Rein Prank

Prospects of Automatic Assessment of Step-by-Step Solutions in Algebra

The paper describes how the features of sufficiently intelligent expression manipulation drill programs can be utilized to calculate numeric scores. The issues discussed include the ways of grading the progress achieved in unfinished solutions, penalization of mistakes, and measuring of economy. The treatment is based mainly on one existing program, T-algebra. The concluding part of the paper points out the key features required for different aspects of numeric grading.

Using Computerised Exercises on Mathematical Logic

At the end of 1987 we started a teaching Software project for the Basic Course on Mathematical Logic for first-year students. The decision to use the Computers was initially caused by poor Performance of the students in two subjects: programming Turing Machines and the construction of the proofs in formal theories. In the process of the work we have added two more simple themes: truth-table exercises and the algebraic manipulation of the formulas.

Input design in interactive learning environment T-algebra

T-algebra is an interactive learning environment for step-by-step solving of algebra problems. To make the diagnosis of mistakes more complete, each solution step in T-algebra consists of three stages: selection of the transformation rule, marking the parts of expression, entering the result of the operation. This article describes the last stage that can proceed in three different modes: free input, pattern-driven input and input of some components of the result.

Software for evaluating relevance of steps in algebraic transformations

Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task. With our current project, we add a program component for checking relevance of the steps.

Using a learner- and teacher-friendly environment for turing machine programming and testing

The paper describes a learning and assessment environment for Turing Machine programming. The interpreter allows to explore different phases of running a particular test in different working modes: step by step, until a change on the tape, until termination, take a step back, etc. The program enables to display the results of testing with a set of tests together with error messages, numbers of steps, etc. We try to describe small details of the program that are important for learner and for instructor.

Designing next-generation training and testing environment for expression manipulation

T-algebra is a project for creating an interactive learning environment for basic school algebra. Our main didactical principle has been that all the necessary decisions and calculations at each solution step should be made by the student, and the program should be able to understand the mistakes. This paper describes the design of our Action-Object-Input dialogue and different input modes as an instrument to communicate three natural attributes of the step: choice of conversion rule, operands and result.

What Should We Add to Syntax-oriented Generation of Random Expressions to Meet Pedagogical Needs?

The paper looks for an exercise environment where the teacher program would enable to fix parameters of random generation so that the generated tasks have desired pedagogical properties. In particular, it should be possible to prescribe qualitative content and size of the solution and its parts, opportunities to make certain errors, probabilities of different decisions to be made by the student. We analyse two existing environments for algebraic exercises in Propositional Logic and identify what additional options are necessary and what computational engines or precomputed resources could produce the desired properties.

Today - Only TEA and no CAAffee. But Tomorrow?

In this paper we consider two environments for algebraic tasks in Propositional Logic: Truth-Table Checker and Formula Manipulation Assistant. From the very beginning our environments were designed not only for exercise labs but also for assessment of homework and tests. Currently our programs produce detailed data for easy and quick human grading but do not accomplish full Computer Aided Assessment where the output would be a numeric score. We set the goal to take into account five aspects of solutions: what part of the task is solved, errors, hint requests, solution economy or conformity with standard algorithm, and quality of answer. We analyse for different task types what is missing from fully automated grading. We conclude that exploitation of our existing automated solver and integration of some our supplementary programs would enable to provide quite satisfying assessment.

Tools for acquiring data about student work in interactive learning environment t-algebra

T-algebra is an interactive learning environment for elementary algebra The main program of T-algebra enables visualizing information about a particular student in tables, indicating solution times, the numbers of errors (in 20 categories) and hint usage for each task Additional software for teachers allows examination of solution results in group views.