So, the end of the year approaches and it’s a good time as so many bloggers do to look back on the past year. Looking at the top 20 posts of 2013 (I’ll
publish those on Jan 1st), many of the old favourites are still there as well as some new entries which were written during 2013. In my never ending quest to make sure posts are easy to find again I have been busy editing posts with categories and tags, hence the new ‘Search posts by category’ menu available on the right and a new look to the ‘I’m Looking For’ pages.
Note also some other changes to the menus on the right – you can see the top 10 posts for the last 48 hours portrayed by an image from the post. Continuing down the right hand side – you can see a gallery – that’s an experiment! Further down you can like the blog on Facebook should you feel so inclined, see some Blog stats and a tag cloud for searching posts! I am still working on all the categories and tags to refine the system!
….. Looking at just the top 20 posts of the year can be rather artificial, I’d like to mention these posts from 2013 that whilst popular didn’t quite make the top 20…..
“The most powerful single modification that enhances achievement is feedback. The simplest prescription for improving education must be “dollops of feedback” John Hattie. Note – now that posts are categorised, it is possible to see all the posts in the feedback category – simply select the category Feedback from the drop down menu and these posts will be returned. (Click on the image if you are wondering about the verbal feedback!)
So important to consider student misconceptions when thinking about their learning. I have recently updated the above post, an important addition being the excellent diagnostic questions site.
Math Centre This is a site I’ll always recommend to students if they want to look at some additional material. The resources are very clear and are available in several formats including some excellent summary notes.
Reviewing popular posts and checking for correct links caused me to revisit my post on handwriting recognition and LaTeX. The original post has now been corrected (in case people have it bookmarked). I have also reproduced the post below.
Web Equation by Vision Objects
A consistently popular post on this blog is that on online whiteboards. If I want to communicate mathematics online to answer a student query for example I find it quicker to use a graphics tablet and an online whiteboard.
I do keep an eye on various LaTex generators, one that has come to my attention is Web Equation; from MyScript. What I like about this is that handwriting is turned into LaTex (only one line at a time). The handwriting recognition is impressive and I found it easy using my graphics tablet to enter expressions accurately; see the quadratic formula below for example.
Web Equation by MyScript
So you scribble an expression and it get turns into LaTex for you – it works:
Note that if you want to copy / edit the Latex then just select the LaTex expression and you will have the opportunity to copy or edit it.
But I must confess I was just as excited to note that now you can immediately see a graph where appropriate, powered by my favourite Desmos graphing calculator (it appears the scales are fixed) and by the option to ‘Compute with WolframAlpha’! (see above image).
..and finally if you wish to be distracted by some more fun applications there are some other great demonstrations from VisionObjects. Try Web Shape or example and turn your sketches into vectorized shapes. This should work well on the interactive whiteboard.
My Year 12 students have just completed a Decision Mathematics mock examination. Preparing solutions to questions causing the most problems made me realise how often I use colour and highlighting in my explanations where I think this helps clarity. The following slideshow demonstrates the solution to a question on Dijkstra’s algorithm for finding shortest paths in network. I have changed colour once a new vertex has been chosen.
See also Colour in Mathematics a presentation with examples showing how colour can help to make explanations clearer. I have many examples I have used for students of all ages, particularly in Algebra.
I have used the excellent diagnostic questions site on several occasions and last week set Year 7 the task of writing some diagnostic questions on two topics we have been studying recently – Sequences and Co-ordinates. The questions in the above slideshow were all written by Year 7 students and are typical of their questions.
Not only did they have to write the questions but indicate the correct answer and explain the reasoning behind the multiple choice answers they had given. This proved an excellent homework in that students showed that they really understood the topics and the possible misconceptions that can arise. Some students commented that they had included particular answers because they were typical of the mistakes they or their friends made. I believe that thinking about possible wrong answers has given them a deeper understanding.