Sharing Teaching Ideas: Graphical Transformations and Calculator Greeting Cards

2001 ◽  
Vol 94 (2) ◽  
pp. 106-110
Keyword(s):  
Mathematics Classroom ◽  
Linear Equations ◽  
Linear Functions ◽  
Advanced Mathematics ◽  
Algebraic Equations ◽  
Mathematics Students ◽  
Algebra Students ◽  
Greeting Cards ◽  
Rectangular Coordinates ◽  
Different Characteristics

Greeting cards exist in many forms—homemade, store-bought, musical, and Internet cards—just to name a few. With the availability of graphing calculators, the creativity and fun of making greeting cards can be brought into the mathematics classroom to enhance students' understanding of functions. Graphing-calculator greeting cards can take on different characteristics and can be created by students at different mathematics levels. A central objective of the task is to use algebraic equations to create desired graphical designs that, along with strategically placed text, extend a calculator greeting. The algebraic equations used can range in difficulty from linear functions in rectangular coordinates to polar or parametric equations. Algebra students who are learning about linear equations, as well as advanced mathematics students who are working with a broad range of families of functions and relations, can create calculator greeting cards.

scholarly journals Mathematics Instruction to Promote Mathematics Higher-Order Thinking Skills of Students in Indonesia: Moving Forward

TEM Journal ◽  
2021 ◽  
pp. 1945-1954
Author(s):  
Benidiktus Tanujaya ◽  
Rully Charitas Indra Prahmana ◽  
Jeinne Mumu
Keyword(s):  
Active Learning ◽  
Literature Review ◽  
Teaching And Learning ◽  
Mathematics Classroom ◽  
Mathematics Learning ◽  
Thinking Skills ◽  
Mathematics Textbooks ◽  
Mathematics Students ◽  
Classroom Activities ◽  
And Mathematics

HOTS instruction in mathematics is rarely explicitly programmed by the schoolteacher. As a result, students' HOTS is at the lowest level, especially in national or international assessments. The purpose of this research is to determine why mathematics education in Indonesia does not have a significant effect on student HOTS by conducting a review of several Indonesian publications on the subject. This research is a qualitative method of literature review related to the HOTS of Indonesian mathematics students, and an organized interview triangulated to support the data and information from the literature review. The interview consisted of two critical questions administered using Google Form: implementing active learning and mathematics textbooks on mathematics classroom activities. The results concluded that there were two primary sources of error in mathematics learning to increase HOTS in Indonesia: active learning and current mathematics textbooks. Besides, in teaching and learning practices, the active learning model is rarely used when using official texts that do not promote HOTS for mathematics students in Indonesia.

scholarly journals INDOOR AIR TEMPERATURE DISTRIBUTION – AN ALTERNATIVE APPROACH TO BUILDING SIMULATION

2003 ◽  
Vol 2 (1) ◽  
Author(s):  
A. T. Franco ◽  
C. O. R. Negrão
Keyword(s):  
Temperature Distribution ◽  
Air Temperature ◽  
Indoor Air ◽  
Linear Equations ◽  
Three Dimensional ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Algebraic Equations ◽  
Conservation Of Energy ◽  
Energy Conservation Equation

The current paper presents a model to predict indoor air temperature distribution. The approach is based on the energy conservation equation which is written for a certain number of finite volumes within the flow domain. The magnitude of the flow is estimated from a scale analysis of the momentum conservation equation. Discretized two or three-dimensional domains provide a set of algebraic equations. The resulting set of non-linear equations is iteratively solved using the line-by-line Thomas Algorithm. As long as the only equation to be solved is the conservation of energy and its coefficients are not strongly dependent on the temperature field, the solution is considerably fast. Therefore, the application of such model to a whole building system is quite reasonable. Two case studies involving buoyancy driven flows were carried out and comparisons with CFD solutions were performed. The results are quite promising for cases involving relatively strong couplings between heat and airflow.

A Diagonally Dominant Solution for the Cylinder End Problem

1981 ◽  
Vol 48 (4) ◽  
pp. 876-880 ◽  
Author(s):  
T. D. Gerhardt ◽  
Shun Cheng
Keyword(s):  
Infinite System ◽  
Linear Equations ◽  
Infinite Cylinder ◽  
Algebraic Equations ◽  
Precise Calculation ◽  
Linear Algebraic Equations ◽  
Present Solution ◽  
Diagonally Dominant ◽  
Expansion Coefficients

An improved elasticity solution for the cylinder problem with axisymmetric torsionless end loading is presented. Consideration is given to the specification of arbitrary stresses on the end of a semi-infinite cylinder with a stress-free lateral surface. As is known from the literature, the solution to this problem is obtained in the form of a nonorthogonal eigenfunction expansion. Previous solutions have utilized functions biorthogonal to the eigenfunctions to generate an infinite system of linear algebraic equations for determination of the unknown expansion coefficients. However, this system of linear equations has matrices which are not diagonally dominant. Consequently, numerical instability of the calculated eigenfunction coefficients is observed when the number of equations kept before truncation is varied. This instability has an adverse effect on the convergence of the calculated end stresses. In the current paper, a new Galerkin formulation is presented which makes this system of equations diagonally dominant. This results in the precise calculation of the eigenfunction coefficients, regardless of how many equations are kept before truncation. By consideration of a numerical example, the present solution is shown to yield an accurate calculation of cylinder stresses and displacements.

Devices for a Mathematics Classroom: An individual laboratory kit for the mathematics student

1954 ◽  
Vol 47 (2) ◽  
pp. 100-105
Author(s):  
Nona Mary Allard
Keyword(s):  
Mathematics Classroom ◽  
Mathematics Students ◽  
Individual Laboratory ◽  
Mathematics Student ◽  
Discovery Method ◽  
Powerful Incentive

The thrill of discovery is a powerful incentive to students of physics and chemistry. Mathematics students, too, can be motivated by discovery experiences. However, the collection, care, and distribution of the materials needed to employ the discovery method can be a prohibitively time-consuming chore for the teacher.

scholarly journals On the Solubility of Linear Algebraic Equations (Contd.)

1913 ◽  
Vol 12 ◽  
pp. 137-138
Author(s):  
John Dougall
Keyword(s):  
Linear Equations ◽  
Homogeneous System ◽  
Algebraic Equations ◽  
Similar Reasoning ◽  
Null Solution ◽  
Linear Algebraic Equations ◽  
The Given ◽  
Homogeneous Linear

A system of n non-homogeneous linear equations in n variables has one and only one solution if the homogeneous system obtained from the given system by putting all the constant terms equal to zero has no solution except the null solution.This may be proved independently by similar reasoning to that given for Theorem I., or it may be deduced from that theorem. We follow the latter method.

Large Displacement Analysis of a Marine Riser

1985 ◽  
Vol 107 (1) ◽  
pp. 54-59 ◽  
Author(s):  
T. Huang ◽  
S. Chucheepsakul
Keyword(s):  
Strain Energy ◽  
Equilibrium Configuration ◽  
Numerical Procedure ◽  
Stationary Condition ◽  
Arc Length ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Marine Riser ◽  
Highly Nonlinear ◽  
Rectangular Coordinates

A method of static analysis for a marine riser experiencing large displacements is presented. The method is suitable for analyzing a riser having a known top tension and a possible slippage at the top slip joint. Utilizing the stationary condition of a functional coupled with an equilibrium equation, one can conveniently obtain the equilibrium configuration numerically. The configuration is expressed in terms of the rectangular coordinates. The functional representing the energy and work of the riser system is expressed in terms of the horizontal coordinate which is parameterized in terms of the vertical depth instead of arc length. For a two-dimensional problem, two multipliers must be included in the functional. One of the two represents the variable axial force along the length of the riser and the other corresponds to the strain energy per unit riser length due to bending. Utilizing the finite element method, a numerical procedure to obtain the configuration of static equilibrium is given. The resulting algebraic equations are highly nonlinear and the Newton-Raphson iterative procedure is used to solve the equations. An example is given.

scholarly journals UniDoodle: A Multi-Platform Smart Device Student Response System – Evaluated in an Engineering Mathematics Classroom

2017 ◽  
Vol 15 (3) ◽  
pp. 44
Author(s):  
Seamus McLoone ◽  
Christine Kelly ◽  
Conor Brennan ◽  
Caitriona NiShe
Keyword(s):  
Mathematics Classroom ◽  
Evaluation Process ◽  
Student Response ◽  
Smart Device ◽  
Student Response System ◽  
First Year ◽  
Mathematics Students ◽  
Response System ◽  
Engineering Mathematics ◽  
Mathematical Equations

Most of the existing student response systems, such as clickers, have limited input capabilities, typically only offering students a multiple-choice selection. In some instances, students can input a numerical or textual response. However, mathematical equations, diagrams, etc. are all beyond the capabilities of such systems. This paper proposes and presents a novel multi-platform smart device-based student response system, called UniDoodle, that allows for a more generic and flexible input. This system consists of a student application that allows for freeform input through sketching capabilities, a lecturer application that allows easy viewing of multiple sketch-based responses and a cloud-based service for co-ordinating between these two applications. In essence, students can now respond to a question posed by the lecturer using sketches and, hence, mathematical equations, circuit diagrams, graphs, etc. are all possible on the UniDoodle system. In addition, the lecturer can now gain a richer and more useful insight to the students’ understanding of the relevant material. This paper also evaluates the UniDoodle system in a large class of first year Engineering Mathematics students. Details of the UniDoodle system, the evaluation process and the feedback obtained are all presented within.

scholarly journals On the economical solution method for a system of linear algebraic equations

2004 ◽  
Vol 2004 (4) ◽  
pp. 377-410 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Vadim A. Krysko ◽  
Anton V. Krysko
Keyword(s):  
Differential Equations ◽  
Boundary Value ◽  
Linear Equations ◽  
Three Dimensional ◽  
Boundary Element Methods ◽  
Minimal Amount ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Point Of Intersection ◽  
Stationary Heat Transfer

The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped inℝ3is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error ofO(hx12+hx22). The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

Use of a tree volume equation based on two lower-stem diameters to estimate forest volume from sample tree counts

1995 ◽  
Vol 25 (6) ◽  
pp. 871-877 ◽  
Author(s):  
Thomas B. Lynch
Keyword(s):  
Linear Equations ◽  
Stem Diameter ◽  
Linear Functions ◽  
Individual Tree ◽  
Point Sampling ◽  
Sample Tree ◽  
Fixed Radius ◽  
Volume Equation ◽  
The Individual ◽  
Lower Stem

A recently developed method of individual-tree volume prediction uses measurements of two lower-stem diameters, rather than the more traditional DBH and height measurements, to estimate stemwood. One form of the equation is linear with respect to volume between the two diameter measurements, as computed by Smalian's formula, and can be algebraically rearranged into the sum of two equations, one linear with respect to the square of the topmost lower-stem diameter, the other linear with respect to the square of the bottom lower-stem diameter. These two equations have the same form as local volume equations that are linear functions of the square of diameter. Because of this, a variation of horizontal point sampling can be used to select trees with probability exactly proportional to each of the equations. Forest volumes can be estimated from counts of trees obtained by comparing the point sampling gauge angle with individual tree diameters at the lower-stem diameter measurement points used by the individual-tree volume equation. To account for the negative intercept term in the linear equations, trees within a small fixed-radius plot are not included in the counts.

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