Abstract
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.
Highlights
IntroductionMathematics education is constantly evolving based on the requirements of contemporary society
Mathematics education is constantly evolving based on the requirements of contemporary society.the curriculum development is strongly influenced by 21st-century learning skills in particular critical thinking, problem solving, communication and collaboration [1]
The goal of Mathematics B-day 2018 assignment [55] was inspired by the mathematical open ended problem called “The Moser’s Worm Problem” formulated as follows: “What is the surface of the smallest flat shape that can cover all lines of length 15 cm?” [56] (p.153)
Summary
Mathematics education is constantly evolving based on the requirements of contemporary society. The curriculum development is strongly influenced by 21st-century learning skills in particular critical thinking, problem solving, communication and collaboration [1]. Students intending to inquire as defined in [3] feature the following characteristics: asking questions, attempting and experimenting, identifying the problem, choosing the right strategy in problem solving. The nature of open-ended problems represents the means how to implement the inquiry in mathematics education [4] and help students to learn how to think independently for using the problem solving strategies [5]. Over the course of many years, solving open-ended problems in mathematics has evolved into an activating method that supports the 21st-century learning skills mentioned above
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