Communication and Mathematic reasoning: Theory of planned behavior and inquiry

The purpose of this study is to investigate the aspects of communication and mathematical reasoning. In investigating the aspects of mathematical communication with an inquiry approach, of course there are several things observed related to learning mathematics. The focus of the material aims at observing communication and mathematical reasoning within the framework of inquiry, and the theory of planned behavior (TPB) is geometry and algebra. The research method used a qualitative research by looking at case studies with research subjects consisting of 31 prospective mathematics teachers in Semarang city. From the aspect of communication and mathematical reasoning that exists, it can be seen from the answers of 31 prospective mathematics teachers with an authentic point of view of inquiry and a theory of planned behavior for problem solving. From the observation, several cognitive processes are adapted to the authentic framework of inquiry and the theory of planned behavior for algebra and geometry material. In reasoning, a wedge appears between mathematical reasoning and communication adapted to the framework of inquiry and the theory of planned behavior. The contribution of this study is to determine the communication framework and mathematical reasoning from the theoretical aspects of planned behavior and inquiry. It is important to know aspects of communication and mathematical reasoning from a different perspective.

GeoGebra Training for Making Mathematics Learning Media at SMPN 11 Depok

The purpose of this community service activities is to introduce and provide a GeoGebra training to Mathematics teachers at SMP Negeri 11 Depok. GeoGebra is a software that is used as a learning media in Geometry and Algebra as an innovation in learning Mathematics. So far, teachers are using simple tools only to explain about some topics in Mathematics to the students. The community service team will introduce and give a GeoGebra training. The methods that are used are training methods, accommodation, and discussion. The training is carried out by providing theories and practices to the teachers to operate the GeoGebra for Geometry and Algebra. The output target in this community service is the teachers can use GeoGebra as a learning media in Mathematics especially in Geometry and Algebra, GeoGebra module, and scientific articles.

Predicting Fraction and Algebra Achievements Online: A Large-Scale Longitudinal Study Using Data from an Online Learning Environment

Background: Mastering fractions seems among the most critical academic skill for students to acquire in school as fraction understanding significantly predicts later academic and vocational prospects. As such, identifying longitudinal predictors of fraction understanding (e.g., mastery of numbers and operations) is highly relevant. However, almost all existing studies identifying more basic numerical skills as predictors of fraction understanding rest on data acquired in face-to-face testing - mostly in classrooms. Objectives: In this article, we evaluated whether obtained results generalize to data from the curriculum-based online learning environment Bettermarks for mathematics used in schools in the Netherlands. In particular, we i) evaluated whether fraction understanding can be predicted by prior skills on different more basic mathematical topics before we ii) examined whether fraction understanding predicted achievements in algebra over and beyond the influence of basic mathematical skills. Methods: We considered data from more than 5,000 students who solved over 1 million mathematical problem sets. Results and Conclusions: In line with previous findings, we found that fraction understanding was predicted significantly by prior skills on basic mathematical topics. Our analyzes also revealed that algebra achievements were predicted significantly by fraction understanding beyond influences of basic mathematical skills. Implications: Together, these findings substantiated previous results based on face-to-face testing and, thus, indicate that data from large-scale online learning environments may well qualify to provide significant insights into the development of mathematical skills.

Differences Between Schools of Choice and Traditional Comprehensive Schools in Their Grade 9 Academic Performance

This study was conducted to determine the differences between schools of choice and traditional comprehensive high schools in terms of their Grade 9 State of Texas Assessments of Academic Readiness (STAAR) End-of-Course (EOC) exams in Biology, English 1, and Algebra 1 during the 2017-2018 school year. Inferential statistical analyses revealed the presence of a statistically significant difference between the two types of schools on their EOC exam passing rates in all three content areas for students who were not at-risk and for students who were not in poverty. In contrast, statistically significant differences were not revealed between the two types of schools in terms of the EOC exam passing rates of their CATE and Non-CATE students. Knowing that students who have choice appear to perform better academically, policymakers are encouraged to study the feasibility of channeling more funding to help school districts expand their school choice programs to (a) motivate more students to find the school that fit their needs and their future college and career aspirations, and (b) to solicit more support from parents and community businesses to invest in their communities to improve schools through taxes. Given that the data for this research were gathered for only 16 school districts in South Texas, researchers are encouraged to conduct a study that will involve all school districts in the whole state and possibly the whole nation to reach more conclusive evidence on the differences between schools of choice and neighborhood schools.

An analytical and probabilistic model with concordance for detecting mine-like objects with mirror symmetry

PurposeThe purpose is to develop search and detection strategies that maximize the probability of detection of mine-like objects.Design/methodology/approachThe author have developed a methodology that incorporates variational calculus, number theory and algebra to derive a globally optimal strategy that maximizes the expected probability of detection.FindingsThe author found a set of look angles that globally maximize the probability of detection for a general class of mirror symmetric targets.Research limitations/implicationsThe optimal strategies only maximize the probability of detection and not the probability of identification.Practical implicationsIn the context of a search and detection operation, there is only a limited time to find the target before life is lost; hence, improving the chance of detection will in real terms be translated into the difference between success or failure, life or death. This rich field of study can be applied to mine countermeasure operations to make sure that the areas of operations are free of mines so that naval operations can be conducted safely.Originality/valueThere are two novel elements in this paper. First, the author determine the set of globally optimal look angles that maximize the probability of detection. Second, the author introduce the phenomenon of concordance between sensor images.

The impact of Fishers Reproductive Compensation on raising equilibrium frequencies of semi-dominant, non-lethal mutations under mutation/selection balance.

Fishers reproductive compensation (fRC) occurs when a species demography means the death of an individual allows increased survival of his/her relatives, usually assumed to be full sibs. This likely occurs in many species, including humans. Several important recessive human genetic diseases cause early foetal/infant death allowing fRC to act on these mutations. The impact of fRC on these genetic conditions has been calculated and shown to be substantial as quantified by w, the fold increase in equilibrium frequencies of the mutation under fRC compared to its absence i.e. w=1.22 and w =1.33 for autosomal and sex-linked loci, respectively. However, the impact of fRC on the frequency of the much large class of semi-dominant, non-lethal mutations is unknown. This is calculated here by a mixture of simulation and algebra and shown that w is approximately 2-h*s and 2-0.19s-0.85h*s for autosomal and sex-linked loci respectively where h is dominance (varied between 0.05 and 0.95) and s is selection coefficient (varied between 0.05 and 0.9). These results show that the actions of fRC can almost double equilibrium frequency of mutations with low values of h and/or s. The dynamics of fRC acting on this type of mutation are also identified and discussed.

Polynomials, numerical triangles and sequences associated with the probability distribution of the hyperbolic cosine type for odd values of the parameter

The article introduces a new class of polynomials that first appeared in the probability distribution density function of the hyperbolic cosine type. With an integer change in one of the parameters of this distribution, polynomials in the form of a product of positive factors are written out with an increasing degree. Earlier, the author found a connection between the distribution of the hyperbolic cosine type and numerical sets, in particular, in the simplest cases with the triangle of coefficients of Bessel polynomials, the triangle of Stirling numbers, sequences of coefficients in the expansion of various functions, etc. Also from the distribution formed numerous numerical sequences, both new and widely known. Consideration of polynomials separately from the density function made it possible to reconstruct numerical sets of coefficients, ordered in the form of numerical triangles and numerical sequences. The connections between the elements of the sets are established. Among the sequences obtained, in the simplest cases, there are those known from others, for example, physical problems. However, the overwhelming majority of the found number sets have not been encountered earlier in the literature. The obvious applications of this research are number theory and algebra. And the interdisciplinarity of the results indicates the possibility of applications and enhances their practical significance in other areas of knowledge.