Severe Mathematical Difficulties Research Articles

Reducing Math Anxiety in School Children: A Systematic Review of Intervention Research

Recent studies indicate that math anxiety (MA) can already be found in school-aged children. As early MA depicts a potential risk for developing severe mathematical difficulties and impede the socio-emotional development of children, distinct knowledge about how to reduce MA in school-aged children is of particular importance. Therefore, the goal of this systematic review is to summarize the existing body of research on MA interventions for children by identifying the approaches, designs, and characteristics as well as the effects of the interventions.

Instructional Interventions to Address Mathematics Anxiety in Sub-Saharan Africa: A Systematic Review (1980–2020)

Research indicates that mathematics anxiety is among the factors that contribute to poor performance in mathematics. Learners have a risk of developing severe mathematical difficulties that might impede their socio-emotional development and future mathematics careers; therefore, an understanding of instructional strategies to reduce mathematics anxiety is important. The objective of this systematic review is to summarise the existing body of research on instructional interventions for addressing mathematics anxiety in the classroom. Nine articles that met the inclusion criteria were identified. To address mathematics anxiety in learners, two of the identified articles used problem-solving, one collaborative learning, two personalised instruction, one peer teaching using a photovoice approach, one brain-based instructional strategy, and one team-assisted individualised instructional strategy, whilst one was computer-based. All nine interventions had a positive effect on reducing mathematics anxiety as well as improving performance among learners. The systematic review revealed that little has been done in terms of research on instructional strategies that reduce mathematics anxiety in Sub-Saharan Africa. It is recommended that more studies on instructional strategies that address mathematical anxiety in Sub-Saharan Africa need to be conducted.

Identifying Children with Persistent Developmental Dyscalculia from a 2‐min Test of Symbolic and Nonsymbolic Numerical Magnitude Processing

ABSTRACTDevelopmental dyscalculia (DD) is a mathematical learning disability that occurs in around 5%–7% of the population. At present, there are only a handful of screening tools to identify children that might be at risk of developing DD. The present study evaluated the classification accuracy of one such tool: The Numeracy Screener, a 2‐min test of symbolic (Arabic numerals) and nonsymbolic (dot arrays) discrimination ability. A sample of 222 children who demonstrated persistent deficits (n = 55), inconsistent deficits (n = 51), or typical performance (n = 116) on standardized tests of math achievement over multiple observations was tested. The Numeracy Screener correctly classified children in all three groups. Notably, the symbolic condition has greater sensitivity in discriminating children with persistent DD from the other two groups. Screening tools that assess early numeracy skills may be promising for identifying children at risk for developing severe mathematical difficulties.

Kindergarteners at Risk for Severe Mathematics Difficulties: Investigating Tipping Points of Core Mathematics Instruction

A concerning number of students enter kindergarten facing an intractable variation of mathematics difficulties (MD). This study investigated the impact of an explicit, core kindergarten mathematics program on the mathematical outcomes of kindergartners who demonstrated risk for severe MD at kindergarten entry and examined whether these students improved from a category of high MD risk (i.e., <10th percentile) to a lower risk of MD (i.e., norm-referenced performance at or above the 10th, 20th, 30th, and 40th percentiles) between the fall and spring of kindergarten. Differential response to the program based on the classroom-level proportion of students with severe MD was also explored. A total of 795 kindergarteners with severe MD from 122 classrooms were included in the analyses. Results suggested students with severe MD in treatment classrooms improved from fall to spring at a greater rate than their control peers. Treatment students also demonstrated higher rates of improvement from below the 10th percentile to a performance at or above the 20th, 30th, and 40th percentiles across the school year. No evidence of differential efficacy of the program by the classroom-level proportion of students with severe MD was found. Implications for using explicit mathematics programs to thwart the onset of severe MD among academically vulnerable students are discussed.

Tier 3 Intensified Intervention for Second Grade Students with Severe Mathematics Difficulties

Abstract&#x0D; A multiple baseline design was employed to examine the effects of an intensive mathematics intervention, which focused on early numeracy concepts and skills. Thirty-three second grade students participated in the study. Students attended five different schools in one school district and received the intervention in a total of 12 groups from mathematics interventionists. The intervention occurred for about 30 min per session, 5 days a week for 8 weeks with a maintenance phase two weeks later and generalization testing four weeks later. The intervention consisted of explicit instruction, strategies, and mathematics practices. Visual analyses of the data showed improvement for the majority of the groups. Effect size calculations showed no evidence of overlapping data between baseline and intervention for nine out of twelve groups. Maintenance data revealed positive results and five students had a posttest score at or above the 25th percentile on the generalization measure. Implications for practice with limitations and future research are discussed.&#x0D; &#x0D;

Intensifying Intervention for Students With Persistent and Severe Mathematics Difficulties

Intensifying Intervention for Students With Persistent and Severe Mathematics Difficulties

The Effects of a Tier 3 Intervention on the Mathematics Performance of Second Grade Students With Severe Mathematics Difficulties

The purpose of this study was to determine the effectiveness of a systematic, explicit, intensive Tier 3 (tertiary) intervention on the mathematics performance of students in second grade with severe mathematics difficulties. A multiple-baseline design across groups of participants showed improved mathematics performance on number and operations concepts and procedures, which are the foundation for later mathematics success. In the previous year, 12 participants had experienced two doses (first and second semesters) of a Tier 2 intervention. In second grade, the participants continued to demonstrate low performance, falling below the 10th percentile on a researcher-designed universal screener and below the 16th percentile on a distal measure, thus qualifying for the intensive intervention. A project interventionist, who met with the students 5 days a week for 10 weeks (9 weeks for one group), conducted the intensive intervention. The intervention employed more intensive instructional design features than the previous Tier 2 secondary instruction, and also included weekly games to reinforce concepts and skills from the lessons. Spring results showed significantly improved mathematics performance (scoring at or above the 25th percentile) for most of the students, thus making them eligible to exit the Tier 3 intervention.

Nonisothermal nematic liquid crystal flows with the Ball–Majumdar free energy

In this paper, we prove the existence of global-in-time weak solutions for an evolutionary PDE system modelling nonisothermal Landau–de Gennes nematic liquid crystal (LC) flows in three dimensions of space. In our model, the incompressible Navier–Stokes system for the macroscopic velocity $$\mathbf{u}$$ is coupled to a nonlinear convective parabolic equation describing the evolution of the $$Q$$ -tensor $$\mathbb {Q}$$ , namely a tensor-valued variable representing the normalized second-order moments of the probability distribution function of the LC molecules. The effects of the (absolute) temperature $$\vartheta $$ are prescribed in the form of an energy balance identity complemented with a global entropy production inequality. Compared to previous contributions, we can consider here the physically realistic singular configuration potential $$f$$ introduced by Ball and Majumdar. This potential gives rise to severe mathematical difficulties since it introduces, in the $$Q$$ -tensor equation, a term that is at the same time singular in $$\mathbb {Q}$$ and degenerate in $$\vartheta $$ . To treat it, a careful analysis of the properties of $$f$$ , particularly of its blow-up rate, is carried out.

On the analysis of cross-ply laminates with micro-cracks and inelastic deformation

For cross-ply laminates micro-matrix cracks in the 90° plies and inelastic deformation in the 0° and 90° plies are two major forms of damage which affect the long-term durability of the materials. It is crucial to develop a mechanics based approach to incorporate both micro-cracks and inelastic deformation of the composite materials based on the response of the 0° and 90° plies in order to accurately predict the response of the materials in service environments and to assist in optimizing the materials system for best performance. However, such a task leads to severe mathematical difficulties, primarily due to the zero traction conditions on the crack surfaces, the complicated constitutive relations governing the inelastic deformation and the interaction between the cracks and the inelastic deformation. In this paper, a general framework for the analysis of crossply laminates with micro-matric cracks and inelastic deformation is proposed. For this purpose admissible stress fields are constructed which satisfy equilibrium and all boundary and interface conditions. The principle of minimum complementary energy is utilized to derive a differential equation for the stress function from which the stress field of the composite can be derived. The inhomogeneous terms of the differential equation involve the inelastic strains which are loading history dependent. The Green's function of the differential equation is then obtained. Using the Green's function and a constitutive equation, two-dimensional stress and strain states in the composite at any time are represented by an integral of the Green's function and the inelastic strains accumulated up to that time. This new analysis takes into consideration the microcrack-microcrack interaction, as well as the interaction between the microcracks and the inelastic deformation, and provides a point-wise variation of the stress field instead of average stress field as most of the analytical approaches yield.The interactions of matrix cracks and creep deformation of an eight-harness satin weave (SHSW) Nextel 610/Aluminosilicate ceramic matrix composite is studied using the proposed model. The predicted creep strain of the composite shows good correlation with experimental data at different levels of temperature and stress conditions. The distribution of stresses and strains provides important information on the response of the composite.

Calculation of molecular electronic structure with the help of the Σ-separation method: preliminary results and prospective development

Severe mathematical difficulties arise in the calculation of molecular integrals with exponentially decaying functions, particularly in the case of polyatomic molecules and heavy atom compounds. In an attempt to overcome this, the Σ-separation approach was chosen as the basis for a numerically advanced tabulation—restoration algorithm.

Matched-asymptotic analysis of low-Reynolds-number flow past two equal circular cylinders

Jeffery's solution in bi-polar co-ordinates of the two-dimensional Stokes equations cannot be applied to the low-Reynolds-number flow past two parallel circular cylinders because of severe mathematical difficulties. These difficulties can be overcome by considering the flow field far from the cylinders and then modifying the solution near the cylinders so that it becomes the inner expansion for an application of the method of matched asymptotic expansions. After the calculation of the drag, lift and moment coefficients of two adjacent equal circular cylinders to O(1) in the Reynolds number R, the analysis is extended to incorporate partially the effects of fluid inertia of order R. The results show fairly good agreement with Taneda's experimental data.

Certain problems concerning the origin and maintenance of cosmic magnetic fields

How regular magnetic fields in a plasma originated and are sustained is a question of considerable interest, since various objects in space such as spiral arms of galaxies, many stars, and planets have a regular magnetic field [1–3]. Several theoretical studies have been devoted to this theme [4–9]. However, because of the severe mathematical difficulties which arise in solving this problem, its study in the general form is still not possible, and its kinematic aspects are usually considered. In [5] a study is made of the induction of a toroidal magnetic field from the dipole field of a rotating spherical mass under the influence of radial convection. For the process to be undamped it is necessary to maintain a poloidal field, which according to the Cowling theorem may be induced by asymmetric motions from a toroidal field. Parker [6] suggested a specific model for the field increase by motions of the cyclonic type and indicated the possibility of self-regulation of the field maintenance process. Under certain conditions this process has a wave nature, the so-called “dynamo-waves.” In [7, 8] Braginskii considered the question of maintaining a quasi-stationary field by motions of the medium which differ little from axisymmetric motions. As a result of the large magnetic Reynolds numbers Rem≫1 the field decays slowly, and a weak generation mechanism is adequate for maintaining the field.

Wave formation in laminar flow down an inclined plane

This paper deals theoretically with a problem of hydrodynamic stability characterized by small values of the Reynolds number R. The primary flow whose stability is examined consists of a uniform laminar stream of viscous liquid running down an inclined plane under the action of gravity, being bounded on one side by a free surface influenced by surface tension. The problem thus has a direct bearing on the properties of thin liquid films such as have important uses in chemical engineering.Numerous experiments in the past have shown that in flow down a wall the stream is noticeably agitated by waves except when R is quite small; on a vertical water film, for instance, waves may be observed until R is reduced to some value rather less than 10. The present treatment is accordingly based on methods of approximation suited to fairly low values of R, and thereby avoids the severe mathematical difficulties usual in stability problems at high R. The formulation of the problem resembles that given by Yih (1954); but the method of solution differs from his, and the respective results are in conflict. In particular, there is dis-agreement over the matter of the stability of a strictly vertical stream at very small R. In contrast with the previous conclusions, it is shown here that the flow is always unstable: that is, a class of undamped waves exists for all finite values of R. However, the rates of amplification of unstable waves are shown to become very small when R is made fairly small, and their wavelengths to become very large; this provides a satisfactory explanation for the apparent absence of waves in some experimental observations, and also for the wide scatter among existing estimates of the ‘quasi-critical’ value of R below which waves are undetectable. In view of the controversial nature of these results, emphasis is given to various points of agreement between the present work and the established theory of roll waves; the latter theory gives a clear picture of the physical mechanism of wave formation on gravitational flows, and in its light the results obtained here appear entirely reasonable.The conditions governing neutral stability are worked out to the third order in a parameter which is shown to be small; but a less accurate approximation is then justified as an adequate basis for an easily workable theory providing a ready check with experiment, This theory is used to predict the value of R at which observable waves should first develop on a vertical water film, and also the length and velocity of the waves. These three predictions are compared with the experimental results found by Binnie (1957), and are substantially confirmed.