The UKEdChat Mathematics Subject Special was on Thursday 23rd October, the previous link now includes a record of the chat.
Note the questions raised during the chat:
- What are some of your key mathematical questions you use in lessons? Share your favourite maths starter activity.
- What are your favourite maths resource sites for inspiration? Who are inspired maths tweeters you follow?
- Which maths topic do your students struggle the most with? What support strategies do you use for them?
- Homework … Which are the most successful strategies you use for maths?
- Maths and computing go hand in hand. How are you tapping into this connection?
- Final call. Please showcase your favourite aspects of maths teaching / resources / tips.
I have mentioned many resources you may find useful in connection with many of the questions in my ‘Resolutions for Mathematics Teachers” reproduced here:
How time flies – it is almost half term and I realised that I had not set my new classes up on Manga High or Sumdog which I have now rectified. Looking at the games again on Manga High in particular I was struck by the excellent variety of Mathematics skills involved. So many so called Mathematics games are simply Arithmetic but on Manga High students can use games to practise Algebra and Geometry as well as Arithmetic Skills. The Basic Package (free) allows access to all the games and teachers can set the excellent Prodigi Quizzes for a week at a time; teachers will find clear Getting Started Guides here. Scroll down this page to see some samples of the quizzes and for a very comprehensive guide to the content check the information here selecting Algebra for example shows the extensive resources available.
With my Year 9 (UK age 13-14) class we have been studying simultaneous equations and for their homework as well as the text exercises I have given them some alternatives online to support their work, as a school we use MyMaths (subscription site), I have also linked to David Smith’s excellent site (free) and I have just added three Prodigi quizzes to the list! It will be interesting to see which they like – I feel a survey coming on!
Returning to the games, hover over any game to check the skills tested; for example try Algebra Meltdown or The Wrecks Factor for algebraic skills.
I have written on Sumdog before, that post has various useful links. You will see from the Sumdog blog that you can now choose skills appropriate for your school; having initially chosen the UK National Curriculum – I changed my mind and went back to the Classic set – skills for 5-14 year olds, worldwide.
Reviewing some TES resources I was reminded that Loop cards can make a great starter or plenary. This rather attractively presented resource on Significant Figures by Natasha Keyes is a Word file so could easily be adapted for short question types.
Before you create your own though, try this TES collection! See this great set of Trigonometry Loop Cards from Interactive Maths for example or a Quadratics Treasure Hunt by Nicole Cozens or perhaps some Inequalities from James Lockhart. Note you can narrow the search by Key Stage and then by topic. (There are Loop Card activities available for many subjects, not just Mathematics).
The wonderful Tarsia software has Follow Me cards as one of the output types so this could be a good way to create any new sets, the maximum size for a single set is 24.
The more sophisticated versions of loop activities like treasure hunts, can make an excellent main lesson activity. MATHSLOOPS from the creator of MathsBox shows how sophisticated loop cards can be; there are three free sample sets available, questions aimed at (current!) GCSE grades A, C and G.
Of course Treasure Hunts are very similar in that the answer to a question leads to the next question. I have found Treasure Hunts make a real change in that we are all moving round the room; I find this a good opportunity to also wander round the room and talk to lots of students. With Year 9 this week a Trigonometry treasure hunt worked really well and I learned from them that a witty colleague of mine had hidden one of the questions on the inside of the cupboard door when doing a treasure hunt with them! Returning to MathsBox again there are several free samples available. (To see the collection of free samples, see this page then choose Samples and choose a resource type from the menu on the left.) There are many Treasure Hunts on TES resources – they seem to turn up in the Loop Card search, but you can also search for Treasure Hunts.
The simple short answer type loop cards (also sometimes called ‘I have you, who has..’) make ideal starters or plenaries as a whole class activity, each student could have a card each, alternatively perhaps a group of students could have a set of cards for the group.
With my Year 12 classes (UK age 16-17) we have been looking at quadratic inequalities and it struck me that as always a really good picture is what we needed – so of course I turned to my favourite graphing calculator and created a couple of Desmos pages for them. I have written a post for them on Mathematics for Students with the links to the graph pages, also a link to David Smith’s The Maths Teacher site and a reminder that you can of course just enter your inequality as a WolframAlpha query.
In other classes this week – yes it was a good idea to have Year 9 measuring triangles to introduce trigonometry – so far so good – I believe they understand the trigonometric ratios – I’ll be more convinced when I see their books this coming week.
Year 11 now regard Circle Theorems as good puzzles and Geogebra applets worked really well for demonstrations. Talking of GeoGebra – look at their newly designed website.
Year 13 Further Mathematicians have seen the benefits of throwing a matrix into WolframAlpha (just enter the matrix and you’ll get the inverse, eigenvalues, eigenvectors & vectors & more). When I get email queries including the words ‘I checked it on WolframAlpha….;’ I know I’m onto a good thing helping them to help themselves.
And finally I’ll mention a rather interesting looking app Math Chat which I learned about on Richard Byrne’s wonderful Free Technology for Teachers – currently only for iPad and iPhone – but I am assured by Math Chat that they are planning on expanding to Android soon and expanding onto the web too. When they do I’ll come back to it. It is interesting that my post on Writing Mathematics online has been one of the most consistently popular posts since the early days of this blog. LaTeX is all very well but to be realistic – our students are not going to be writing lots of LaTeX any time soon.
This week I will be introducing Trigonometry to Year 9 (UK Key Stage 3, age 13-14). I always like to begin trigonometry with students actually measuring lengths in triangles, I believe they get more of a feel for the meaning of the ratios of the sides of a triangle if they have actually measured the length of the sides and calculated the ratios themselves.
I decided what I need is some accurate drawings of triangles of various dimensions that they could work on. It took a few seconds (the third entry in the search results for introducing trigonometry) to discover not only the drawings I wanted but a perfect recording sheet! From NZmaths (New Zealand Maths) – a site I have mentioned before for its excellent resources comes Introducing Trig. As well as the resources, teachers’ notes are provided. (Scroll to the end, past the teachers’ notes for the resources)
So after an introduction including a reminder of Pythagoras they met last year, we’ll just need to be clear on the terms opposite, adjacent and hypotenuse, how to complete the recording sheet and the measuring can begin! This is a very able group of students and I suspect several of them to be telling me for example by the end of the lesson that sin 60° is the same as cos 30°.
Checking a few more links in the results of the search I see the excellent Math Open Reference site which I have referred to on several occasions. I also see that I am in very good company in my desire to get the students measuring themselves and using the nzmath resource – see Dan Pearcy’s post.
Something else I like to do when discussing trigonometry is to discuss all the possible types of problems that can come up because whether they are disguised as buildings / trees / ladders or whatever there are still only a limited number of problem types, eg find the angle given the opposite and hypotenuse. The students can work out how many problems there are.
I’ll update this post with how we got on!
At the moment I am introducing calculus to my sixth form classes and I wanted to use Desmos to illustrate drawing a tangent to a curve. A quick search found this. Copying the page to my own account I then modified the page to show a simple quadratic (f(x) = x2).
Desmos – tangent to a curve
Something I have been meaning to do for a while is try the folder feature on Desmos, a rather neat way to create a tidy looking set of items.
Desmos page notes
Show / hide folder contents
Folders are easy to create:
Desmos – add folder item
Having created a folder, press enter and the next item will be placed in the folder. If you want to add items later, ‘nudge’ your item into the contents of the folder.
I recommend that students use Desmos to help them understand any questions they do; finding the equation of a tangent to a curve is a good example, Desmos can be used very quickly to illustrate a correct (or not!) solution.
For checking calculus examples students can use WolframAlpha, examples are included in the fourth slideshow here).
Update ….and along came @Desmos! (select either picture for graph page)
Tangent to curve – fabulous version by Desmos!
Thank you @Desmos! (Think I’ll put in a few requests!)
…such a busy one – so I’ll be brief (but can’t break that new year resolution of January 2011, the only one I have ever kept, to write a post each week!)
So this week – I have been using my name cards – I’m learning names fast! My classes all know that I think WolframAlpha and Desmos are rather useful and we have had some great discussions on the learning behaviours I’ll be noting about them all on ClassCharts.
I must recommend the free samples from Bring On the Maths, the Core 3 activity – Logarithmic equations worked really well with my Year 13 class and next week I’ll use the C4 Binomial Expansion resource when we are talking about the validity of a given expansion. I have used the Trigonometric Ratios resource before – and will again; there are several other great resources in that list of samples – explore!
Now to hand over to a master (and his son), I love this TED talk from Hans and Ola Rosling. Can you do better than the chimps? Why we are all so statistically ignorant! (More on The Ignorance Project)
Planning some lessons for the week I realised that I will be telling all my students about Craig Barton’s and Simon Woodhead’s wonderful Diagnostic Questions website so thought I would write this week’s post on that (again!). By some amazing coincidence as I started typing – into my inbox comes notification of a new post from Craig! He has been writing lots of lovely new questions and we can look forward to more (thank you so much Craig!).
Diagnostic Questions can make a great start (or any time!) to a sixth form lesson. I will be teaching Year 13 (UK age 17-18) this week about logs and exponentials. The Post 16 – Pure section has a growing and great selection of questions. Checking Logarithms and Exponentials I think those will do nicely as part of my lesson! As a registered user I was able to create a quiz consisting of all these questions. By creating a quiz one can order the questions exactly as required and also very easily create a PowerPoint slideshow for offline use, alternatively or as well – simply download the pdf version.
I find the easiest way to create quizzes is to use the Instant Quiz Facility which I have written about before; I thought it would be worth putting all the instructions together so created the following slideshow showing how I created the quiz on logs and exponentials. To create a new quiz I make sure that the Instant Quiz has no questions currently in it so have got into the habit of clearing it out once I have created a new quiz. The instructions for doing so are included here.
Using the option to download images I created the following PowerPoint:
Logarithms & Exponentials diagnostic questions
For completeness this slideshow gives instructions for downloading a quiz you have created and quickly creatng a PowerPoint slideshow for offline use.
To see the pdf version choose this file: Logs & Exponentials Diagnostic Questions
To view the quiz online then follow this link.
So – back to school again and I thought I would make a final and rather important update to Resolutions for (Mathematics) Teachers. Reading John Hattie’s Visible Learning for Teachers is such an important reminder that we should really be looking at the impact of all we do on our students. We might think a particular method or resource is amazing, but do we think so because we have considered very carefully how it will help our students learn?
For a summary of the book, read this from The Main Idea.
The five dimensions of Expert Teachers Hattie identified were based on a review of the literature.
- Expert teachers identify the most important ways to represent the subjects they teach
- Expert teachers create an optimal classroom climate for learning
- Expert teachers monitor learning and provide feedback
- Expert teachers believe all students can reach the success criteria
- Expert teachers influence a wide range of student outcomes not solely limited to test scores
Dimensions 4 and 5 remind me of Carol Dweck, I wrote recently that these points she made struck a chord with me: for teachers to develop a growth mindset in their students they need to develop their own growth mindset; do we ever judge our students too quickly? Also, such a useful reminder that we may sometimes worry too much about ‘teaching to the test’ when we just need to remember that ‘The outcomes are natural byproducts of engaging in good practice’.
A thought provoking interview with John Hattie can be found here in an issue of ‘In Conversation’ (Spring 2013). The interview is structured round the eight “mind frames” discussed by Hattie in Visible Learning for Teachers.
I have sometimes listened to audio books as I do like to hear authors read their own work, I believe it helps understanding. You can hear John Hattie himself on the principles discussed in Visible Learning in these two videos: Visible Learning Part 1: Disasters and below average methods and Visible Learning Part 2: effective methods. If you are in a hurry you might want to skip straight to the last part of the second video! For anyone who can’t get enough of Hattie, he was interviewed recently as part of Radio 4’s series The Educators, you can listen here.
For further reading of current ideas, see Tom Sherrington’s excellent collection: Contemporary educational ideas all my staff should know about.
If you are about to return to school (or have already done so) then I wish you and your students a great year.
One of my personal resolutions for the coming year is to carry on with my practice of using resources that students can then refer to or use at home if they wish. Mathematics notes and calculators are a good example of such resources.
To consider an example, early this term with the Further Mathematicians I will be studying matrices and I will let them know the sources of any resources I use in lessons. I use a blog to provide the details of my students’ homework so I can simply add the links to their homework page. Sometimes where there are several useful resources I think maybe of interest to a wider audience I also add a post to Mathematics for Students, see for example, Polar Coordinates. In fact I think I will do that more this year.
To return to matrices, some useful resources include the following:
On the AQA website the Teaching and learning resources page for A Level Further Maths includes three online textbooks under the Resources for students heading. For example if I want a worked example of finding the inverse of a 3×3 matrix then we can look at Chapter 5 of AQA’s Further Pure 4 text. This also has an exercise with the answers at the back if they want additional examples.
The Math Centre
More sources of notes and examples include Chapter 9 on Matrices and Transformations from the CIMT Further Pure Mathematics A Level material, Just the Maths, the Math Centre and The HELM Project. If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include clear worked examples. You can see on the list that a very small number of titles (that you are unlikely to want A Level) are ‘not ready yet'; for the sake of completeness I discovered the complete set hosted by the Open University. To access the Open University resources you will need to create an account (easy and free), this will also give you access to the numerous free online courses.
Obviously we need to keep an eye on the specification when looking at alternative sources of examples but surely that can only be a good thing, particularly for our students who will be off to university in the near future.
Matrices is an example of a topic where it can be very useful to check work with WolframAlpha; I have created a new slideshow of Matrix Examples to add to the WolframAlpha slideshow series so we can easily check any work.
The series is on Mathematics for Students also and a post including the matrices resources discussed here has been added also.