Analysis of Junior High School Students' Mathematical Connection on The Ratio and Proportion Concepts

The purpose of this study was to obtain an overview of the mathematical connections of junior high school students on the concepts of ratio and proportion. This research uses a descriptive qualitative method with data triangulation. The research participants were four junior high school students in Sukabumi. The instrument used in this study consisted of a description test of three questions that had been consulted with experts and based on considerations regarding indicators of mathematical connection ability. Based on the results of the study, it is known that the ability of students to recognize and use connections between mathematical ideas is 50%, the ability of students to connect and apply mathematical concepts with other disciplines is 50%, and the ability of students to connect and apply mathematical concepts to problems in everyday life with a percentage of 50%. The results showed that the mathematical connection ability of some junior high school students in Sukabumi on the concept of comparison was included in the poor category.

The Effectiveness of Inquiry-based Learning on Middle School Students’ Mathematics Reasoning Skill

This study investigated the effectiveness of inquiry-based learning (IBL) approach in ratio and proportion on the mathematics reasoning skill of seventh-grade students. The study was carried out in a seventh-grade mathematics course in a middle school located in the Central Anatolia region of Turkey during the 2016-2017 academic year. The IBL content was prepared and implemented about the ratio and proportion topics on which the reasoning skill is effective in the 7th grade curriculum. The IBL teaching implementations were conducted with 30 seventh grade students, but nine students, who represented different math achievement levels, were selected for the study’s analysis. Course video recordings, worksheets, student interviews, and diaries were used as data collection tools. The results showed that the students' predictive, explanation, generalization and justification skills emerged as indicators of reasoning skill. Students made different predictions and generalizations based on their existing knowledge and they developed solutions to problems using different strategies in IBL process. According to these findings, it was concluded that students' reasoning skill were effective during IBL. Keywords: Inquiry-Based Learning in Mathematics (IBL-M), Reasoning skill, Ratio and proportion, Middle school students

Achieving Ultra-High Performance Concrete by Using Packing Models in Combination with Nanoadditives

This paper describes the packing models that are fundamental for the design of ultra-high-performance concrete (UHPC) and their evolution. They are divided into two large groups: continuous and discrete models. The latter are those that provide the best method for achieving an adequate simulation of the packing of the particles up to nanometric size. This includes the interaction among the particles by means of loosening and wall coefficients, allowing a simulation of the virtual and real compactness of such particles. In addition, a relationship between virtual and real compactness is obtained through the compaction index, which may simulate the energy of compaction so that the particles are placed in the mold. The use of last-generation additives allows such models to be implemented with water–cement (w/c) ratios close to 0.18. However, the premise of maximum packing as a basic pillar for the production of UHPC should not be the only one. The cement hydration process affected by nanoadditives and the ensuing effectiveness of the properties in both fresh and hardened states according to the respective percentages in the mixture should also be studied. The characterization tests of the aggregates and additions (dry and wet compactness, granulometry, density and absorption) have been carried out in order to implement them numerically in the polydisperse packing model to obtain the compactness of the mixture. Establishing fixed percentages of nanoadditives in the calculation of the mixture’s compactness. The adequate ratio and proportion of these additions can lead to better results even at lower levels of compactness. The compressive strength values obtained at seven days are directly proportional to the calculated compactness. However, at the age of 28 days, better results were obtained in mixes with lower cement contents, fewer additions and lower compactness. Thus, mixes with lower cement contents and additions (silica fume and limestone filler) with a compactness of φ = 0.775 reached 80.1 MPa of strength at 7 days, which is lower than mixes with higher cement contents and number of additions (SF, limestone filler and nanosilica), which achieved a compactness of φ = 0.789 and 93.7 MPa for compressive strength. However, at 28 days the result was reversed with compressive strengths of 124.6 and 121.7 MPa, respectively.

Extending a Euclidean Model of Ratio and Proportion

This paper is written for mathematics educators and researchers engaged at the elementary and middle school levels and interested in exploring ideas and representations for introducing students to ratio and proportion and for making a smooth transition from multiplication and division by whole numbers to their counterparts with fractions. Book V of Euclid’s Elements offers a scenario for deciding whether two ratios of magnitudes, embodied as a pair of line segments, are equal based on whether the ratios of magnitudes, when multiplied by the same whole numbers, n and m, each yield common products. This test of proportion can be performed using an educational software application where students are presented with a target ratio of commensurable magnitudes, A:B, and challenged to produce a selected ratio, C:D, that behaves like the target ratio under the critical conditions. The selected ratio is automatically constructed such that C:D = m:n, on the basis of a lattice point (n, m) chosen by the student. By adding partitive and Euclidean division to Euclid’s model, five new scenarios with similar goals are proposed. Representations in the Euclidean plane, on a number line, and in the Cartesian plane provide feedback that students may use to help identify a ratio of whole numbers corresponding to the targe ratio of magnitudes. The representations serve to highlight fractions as members of equivalence classes. The model remains to be investigated with teachers and students.

Achieving Ultra-High Performance Concrete by Using Packaging Models in Combination with Nanoadditions

This paper describes the packaging models that are fundamental for the design of ultra-high-performance concrete (UHPC), and their evolution. They are divided into two large groups: continuous and discrete models. The latter are those that provide the best answer in obtaining an adequate simulation of the packing of the particles up to nanometric size. This includes the interaction among the particles by means of loosening and wall coefficients, allowing a simulation of the virtual and real compactness of such particles. In addition, a relationship between virtual and real compactness is obtained, through the compaction index, which may simulate the energy of compaction that the particles undergo in their placement in the mold. The use of last-generation additives allows such models to be implemented with water-cement (w/c) ratios close to 0.18. However, the premise of maximum packing as a basic pillar for the production of UHPC should not be the only one. The cement hydration process affected by nanoadditions and the ensuing effectiveness in the properties in both fresh and hardened state according to the respective percentages in the mixture should also be studied. An adequate ratio and proportion of these additions may lead to an obtaining of better results even with lower levels of compactness.

GENDER PERSPECTIVE AND NEWMAN'S THEORY IN ERROR ANALYSIS OF STUDENTS' ANSWERS IN RATIO AND PROPORTION

This research was conducted to find out how the gender perspective affects the mistakes made by students in the ratio and proportion questions. Mindset’s differences between male and female will affect how they solve problems and it will also affect their mathematics learning outcomes. Errors made by students were analyzed using the Newman error analysis indicator. Error analysis indicators used are reading errors, misunderstanding errors, transformation errors, process errors, and error writing answers (encoding). This research uses descriptive qualitative research method. This research was conducted at SMPN 2 Cimahi. The instruments in this study were test and non-test questions. It can be concluded from this research that there are differences between male and female students when working on ratio and proportion concept questions based on the mistakes they’ve made. The most common mistakes made by male students are mistakes in the process of writing answers. This error occurs because they do not write down the complete answer details, it’s because male tend to be simpler in solving problems. The most common mistake made by female is an error in understanding. It’s because female tend to use logic-less when understanding the mathematical problems presented in the questions.