RETROSPECTIVE OF THE TEACHING MATHEMATICS
BY
NORM REFERENCED AND CRITERION
REFERENCED exercises
Anna MACUROVA, Dushan MACURA, Stanislaw
BALCZAK
Abstract. The
retrospective of the teaching mathematics is investigated by the educational
psychology. The retrospective of the teaching is analyzed by the typology of
the mathematical exercises. We using the exercises norm referenced and
criterion referenced. The intellectual classes differently of the students are
accepting.
Key words:
Retrospective of the teaching mathematics, mathematical exercises, exercises
norm referenced, exercises criterion referenced.
Introduction
The selection mathematical exercises for the identification
retrospective of the teaching mathematics are complicated pedagogical activity
operation. The selection is prosperous operation with by quantity lessons
mathematics. The compliance of the proportion curriculum of the mathematics is
indispensable in the selection exercises.
The package of the mathematical exercises for identification
retrospective of the teaching mathematics are write down with the convention
for construct the non-standardize testes.
The packages of the exercises are discriminate for norm
referenced (NR) and for criterion referenced
(CR) exercises.
The discrimination is by the activity the students.
The norm referenced NR packages
exercises expressed the learning results of the student on the confrontation
with classmates.
The criterion referenced CR packages exercises expressed the learning results of the students on
the confrontation in the quantity of the learn curriculum.
Purposes
of the suggestions packages exercises
Suggestions packages exercise are construct for the alumnus of the high
school.
Suggestions packages are integrate in the read up on after teaching
given thematic complex.
Range curriculum of the package exercises represented fundamental
sciential requirement of the students on the levels.
Levels resolve the exercises on the prepared the pieces of paper.
Packages of the mathematical exercises motivate the mathematical
teachers.
Form of the exercises in the packages
The thesis of the exercises NR and CR packages
transcend the fundamental curriculum. The teacher determine about the exercises
for the monitoring retrospective of the teaching the mathematics.
If the exercises represented the fundamental
curriculum, then the packages monitors remember and understanding of the
know-how of the students.
The form of the exercises is dichotomous, the
exercises have the answer with selection or the structured exercises with the
extensive answer or creative exercises and the gap-fill exercises.
In the packages are the open ended exercises
and bounded exercises.
The students create the answer in the open-ended exercises or the students
choose the correct answer of the designated alternatives.
Students fill to satisfy allowed in the form the mathematical
algorithms by determined the solution open ended structured exercises.
Students present the answer in the form number, graphic symbol,
definition, word for the open-ended structured mathematical exercises.
Students fill in the open ended exercises with the short answer, The
exercises has form incomplete theorem and they called cloze exercises.
Students choose the correct answer of the many answers in the package
mathematical bounded exercises with selection answer (optimal number answer is 5).
In the bounded mapping mathematical exercises the students determine corresponding results.
In the bounded systemization mathematical exercises the students create group elements by the specific property.
Bounded dichotomous mathematical exercises are not in the packages mathematical exercises. In the dichotomous
exercises the students determine of the two eventuality: yes-no, correct
non-correct.
Open-ended non-structured mathematical
exercises with large answer are not in the packages. In this
exercises the students have the problem choose the answer.
Conclusion
The mathematical exercises
packages have the properties of the
didactic testes validity the degree correspondence
with the mathematical curriculum of the thematic complex. Analogical by
didactic testes - the mathematical exercises packages have
a)
Content validity,
b)
Aspect validity,
c)
Conceptual validity.
Content validity represented
regular contain mathematical curriculum for the packages. Aspect
validity represented
the extent correspondence with the result of the other mathematical test.
Conceptual validity represented
extent for the know-how acquired in the teaching.
The mathematical exercises
packages have the properties of the
didactic testes reliability is the criterion of the
precision and infallibility of the measure the adjusted teacher result.
The measure is reliability
if the multiple measure the given mathematical complex we have identical
results. (The test is validity if he is too much reliability. The too much
reliability not guarantees the validity of the test.)
The package of the mathematical
exercises is practical. The practical of the package is the requirement economical.
The economical packages has the exercises where the extensive curriculum the
great quantity students is verify in the short time
Literature
1. Balczak, S.: The
Proposal of the Didactic Test in the Mechanical Technology Discipline. The finals work of the complementary
pedagogically studies. Faculty of Manufacturing Technologies of the
University of Technology in Koshice. 2001, p. 40.
2. Macura, D.: The Entrance
Examination, Exercises, and Their Solutions. Faculty of Natural and
Humanitarian Science University of Preshov, 1999,
pp.85. ISBN 80-88722-47-0.
3. Macura, D. - Macurova, A.: NR and
CR packages of the mathematical exercises for the secondary school. Methodically-pedagogically
center in Preshov. 2003, s. 44. ISBN 80-8045-290-3.
4. Macurova, A. Hrehova, S.: Solution of the Poisson Equation by the EXCEL.
In:Proceeding of the Scientific International
Conference Modernization of the teaching
technically oriented discipline. Pedagogically Faculty Palacky
University in Olomouc.
Olomouc, 1999, Czech Republic.
5. Macurova, A. Hrehova, S.: Some
Annotation for Periodic Solution of the Differential Equations System with
Periodic Coefficients.In: Proceedings of the
Scientific Conference with International Participation: Informatics and Algorithms ´98 , Technical University Preshov, 1997, Slovak Republic. Pp. 123 129.
6. Hrubina, K. Macurova, A.: On the Approximation Method Applied to the
Solution of Mathematical Model Expressed by Differential Equation of the Second
Order. Transactions of the Universities
of Koshice. Pp.36 46. 3/2003, ISSN 1335 233.
7. Tirpakova, A.:
On a sum of observables in F-quantum spaces and its applications to
convergence theorems. In: Proceeding from the First Winter School on Measure
Theory, Liptovsky Jan . Slovak Republic.1988, p.161-165.
8.Vasilko, K. Macurova,
A.: The New Mathematical Description of the Dependency 
. In: CEEPUS. SCIENCE
REPORT, Project PL 1, Computer Aided Systems for Manufacture and
Measurement of Machine Elements. Kielce 2004, Poland.
Pp. 173 178, p. 253. ISBN 83-88906-65-8.
Address authors
EdDr. Anna MACUROVA,
PhD., Eng. Stanislaw BALCZAK, The Department of Mathematics, Informatics and
Cybernetics, Faculty of Manufacturing Technologies of the University of
Technology in Koshice. Bayerova 1, 08001 Preshov,
Slovak Republic.
e-mail:
macurova.anna@fvt.sk., e- mail:balcak@condornet.sk.
Mgr. Dušan
MACURA, PhD., Department of the Mathematic, Faculty of Natural and Humanitarian
Science University of Preshov, 17 November, 080 01 Preshov, Slovak Republic, e-mail:macura@unipo.sk.