# GeoGebra Conference Budapest 23-25 January 2014

GeoGebra conference in 2014. We will meet in Budapest, Hungary on 23-25 January 2014 for a promising conference: http://events.geogebra.org/budapest2014/

Plenary talks will be delivered by Markus Hohenwarter, Zsolt Lavicza , Celina Abar, Tomas Recio, and Balazs Koren. Also, there will be parallel sessions with talks and workshops.

The deadline for abstract submission is 1 December and registration is already open:
http://events.geogebra.org/budapest2014/registration/ Payment methods will be announced later, but register for early bird fees and to receive further information.

# Seb Schmoller: Second report from Keith Devlin’s and Coursera’s Introduction to Mathematical Thinking MOOC

About a month ago I finished Keith Devlin’s 10 week introduction to mathematical thinking course. This report supplements the one I published in April, which I’d based on my experience and observations during the first six weeks of the course.

# Seb Schmoller: A report from Keith Devlin’s and Coursera’s “Introduction to Mathematical Thinking” MOOC

This report was first published on 14 April 2013 in Seb Schmoller’s Fortnightly Mailing, and is reproduced here with Seb’s permission.

I’m six or so weeks into Keith Devlin’s 10 week Introduction to Mathematical Thinking, along with some tens of thousands of others.

Here is a longish thumbnail sketch of the design of the course, followed by two appendices. Appendix 1 concerns peer review. Appendix 2 is what the course web site has to say about grading and certificates of completion.

# Developing a Healthy Scepticism About Technology in Mathematics Teaching

 Developing a Healthy Scepticism About Technology in Mathematics Teaching,  a paper by Peter Rowlett (Nottingham Trent University). Abstract:  A reflective account is presented of experiences which took place alongside a research project and caused a change in approach to be more sceptical about implementation of learning technology. A critical evaluation is given of a previous e-assessment research project, undertaken from a position of naive enthusiasm for learning technology. Experiences of teaching classes and designing assessment tasks lead to doubts regarding the extent to which the previous project encouraged deep learning and contributed to graduate skills development. Investigations of the benefits of another technology—in-class response systems—lead to revelations about learning technology: its enthusiastic introduction in isolation cannot be expected to produce educational benefit; instead it must address some pedagogic need and should be evaluated against this. Overall, these experiences contribute to a shift away from a naive enthusiasm to an approach based on careful consideration of educational need before technology implementation.

# Beamer handouts

During my career I’ve seen great changes in the presentation of lectures and the production of handouts.

The original lecture technology, writing on a blackboard with a piece of chalk, is hopelessly old-fashioned now, though I still prefer it for teaching. It was replaced first by whiteboards, whose pens originally used foul-smelling chemicals (they have improved but I am not convinced they are healthier than chalk). Then came overhead projectors. Originally these tried to emulate boards: the acetate was on a roll, and you could turn the handle as you went and write continuous text, and could scroll back (the word seems more fitting for this than for a computer screen). Now OHPs are a health hazard: not, as you might think, because you might injure your back picking them up from the floor, or because you might trip over the lead, but because you might walk through the beam and damage your eyes.

Currently, computer and data projector rule, until they are superseded by the next thing, which might be some sort of smart paper. Mathematicians like the current set-up because the Beamer package gives us access to all the facilities and power of LaTeX.

What about the production of lecture notes or handouts?

I’ve always regarded lecture notes as not identical to what I write on the board or display on the screen, and write them with some care. But this effort, while fine for teaching, is not always appropriate. For seminars or conference presentations, a copy of the slides might be better.

Technology has changed things here as well. Once, lecture notes were handwritten or typed onto stencils, and duplicated by machines using even more unpleasant chemicals. Then came the photocopier, which took the pain out of duplication; high-quality laser printers and LaTeX did the same for preparation.

But reproducing slides has always posed problems of its own. By their nature, they are large format, one slide to a page (or many, if you use Beamer, since each \pause command starts a new page in the PDF). There was a program called mpage which took your PostScript slides and put them four (or two or eight) to a page. To produce PostScript from LaTeX, the standard route was via DVI. But now I only use pdfLaTeX, so this is not immediately viable. You can convert PDF to PostScript by the “print to file” command, and re-convert to PDF using ps2pdf.

The gap was filled, for a time, by various packages (my colleague Peter Kropholler produced one) which took the input file for the sldes and printed it out as a continuous document. Indeed, there is a package called beamerarticle which does this for Beamer input. This is how I produced the notes for my previous LTCC intensive course onSynchronization, which you can find here.

But recently I have found that there is a way to print the Beamer slides as a handout; I shall probably use this method for this month’s LTCC intensive on Laplacian eigenvalues and optimality. This may be useful to others, so here are the details.

The first step is to persuade Beamer to print one frame to a page, ignoring the \pausecommand and its refinements. This is easily done with the option handout. So if you compile your document with first line

\documentclass[12pt,handout]{beamer}

you will have taken this step.

To put several slides on a page, the versatile pdfpages package is what you need. Make a LaTeX input file using this package which has a single line between \begin{document}and \end{document}, reading

\includepdf[<options>]{file.pdf}

where file.pdf is the output from the previous step. Options include page layout (landscape or not, number of slides across and down, spacing, whether they are framed). I recommend you to this page; I have used it as is, except for putting six rather than four slides on a page.

I re-did my Lisbon lecture slides this way: take a look here.

Only one small problem remains. If you called the file that invokes pdfpages something generic like handout.tex, then of course the output will be called handout.pdf. I would prefer to have a name based on that of the input PDF. Probably someone has already done this; but when I am not so busy (maybe when I retire) I might try to produce my own.

[Reposted from Peter Cameron's Blog]

# QAMA: The Calculator That Makes You Better At Math

From a post by Alex Knapp on Forbes blog:

QAMA [...] is a calculator designed to reverse the last several decades of education by actually improving students’ intuitive understanding and appreciation of math skills.  It does this in a deceptively simple way.

The name itself gives the method away – QAMA stands for “Quick Approximate Mental Arithmetic” (and in Hebrew, it means “How much?”). As with most calculators, to solve a problem with a QAMA, you first do what you’d do with a regular calculator: type in the problem. But rather than just give you the answer right away, QAMA asks you for one more step: you have to estimate the answer. If your estimation demonstrates that you understand the math, the calculator will give you the precise answer. If your estimation isn’t close, then you have to try again before you get the precise answer.

Quick – what’s the square root of 2? What do you mean you don’t have a calculator? Well, you can start guessing, right? So let’s work this through. You know you have an upper bound – it has to be less than 1.5, because 1.5 x 1.5 is 2.25.  And it has to be more than 1, because 1 x 1 is just 1. But 2.25 is pretty close, right? So what if you guess 1.4? Well, then you’d be pretty close. 1.4 x 1.4 is 1.96, and the square root of 2 is about 1.414.

But did you notice something? Without your calculator, you had to estimate. In order to estimate, you had to think about and engage with the math behind exponents and square roots. Which means, hopefully, that you came out of that first paragraph with a bit better understanding of math.

That’s the theory behind QAMA, which is a calculator designed to reverse the last several decades of education by actually improving students’ intuitive understanding and appreciation of math skills.  It does this in a deceptively simple way.

The name itself gives the method away – QAMA stands for “Quick Approximate Mental Arithmetic” (and in Hebrew, it means “How much?”). As with most calculators, to solve a problem with a QAMA, you first do what you’d do with a regular calculator: type in the problem. But rather than just give you the answer right away, QAMA asks you for one more step: you have to estimate the answer. If your estimation demonstrates that you understand the math, the calculator will give you the precise answer. If your estimation isn’t close, then you have to try again before you get the precise answer.

How close is close? Well, that depends on the calculation. If you put in 5×6, you have to estimate 30 – the calculator expects you to know your multiplication tables. For exponent problems, if you have an integer – say something like 23^2, the tolerance is such that you still have to be pretty close, but there’s a wider berth for say, 23^2.1, because non-integer exponents are a tougher problem.

Developing the calculator to have these different tolerances for different types of calculations was the key challenge for QAMA inventor Ilan Samson.

# Using Adaptive Comparative Judgement to Assess Mathematics

Ian Jones & Lara Alcock
Loughborough University

Adaptive Comparative Judgement (ACJ) is a method for assessing evidence of student learning that offers an alternative to marking (Pollitt, 2012). It requires no mark schemes, no item scoring and no aggregation of scores into a final grade. Instead, experts are presented with pairs of student work and asked to decide, based on the evidence before them, who has demonstrated the greatest mathematical proficiency. The outcomes of many such pairings are then used to construct a scaled rank order of students from least to most proficient.

ACJ is based on a well-established psychophysical principle, called the Law of Comparative Judgement (Thurstone, 1927), which states that people are far more reliable when comparing one thing with another than when making absolute judgements. The reliability of comparative judgements means “subjective” expertise can be put at the heart of assessment while achieving the sound psychometrics normally associated with “objective” mark schemes.

Until recently comparative judgement was not viable for educational assessment because it is tedious and inefficient. The complete number of required judgements for producing a rank order of $$n$$ scripts is $$\frac{n^2-n}{2}$$.However the development of an adaptive algorithm for intelligently pairing scripts as more judgements come in means the number of required judgements has been slashed to around $$6n$$.