Future jobs will require students to handle interdisciplinary knowledge that goes beyond computing techniques when it comes to mathematics education. The traditional approach to education insufficiently develops the needed mathematical skills and mathematical literacy and there is a need to devise new methods of teaching and learning. We introduce game-based learning in mathematics education through carefully designed activities aiming at interdisciplinarity and increasing students’ motivation, mathematical and digital literacy, physical activity, level of knowledge, etc. We propose the treasure hunt cantered around cryptography as an example activity that satisfies the described criteria. Parts of the clues leading to the treasure are hidden using different ciphers, following the historical development of cryptography. The treasure hunt is time-limited to one hour and, to successfully complete the search, students need to learn, adapt, and apply different methods of encryption and decryption. To complete the hunt in time, students must work as a team and effectively divide the tasks among themselves. Students have at their disposal all instructions and manuals in written form, and they are compelled to read with comprehension. We conducted the activity with several groups of high school students with no previous knowledge and skills in the field of cryptography. Students were asked to take a pre-test and post-test survey about their experience and familiarity with cryptography concepts. Most teams completed the search and achieved all learning outcomes. In the paper, we will describe the activity in detail, analyse the test results and give additional examples of game-based activities in mathematics education.
In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described by Tonchev in [12] in order to obtain selforthogonal codes over an arbitrary field. We extend construction self-orthogonal codes from orbit matrices of self-orthogonal designs and weakly self-orthogonal 1-designs such that block size is odd and block intersection numbers are even described in [5]. Also, we generalize mentioned construction in order to obtain self-orthogonal codes over an arbitrary field. We construct weakly self-orthogonal designs invariant under an action of Mathieu group M 11 and, from them, binary self-orthogonal codes.Let D be weakly self-orthogonal design and let M be its bˆv incidence matrix. Using suitable extension of M one can obtain self-orthogonal binary code C.Theorem 1 Let D be weakly self-orthogonal design and let M be its b ˆv incidence matrix.1. If D is a self-orthogonal design, than CpDq is a binary self-orthogonal code.2. If D is such that k is even and the block intersection numbers are odd, then the matrix rI b , M, 1s, generates a binary self-orthogonal code.3. If D is such that k is odd and the block intersection numbers are even, then the matrix rI b , M s, generates a binary self-orthogonal code.
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