Dhiya Al-Jumeili and I are working on a rule-based system for students to practise their maths skills on. The PC-based system TREEFROG (see description below) simply checks each step of the student's argument for consistency, and recognizes if the correct finishing point has been reached. The online prototype (which only covers polynomial algebra at present), gives rudimentary feedback using malrules if a mistake is made in a step. If you have any thoughts, positive or negative, please email me at P.M.STRICKLAND@LIVJM.AC.UK
Treefrog for Windows Simple equations and polynomial algebra are
now catered for in a full Windows application. As this product is under very
rapid development at the moment, please email me if you are interested
Follow this link
to get an idea of what is available.
Treefrog 2.0 for MSDOS
This version of TREEFROG incorporates several new features;
Software fits one a single floppy, which can be run on any
compatible PC.
Context-sensitive hints.
The ability to include fully- or partly-worked examples.
Student logs created on the floppy disk which can be browsed
by teachers/ lecturers.
Go straight to download
A fuller article on TREEFROG 1.x, written for the MathSkills newsletter, is available here . TREEFROG is a MS-DOS based program, which is based on mathematical rules. A student is presented with an expression (say integral of x cos x d x, or x²+3x+2 = 0) and told to convert it to another form (function of x + constant, x = .. or x = ..) which is equivalent. They can enter expressions one step at a time
(e.g. x²+3x+2 = 0 -> (x+1)(x+2) = 0)
and at each step the system checks for syntax and logical errors.
You can use LET to define your own variables, for example in differentiation by the product rule, or integration by substitution.
You can also use ? to check an equation, such as making sure that its derivative is correct.
See this screenshot;
The lines starting with 'let' were typed just as you see them; the lines with equations on were typed with a question mark, e.g. ?du/dx = 1.
MATHQUIZ is an older program, with some redeeming features, which allows questions to be set with slightly more detailed feedback.
MACFROG is an authoring tool, which allows lecturers to set their own questions (e.g. integrate any function, solve any equation) within the limitations of the existing rules.
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