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

Abstract

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.

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

“…When students are asked to solve a combinatorial task using an expression or formula, then they should be able to generalize algebraically. Similarly, to our previous study [29] the role of algebraic generalization in solving problems from the different parts of mathematics was confirmed. Thus we can conclude that the algebraic generalization abilities should be in the focus of the upper-secondary mathematics education.…”

“…On the other hand, the algebraic generalization raises specific problems for almost every student, even in the course of studying higher grades [28]. Our recent research findings indicate an ability to produce some general algebraic expressions as a crucial factor in solving open-ended non-routine problems in mathematics, even by high-achievers [29].…”

Relation between Pupils’ Mathematical Self-Efficacy and Mathematical Problem Solving in the Context of the Teachers’ Preferred Pedagogies

“…This also seems to hold true in reverse, i.e., students who have a positive attitude to mathematics are more successful at solving mathematical problems [53][54][55][56][57]. The results of several authors show that success in solving mathematical problems is influenced by students' procedural skills, including their ability to use (dominantly mathematical) tools productively and to choose an appropriate representation in the mathematization of problem situations [58][59][60][61]; their level of control of processes related to mathematical activity, such as reasoning, communication, generalization, or mathematical modeling [62][63][64][65][66][67][68]; and the level of their conceptual understanding of mathematical concepts [69][70][71][72][73].…”

A Joint Assessment of Reasoning about General Statements in Mathematics and Biology

“…Thus, it consists of classroom activities involving students that observe, pose questions, reason, search for information, collaborate, collect data and interpret them, discuss obtained results (Dorier and Maass, 2014). Such an environment is naturally rich in generalisations (Bulková, Medová and Čeretková, 2020) and general statements of various appearances and validity are frequently voiced in the classroom.…”