With older students in mind including those about to enter higher education, there are many free resources available to support students in their study of Mathematics.
Note that a new blog aimed at students is now available.
There are many sources of excellent notes online. See this Evernote shared notebook: Mathematics notes for useful links. (You do not need an Evernote account to view the notebook). Some of these sites include videos, for an extensive collection of videos try Khan Academy.
Alternatively, use the Livebinders version of Mathematics Notes.
On the subject of Evernote - it is a valuable tool for any student or teacher.
Other tools which may be of interest are on Digital Tools for Students.
Students going on to study Mathematics degrees have a look at Kevin Houston’s ‘How not to get a good mathematics degree‘ and ‘How to get a good mathematics degree‘. He also has provided a pdf file you can download: 10 Ways to Think Like a Mathematician. Kevin Houston works at the University of Leeds.
I would advise students of any subject to learn to use WolframAlpha. Suppose you wish to do some revision on techniques for differentiation for example – ask WolframAlpha to differentiate x2sinx, and the derivative will be returned with possible working available if ’Show steps’ is selected. (Further Calculus examples). WolframAlpha provides an excellent way to check your work.
WolframAlpha will plot graphs, there are many other free and excellent online graphing tools, see the Desmos Graphing Calculator for example and many other online graphing tools. (See this page for polar curve plotters).
Thinking longer term – have a look at the excellent Maths Careers site.
WolframAlpha can be used for vocabulary, for example try typing ‘plus’ into WolframAlpha.
Note that WolframAlpha has assumed plus is a character but you can choose to refer to a mathematical definition or a word (or an internet architecture topic). Choosing word will not only give definitions but a wealth of other information that you would not find in a dictionary such as the first known use of the word, frequency of use, rhyming words and much more!
Other sites of interest for Mathematics vocabulary have been mentioned in this Mathematics Reference post. If you are interested in the first know use of mathematical words then try Jeff Miller’s ‘Earliest Known Uses of Some of the Words of Mathematics‘.
This is the first in a series of examples showing the syntax to use for WolframAlpha.
These examples are intended for 11-14 year old students.
All the examples will be added to the WolframAlpha pages where you will find further information.
Busy in a computer room this morning one of my year 9 (UK age 13-14) students informed me that WolframAlpha is 2 today!
I show all my students WolframAlpha in class and sometimes use it in class to check a result. I have been pleased to see students using it themselves.
See the WolframAlpha page and subpages for further details of WolframAlpha including several useful links.
WolframAlpha now has a dedicated page (and sub-pages) on this blog to make resources easy to find.
Hover over a page tab to see any associated pages.
This will be developed further.
Check Fred Feldon’s presentation on Slideshare which discusses the implications of WolframAlpha for Mathematics education and also includes many examples.
WolframAlpha have now launched Fun Facts on Twitter. Note that you can read these facts even if you are not a Twitter user.
WolframAlpha have written on this in their own blog.
Now here’s an impressive fact from WolframAlpha on just how popular WordPress is:
On the subject of Mathematics Fun Facts – a reminder of these sites mentioned in earlier posts.
Mudd Math Fun Facts
Tanya Khovanova’s Number Gossip
Amazing Number Facts from Madras College.
MAA NumberADay blog.
There are many excellent resources online for solving equations.
A simple way to see a complete solution to an equation is to enter it into WolframAlpha then select ‘Show Steps’. (Update 2012 – using the free version of WolframAlpha allows you an unlimited number of queries, so excellent for checking any work but you can only use ‘Show Steps’ three times a day!)
From John-Paul Green’s Flashy Maths try ‘Sequences‘ to generate linear sequences and predict the nth term.
To identify an integer sequence try the Online Encyclopedia of Integer Sequences.
Simply type in your sequence and choose Search.
WolframAlpha Widgets are mini applications built on Wolfram Alpha queries. You can share them in several ways - Facebook and Twitter for example or embed them in a blog or website. Either use a widget from the growing gallery (note the categories on the right) - see Mathematics here or create your own.
See Wolfram Alpha’s own blog entry.
For further information on WolframAlpha these links may be useful:
WolframAlpha YouTube Channel
Gallery of Examples
From h+ Magazine a comprehensive Users Guide to WolframAlpha
Using WolframAlpha in the Classroom
Step-by-Step Math – WolframAlpha blog post
Training Video from Russell Stannard – Teacher Trainng Videos
Mathematics Lesson Plans from WolframAlpha for Educators
10 questions younger children could try – Wolfram Alpha Blog entry
….and on a lighter note from Mashable we have some Easter Eggs!
WolframAlpha – this is definitely worth taking a look at if you have not seen it before.
For example type in: solve 3x+7 = 13
(or any equation of your choice, use x^2 for example for powers!)
Note that you have the option to view the steps when the results are returned.
Have a look at the gallery of examples for inspiration, including Mathematics.
Update 12th April:
Recently introduced Wolfram Alpha for Educators has examples of how it can be used in the classroom, note the Wolfram Alpha blog post on Step-by-Step Math and the Mathematics Lesson plans.