Course: Mathematical thinking in practice

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Course title Mathematical thinking in practice
Course code KMA/EIPM1
Organizational form of instruction Seminary
Level of course not specified
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
  • Hašek Roman, Mgr. Ph.D.
  • Pech Pavel, prof. RNDr. CSc.
  • Petrášková Vladimíra, doc. RNDr. Ph.D.
  • Samková Libuše, RNDr. Ph.D.
Course content
The course is divided into four three-hour blocks, each of which is taught by different teacher: 1) Concept Cartoons. Building the elementary foundations of the principles of mathematical thinking is introduced through so called Concept Cartoons. Participants taking part in the group work with this means of active learning. 2) The role of numbers in our life. Every day of our lives we meet mathematics through various numbers and their characteristics. In this block the participants will become practically familiarized with the role of numbers, e.g. primes or basic mathematical constants, in their lives. 3) Geometry of real life. Geometry is an integral part of practice. In both technical practice and natural phenomena, basic geometric principles are often applied, mostly interfering with other fields of mathematics. The participants will become acquainted, among other topics, with isoperimetric inequality, A-G inequality, the Fibonacci series or with simple visual proofs of selected geometric properties. 4) Financial literacy. The fourth block of the course is devoted to financial literacy. The participants will focus on the history of money and the development of monetary systems in the context of the 21th century. Applying elementary mathematics, they practice the process of pricing, family budgeting and they get to know the principles of interest.

Learning activities and teaching methods
Work with text (with textbook, with book), Work activities (workshops), Activating (simulations, games, drama), Work with multi-media resources (texts, internet, IT technologies), Individual tutoring, Flipped classroom
Learning outcomes
The course is focused on the development and practical application of mathematical methods. At first, by means of particular activities, the participant will become acquainted with the basis of mathematical thinking and the methods of its development. Then, when solving specific real life situations, the participant applies selected mathematical procedures appropriate to these situations and which are also applicable in other practical situations. In order to do so, a basic knowledge of upper secondary school mathematics is sufficient. If the development of a mathematical model or the solution of a real life problem appears to be too complex, the intuitively operated mathematical software or mobile application is provided for the participant to do so. The scope of the course spans from the development of the basic processes of mathematical thinking, through the reflection of the principles of number theory and geometry in real life, to the application of mathematical methods in everyday financial issues.
At first, by means of particular activities, the participant will become acquainted with the basis of mathematical thinking and the methods of its development. Then, when solving specific real life situations, the participant acquire to apply selected mathematical procedures appropriate not only to these situations but also applicable in other practical situations.
Common knowledge of secondary school mathematics. Ability to communicate, read and write in English.

Assessment methods and criteria
Student performance assessment, Combined exam, Seminar work

Active participation in the course activities. Writing a seminar paper. Passing the exam by solving a specific task from the subject content.
Recommended literature
  • Plus magazine.. living mathematics [online]..
  • The 10 Most Important Numbers In The World. Business Insider [online]..
  • ARTHUR, C. J. Financial literacy education: Neoliberalism, the consumer and the citizen.. Rotterdam, 2012.
  • BOGOMOLNY, A. Cut The Knot: Interactice Mathematics Miscellany and Puzzles [online]..
  • CAPINSKI, M. & ZASTAWNIAK, T. Mathematics for finance: An introduction to financial engineering.. London: Springer., 2008.
  • DEVLIN, K. Introduction to Mathematical Thinking [online]. 2012.
  • KIRKBY, D. Go Further With Investigations.. London: HarperCollins Publishers, 1996.
  • KIRKBY, D. More Investigations.. London: HarperCollins Publishers, 1995.
  • STACEY, K. et al. Specific mathematics assessments that reveal thinking. Smart tests research and development project [online]..
  • ULM, V. (ED.). Inquiry-based mathematics education for gifted children in primary school.. Augsburg: University of Augsburg, 2011.

Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester