Unimodular matrix and bernoulli map on text encryption algorithm using python

One of the encryption algorithms is the Hill Cipher. The square key matrix in the Hill Cipher method must have an inverse modulo. The unimodular matrix is one of the few matrices that must have an inverse. A unimodular matrix can be utilized as a key in the encryption process. This research aims to demonstrate that there is another approach to protect text message data. Symmetric cryptography is the sort of encryption utilized. A Bernoulli Map is used to create a unimodular matrix. To begin, the researchers use an identity matrix to generate a unimodular matrix. The Bernoulli Map series of real values in (0,1) is translated to integers between 0 and 255. The numbers are then inserted into the unimodular matrix's top triangular entries. To acquire the full matrix as the key, the researchers utilize Elementary Row Operations. The data is then encrypted using modulo matrix multiplication.

Error analysis of prospective mathematics teachers in solving of applying radian measurement problem in trigonometry courses

This research aims to describe the mistakes of the prospective teachers in solving the application of radian measurement problems and their causes. This type of research is qualitative descriptive research with a case study approach. The types of data collection in this research consisted of the results of the subject's work and transcripts of interviews with research subjects. By following the type of data, this research instrument consists of one question about the problem of applying radian measurement and interview guidelines developed by the researchers. Data analysis of the subject's work is carried out by classifying the types of errors to know the types of errors that arise in solving the problem of applying the radian measurements. While the transcript analysis of the interview results was carried out by coding the words to determine the factors causing the errors that appeared. The results of the research indicate that the error in solving the problem of applying the radian measurement are misconceptions and factual errors. This misconception is generally caused by intuitive thinking, while this factual error is generally caused by not paying careful attention to the information in the question. The solution to these errors is to analyze the elements of the circle that are interconnected in solving the problem of applying the radian measurements and to be careful in writing the information that is known in the question.

Improving students’ mathematical logical intelligence through the online-based integration of local wisdom of Sulapa Eppa Walasuji

Mathematical logical intelligence is one of the skills that are needed in the 21st century related to mathematical problem-solving skills. The importance of this skill is not in line with the facts on the ground, where students are still weak in counting and using logic in problem solving. The purpose of this research is to improve students’ mathematical logical intelligence through the online-based integration of local wisdom of Sulapa Eppa Walasuji. Sulapa Eppa Walasuji is one of the Bugis-Makassar local wisdoms with a unique pattern, appropriate to be used as a medium for learning transformation of geometry. Through the integration of local wisdom, Sulapa Eppa Walasuji can create contextual mathematics learning, so that students can easily understand the material by connecting real-life concepts. This research includes experimental research with a quasi-experimental design of the nonequivalent control group design type. The research instrument used was a mathematical logical intelligence test consisting of five essay questions. The data analysis used is descriptive statistics with gain score and effect size testing. The results showed that the mathematical logical intelligence of experimental class students increased by 43.16 with the effective contribution of the r effect size being 0.910. This indicates that the online-based integration of Sulapa Eppa Walasuji can improve students’ mathematical logical intelligence.

Assessing moodle-assisted e-learning for students’ concept understanding and critical thinking skills in algebra

Conceptual understanding and critical thinking skills are necessary for all students to help them in their learning process. This research aims to determine the effect of Moodle-assisted e-learning on (1) conceptual understanding, (2) critical thinking skills, and (3) conceptual understanding and critical thinking skills combined. This research employed a quasi-experimental design with random cluster sampling was used as the sampling technique. An algebra written test was used to collect research data. Furthermore, the researchers performed the normality test, homogeneity test, and MANOVA analysis to analyze the data. The researchers discovered that Moodle-assisted e-learning influenced students' conceptual understanding, critical thinking skills, and conceptual understanding and critical thinking skills.

Metacognitive failure in constructing proof and how to scaffold it

This research aims to describe the students’ metacognitive failure in constructing proof and the scaffolding support. The participants of this qualitative case study were eight preservice mathematics teachers of six-semester, State University of Malang. We carried out a test about proof construction problems in Abstract Algebra. Then we verified the data using triangulation of constant comparative method from a test and a task-based interview with the stimulated recall. The results indicated two groups of students in proving strategy. Group I performed “appropriate” syntactic strategy and Group II vice versa. Blindness was experienced by the subject that does not recognize errors detection or the ambiguity of the proof. Mirage occurred when the subject recognizes an error detection on the proper strategy or application of a theorem, then is unable to verify the truth of his work. Misdirection appeared when the subject recognizes a lack of progress, then uses an incomplete or irrelevant concept. Vandalism emerged with no progress or detection of errors of the strategy then the subject performs some irrelevant steps to the issue or uses a misconception. Practically, the teachers can use these results for learning innovations in scaffolding-based proof courses. The scaffolding might need some development and application in supporting students to overcome difficulty in proving mathematical sentences.

Rasch model item response theory (IRT) to analyze the quality of mathematics final semester exam test on system of linear equations in two variables (SLETV)

A high-quality test has a balanced level of difficulty and can be completed by the respondent with their level of abilities. This study analyzed the test instrument used to measure students' mathematics abilities in the semester final exam on System of Linear Equations in Two-Variables. The purposive sampling technique was applied to select the respondent students (N=195). The test items were twenty multiple-choice questions. The researchers performed the data analysis using Rasch model Item Response Theory (IRT) approach with the QUEST program. The analysis revealed that the twenty items’ validity matched the Rasch model with a range of INFIT MNSQ values between 0.89 – 1.17. Items on the final semester exam can be used based on the estimated OUTFIT t-value less than equal to 2.00. The OUTFIT t analysis obtained nineteen qualified items and one unqualified item.

Designing interactive games for improving elementary school students’ number sense

Number sense is an essential primary mathematics material in elementary school that students must master. Learning media may be utilized in elementary schools' teaching and learning process to engage and inspire students to participate in learning activities, particularly mathematics. Therefore, the researchers designed an interactive game using Genially to improve students' number sense. The ADDIE development model was applied in the research and development procedure. In this research, the ADDIE development model began by analyzing problems related to the mathematics learning process in elementary schools, analyzing the environment and work situation, designing an interactive game, developing the game based on validation results from three media experts and two concept experts, and conducting a one-on-one trial. The product feasibility was tested on 46 students who were divided into two classes. Class B served as the experimental class, while Class A served as the control class. The interactive game's validation findings showed that the developed interactive learning media was practical and useful. As a result of the implementation, the experimental class students' grasp the material better than the control class.

Problem-based learning model on mathematical analytical thinking ability and science process skills

This research serves as a reference for teachers to implement problem-based learning models on analytical thinking skills and science process skills in mathematics subjects. This research examines the differences and relationships between students' analytical thinking skills and science process skills with problem-based learning models in mathematics. The sample of this research consisted of 180 students. This research is a quantitative study with a questionnaire as the instrument. The obtained data were analyzed using the t-test and correlation test. The results showed a significant difference between analytical thinking skills and students' science process skills, especially on the indicators of Observation and Classification at SMPN 35 Batanghari and SMPN 8 Batanghari students who applied the problem-based learning model in mathematics. Furthermore, it was found that there was a relationship between analytical thinking skills and science process skills because students with analytical thinking skills possessed better science process skills in problem-based learning models in mathematics subjects.