it. More to explore – Canva and I see Richard Byrne has posted on Canva new features.

Low Stakes Testing in the Mathematics Classroom

Low Stakes Testing in the Mathematics Classroom (PowerPoint File, takes a few moments to download)

Or use this shorter version to see the slides on the student survey on low stakes tests.
Mini Tests Colleen Young for PowerPoint

Slides from the BERA Conference, Learning from the classroom – Practitioner research in mathematics education – July 2016

There are many hyperlinks provided in the presentation, for ease of access these are also provided below:

Solving Linear Equations

A collection of resources to use to demonstrate and practise solving equations.

Student Exercises
I find Owen Elton’s worksheet, Balancing Equations on TES Resources very useful when introducing equations, the diagrams emphasise that we must do the same to both sides.
(See Diagrams in Mathematics, for more on the use of diagrams to help understanding).

Balancing Equations – Owen Elton

Linear Equations – Don Steward

As an alternative to the balance approach, consider this doing / undoing approach, described here by Don Steward, this is an approach I use for finding inverse functions. The exercises Don refers to are here.

A2 – Mostly Algebra

One of the Standards Unit resources, A2 Creating and solving equations (in Mostly Algebra) uses this approach, students create an equation and  then undo it; this is a great exercise for demonstrating notation. Another resource with this approach comes from the Mathematics Assessment Project (the design and development was led by the MARS Shell Center team at the University of Nottingham) Building and Solving Linear Equations lesson

For a superb collection of ideas and student exercises for solving linear equations see all Don Steward’s posts tagged linear equations. Many of these outstanding resources use a very visual approach with very clear diagrams to help students’ understanding.

Diagnostic Questions

There are numerous questions on linear equations on Diagnostic Questions.

A simple way to check a solution to an equation of any type is to simply enter your equation as a WolframAlpha query. Note that WolframAlpha includes a graphical illustration; it is so important for students to understand how equations may be solved graphically; I always illustrate graphical solutions when we are working with Algebra to help students make these links. Desmos of course, is ideal here.

Centre for Innovation in Mathematics Teaching

CIMT
have tutorials on equations: Linear Equations 1, Linear Equations 2, and Linear Equations with Brackets in their Interactive Resources

The following three resources work well for demonstrating the balance method of solving linear equations.

Duncan Keith’s Linear Equation Calculator is available on STEM Learning.

Choose the type of equation you require then the sequence of operations required to solve the equation.
Select Do it after each operation, for example -32 Do it were the keys selected to start the above problem.

The slideshow below shows how to use the calculator to solve equations where the unknown is on both sides.

Mathisfun

Mathisfun

Mathisfun has this very clear and easy to use interactive illustrating the solution of linear equations.

Top 100 Tools For Learning – 10th Anniversary

Jane Hart is the Founder of the Centre for Learning & Performance Technologies and as you can see from her blog, 2016 marks the 10th year of her annual Top 100 Tools for Learning list.

Jane has put together all the presentation slidesets as well as an alphabetical list of ALL the tools which have appeared on any of the lists.

The 2015 slideset is shown here.

Voting is now open for the Top 200 Tools for Learning 2016 and will close on Friday 30 September 2016, and the 10th annual list will be released on Monday 3 October 2016. You can find all the voting guidance and forms here. Note the 200, not 100; as you can see from Jane’s description she is making some changes to celebrate the anniversary.

From the voting guidance you can see that there are three methods of voting, my choice is:

So these are my own 2016 choices as top tools for learning because these are tools I use all the time in my job, both in my teaching and in my role as a senior leader. Note that we are not discussing subject specialist resource sites here (that’s another whole (updated) story), but tools for education generally; I think it is very useful to remind ourselves of Jane Hart’s own definition:

“Any software or online tool or service that can be used for your own personal learning or for teaching or training”.

 CY 2016 votes Education Personal Learning & Productivity Place in Top 100 2015 Evernote x x 10 WordPress x x 8 Google (search) x x 3 Twitter x x 1 Slideshare x 20 PowerPoint x 5 Excel x x 56 Moodle x 15 WolframAlpha x – Desmos x –

Looking at Jane’s alphabetical list of ALL the tools which have appeared on any of the lists, I thought it would be interesting to see which tools have been on all nine lists to date and also at popular tools from the last 5 lists, 2011-2015. I used a favourite tool, Excel to create these, the file is available if of interest: Jane Hart Top 100 Tools – Colleen Young analysis Note the tabs at the bottom, the first three worksheets show the tools which have been in every list, 2007-2015, the last two look at the longer list of tools which have been in the list for the last 5 years. You can read Jane’s fascinating analysis of trends for work place learning.

Tools on the list every year since 2007

Average Rank 2011-2015

To elaborate further on my choices
Evernote
– an outstanding note-taking tool and something I use every day. I have a notebook for each of my classes to which I upload any resources I want for that class; I also jot down any ideas I have for each class. I can use it on any PC, tablet or my phone. It is also a good way to share for example a list of websites with students – using a shared notebook. I have many notebooks both for my job and life generally; the search facility in Evernote is awesome and the ability to link from one note to another, very powerful. (Blog post on Evernote).

WordPress  – obviously – you are reading a WordPress blog right now! I have several other blogs, GamesStarters and for students I have created Mathematics for Students and something I am very pleased with is a blog I use to give the details of homework for each of my classes. I created ‘What was that homework?’ as a result of a survey of students across several schools where many students said that they would like homework details online. No student can ever say to me that they didn’t know what their homework was! I also have blogs on useful tools for students and teachers generally. (The very first post on this WordPress blog – which includes some useful WordPress links).

Twitter  – great for professional development – I have contacts in education all over the globe and have been led to many useful resources by my virtual colleagues! See Mathematics Conversations. and this post on Twitter.

Slideshare  – it is very easy to upload presentations to this (free) presentation sharing site; the two shows above are examples. Presentations for teachers or students could be uploaded for example.

PowerPoint I can’t really have Slideshare without including PowerPoint in my list because that’s where I start with my presentations, often with a little help from the interactive whiteboard software. It is interesting to see how popular PowerPoint was last year at number 5, other presentation software such as Prezi is also useful, but it’s so important to remember that it’s the content that matters! See this post, Presentations for some reading and resources on presentations.

Excel is something I use everyday in my job to analyse and present data; I also use many spreadsheets for teaching. Of all the applications in the Office suite this stands out for me, the changes from Excel 2003 to 2007 with the massive improvements to conditional formatting for example make this one outstanding application. There are also many Excel spreadsheets out there too to help in Maths lessons – see Maths Files for example.

Moodle We have a Moodle course for each year group in school; each course has links to any websites that we use in class so students can investigate further themselves if they wish. VLEs are sometimes criticised for being no more than ‘filing cabinets’; I would argue what useful filing cabinets they are – containing resources chosen by teachers for their students all in one organised place. For example we see that in the run up to examinations the relevant Moodle courses receive hundreds of hits as everything students need was available, not only syllabus information and papers but worked examples that we have uploaded. It is also of course possible to use forums and quizzes on a VLE and being a secure site for the school we can include information intended for our students only.

WolframAlpha.  WolframAlpha is not just all about Maths, it covers so many subjects and even though they would love us to pay for WolframAlpha pro, the free model still offers unlimited queries everyday!

Desmos, the outstanding graphical calculator deserves a vote in my opinion, it is wonderful for learning mathematics, accessible for young students yet has the sophistication required for university students. Brilliant. It is entirely free, very simple to use even for young students and brilliant for projecting in lessons. There are also free apps for both Android and iOS.

So that concludes the voting from Colleen as 10 tools are needed for a valid voting entry!

Circles & Tangents

Desmos – Circles & Tangents

Use Desmos to explore tangents to circle through given point

Teaching Year 10 about the equation of a tangent to a circle at a given point I have created a Desmos page. I have also created a Diagnostic Questions Quiz using questions on circles (centre the origin) from Diagnostic Questions.
(pdf: quation of a Circle & Gradient of Tangent)

(Also added to GCSE New Content page)

An early introduction – plot some points and functions
Desmos – points & functions (for PowerPoint file)

Graphs-GCSE for PowerPoint file

Writing Mathematics Online

I have written various posts on the available tools online for writing Mathematics and this is a topic which remains consistently popular. Time for yet another revisit and update as new possibilities are now available – all resources / links here have been checked. I have removed resources where blogs / twitter have not been updated for some considerable time as I think this is a cause for concern regarding the longevity of the resource.

Something I use a lot. I should explain my requirements – I want tools to communicate Mathematics online, for example I may wish to provide some model solutions or answer students’ questions. Writing mathematics can be a pain (and yes I know about LaTeX). Note that there are various possibilities – sometimes just a static picture is required, sometimes you may want to display how to solve a problem in stages, or perhaps you require a collaborative space. You will also need to consider if you want the examples to be permanent or whether you just want a collaborative space for discussion. A graphics tablet is essential.

My favourite method for illustrating Mathematics online (and in fact the one I use most often) when I just need a series of static displays is to turn an interactive whiteboard flipchart (or a PowerPoint) into a pdf file; the pdf file can then be sent to students or uploaded to whatever virtual learning environment or online storage your school uses. If you do not have access to interactive whiteboard software there are alternatives, one could use Windows Paint for example; there are also various free online tools available; see some of the resources below.

flipchart to pdf example

For sharing resources, it is possible to upload a PowerPoint or pdf file to Slideshare. There are many examples on this blog of my SlideShare slideshows – see this for example

I should mention that I find Slideshare excellent – I use the free version which offers me everything I need – it works every time – I use it a lot!
I created the PowerPoint for the slideshow above by writing on the interactive whiteboard software using my graphics tablet and taking a picture of each page using the Windows snipping tool (it’s in Accessories) – this takes seconds – the snipping tool is something I use every day! (Alternatively I could have saved the interactive whiteboard flipchart as a pdf).

There are as always several options:

Screencastomatic

If you wish to record a screencast of the moving pen / step by step solution variety and save your work, Screencast-o-matic is an excellent option. It is very easy to use to capture the screen and your recording can then be uploaded to YouTube if you wish.

Illustrating how to simplify an algebraic fraction :

Screencast-o-matic offers everything I want in this category. It is very easy to use indeed – I can write very smoothly whilst recording.

Further resources offering various solutions for writing Mathematics online:

Twiddla

For a collaborative board, try twiddla which seems excellent for collaboration – voice as well if you want. Twiddla offers some very sophisticated features including the ability to use mathematical formulae and upload files and images. Use of the board with all it’s features is free but you cannot save any of your work (possible with a subscription). This would be good for working online with a group of students.

Doodle.ly

Doodle.ly offers a very easy way to have a quick scribble and then share your thoughts! See quadratic example (and note that I created that just to test Doode.ly years ago – a good sign that it’s still there!) Select Doodle Now, doodle, then if you want to publish you will need to sign in. You can sign in with Twitter or Facebook. I like the different pen tools available, the full screen option and the ease of publishing. Apps are available for Android and iOS

Glencoe – virtual manipulative

Richard Byrne on his wonderful Free Technology for Teachers blog wrote a post, “Seven Free Online Whiteboard Tools for Teachers and Students”. Richard has also written more on Screencasting tools.

If you are looking for more online whiteboard applications then you could try the interactive whiteboard manipulative from Glencoe  (I came across this in a Google search). Note the various backgrounds and manipulatives available.

Bruno Reddy – Geometry Toolbox

I can’t mention online whiteboard tools without mentioning Bruno Reddy’s lovely Geometry toolbox – this is great for demonstrating constructions and is on the teachers’ section of his excellent site.

If you want to draw some pictures and like the idea of more crayons and pens then you might enjoy these tools!

Finally – your students may find this amusing – the Writing Repeater – write something and play it back – now this is a lovely tool for little ones learning to write but I’m sure we can think of some uses!

By Colleen Young