Nonsymbolic and Symbolic Numerical Magnitude Processing in the Brazilian Children with Mathematics Difficulties

ABSTRACT It is still debated if the main deficit in mathematical difficulties (MD) is nonsymbolic or symbolic numerical magnitude processing. Objectives: In the present study, our main goal was to investigate nonsymbolic and symbolic numerical magnitude processing in MD and the relationship between these abilities and arithmetic. Methods: The Brazilian school-age children with MD completed a nonsymbolic and a symbolic numerical magnitude comparison task and an arithmetic task. We compared their performance with a group of children with typical achievement (TA) and investigated the association between numerical magnitude processing and arithmetic with a series of regression analyses. Results: Results indicated that children with MD had low performance in the nonsymbolic numerical magnitude comparison task. Performance in both nonsymbolic and symbolic numerical magnitude comparison tasks predicted arithmetic abilities in children with TA, but not in children with MD. Conclusions: These results indicate that children with MD have difficulties in nonsymbolic numerical magnitude processing, and do not engage basic numerical magnitude representations to solve arithmetic.

Development and use of the program of automatic problem solving when conducting practical classes in physics at the university

The creation of a virtual educational environment, consisting of an information space that ensures the availability of unlimited educational material through communication means, a virtual or real communication channel between a student and a teacher, increases the role of self-education, the dominance of learning over teaching. Paraphrasing [1], we can say that physics is owned not by the one who knows the formulas and definitions, but by the one who, with their help, can solve physical problems (PP). Similarly to the words of E. Fermi [2]: "A person knows physics if he/she can solve problems." The ability to solve PP contributes to the concretization of students' knowledge; without it, there is a separation of theoretical, lecture, educational material from the main task of any learning process – the practical application of accumulated knowledge and skills. Solving of PP contributes to the development of mental activity, the formation of creativity, intelligence, observation, independence and accuracy, is one of the forms of repetition, control and assessment of knowledge. At the same time, it is the solution of problems that is the most difficult element of physical education, causing methodological, didactic, psychological, and mathematical difficulties. It is known, that along with the traditional methods of solving PP: arithmetic, algebraic, geometric, graphic, experimental, since the beginning of the 2000s, information technology, computer technology, and programs - answer books have been actively used. The traditionally difficult issue of solving problems in physics requires both the improvement of classical methods and the development of new software tools for solving problems. The paper discusses the possibilities of using computers to solve various types of physical problems, the use of a site, created by the author, with considered examples of solving more than 2500 problems in physics, a developed program for automatic solution of problems in physics (APS - automatic physics solver) during practical exercises.

Mathematical Difficulties of 7th Grade MTs Students Analysis in Online Learning Based on The Realm Bloom’s Taxonomy

Online learning is a new alternative for the continuity of learning activities during the Covid-19 period, where learning is carried out online through various media or ICT used. This research aims to see the analyze how difficult students mathematical in working on mathematical problems, especially in quadrilateral and triangular material. The subject of this study were students of class VII at MTs Negeri Kabupaten Bandung Barat. The instrument used were written tests in the form of essays which numbered 5 questions and a student questionnaire via a google form. This research method uses descriptive analysis, to find out the student's mistakes in solving problems. Processing data is calculated in the form of average student scores obtained by analysis used on Taksonomi Bloom cognitive. The results showed that students achievement in the process of solving triangular and quadrilateral problems based on the stage of Taksonomi Bloom is based on the stage of Taksonomi Bloom, namely, at the cognitive stage the most is in stage C5 and C6 there is evaluation and creation, then in C2, C3, and C4 also still less than 60%. Thus it can be seen that the level of student understanding of rectangular and triangular material is still relatively low so that there is difficulty in solving students' problems on rectangular and triangular material based on Taksonomi Bloom stages. Keywords: student difficulties, online learning, quadrilateral, and triangular, taxonomy bloom

Anisotropic 𝑝-Laplacian Evolution of Fast Diffusion Type

We study an anisotropic, possibly non-homogeneous version of the evolution 𝑝-Laplacian equation when fast diffusion holds in all directions. We develop the basic theory and prove symmetrization results from which we derive sharp L 1 L^{1} - L ∞ L^{\infty} estimates. We prove the existence of a self-similar fundamental solution of this equation in the appropriate exponent range, and uniqueness in a smaller range. We also obtain the asymptotic behaviour of finite mass solutions in terms of the self-similar solution. Positivity, decay rates as well as other properties of the solutions are derived. The combination of self-similarity and anisotropy is not common in the related literature. It is however essential in our analysis and creates mathematical difficulties that are solved for fast diffusions.

Two Dyscalculia Subtypes With Similar, Low Comorbidity Profiles: A Mixture Model Analysis

Several studies have aimed to identify subtypes of dyscalculia. In many of these studies, either pre-defined groups (e.g., children with reading and mathematical difficulties vs. children with isolated mathematical difficulties) were analyzed regarding their cognitive profiles (top-down approach), or clusters of children with dyscalculia (CwD) were identified based on a narrow range of cognitive and mathematical skills (data-driven or bottom-up approach). However, it has remained difficult to establish robust subtypes of dyscalculia across studies. Against this background, we conducted a mixture model analysis in order to explore and identify subtypes of dyscalculia based on a broad range of variables (intelligence, reading fluency, working memory, attention, and various mathematical skills). The total sample comprised 174 elementary school CwD (IQ > 70; mathematical abilities: percentile rank <10), which consisted of two subsamples. The first subsample was based on a diagnostic test focusing on calculation (HRT 1–4; n = 71; 46 girls, 25 boys; age: M = 9.28 years, SD = 0.94) whereas the second subsample was based on a diagnostic test with a strong focus on basic numerical capacities (ZAREKI-R; n = 103; 78 girls, 25 boys; age: M = 8.94 years, SD = 1.05). Results provided convincing evidence for the existence of two subtypes in CwD: A slightly impaired subtype and a strongly impaired subtype. Subtypes differed most strongly regarding mathematical abilities, but the analyses suggest that differences in attention could also be a key factor. Therefore, comorbid attention difficulties seem to be a relevant factor that needs to be considered when establishing subtypes. Substantial intelligence differences between dyscalculia subtypes could not be found. Differences in working memory and reading fluency were negligible. Overall, the results seemed to be robust regardless of the diagnostic test used for assessing dyscalculia. When planning interventions for CwD, the existence of a subtype with substantial attention problems should be kept in mind.