I have recently rewritten many of the questions from the Essential Maths for Medics and Vets modules using Numbas – an open e-assessment system and this post is about my experiences of using Numbas. I am not a mathematician and not a programmer (though I have done a little programming in the past) – my background is in biological chemistry and I have taught maths for first year biologists, medics, vets and psychology students at the University of Cambridge. The maths questions cover the techniques and concepts that beginning undergraduate students need in physiology, biochemistry, pharmacology and pathology. From what I can tell many of the questions are useful for non-medical biologists too.
What is Numbas?
“Numbas is a web-based e-assessment system that helps users create online tests. It was designed with numerical tests in mind, but is equally suitable for a range of other subjects. … We have created Numbas to be a valuable resource for educators, regardless of their budget. This is why the system is free and open-source, meaning that anyone can edit or adapt it to their needs.
Educators can set up a free account and choose from a public database of questions, or start creating their own. When they have put together their test, they can share it to places where students are already learning. Exams can be shared to a wide variety of locations, online and offline, and can be viewed on tablet, mobile or desktop.[1]”
Variables
One of the most powerful aspects of Numbas is that you can create variables that change each time a student views the question so they can attempt the question as many times as they like. For example in the following question, the numbers change randomly (within a predetermined range).
(click on the image to enlarge)
And if the student clicks on “Reveal Answer” then can get advice that is tailored to the particular instance of the question:
Randomisation works well sometimes – but not others.
For questions like the one above this works well but for more specific scenarios such as the question below it becomes a lot more difficult.
The tutorials get you up to speed pretty quickly and writing simple questions like these with a few variables was possible after viewing a couple of short videos and reading the documentation.
LaTeX and JME
However… getting the equations to look good requires the use of LaTeX and this is well known to have a pretty steep learning curve but there is plenty of online help – even a tool that allows you to write a mathematical expression by hand and it displays the LaTeX. Compare the following question display
With the LaTeX
In my opinion setting out the equations clearly is really important, especially for dyslexic or dyspraxic students and particularly for things like fractions and exponents, so LaTeX is really worth learning. The other thing that’s important for this group is font choice. It’s worth noting that any text written within the $ signs that designate the LaTeX input has Times New Roman as its default font. So when you want to include units in with an equation or some variables you need to either put them after the final $ or use the instruction \text to tell LaTeX to display as text rather than as mathematics. I decided in the end that I wanted the numbers to display in Times New Roman so that a one (1) wouldn’t look like an ell (l) but that the prefixes and units would be in the default web font (usually calibri). And whilst on the subject of prefixes, it’s worth knowing that to get a micro sign on a webpage you can go to a website called http://www.unicodeit.net/ and type in the LaTeX code for the symbol, in this case \mu and it’ll display the Unicode symbol which you can then copy and paste into Numbas. This is the way of ensuring that the micro displays correctly.
Re-using and copying questions
In my view, one of the most powerful aspects of the Numbas system is the potential to copy, modify and/or re-use someone else’s questions. The first time I did this was when I was trying to figure out how to display standard form. I found a question by Martin Jones (thank you Martin!) and copied it, had a look at how he’d put it together, and then shamelessly created a similar question for myself using the same approach. It’s been quite handy being able to look at other people’s questions – sometimes to just copy and adapt but other times to see how they actually implemented it and to get other ideas for ways of presenting the info or asking the question.
Requiring a student to input their answer in standard form rather than just in scientific notation (i.e. as 1.3 x 106 rather than 13 x 105 or 130 x 104) turned out to be somewhat challenging. Of course 1.3 x 106 is equal to 13 x 105 so the Numbas system considers them the same as it should do. There were occasions when I particularly wanted the answer in standard form. However with thanks to Christian Perfect, the Numbas developer, the problem was solved. I kicked myself when I saw Christian’s solution as I really should have thought of that myself. If you’re interested in the details, have a look at Christian’s version of my question https://numbas.mathcentre.ac.uk/question/8400/christians-copy-of-test1a-1/
Another reason for copying someone else’s question is to add your own context. Because my students are primarily biomedical many of my questions have a biomedical context, so I ask for the concentration of adrenaline solution and express the answer with an appropriate unit or in standard form but it would be very easy to just copy my question and then modify the text to suit whichever field you’re in.
Sharing and Re-using
All of the Essential Maths for Medics and Vets are creative commons licensed (attribution, non-commercial, share-alike – see https://creativecommons.org/licenses/by-nc-sa/4.0/) To download the question sets just go to the following link, select the question set you’re interested in (they have the tick icon in front) and choose which download option works best for you.
http://www.mathcentre.ac.uk/resources/uploaded/EssentialMaths.html
This link also contains the original audiovisual tutorials and pdf documents and you can link to this so students can revise the material before and/or after attempting the questions.
Alternatively you can create your own exams by putting together a selection of questions – either ones you’ve created yourself of copies you’ve made of other questions. Questions are generally tagged with keywords so you can find them.
Thanks
To Christian Perfect and Bill Foster at Newcastle University for their prompt and helpful responses to my queries
To everyone who tested the questions and provided feedback: Nigel Atkins, Kingston University; Rebecca Barnes, University of Sheffield; Chrystalla Ferrier, Westminster University; Dawn Hawkins, Anglia Ruskin University; Robert Jenkins, University of Sheffield; Bernadette Leckenby, Sunderland University; Gemma Marsden, University of Northampton; Rosanne Quinnell, University of Sydney; Lois Rolling, University of East London; Felicity Savage, Anglia Ruskin University.
[1] http://www.numbas.org.uk/faq/
Biomaths Education Network 
A MOOC for How to Learn Math(s)
I can thoroughly recommend the MOOC, by Prof Jo Boaler on the Stanford EdX platform “EDUC115N How to Learn Math.” It is available until Sept 27th and you can start it anytime until then. Whilst I have started other MOOCs and not got past the first section, I found this one so compelling that I stayed up late into the night and pounced immediately when they released the next section.
According to the course info:
The course gives an accessible and jargon-free explanation of some of the research in maths learning and gets you to think about how you’d relate that to your own practice, either as a teacher or as a parent helping their child with homework.
Why do I think it’s so important? There are a number of reasons:
1- The course gets you to think about how people get negative messages about maths and why people can be so strongly affected by them. Within this there was an excellent section on stereotype threat which brought in a number of aspects I wasn’t previously aware of. You also consider how powerful mindset is and the sorts of techniques you can use to try to change mindset (this is based on the work of Carol Dweck – ref below).
2. There was a good discussion about how to handle mistakes and some accompanying videos of a classroom teacher putting this theory into practice. This is something I find really difficult – I want to jump in with the right answer rather than guide them towards realising how to get to the answer.
3. There were hints and tips (incl video demonstration) of how to encourage students to communicate their answers in different ways, visual, verbal, diagrammatic, symbolic etc. This is a really important skill which is often neglected. It also showed the importance of getting students to explain different ways of reaching an answer and valuing those different perspectives.
4. The course considered how to help develop a positive attitude about maths. I don’t think I can do it justice here – you really need to watch the videos.
Some excellent references:
Paul Lockhart’s: A Mathematician’s Lament
Steele, Claude M. (2011). Whistling Vivaldi: How stereotypes affect us and what we can do (issues of our time). New York, NY: W. W. Norton and Company.
Dweck, Carol S. (2007). Mindset: The new psychology of success. New York, NY: Random House.
Jo Boaler’s book “Elephant in the Classroom” covers much of this course’s material.