ANALISIS KESULITAN BELAJAR SISWA BERKEMAMPUAN MATEMATIKA RENDAH BERDASARKAN GENDER

This study aims to fully describe the learning difficulties of students with low mathematical abilities in solving arithmatic division operations based on gender. This research is a descriptive qualtative research with research subjects consisting of 1 female student and 1 male student with low math ability in class IV-A SDN Bugih 1 Pamekasan with the test instrument for the comlpetion of the division count operations aninterviews. The results showed that on thr indicators of difficulty in understanding the concept, the results of the study learning difficulities in female subject (S1) and male subject (S2) in solving the division arithmetic operation, namely the two subjects did not know the concept of division as repeated subtraction. On the indicator of difficulty in applying the principle, the two subjects were unable to do the tiered division correctly because the wo principle of division to the long division. Whereas in the indicator of difficulty in solving verbal problems, the two subjects were unable to write down what wa known and what was asked of the story problem correclty.

Low latency Montgomery multiplier for cryptographic applications

In this modern era, data protection is very important. To achieve this, the data must be secured using either public-key or private-key cryptography (PKC). PKC eliminates the need of sharing key at the beginning of communication. PKC systems such as ECC and RSA is implemented for different security services such as key exchange between sender, receiver and key distribution between different network nodes and authentication protocols. PKC is based on computationally intensive finite field arithmetic operations. In the PKC schemes, modular multiplication (MM) is the most critical operation. Usually, this operation is performed by integer multiplication (IM) followed by a reduction modulo M. However, the reduction step involves a long division operation that is expensive in terms of area, time and resources. Montgomery multiplication algorithm facilitates faster MM operation without the division operation. In this paper, low latency hardware implementation of the Montgomery multiplier is proposed. Many interesting and novel optimization strategies are adopted in the proposed design. The proposed Montgomery multiplier is based on school-book multiplier, Karatsuba-Ofman algorithm and fast adders techniques. The Karatsuba-Ofman algorithm and school-book multiplier recommends cutting down the operands into smaller chunks while adders facilitate fast addition for large size operands. The proposed design is simulated, synthesized and implemented using Xilinx ISE Design Suite by targeting different Xilinx FPGA devices for different bit sizes (64-1024). The proposed design is evaluated on the basis of computational time, area consumption, and throughput. The implementation results show that the proposed design can easily outperform the state of the art

PENGEMBANGAN LEMBAR KERJA PESERTA DIDIK MATERI KELILING DAN LUAS BANGUN DATAR MENGGUNAKAN KALKULATOR DENGAN PEMBELAJARAN DELIKAN

This research is a research development (Research and Development) that aims to determine the feasibility of LKPD Mathematics products as well as the supporting and inhibiting factors of using LKPD. This study uses the Borg and Gall development model. The instruments used were tests, interviews, and questionnaires. There are 3 types of questionnaires used, namely expert validation questionnaires, student response questionnaires, and teacher response questionnaires. The results of the validation that have been carried out by the three validators obtained an overall average value of 4.16 with valid criteria. The LKPD trials were carried out by the Delikan learning steps (listen, see, and do). The average score of the students' questionnaire response was 4.58 with very good criteria. The teacher response questionnaire to the mathematics LKPD obtained a result of 4.2 with a good category. The use of LKPD received a very good response from students because the use of calculators was something new, but some students did not understand the concept of multiplication and long division so they needed guidance from the teacher. LKPD Mathematics of the circumference and area of a flat shape using a calculator with Delikan learning in Class IV SD UMP is said to be feasible and can be used as an alternative teaching material to improve skills in calculating the circumference and area of a flat shape using a calculator calculating tool.

New Method of Solving the Economic Complex Systems

In this study, the authors first develop a direct method used to solve the linear nonhomogeneous time-invariant difference equation with the same number for inputs and outputs. Economic cybernetics is the crystallization for the integration of economics and cybernetics. It analyzes the stability, controllability, and observability of the economic system by establishing a system model and enables people to better understand the characteristics of the economic system and solve economic optimization problems. The economic model generally applies the discrete recurrence difference equation. The significant analytic approach for the difference equation is the z-transformation technique. The z-transformation state of the economic cybernetics state-space difference equation generally is a rational function with the same power for the numerator and the denominator. The proposed approach will take the place of the traditional methods without all annoying procedures involving the long division of some complicated polynomials, the expanded multiplication of many polynomial factors, the differentiation of some complicated polynomials, and the complex derivations of all partial fraction parameters. To highlight the novelty of this research, this study especially applies the proposed theorems originally belonging to engineering to the field of economic applications.

Exploring Real Numbers as Rational Number Sequences With Prospective Mathematics Teachers

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students’ understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real numbers as rational number sequences. We found that the instructional sequence enhanced prospective teachers’ understanding of real numbers by considering them as quantities and explaining them by using rational number sequences. In particular, results showed that prospective teachers reasoned about fractions and decimal representations of rational numbers using long division, the division algorithm, and diagrams. This further prompted their reasoning with decimal representations of rational and irrational numbers as rational number sequences, which leads to authentic construction of real numbers. Enacting the instructional sequence provides lenses for mathematics teacher educators to notice and eliminate difficulties of their students while developing relationships among multiple representations of real numbers.