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.
This week Year 10 (UK age 14-15) have been exploring different graph types and also transformations and graphs.
For homework I asked them to draw just a small number of graphs by hand but wanted them to check their work and explore further graphs using the Desmos graphing calculator. Early in the week I made sure they could all use Desmos including the use of tables so in an IT room they used the slideshow here and created several graphs of their own.
Once all the students were confident to use Desmos to create various lines and curves I asked them to explore a series of graphs so that this coming week we can discuss transformations and graphs. Using Desmos allowed them to explore many graphs in a short space of time and several students chose to take screenshots and make notes for themselves.
Desmos – simple transformations example
Having used sliders they were able to create this type of graph page.
I have created the slideshow below to use in class to summarise our work and act as a revision aid for them.
These slideshows are both available here for students.
One of the most popular posts on this blog is Top >10 Mathematics Websites. It struck me that it might be useful to think about my top recommendations for students; once again using some categories as well as individual sites gives me the excuse to mention more than 10! So for your students:
Top >10 Mathematics Websites for Students
Back to the teachers!
I have mentioned TED-Ed before with its collection of Mathematics videos, note the feature now offered by TED-Ed to ‘find and flip’ which allows you to use a video and turn it into a lesson; see ‘Flip This Video’.
Looking at some videos, it struck me that something like Gaurav Tekriwal’s The magic of Vedic Math would be ideal to tinker with! (These ‘tricks’ can make ideal starters, I have linked to some further videos on this page on Number on Mathematics Starters.)
On the subject of videos and TED, have you heard Ken Robinson’s latest talk,
How to escape education’s death valley?
Below I have given details of some resources I am currently using with my classes or have recommend to my students so they can explore examples further themselves.
Year 12 (age 16-17)
I want to talk about quadratic inequalities this week so I thought I’d use the Desmos graphing calculator to draw some pictures! Click on the image for the Desmos page and select ‘projector ‘ mode for display on the interactive whiteboard. Last week a student in this class asked where she could find some additional resources on polynomial division.
Note: I use the Desmos calculator so much I have decided it deserves a page of its own here (under Resources).
Year 13 (age 17-18)
Some students in a Further Maths class asked for some Polar coordinates resources to support their studies – so a post for them on my blog for students – these resources would also work well on the interactive whiteboard for use in class. As regular readers know I am a great fan of WolframAlpha and use it with all my classes (WolframAlpha now have a paid for service but it is still completely free to use to check answers for an unlimited number of queries, the free use limits step by step solutions to 3 a day). One of this class showed me that he has the WolframAlpha app on his phone.
Year 11 (age 15-16)
My Year 11 group are studying the AQA Level 2 Certificate in Further Mathematics (a course I am very much enjoying teaching) as well as completing their GCSE course this year. We have been studying calculus and I have found the Desmos graphing calculator very useful to illustrate problems we have been solving. This class have mock examinations coming up and I wanted to recommend some additional resources for them (we have various texts and the AQA support is excellent but the more the better and there is currently no textbook for the course); one site with some very useful resources for some parts of the course such as introductory Calculus is David Smith’s ‘The Maths Teacher.’
Year 8 (age 12-13)
I have a Year 8 class this year, none of whom I have taught before, we have been looking at surface area and volume. Math Open Ref has a rather nice animation which helps when looking at the surface area of a cylinder. (More on John Page’s Math Open Ref). I will also use this site when we look at constructions soon. Most had not seen WolframAlpha before so were quite impressed at how easy it is to check working! There are slideshows available for students showing the syntax for a selection of examples on my blog for students.
It struck me recently that so many blogs are addressed to the teachers, so perhaps it’s time to provide one for the students!
Hence the new Mathematics for Students a companion blog to this one but addressed to students.
Any thoughts / ideas / comments – please let me know.