Items tagged with history history Tagged Items Feed

I think we all know the routine. We walk to a large classroom, we sit down for a test, we receive a large stack of questions stapled together and then we fill in tiny bubbles on a separate sheet that is automatically graded by a scanning machine. We’ve all been there. I was thinking recently about how far the humble multiple choice question has come over the last few years with the advent of systems like Maple T.A., and so I did a little research.

Multiple choice questions were first widely-distributed during World War I to test the intelligence of recruits in the United States of America. The army desired a more efficient way of testing as using written and oral evaluations was very time consuming. Dr. Robert Yerkes, the psychologist who convinced the army to try a multiple choice test, wanted to convince people that psychiatry could be a scientific study and not just philosophical. A few years later, SATs began including multiple choice questions. Since then, educational institutions have adopted multiple choice questions as a permanent tool for many different types of assessments.

One of the biggest advances in the use of multiple choice questions was the birth of automatic grading through the use of machine-readable papers. These grew in popularity during the mid-70s as teachers and instructors saved time by not having to grade answer sheets manually.

Until recently, there has not been much advancement in this area.  It’s true, Maple T.A. can do so much more than just multiple choice questions, so this style of question is less important in large-scale testing than it used to be. But multiple choice questions still have their place in an automated testing system, where uses include leveraging older content, easily detecting patterns of misunderstanding, requiring students to choose from different images, and minimizing student interaction with the system. Luckily, Maple T.A. takes even the humble multiple choice questions to the next level. Now you might be thinking, how is that even possible given the basic structure of multiple choice questions? What could possibly be done to enhance them?

Well, for starters, in Maple T.A., you can permute the answers. This means you have the option to change the order of the choices for each student. This is also possible with machine-readable papers, but this does require multiple solution sets for a teacher or instructor to keep track of. With Maple T.A., everything is done for you. For example, if you have a multiple choice question in Maple T.A. with 5 answer choices, there are 120 different possible answer orders that students can be presented with. You don’t have to keep track of extra solution sets or note which test version each student is receiving. Maple T.A. takes care of it all.

Maple T.A. allows you to create Algorithmic questions - multiple choice questions in which you can vary different values in your question. And you aren’t limited to selecting values from a specific range, either. For example, you can select a random integer from a pre-defined list, a random number that satisfies a mathematical condition, such as ‘divisible by 3’ or ‘prime’, or even a random polynomial or matrix with specific characteristics. It allows an instructor to create a single question template, but have tens, hundreds, or even thousands of possible question outcomes based on the randomly selected values for the algorithmic variables. The algorithmic variables not only apply to the question being asked by a student, but also the choices they see in a multiple choice question.

You can even create a question where every student gets the same fixed list of choices, but the question varies to ensure that the correct response changes.  That’s going to confuse some students who are doing a little more “collaboration” than is appropriate!

Some of the other advantages of using Maple T.A. for multiple choice are also common to all Maple T.A. question types. For example, you can provide instant, customized feedback to your students. If a student gets a multiple choice question correct, you can provide feedback showing the solution (who is to say the student didn’t guess and get this question correct?) If a student gets a multiple choice question incorrect, you can provide targeted feedback that depends on which response they chose. This allows you to customize exactly what a student sees in regards to feedback without having to write it out by hand each time.

And of course, like in other Maple T.A. questions, multiple choice questions can include mathematical expressions, plots, images, audio clips, videos, and more – in the questions and in the responses.      

Finally, let’s not forget, in an online testing environment, there is no panic when you realized you accidently skipped line 2 while filling out your card, no risk of paper cuts, and no worrying about what kind of pencil to use!

References:

http://www.edutopia.org/blog/dark-history-of-multiple-choice-ainissa-ramirez

http://xkcd.com/499/

http://io9.com/5908833/the-birth-of-scantrons-the-bane-of-standardized-testing

I would like to pay attention to http://www.ams.org/samplings/feature-column/fc-2013-05 .
Comparing the Galileo's calculation 87654/53 with the capacity of Maple, the question arises:
"Are we  cleverer than Galileo Galilei?". I don't know the answer.

A set of three taped video interviews with famous physicist and mathematician Cornelius Lanczos (1893-1974) has been made available online by the University of Manchester.

Can someone explain to me how I flush the memory build up that occurs as Maple keeps track of historical execution?

If I, for example, write a FOR loop that iterates a huge amount of times and don't include the colon after "end do", but rather use the semicolon, the memory usage keeps creeping up and then finally Maple just goes off into never land and never comes back.

I tried this in Windows and Mac OS X.  Same results.

I thought I could add an interface(historysize=?...

Back when I was working at the University of Waterloo, I found several copies of a VHS tape sitting on a dusty bookshelf full of old Maple boxes and manuals. The tape's cover had a line drawing of Issac Newton on it and the title "Maple V: The Future of Mathematics".

There was...

One of the best things about growing up in the “Hood” is that it feels really good when you leave. I grew up in a neighborhood called Downsview in Toronto whose claim to fame used to be it was the home to the DeHavilland Aircraft company but today is more associated with ongoing issues of crime, poverty, and many other urban illnesses. So every time I hear that someone from the Hood did something great, I take notice and I take special pride. This is the story about...

The term “from months to days” is a favorite slogan of mine and I have relied on it religiously for over two decades to illustrate the fundamental benefit of symbolic computation. Whether it’s the efficient development of complex physical models using MapleSim, or exploration of parametric design surface equations (my dissertation) using good old fashioned Maple V Release 2, the punch that symbolic computation provided was to automate the algebraic mechanics...

I've never been to Ireland, but this was the first thing that popped into my head when I heard of "mathematical tourism":

As the story goes (recounted here among other places), on October 16, 1843, the Irish mathematician William Rowan Hamilton was walking along the Royal Canal in Dublin with his wife, when he invented the basic relation defining the quaternions. (He had previously been thinking about ways of extending the complex numbers to higher dimensions.) Supposedly, he was so excited by this that he carved i=j=k=ijk=-1 into nearby Brougham Bridge, which must have been one of the most spectacularly opaque pieces of graffiti in history. Unfortunately, there is no trace of such a carving now, but there is a plaque commemorating Hamilton's idea.

William Rowan Hamilton Plaque - geograph.org.uk - 347941

Licence: JP [CC-BY-SA-2.0 (http://creativecommons.org/licenses/by-sa/2.0)], via Wikimedia Commons

According to the article, since 1989 mathematicians from the National University of Ireland, Maynooth have organized a pilgrimage from Dunsink Observatory to the bridge on the anniversary of Hamilton's discovery. So if you're ever in Dublin in October, you assuredly have someplace to go.

(But be sure not to commute there! :))

Page 1 of 1