Rein Prank | University of Tartu (original) (raw)

Papers by Rein Prank

EDULEARN15 Proceedings, 2015

Algebra and Logic, Jul 1, 1981

The paper describes some findings from a programming task book project. The book contains tasks o... more The paper describes some findings from a programming task book project. The book contains tasks on arithmetic (operations, calculating the value of numeric expressions, common fractions etc), number theory (factors, prime numbers, GCD, LCM, Euclid algorithm), constructions in planar geometry, algebra (linear equations and inequalities, systems of linear equations, polynomials), some types of nonroutine tasks. The paper also brings up the necessary information processing that is not explicit when mathematical tasks are solved by paper-and-pencil method: parsing of algebraic expressions, finding the coordinates of intersection points by planar constructions, programming of algorithms for the tasks that appear in textbooks only in the form of one single numerical example. Some warnings are given about the impact of "brute force" computer solutions of reasoning-oriented tasks.

About ten years ago we started the computerisation of the exercises of our basic course in Mathem... more About ten years ago we started the computerisation of the exercises of our basic course in Mathematical Logic in Tartu University. As a result, we implemented a package of four programs designed for the following types of exercises: 1) truth-table exercises, 2) formula manipulation, 3) proofs in Propositional and Predicate Calculus, 4) Turing Machines. A general description of the package and our first experience is given in [1] and some concrete items are discussed in [2] and [3]. Having now exploited the package during six years with the yearly enrolment of 70-100 students, we have made some corrections and additions to our first versions of the programs. Also, some problems for which we do not have good solutions have arisen.

In this paper we consider two environments for algebraic tasks in Propositional Logic: Truth-Tabl... more 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.

In this paper we define Pedagogical CAS as an exercise and assessment environment for exercises o... more In this paper we define Pedagogical CAS as an exercise and assessment environment for exercises on numeric, fractional and algebraic expressions, equations, inequalities and equation systems. We assume that the student solves tasks step by step, performing arithmetic and algebraic operations. The system checks correctness of the student’s steps, provides feedback about errors and requires correction, records the student’s solutions and information about errors, is able to provide hints, has tools for visualizing recorded information and for automated assessment. The paper describes our ideas on the following issues: • Solution interface and working modes for students, • Error diagnostics, • Features and role of an automated Solver, • Using random generation of expressions, • Features and user interface of a Teacher Program for preparing tasks, analyzing the work of one student and groups of students, preparing tests with automated grading, • Database and server architecture of the s...

Mathematics in Computer Science

Proceedings of the 8th International Conference on Computer Supported Education, 2016

The paper looks for an exercise environment where the teacher program would enable to fix paramet... more 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.

International Journal for Technology in …, 2006

Journal of Symbolic Computation, 2014

In this paper we consider student solutions to tasks on the conversion of propositional formulas ... more In this paper we consider student solutions to tasks on the conversion of propositional formulas to disjunctive and conjunctive normal forms. In our department, students solve such exercises using a computerized environment that requires correction of every direct mistake but does not evaluate suitability of the steps. The paper describes implementation of an additional tool for analyzing these steps. This tool compares the students' steps with an "official algorithm" and possible simplification operations and checks for 20 deviations from the algorithm. The tool is applied to solutions from two student sessions and the paper analyzes the data on algorithmic mistakes.

Informatik-Fachberichte, 1991

... table of contents. Pages: 34 - 38. Year of Publication: 1991. ISBN:3-540-54619-7. Author,Rein... more ... table of contents. Pages: 34 - 38. Year of Publication: 1991. ISBN:3-540-54619-7. Author,Rein Prank, Publisher, Springer-Verlag London, UK. Bibliometrics, Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 0. ...

Lecture Notes in Computer Science, 2011

The paper describes a learning and assessment environment for Turing Machine programming. The int... more 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 ...

Infos, 1991

TARTU ÜLIKOOL ARVUTITEADUSE INSTITUUT Reimo Palm Rein Prank SISSEJUHATUS MATEMAATILISSE LOOGIKASS... more TARTU ÜLIKOOL ARVUTITEADUSE INSTITUUT Reimo Palm Rein Prank SISSEJUHATUS MATEMAATILISSE LOOGIKASSE Tartu 2004 Käesoleva raamatu väljaandmist on toetanud Eesti Infotehnoloogia Sihtasutus projekti Tiigriülikool raames. ...

International Journal for Technology in Mathematics Education

T-algebra is a project for creating an interactive learning environment for expression manipulati... more T-algebra is a project for creating an interactive learning environment for expression manipulation tasks of elementary 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 steps: choice of conversion rule, operands and result.

Abstract. In Tartu University the exercises in Mathematical Logic were computerised about ten yea... more Abstract. In Tartu University the exercises in Mathematical Logic were computerised about ten years ago. The paper investigates the changes in the course induced by Computerised Teaching of Formal Proofs. In many cases we have now included the references to the students' ...

Lecture Notes in Computer Science, 2013

Students of our department solve algebraic exercises in mathematical logic in a computerized envi... more 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.