Graphing Calculator Research Articles

Table Techniques

There is a distinction between using technology as a tool for doing mathematical tasks and using it to develop conceptual understanding (Dick and Hollebrands 2011). In this article, the table feature of the TI-84 Plus graphing calculator is used in the second role, enabling students to participate in the reasoning and sense-making process. This article showcases four classroom activities that use tables as a dynamic tool for inquiry, applying numerical representations to algebraic, graphical, and geometric phenomena. Although these activities are presented using the TI-84 Plus CE graphing calculator, other calculator and computer platforms can be employed; see the Teacher Guide in more4U for details.

Behavior of an Electrochemical Integrator Based on Solid Electrolyte in the Galvanoharmonic Charging Mode

The behavior of an electrochemical integrator based on a solid electrolyte is studied in the galvanoharmonic charging mode. The possibility of applying simpler and more graphic calculation techniques and separating the impedance of electrochemical systems into active and reactive components is shown. The plotting of the dependences of the active and reactive impedance components on the ac frequency is used to determine the parameters of the studied equivalent electric cuircuits.

Fostering Pre-Service Teachers’ Mathematical Thinking and Reasoning by Using TI-Nspire CX Graphing Calculator- A Review of Literature

Fostering Pre-Service Teachers’ Mathematical Thinking and Reasoning by Using TI-Nspire CX Graphing Calculator- A Review of Literature

О построении моделей объектов пространства четырех и более измерений в учебном процессе

In this paper the visibility concept in the context of modeling of multidimensional spaces’ objects is clarified. It is concluded that such model’s visibility should be defined as unambiguity and completeness of information presented in this model and consistent with the student’s experience in the area of modeling a space of higher dimension (3D) by elements of spaces of lower dimension (2D). Such possibilities are presented by the generalized complex drawing. Examples for objects 4D-modeling using two 3D or three 2D flat projections are presented, some properties of the 4D generalized drawing are listed. The solution of problems with 4D-objects is considered on the example of 4D-pyramid section construction, and deploying its lateral surface. It is shown that to simplify the solution of these problems is required a system allowing automatically perform repetitive sequences of constructions. A list of elementary constructions is presented, and a method for recording of composite constructions and based on them algorithms for problems solving is shown. It is demonstrated that a 3D-scan of 4D-pyramid’s lateral surface, constructed with 2D drawing, can be imported into CAD as a 3D-model. The deploying of the 4D-cone’s lateral surface is considered. The resulting scan’s surface 3D-model imported into CAD is shown. Cases are indicated when a multidimensional space’s object 3D-model may be more visual than a flat one. As an example, 2D-models for imaginary continuations of lines and circles of the complex plane (simulated by Euclidean 4D-space) are presented. Two 3D-projections for imaginary continuations of a circle with a real radius as 3D-space surfaces are shown. It is noted that in order to combine in an educational course the multidimensional space’s objects modeling and work in CAD the tasks on designing of complex technical surfaces by means of output in multidimensional space are suitable. A brief review of sources is given, in which theoretical foundations and the use of key geometrical methods for surfaces construction are considered; an example of a surface constructed by a progressive key method and imported into CAD is shown. The concept of a product’s electronic model (PEM) is described, in which the modeled object’s 3D-simulator as its visual representation is combined with numerous 2D-layers, which elements automatically perform geometrical and graphical calculations in spaces of any dimensions, and control 3D-model’s dimensions and shape through constructive and parametric links. Conclusions are drawn about the possibility of visual multidimensional modeling in the educational process, the advantages of using a complex drawing for solving of problems with multidimensional objects, the need to use special systems of constructive geometric modeling that automate repetitive sequences of constructions. It is also concluded that multidimensional objects’ 2D-models can and should be directly involved in the PEM formation.

Behaviour of the electrochemical intrgrator on the basis of solid electrolyte in galvanoharmonic charging mode

Behaviour of the Electrochemical integrator on the basis of Solid Electrolyte is studied in the galvanoharmonic charging mode. The possibility of application of simpler and more graphic calculation technigue and separation of impedance of electrochemical systems into active and reactive components is shown. The plotting of the dependences of the active and reactive impedance components on ac freguency was used to find the values of parameters of the studied equivalent electric cuircuits.

A Novel Dual-Motor Two-Speed Direct Drive Battery Electric Vehicle Drivetrain

Although the demand of battery electric vehicle (BEV) growths fast as the requirement of reducing greenhouse gas emission and the usage of fossil fuels, the limited driving range and unfriendly retail price present barriers to BEV to provide comparable performance as a traditional vehicle. This paper proposes a dual-motor two-speed direct drive BEV powertrain to boost average motor operational efficiency in daily driving without increasing any complexity of manufacturing or control, ultimately, saving limited battery energy and manufacturing cost. The specifications of the proposed powertrain are first identified through mathematical and graphical calculations, which split traditional one propelling motor to two with separate permanent engaged gears to maximize the motor efficiency. Based on dynamic powertrain modeling in a Simulink/Simscape, economic shifting strategy, and dynamic torque transfer control are designed and tested. According to the simulation results, it is noticed that significant energy efficiency improvement can be achieved. Thanks to the optimized torque transfer control strategy, extremely low vehicle jerk are recorded during the shifting process. At last, conclusions can be made that the proposed dual-motor powertrain superior to the traditional single motor counterpart in terms of fuel economy, driving range, and cost.

The Quest of the Important in Mathematics Classroom

In this article, some ideas are exposed to take out profit of the properties of the straight line to know and to explore many interesting properties of functions as polynomials or rational functions. Some ideas are also presented to use the graphic calculators in a sequence that allows integrating the arithmetic language with the graphic and algebraic languages. This proposal has been applied in initial mathematic courses of future economists and engineers, obtaining interesting results related to the development of the graphic thought.

Aplicación de la estadística robusta en la identificación de valores “OUTLIERS” en análisis de residuos de clorpirifos en maní. programa elaborado en Hp-Basic utilizando la calculadora gráfica HP Prime

En el presente trabajo se ha aplicado la estadística robusta para la identificación de valores “outliers” en la determinación del factor recobrado en el análisis de residuos de clorpirifos en maní por cromatografía de gases con detector ECD. Para ello fue elaborado un programa en lenguaje HP-BASIC, basado en la estadística robusta y específicamente en el algoritmo de Huber y el cual fue editado en la calculadora gráfica de última generación HP PRIME Graphing Calculator. El programa fue ejecutado ingresando los datos obtenidos de los resultados de la evaluación del factor de recobrado para el método de análisis de clorpirifos en una muestra de referencia interna de maní, obteniéndose como resultado un estimado de los parámetros de la población y la identificación de 3 “outliers”. Este programa fue validado con uno de referencia elaborado en Excel por el Comité de Métodos Analíticos de la Royal Society of Chemistry, observándose que la desviación de los parámetros de la población (m,s) fueron menores que la precisión iterativa, lo que indica que no hubo diferencias significativas entre los dos programas. Por otro lado, estos resultados se compararon con los obtenidos por las pruebas clásicas de Dixon y de Grubbs, concluyendo que el método de Huber es el más sensible. El menos sensible es el test de Dixon, dado que su aplicación no detectó ningún outlier, mientras que el test de Grubbs identificó los dos valores más pequeños.

The effect of DNA backbone on the triplet mechanism of UV-induced thymine-thymine (6-4) dimer formation.

Density functional theory calculations were carried out to investigate the formation mechanism of the thymine-thymine (6-4) dimer ((6-4)TT), which is one of the main DNA lesions induced by ultraviolet radiation and is closely related to skin cancers. The DNA backbone was found to have nonnegligible effects on the triplet reaction pathway, particularly the reaction steps involving substantial base rotations. The mechanism for the isomerization from (6-4)TT to its Dewar valence isomer (DewarTT) was also explored, confirming the necessity of absorbing a second photon. In addition, the solvation effects were examined and showed considerable influence on the potential energy surface. Graphical Abstract DFT calculations on the influence of DNA backbone on the mechanism of UV-induced thymine-thymine (6-4) dimer formation.

Fases das tecnologias digitais na exploração matemática em sala de aula: das calculadoras gráficas aos celulares inteligentes

Este artigo apresenta pesquisas relacionadas ao uso de tecnologias na exploração matemática nas diferentes fases das tecnologias digitais. A divisão dessas fases inicia-se por volta dos anos 1980 e compreendem os dias atuais, de modo a se formar quatro fases que não são disjuntas. Para isso, enfatiza-se uma mesma atividade investigativa nas mídias calculadora gráfica, computadores e celulares inteligentes, discutindo as possibilidades e limitações de cada mídia. Aponta-se os celulares inteligentes como a principal tendência futura no que tange as tecnologias digitais em sala de aula de Matemática na Educação Básica. Com a discussão realizada é possível afirmar que o sucesso de uma atividade com o uso de tecnologias se dá a partir de uma atividade bem elaborada, que favoreça a investigação e a criação de conjecturas pelos alunos. Além disso, fatores como pouca formação do professor no que tange o uso das tecnologias para o ensino da matemática, estrutura curricular não flexível e a dificuldade na elaboração de atividades com tecnologias, geram barreiras no trabalho do professor.

Graphics Calculators in the Primary Classroom: Student-Teachers’ Beliefs and the TPACK Framework

Graphics Calculators in the Primary Classroom: Student-Teachers’ Beliefs and the TPACK Framework

USING ANDROID-BASED EQUATION PLOTTERS AS SUPPORTING TOOLS FOR TEACHING AND LEARNING ATOMIC ORBITALS

Chemistry undergraduate students are required to master the theory of quantum mechanics as the basic requirement to study the properties of the submicroscopic particle. However, many studies showed the students’ difficulties to bring the quantum mechanical concept to the macroscopic world and vise-versa. The use of computer visualization tool will very useful for teaching and learning the quantum concept, especially electron and its related atomic orbitals. This technological report paper demonstrates some of the Android-based applications i.e FuncXY, TriPlot 3D Graphing, and Graphing calculator to effectively, quickly, and accurately convert wave functions into various hydrogen atomic orbital visualizations. By selecting spherical coordinate and entering wave equation, these smartphone graphical devices visualize three-dimensional atomic orbitals. Users are also easy to rotate, zoom and manipulate the object. Finally, these user-friendly plotters are very recommended to assist chemistry educators in teaching quantum mechanics.

Aspect Ratio Distribution and Chord Length Distribution Driven Modeling of Crystallization of Two-Dimensional Crystals for Real-Time Model-Based Applications

Two-dimensional (2D) crystals, for which the shape is described by two linear sizes, are common in fine chemical and pharmaceutical industries. Since the crystal size and shape are directly related to the performance of active pharmaceutical ingredients, the simultaneous size and shape distribution control is of paramount importance in pharmaceutical crystallization engineering. To efficiently achieve simultaneous size and shape control often requires model-based control strategies; however, the increased computational cost of the process simulation and the substantial differences between the simulated and measurable quantities make the implementation of model-based control approaches challenging. This paper addresses the important problem of the real-time simulation of the most likely measurable chord length distribution (CLD) and aspect ratio distribution (ARD) as well as the concentration variations during the crystallization of 2D needle-shaped crystals. This enables the application of focused beam reflectance measurement (FBRM) and particle vision and microscopy (PVM), two routinely applied probes, as quantitative direct feedback control tools. Artificial neural network (ANN)-based FBRM and PVM soft-sensors are developed, which enable the direct and fast transformation of 2D crystal size distribution (CSD) to CLD and ARD on arbitrary 2D grids. The training data for the ANN are generated by a first principle, geometrical model-based simulation of FBRM and PVM for high aspect ratio crystals, although the ANN approach is applicable for any simulated or experimental training data sets. It is also demonstrated that the in situ imaging-based shape measurement underestimates the real aspect ratio (AR) of crystals, for which a simple correction is proposed. From the model-equation solution perspective, the soft-sensors require full population balance solution. The 2D high-resolution finite volume method is applied to simulate the full 2D CSD, which is an accurate, stable, but computationally expensive technique. The real-time applicability is achieved through various implementation improvements including grid optimization and data-type optimized hybrid central processing unit–graphical processing unit calculations.

BEHAVIOR OF BLOCKING (INERT) ELECTRODE / SOLID ELECTROLYTE INTERFACE IN GALVANOGARMONIC CHARGING MODE. CASE OF DECELERATED DIFFUSION AND ADSORPTION –DESORPTION OF TWO DIFFERENT KINDS OF PARTICLES

Electrochemical behavior of a cell with an interface of blocking electrode /solid electrolyte was studied in galvanogarmonic mode of charge. The possibility of application of simple and more graphic calculation technique and separation of electrochemical impedance schemes into active and reactive constituents was shown. The Jacobsen-West diffusion model was used as an equivalent electric circuit, which is valid for relatively large times or low AC frequencies. The plotting of dependences of active and reactive impedance components on AC frequency was used in order to estimate the values of parameters for studied equivalent electric circuits.

Impact of Using Graphing Calculator in Problem Solving

The purpose of this study is to investigate the impact of graphing calculator on students’ problem solving success in solving linear equation problems and their attitude toward problem solving in mathematics. A quasi-experimental non-equivalent control and treatment group using the pre-test post-test design was employed in this study to test the hypotheses. The sample of the study involved two Form Four classes from one public secondary school in Sarawak, Malaysia. Students in the experimental group received problem solving based instruction using graphing calculator while the control group students underwent the traditional chalk and talk method without the graphing technology. Two instruments were used in this study, namely the Linear Equation Problem Solving Test and the Mathematical Problem Solving Questionnaire. Findings of this study show existence of a significant difference in the mean scores between the two groups; students who used graphing calculator performed better in problem solving tasks compared to students without access to graphing calculator. Furthermore, a questionnaire was used to obtain students’ attitude toward problem solving in mathematics. Results from the survey revealed that students who use graphing calculator have a better attitude toward problem solving in mathematics. This study is pertinent as it investigates a different approach in teaching linear equation through problem solving while integrating the latest graphing calculator technology in the lessons.

Prognostic factors of acute renal failure following partial nephrectomy of solitary kidney

Background. Acute renal failure (ARF) in the postoperative period increases the risk of complications and death. Estimating the risk of ARF prior to surgery is particularly important, because it allows modifying the treatment in high-risk patients.Objective: to develop prognostic models for evaluating the risks of ARF in patients undergoing resection of a solitary kidney by measuring preoperative parameters.Materials and methods. The study included 136 patients with tumors in a solitary kidney that underwent surgical treatment in the N.N. Alexandrov National Cancer Center of Belarus in the last 16 years.Results. Biochemical blood tests demonstrated that 28 patients (20.6 %) had ARF in the early postoperative period. The multivariate model for assessing the risk of ARF included the following three covariates: tumor size, multifocality, and serum potassium level. We identified the cut-off points of tumor size (3.6 and 5.2 cm) and potassium level (4.4 and 4.8 mmol/L) that ensured maximum predictive accuracy. Using the multivariate model, we developed a nomogram that allows graphical calculation of the ARF probability in the postoperative period by measuring preoperative parameters.Conclusion. Our model enables preoperative assessment of the risk of developing ARF after resection of a solitary kidney with an accuracy (С-index) of 85.1 % (95 % confidence interval: 79.3–89.7 %).

Graphical User Interface Calculator for FBGS Performance Optimization Based on New Window Formulas

In this research paper, we develop on one hand a novel theoretical approach to optimize the performance of Fiber Bragg Grating Sensor (FBGS) based on an automated MATLAB-based program, and on the other hand, we propose a new graphical user interface including all design parameters of the FBGS to optimize automatically its window profile based on the sensing system requirement. The main objective of this approach is to obtain the higher reflected power from the FBGS as long as side lobes are kept below the required level. All formulas of the proposed method of optimization are programmed using the Coupled Matrix Theory (CMT) and the Transfer Matrix Method (TMM), which describe the light behavior within the FBGS. The proposed easy-to-use graphical interface allows also researchers to determine easily all parameters required for high FBGS performance providing a high precision and accuracy of numerical results. The proposed theoretical approach has been compared with the window profiles proposed by other authors. All results demonstrate the efficiency of the proposed method.

6I2-13 携帯型ゲーム機でのグラフ電卓(IT ・ メディア利用の科学教育システム(1))

6I2-13 携帯型ゲーム機でのグラフ電卓(IT ・ メディア利用の科学教育システム(1))

Detailed Consideration of Graphical Calculation of Min-Plus Convolution in Deterministic Network Calculus

The convolution operation used in deterministic network calculus differs from its counterpart known from the classic systems theory. A reason for this lies in the fact that the former is defined in terms of the so-called min-plus algebra. Therefore, it is oft difficult to realize how it really works. In these cases, its graphical interpretation can be very helpful. This paper is devoted to a topic of construction of the min-plus convolution curve. This is done here in a systematic way to avoid arriving at non-transparent figures that are presented in publications. Contrary to this, our procedure is very transparent and removes shortcomings of constructions known in the literature. Some examples illustrate its usefulness.

Graphical Calculation of Estimated Energy Expenditure in Burn Patients.

Historically, estimated energy expenditure (EEE) has been related to the percent of body surface area burned. Subsequent evaluations of these estimates have indicated that the earlier formulas may overestimate the amount of caloric support necessary for burn-injured patients. Ireton-Jones et al derived 2 equations for determining the EEE required to support burn patients, 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Evidence has proved their reliability, but they remain challenging to apply in a clinical setting given the difficult and cumbersome mathematics involved. This study aims to introduce a graphical calculation of EEE in burn patients that can be easily used in the clinical setting. The multivariant linear regression analysis from Ireton-Jones et al yielded equations that were rearranged into the form of a simple linear equation of the type y = mx + b. By choosing an energy expenditure and the age of the subject, the weight was calculated. The endpoints were then calculated, and a graph was mapped by means of Adobe FrameMaker. A graphical representation of Ireton-Jones et al's equations was obtained by plotting the weight (kg) on the y axis, the age (years) on the x axis, and a series of parallel lines representing the EEE in burn patients. The EEE has been displayed graphically on a grid to allow rapid determination of the EEE needed for a given patient of a designated weight and age. Two graphs were plotted: 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Correction factors for sex, the presence of additional trauma, and obesity are indicated on the graphical calculators. We propose a graphical tool to calculate caloric requirements in a fast, easy, and portable manner.