| Components of successful education | 69$-$80 |
Abstract
I present a sample of a diagnostic test developed for testing students who enroll into elementary statistics courses. I use the test for observational studies about correlations of students' diagnostic test scores and their subsequent performance in the observed classes. Concrete numerical statistics are given that have proved to be highly reliable and stable to a degree over different classes. The test is more precise than the common generic diagnostic/entrance tests that are administered at universities (meant to gage students' mathematical background). The test has a direct practical value since it is used in everyday teaching practice and is of wider theoretical significance since it addresses one of the components of successful education, namely influence of preparation of students on their success.
Keywords: Diagnostic test
| Using innovative technology for revitalizing formal and informal mathematics: a special view on the interplay between procedural and conceptual knoledge | 81$-$89 |
Abstract
A student often meets a conflict between conceptual and procedural knowledge: does (s)he need to understand for being able to do, or vice versa? Hence an important research question is how pedagogical solutions affect the relation between the two knowledge types. Our theoretical analysis and practical experience evidence that desired links can be promoted when the learner has opportunities to simultaneously activate conceptual and procedural features of the topic at hand. Such activation is considered for interactive learning that utilizes an able technological tool, the ClassPad calculator. In a sequence of examples, we will show how this tool can be exploited to develop both informal and formal mathematical knowledge.
Keywords: Procedural Knowledge, Conceptual Knowledge, Linking Procedural and Conceptual Knowledge, Innovative Technology.
| Is cognitive style related to link between procedural and conceptual mathematical knowledge? | 91$-$95 |
Abstract
This study examined the relation between cognitive style and link between procedural and conceptual mathematical knowledge. It used a sample of 34 mathematically talented eleventh-grade students. A significant positive correlation was found between the students' achievements on the administered Embedded Figures Tests (where ``field-dependence-independence'' cognitive style has a very specific perceptual connotation) and the measures of link between their scores on procedural and conceptual mathematical knowledge. The same relation was again found in a group of particularly talented students who participated in mathematical competitions ($N = 16$), but not in the control group comprising other talented students ($N = 18$).
Keywords: Cognitive Style, Procedural Knowledge, Conceptual Knowledge, Linking Procedural and Conceptual Knowledge, Talented Students, Mathematics Education, Upper Secondary Education.
| Didactical analysis---a plan for consideration | 97$-$104 |
Abstract
Inspired by the idea of Freudenthal's didactical phenomenology, an integrated course of (didactics of) mathematics for primary school teachers is sketched. Based on history of mathematics and education, mathematics as science and psychology, didactical analysis of the subject matter is considered as the core of such a course. Only upon this analysis a proper shaping of didactical transposition of the subject matter is possible which would be, then, widely understood by teachers. A particularly controversial theme---basics of mathematical logic in school is also discussed. A way of elaboration spanning the current contents of school mathematics is suggested, going by interpretation and without the use of truth tables.
Keywords: History of mathematics; courses of teacher training; geometry; arithmetic; logic.
| An introduction to the continuity of functions using Scientific Workplace | 105$-$112 |
Abstract
We recommend the visual presentations shown in this paper as a presentation of the content of continuity in certain grades of secondary schools. In this paper we construct such a programme that can be applied to almost all functions, continuous and discontinues ones, in the programme package Scientific Workplace. This procedure enables teachers to add as many examples as necessary. Thus, the students understand properly this limit process, which is supposed to make the proper accepting of the continuity of function easier.
Keywords: Continuity of functions, visualiztion
| A broader way through themas of elementary school mathematics, V | 113$-$120 |
Abstract
Decimal notation and decade grouping are the basis of traditional elaboration of arithmetic. In the approach that we follow, this elaboration goes gradually through the didactical structuring and extending of number blocks. In this process of block extending, we use sums, applying the principle of permanence of the meaning of addition. Then, finding decimal notations for such sums is a purely calculation task, that is reducible to easier and smaller (already performed) cases. In this paper, the block 1-100 is constructed as the extension of the block 1-20 and its didactical analysis is executed. Due to pedagogical demands, we suggest the replacement of some arithmetic rules by their ``narrative'' substitutes that also have to be meaning-based.
Keywords: Block of numbers up to 100, permanence of meaning of operations, use of brackets.