algorithmically generated questions with non-pure numerical answers

algorithmically generated questions with non-pure numerical answers

by Cristina Berisso -
Number of replies: 2

Hello everyone,

Can the calculated question type in quizzes be easily extended to allow for short answers that contain characters apart from one or more “calculated” numerical answers?

What I would like to do is to be able to include characters among numerical answers so this question type can be used for algorithmically generated questions in algebra. Let me show you an example:

Factor out the following trinomial:

$$x^2+{={a}+{b}}x+{={a}*{b}}$$

Type your answer in the box below. If this trinomial can be factored remember to use parentheses to delimit the binomial factors. If the trinomial is not factorable type the word: NO . Please don't enter any spaces!

The calculated type question allows me to generate datasets with selected positive integers {a} and {b}. I would like to be able to have the students type a string that contains the product of two binomials (in different possible orders-which I could take care of by using different accepted answers):

(x+a)(x+b), where {a} and {b} must be the integers entered in the set.

As you can see, since I’ll be handling Integers, I am not that worried about tolerances different from “0.0”. The important thing is to allow: 1) other characters in the answer, and 2) the ability to identify more than one correct answer (in the case above both {a} and {b}).

Adding such feature to the code would allow also to assess students on solving equations that involve multiple numerical solutions (like quadratic equations). Would this be a not very time consuming feature to add? Can someone do it?

Thank you so much for your time and help!

Cristina

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In reply to Cristina Berisso

Re: algorithmically generated questions with non-pure numerical answers

by Ian Wild -
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Hi Cristina,

Have you taken a look at STACK from Chris Sangwin? It's based on the Maxima CAS and can handle factoring trinomals - and can recognise if a student's answer is algebraically equivalent to a teacher's model answer. As a teacher you can also specify "common errors" and award students marks for "near misses".

Details on STACK can be found at http://www.stack.bham.ac.uk/

Hope this is the sort of thing you are looking for.

Ian.
In reply to Cristina Berisso

Re: algorithmically generated questions with non-pure numerical answers

by Christopher Sangwin -
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Hello Cristina,

Thanks for mentioning STACK Ian.  This question is exactly what STACK is designed to assess. 

In terms of basic algebra, I'm currently putting the finishing touches to questions which test all the algebraic skills outlined in Tony Barnard's "Map of Algebraic Manipulation".

http://www.mth.kcl.ac.uk/staff/ad_barnard/Pocket.pdf

I will be finished before Christmas.  These questions will be available online to try, and the source code distributed with STACK.  Each question is a template which gives randomly generated versions to students and has a full worked solution (reflecting the random numbers).  This represents a significant learning resource, which I hope will be useful.

To give you some idea, attached is a screen shot from one of the "solving quadratics by factoring" problems.  The second part of the question (not shown at the bottom) asks for solutions.

We've put some effort into the feedback, which you can see here.  While it looks a little harsh to give 0 marks for this attempt, students can always try again.  In this case we apply a "penalty" of 10% of the marks deducted for each incorrect attempt, so students who take the touble to read the feedback and act on it will end up with 0.9 marks out of 1.0.  We find students really appreciate this opportunity.  In any case, you can opt not to display anything about marks (grades) or to choose other kinds of marking schemes.  This is up to the teacher.

Chris

Attachment quad1.jpg