Curve Graphing in MS Excel and Applications

Mathematical Progress in Expressive Image Synthesis III, 2016

We propose a method to determine piecewise cubic Bézier curves passing through given points. Our main purpose is to draw accurate graphs of mathematical functions with smaller data. A program drawing such graphs using our method is realized in a computer algebra and outputs the graphs in a source file of T E X and then transforms it into a PDF file. Our method is also useful for numerical calculation of a given area enclosed by a curve and for numerical integration of functions.

School Science and Mathematics, 1992

1988

This report summarizes the work of a two-year project which focused primarily on the problems that students have with algebra in general, and graphs in particular. The first of two major sections in the document deals with the use of computer software to assist in the teaching of graphing. It concludes that thoughtful design and use of graphing software presents new opportunities for teaching about graphing. The next section of the report centers on the development of research instruments that are intended to study scale in the context of graphs of function. It includes a set of problem-based teaching materials that were used as research tools. The appendices contain descriptions of probes designed to see if students can interpret and create graphs of real-world phenomena, along with instruments dealing with mapping, scale, and computer explorations. (TW)

This paper describes the trial of a unit of work on linear and quadratic graphing with six year 10 classes. Two treatments were developed. The computer treatment made use of the ANUGraph software package, while the calculator treatment paralleled the computer treatment but used a combination of previously prepared graphs and graphs constructed by the student with the aid of a calculator. The emphasis in both treatments was on the interpretation of graphs related to real situations. Comparisons between pre-test and post-test results and interviews with twelve students showed that students learnt to handle the software proficiently, and that both groups improved on most of the topics taught. However, the calculator group seemed to be advantaged by practising plotting of points by hand. Implications for future work are discussed. Most secondary schools are now equipped with computers that can run graphing and spreadsheet software, although they are still not frequently used for mathematics teaching. In Asp, Dowsey and Stacey (1992) we described a trial of a teaching unit using spreadsheets to assist students in constructing meaning for the important concepts of variable, expression, equation and solution. This teaching experiment gave an indication of which ideas about equations become easier with appropriate computer technology and what difficulties, both conceptually and in terms of classroom management, result from the use of this technology. In this paper we describe results from a trial of a teaching unit on linear and quadratic functions and their graphs, a topic which seems similarly suited to the use of computers. Frequently all aspects of a complex mathematical idea cannot be expressed with a single representational system. The idea may require multiple, linked representations for its full expression and these different representations may aid the learner's understanding of the idea. Kaput (1992) sees the ability to make translations from one representation of a function to another as a particularly important aspect of mathematical thinking which may be enhanced by technology. The convenient access provided by graphing software to numerical and graphical representations of a variety of functions may assist students to develop a broader and deeper understanding of the function concept.

Futurity Education, 2023

The aim of this paper was to evaluate the effectiveness of the "Mathematica Application" in examining and graphically presenting quadratic functions. This study has the potential to improve teaching and to help choose the most effective tools for examining and presenting quadratic functions. The purpose of this research was to evaluate the effectiveness of the "Mathematica Application" in examining and graphing quadratic functions. The method used to evaluate the effectiveness of the "Mathematica Application" was a combination of qualitative and quantitative analysis. In the qualitative analysis, the students' experience with the Mathematica application in examining quadratic functions and presenting them graphically was examined. The users were music school students who have used the application in order to study quadratic functions in the context of learning mathematics. Also, the quantitative analysis was used to analyse the performance of the Mathematica application in the graphical representation of quadratic functions. The sample of the study is represented by students of the tenth grade, where it is a purposive sample, since these learning units are covered in this class. The results of this evaluation are important to the community of mathematicians and users of the Mathematica application. The findings of the study show a positive assessment by the students on the efficiency and performance of the Mathematica application in examining and graphing quadratic functions. These findings provide implications for improving teaching and establishing the Mathematica application as a suitable tool for studying quadratic functions in the context of mathematics education. By incorporating the Mathematica application into the teaching and learning process of mathematics, students' interaction and understanding of this important mathematical topic can be increased.

2012

Abstract Time-series data are regularly collected and analyzed in a wide range of domains. Multiple simulation runs or multiple measurements of the same physical quantity result in ensembles of curves which we call families of curves. The analysis of time-series data is extensively studied in mathematics, statistics, and visualization; but less research is focused on the analysis of families of curves.

1998

Press <2nd> <GRAPH> (TABLE) and compare the t-table you made with the table in the calculator. Note: Since you changed the function in Y, = the values in the table have changed to match the new function. 4. Repeat Step 3 using y = x2 and y =. 5. Mathercise: Practice the shape of the fundamental equations using arm movements. Stand and demonstrate the shape of the graph when your teacher calls out an equation. Remember the shapes of the four graphs because your teacher will be calling them randomly and rapidly. Eisenhower Regional Consortium for Mathematics and Science Education at AEL Lesson 1/3 13 Graphing Calculators in Mathematics Grades 7-12 Activity Two: Transformations of the "Head of Family" Functions Using the Graphing Calculator Teacher Notes Outline: ()1> Clear the <Y=> menu. Use a table (Activity Two, Handout 1) to record the results of your observations. They will include, for each pair of equations, the graphs and any conclusions that can be made. Graph the "head of family" function in Y1 = , and the transformed graph in K =. Start with Y1 = x and 1/2 = x. Record the results. Clear the <Y=> menu. Next use = ixl and Y2 = lxi. Third use Y1 = x2 and Y2 = x2 and last use Y1 =-N5 , and Y2 =. Fill in the charts each time new equations are used and answer questions at bottom of chart. cg" Clear the <Y=> menu. Use a table (Activity Two, Handout 2) to record your observations. This time, place the "head of family" graph in Y1 = and twice the function in Y2 = (2x , 2lxl , 2x2 , and 2A5 respectively).

Part of my assignment for 2018 SKE in Maths, ST Mary's University, London

Graphing software and graphics calculators are widely used in most of the world's larger economies to facilitate students' development of conceptual understanding of mathematical function analysis. This has proved to be an extremely effective vehicle in making complex mathematics more accessible to the majority of learners. In contrast, its use in South Africa has been limited. Possible reasons may be the cost of graphics calculators, limited availability of supporting study material, and teachers who lack the necessary skills and confidence. At the School of Teacher Training, University of Pretoria, the Master Grapher for Windows was introduced by way of a pilot study in an effort to adapt the training of mathematics teachers in training to meet the specific needs of these students. The experiences of five students were monitored. The aim is to enhance and facilitate trainee teachers' understanding of mathematics, but also to equip them to develop learner centred, group based learning experiences in future teaching situations. Action research was implemented to develop the course.