Unified Mathematics Research Articles

From co‐teaching to co‐mentoring: Transforming special education and mathematics instructional partnerships through shared content‐focused professional development

AbstractCo‐teaching is described as the pairing of a general education teacher and a special education teacher in the general education classroom for the shared instruction of students with and without disabilities. Many teachers struggle to form unified partnerships, especially in mathematics classrooms. The MathMATES project was developed to address a need for joint special education and mathematics professional development aimed to support teachers in merging their individual strengths and expertise through shared content development and relationship‐building exercises. Over the course of the year‐long academy, teachers developed strong knowledge‐sharing partnerships that resembled co‐mentoring partnerships. We compare their progression with research on co‐mentoring to suggest a framework for developing more unified mathematics co‐teaching teams.

Mechanical Behavior of Al-Si10-Mg P-TPMS Structure Fabricated by Selective Laser Melting and a Unified Mathematical Model with Geometrical Parameter.

Compared with the traditional lattice structure, the triply periodic minimal surface (TPMS) structure can avoid stress concentration effectively. Here, it is promising in the fields of lightweight and energy absorption. However, the number of structural parameters and mechanical properties of the TPMS structure is plentiful, and the relationship between them is unclassified. In this paper, for the first time, a unified mathematical model was proposed to establish the relationship between TPMS structural design parameters and mechanical properties. Fifteen primitive models were designed by changing the structural parameters (level-set value C and thickness T) and manufacturing by selective laser melting. The geometric defects and surface quality of the structures were explored by optical microscope and scanning electron microscopy (SEM). The mechanical properties were investigated by quasi-static compression test and finite element simulation. The influence of building direction on structural mechanical behavior (failure mode, stress-strain curve) was studied. The real mechanical properties (Young's modulus and plateau stress) of the structure could be predicted according to different C and T combinations. Finally, the energy absorption characteristics were explored. The results showed that when the C value is 0.6 in the range of 0-0.6, the energy absorption performance of the structure is at the maximum level.

Examining Item Biasness in Terminal Unified Mathematics Examination for Primary School in Lagos State

Examining Item Biasness in Terminal Unified Mathematics Examination for Primary School in Lagos State

Dimensionality assessment of binary response test items: A non-parametric approach of bayesian item response theory measurement

This study investigated dimensionality of Binary Response Items through a non-parametric technique of Item Response Theory measurement framework. The study used causal comparative research type of non-experimental design. The sample consisted of 5,076 public senior secondary school examinees (SSS3) between the age of 14-16 years from 45 schools, which were drawn randomly from three senatorial districts of Osun State, Nigeria. Instrument used for this study was 2018 Osun State unified multiple-choice mathematics achievement test items with empirical reliability coefficient of 0.82. Data obtained were analysed using Non-linear factor analysis, Stout’s Test of Essential Unidimensionality (STEU), Factor Analysis (FA), Full Information Factor Analysis (FIFA) and Bootstrap Modified Parallel Analysis Test (BMPAT). Results showed that both the BMPAT and STEU ascertained violation of unidimensionality assumption of the test items (the observed difference in the second eigenvalue of the observed data and that of second eigenvalue of the simulated data was statistically significant, p = 0.0099; Stout’s test rejected the assumption of essential unidimensionality, T = 10.6260, p<0.05). Non-linear factor analysis and full information factor analysis revealed that four dimensions embedded in the test items and loadings of the items showed within-item multidimensionality respectively. The authors’ concluded that modeling examinees’ performance with unidimensional model when it was actually multidimensional in nature would affect performance of examinees adversely and could lead to blur judgment. Consequently, it is recommended that unidimensional scoring method of Osun State unified mathematics achievement test implicit in Classical Test Theory should be jettisoned and an appropriate scoring model (multidimensional) should be embraced.

Two Contemporary and Efficient Two-Stage Sampling Methods for Estimating the Volume of Forest Stands: A Brief Overview and Unified Mathematical Description

Big Basal Area Factor (Big BAF) and Point-3P are two-stage sampling methods. In the first stage the sampling units, in both methods, are Bitterlich points where the selection of the trees is proportional to their basal area. In the second stage, sampling units are trees which are a subset of the first stage trees. In the Big BAF method, the probability of selecting trees in the second stage is made proportional to the two BAFs’ ratio, with a basal area factor larger than that of the first stage. In the Point-3P method the probability of selecting trees, in the second stage, is based on the height prediction and use of a specific random number table. Estimates of the forest stands’ volume and their sampling errors are based on the theory of the product of two random variables. The increasing error in the second stage is small, but the total cost of measuring the trees is much smaller than simply using the first stage, with all the trees measured. In general, the two sampling methods are modern and cost-effective approaches that can be applied in forest stand inventories for forest management purposes and are receiving the growing interest of researchers in the current decade.

THE UNITY OF MATHEMATICS IN TASKS BASED ON FOUNDATION OF EXPERIENCE IN PICTORIAL MODELING OF THE FUTURE TEACHER

The author offers the development of an innovative curriculum of the unified mathematics based on deployment of clusters of foundation of mathematical knowledge in the course of the future mathematics teachers' research activity. At the heart of the discipline one can find the study of integrative ties in mathematics and their transfer into the didactic field of formation of methods of scientific cognition and sustainable learning motivation among pupils in the context of consideration and examination of the so-called integrative tasks (genesis, maintenance, analysis, application, evaluation, presentation). They are selected through the detection of reasonable criteria. Presentation of educational materials is accompanied by the search and creative activity of future mathematics teachers in the direction of professionalization, enrichment and foundation of experience and development of personal qualities based on actualization of personal meanings of the teachings.

A Unified Mathematical Framework for Coding Time, Space, and Sequences in the Hippocampal Region

The medial temporal lobe (MTL) is believed to support episodic memory, vivid recollection of a specific event situated in a particular place at a particular time. There is ample neurophysiological evidence that the MTL computes location in allocentric space and more recent evidence that the MTL also codes for time. Space and time represent a similar computational challenge; both are variables that cannot be simply calculated from the immediately available sensory information. We introduce a simple mathematical framework that computes functions of both spatial location and time as special cases of a more general computation. In this framework, experience unfolding in time is encoded via a set of leaky integrators. These leaky integrators encode the Laplace transform of their input. The information contained in the transform can be recovered using an approximation to the inverse Laplace transform. In the temporal domain, the resulting representation reconstructs the temporal history. By integrating movements, the equations give rise to a representation of the path taken to arrive at the present location. By modulating the transform with information about allocentric velocity, the equations code for position of a landmark. Simulated cells show a close correspondence to neurons observed in various regions for all three cases. In the temporal domain, novel secondary analyses of hippocampal time cells verified several qualitative predictions of the model. An integrated representation of spatiotemporal context can be computed by taking conjunctions of these elemental inputs, leading to a correspondence with conjunctive neural representations observed in dorsal CA1.

<b>Avaliação do Nível de Conhecimento dos Alunos do Ensino Médio da cidade de João Pessoa com Deficiência Visual sobre as Grafias Química e Matemática Braille</b>

http://dx.doi.org/10.5902/1984686X6832O Sistema Braille é de grande importância na educação do aluno com deficiência visual, pois é através dele que o aluno entra em contato com o conhecimento escrito, sistemático e organizado. Este aluno precisa conhecer os símbolos e as normas de uso destes, para poder escrever, ler e compreender os conteúdos. O conhecimento das Grafias Química e Matemática Braille é importante para que os alunos possam compreender os textos dessas áreas. O objetivo deste trabalho foi avaliar o nível de conhecimento dos alunos com deficiência visual matriculados no Ensino Médio na cidade de João Pessoa, no que tange a essas grafias. Os alunos apresentaram um conhecimento relativamente bom nos símbolos e nas normas da Grafia Matemática Braille, apresentando, na maioria dos casos, dificuldades em reconhecer símbolos pouco usuais. As principais dificuldades dos alunos estavam relacionadas à Grafia Química Braille, pois eles desconheciam grande parte dos símbolos e normas, apresentando um baixo nível de conhecimento.

Chaos, Turbulence and Fractal: Theory and Applications

The paper identifies chaos, turbulence and fractal of quantum and macro gravity and studies their behavior, properties and applications based on the grand unified theory (GUT) and qualitative mathematics and modeling. Applications include devising electromagnetic engines, tornado aborter and terminator and technologies for electromagnetic treatment of genetic diseases such as cancer, systemic lupos erythematosus, diabetes and mental disorder without harm to normal cell and side effect. Typhoon in the Western Pacific which is turbulence is impossible to terminate and impractical to deflect but prediction can be improved because it follows the Northern Pacific Wind Cycle (Southern Pacific Wind Cycle in the Southern Hemisphere) and is affected by the temperature variation over the Philippine Deep and around Mayon Volcano. The electromagnetic engine uses the clean, inexhaustible, free dark matter, specifically, the energy of magnetic flux, in place of conventional fuel, e.g., fossil, nuclear and geothermal. The tornado aborter and terminator utilize the gravitational flux of the Earth, its vortex flux of superstrings as a cosmological vortex which is turbulence. The technologies for electromagnetic treatment of genetic diseases utilize electromagnetic waves based on resonance. All of them are GUT technologies because they are applications of GUT. Except for the magnetic train which is in operation the rest is still at the conceptual and research and development (R&D) phase but the theory is complete and the strategy for R&D are laid down in detail in the cited original papers.

A micro-curricular analysis of unified mathematics curricula in Turkey

This article aims to give a detailed micro-level curricular analysis of the extent to which the intended mathematics curriculum matches the potentially implemented curriculum using the case of Turkey. The article makes inferences about what it means to have a match or mismatch between these two types of curricula. As a result, it is clear that even though there is a close match between the intended and the potentially implemented mathematics curricula, such a match does not seem to be enough to help students to have a solid understanding of targeted mathematical concepts outlined in the overall Turkish curricular standards.

AHT Bézier Curves and NUAHT B-Spline Curves

In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric (AHT) Bezier curves and non-uniform algebraic hyperbolic trigonometric (NUAHT) B-spline curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., tn-5}, n ≥ 5. The two kinds of curves share most of the properties as those of the Bezier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.

Comment on "A Unified Mathematical Framework for Strapdown Algorithm Design"

Comment on "A Unified Mathematical Framework for Strapdown Algorithm Design"

「数学統一試験」と数学教育の質の保証

「数学統一試験」と数学教育の質の保証

The invention of wisdom: from the discovery of audial psychophysics to Plato's politics

Analysis of the mathological musicology in the basic wisdom literatures of several ancient cultures indicates that wisdom derived from the discovery that the human brain's perception of harmony, the vibration nodules of the monochord, and mathematical ratios all possessed homologous structures. Plato developed this into a general audial ontology unifying psychology, physics and mathematics into a Natural Law science that produced the structure of his political dialogues. Platonic form is shown to have a sciential foundation in a phenomenological realism that is compatible with the neo-Pythagoreanism appearing today in physics and biology.

Brief Reports: Children's Discrimination between Enjoyment and Value of Arithmetic

Data that bear on the motivation of children to learn arithmetic—for its own enjoyment or as a means to other ends—were obtained in the evaluation of Unified Science and Mathematics for Elementary Schoois (Shann, 1977a, 1977b). It must be emphasized that the evidence is tentative, for students' attitudes toward arithmetic were not a primary concern of the USM ES evaluation, but the finding that even children can discriminate between enjoyment and value in their attitudes toward arithmetic should not go unnoticed. The clarity and consistency of the evidence from multiple indicators suggest that the issue is indeed a promising one for further investigation.

Statistics in the elementary school

This paper discusses the role of statistics within an interdisciplinary program on real problem solving in elementary schools (through grade 8). We first describe some general features of the USMES (Unified Science and Mathematics for Elementary Schools) curriculum and some situations where the application of statistical principles and techniques can enter the program. Then we present our ideas concerning the kinds of statistical methods that are appropriate in this environment, and we discuss the use of this material with both elementary school students and elementary

The Secondary School Mathematics Curriculum Improvement Study: A Unified Mathematics Program

IN THE early 1950s the mathematicians at the university level began justifiably to criticize the mathematical preparation of high school students for university study. Partly because of this criticism, a number of reform movements arose, of which those of the University of Illinois Committee on School Mathematics, the Commission on Mathematics of the College Entrance Examination Board, and the School Mathematics Study Group were most notable. The activities of these reform groups brought about a great improvement of the mathematics curriculum, though maintaining the traditional separation of mathematics into yearly units of study, especially for algebra and geometry. Included in these programs were quite a few topics not found in the pre-1950 era, such as the structure of the several number systems, the early introduction of the function concept, and a more rigorous presentation of Euclidean synthetic geometry. Likewise, the notions of sets and set operations were used to the advantage of better understanding.

Unified mathematics, by P. B. Lawson Part 3. Pp. viii, 266. With answers 95p, without answers 90p. 1970 (University Tutorial Press) - Unified mathematics, by P. B. Lawson Part 4. Pp viii, 351. With answers £1·20, without answers £1·15. 1972 (University Tutorial Press) - Unified mathematics, by P. B. Lawson Part 5. Pp viii, 335. With answers £1·35, without answers

Unified mathematics, by P. B. Lawson Part 3. Pp. viii, 266. With answers 95p, without answers 90p. 1970 (University Tutorial Press) - Unified mathematics, by P. B. Lawson Part 4. Pp viii, 351. With answers £1·20, without answers £1·15. 1972 (University Tutorial Press) - Unified mathematics, by P. B. Lawson Part 5. Pp viii, 335. With answers £1·35, without answers

Unified Mathematics, Part 3

Unified Mathematics, Part 3

Unified Mathematics. By P.B. Lawson. Part 1, pp. xii, 276; Part 2, pp. xii, 307. 1969. (Universities Tutorial Press.)

Unified Mathematics. By P.B. Lawson. Part 1, pp. xii, 276; Part 2, pp. xii, 307. 1969. (Universities Tutorial Press.)