Identification of Crucial Steps and Skills in High-Achievers’ Solving Complex Mathematical Problem within Mathematical Contest

The aspects of inquiry based learning (IBL) are vigorously and frequently in the focus of recent studies. With the use of inquiry in mathematics in the daily school practice, some further questions are arising there: What kind of problems can be useful for an analysis of students’ competencies in the field of IBL and how to assess the performed level of competencies? In this paper, the Mathematics B-day contest assignment is introduced as a mean to assess the students’ performance in mathematical inquiry skills. Some new rubrics with didactical variables were designed as a tool for assessing students’ competencies. The statistical implicative analysis was used to investigate 29 solutions of Mathematics B-day 2017: Arrow clocks. We identified the key subtasks solutions directly related to the level of the IBL competencies performed in the final mathematical investigation. The subtask which required actually high level of algebraic thinking influenced the level of the final mathematical investigation the most.&nbsp

Designing mathematical computer games for migrant students

International audienc

Analysis of differences between teachers’ activity during their regular and constructivist lessons

International audienceDifferent aspects involved in the constructivist teaching mode were assessed in the eight observed mathematics lessons conducted by four upper-secondary in-service teachers. Four among these lessons were identified as ‘regular’ by the teachers themselves, the other four lessons followed the same constructivist lesson plan designed by the respected educational expert. The main differences were found in the way how the students were working and achieved their independent learning capabilities. The lessons following the constructivist lesson plan were clustered together by the means of hierarchical cluster analysis. The regular lessons were more influenced by the teachers’ personalities then the constructivist lessons

Relations between generalization, reasoning and combinatorial thinking in solving mathematical open-ended problems within mathematical contest

Algebraic thinking, combinatorial thinking and reasoning skills are considered as playing central roles within teaching and learning in the field of mathematics, particularly in solving complex open-ended mathematical problems Specific relations between these three abilities, manifested in the solving of an open-ended ill-structured problem aimed at mathematical modeling, were investigated. We analyzed solutions received from 33 groups totaling 131 students, who solved a complex assignment within the mathematical contest Mathematics B-day 2018. Such relations were more obvious when solving a complex problem, compared to more structured closed subtasks. Algebraic generalization is an important prerequisite to prove mathematically and to solve combinatorial problem at higher levels, i.e., using expressions and formulas, therefore a special focus should be put on this ability in upper-secondary mathematics education. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Slovak Research and Development AgencySlovak Research and Development Agency [APVV-15-0368]; Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic; VEGAVedecka grantova agentura MSVVaS SR a SAV (VEGA) [1/0815/18]; Ministry of Education, Youth and Sports of the Czech RepublicMinistry of Education, Youth & Sports - Czech Republic [RO60201015025]Ministerstvo Školství, Mládeže a Tělovýchovy, MŠMT: RO60201015025; Ministerstvo školstva, vedy, výskumu a športu Slovenskej republiky; Agentúra na Podporu Výskumu a Vývoja, APVV: APVV-15-0368; Vedecká Grantová Agentúra MŠVVaŠ SR a SAV, VEGA: 1/0815/1

Algorithms in mathematics education

International audienceThis paper summarizes my contribution to the plenary panel discussion Big Questions in Mathematics Education and focuses on the role of algorithms in mathematics education. Mathematics and computer science are interrelated from their substance. They share several common concepts including the algorithms, but the way they work with them differ among the two disciplines. Algorithms provide an additional dimension to mathematical knowledge, the deep procedural knowledge. Involvement of coding and work with algorithms in mathematics instruction seems to be a promising activity bridging the two disciplinary approaches. The questions: (i) how the work with algorithms contributes to students' learning and (ii) how to prepare teachers for this kind of activities should be investigated

Relations between Generalization, Reasoning and Combinatorial Thinking in Solving Mathematical Open-Ended Problems within Mathematical Contest

Algebraic thinking, combinatorial thinking and reasoning skills are considered as playing central roles within teaching and learning in the field of mathematics, particularly in solving complex open-ended mathematical problems Specific relations between these three abilities, manifested in the solving of an open-ended ill-structured problem aimed at mathematical modeling, were investigated. We analyzed solutions received from 33 groups totaling 131 students, who solved a complex assignment within the mathematical contest Mathematics B-day 2018. Such relations were more obvious when solving a complex problem, compared to more structured closed subtasks. Algebraic generalization is an important prerequisite to prove mathematically and to solve combinatorial problem at higher levels, i.e., using expressions and formulas, therefore a special focus should be put on this ability in upper-secondary mathematics education

Algorithms in mathematics education

International audienceThis paper summarizes my contribution to the plenary panel discussion Big Questions in Mathematics Education and focuses on the role of algorithms in mathematics education. Mathematics and computer science are interrelated from their substance. They share several common concepts including the algorithms, but the way they work with them differ among the two disciplines. Algorithms provide an additional dimension to mathematical knowledge, the deep procedural knowledge. Involvement of coding and work with algorithms in mathematics instruction seems to be a promising activity bridging the two disciplinary approaches. The questions: (i) how the work with algorithms contributes to students' learning and (ii) how to prepare teachers for this kind of activities should be investigated

Graph problems as a means for accessing the abstraction skills

International audienceComputational thinking is an important 21 st century skill. The ability to design own algorithm, i.e. algorithmic thinking is its integral part. Graph algorithms seem to be a promising mathematical content contributing to development of algorithmic thinking. However, in order to apply the corresponding skills to the problem at hand, first a corresponding representations has to be found. This step of abstraction is crucial for the application of skills to unknown situations and can be seen as a prerequisite for the algorithmic thinking. Solutions of the representation problem of 58 undergraduate students were analysed. Most students chose the diagram as a representation of the situation, only three students used the adjacency matrix and no students chose the incidence matrix or adjacency list, the other known representations. This may indicate that more activities are needed for enhancing students' ability to represent the graph, either by matrices or by a diagram

The effect of different online education modes on the English language learning of media studies students

The implementation of e-learning methods and their efficiency in the process of teaching English for specific purposes, particularly media and journalism, is a rather new phenomenon in Central Europe. The experiment conducted within this study was focused on the efficiency of e-learning and blended-learning modes. We created three groups of students with diverse modes of online education used in each group. The first group (18 students) was educated through the purely e-learning way, the second group (20 students) was taught through the classical face-to-face method, and the third group (18 students) through the blended-learning approach. The online education mode included interactive webinars with a native speaker who was providing live feedback on students’ assignments. Within the study programme of media/journalism the blended-learning mode seems to be the most efficient. Comparing the results of pre-tests to post-tests enabled us to specify the language skills which were improved in the three test groups. Scores of the students in all the four investigated areas (i.e. reading, speaking, listening and vocabulary) increased significantly in the blended-learning group. The vocabulary was the most improved language skill observed in both groups, meaning the e-learning as well as classic group. On the other hand, the online method resulted to an observable improvement in students’ performance as far as for the listening and speaking skills as it might simulate their future workplace

Metacognitive Knowledge and Mathematical Intelligence—Two Significant Factors Influencing School Performance

Metacognitive knowledge and mathematical intelligence were tested in a group of 280 pupils of grade 7 age 12–13 years in the Czech Republic. Metacognitive knowledge was tested by the tool MAESTRA5-6+. Mathematical intelligence is understood as an important criterion of a learner’s ability to solve mathematical problems and defined as the specific sensitivity to the six particular phenomena: causality, patterns, existence and uniqueness of solution, geometric imagination, functional thinking, and perception of infinity. The main objective of the research is to explore relationships and links between metacognitive knowledge and mathematical intelligence of the learners and discover the scope of impacts of their metacognitive knowledge on the school success rate. Based on the collected answers and nearly zero correlation (r = 0.016) between the researched domains, a two-dimensional model considering the correlations between metacognitive knowledge and mathematical intelligence was designed. The developed model enables to describe an impact of the domains on the learner’s school performance within the selected school subjects, and concurrently, it emphasizes their importance within the educational practice as such