The Graphing Calculator

The graphics calculator (GC) is a hand-held technology. With it, students visualize and understand concepts in mathematics and science better. It also allows them to make real-world connections, binding together advanced graphing functionality and conceptual science, technology, engineering, arts and mathematics (STEAM). As they gain a deeper understanding of abstract concepts, they acquire creative and critical thinking and problem- solving skills they need to reach greater academic successes. In learning, GC plays several roles in increasing students’ computational thinking and procedural skills. Despite being a learning tool that satisfies science and mathematics curriculum needs, the calculator often has been used as an add-on to traditional teaching methodology rather than central and in more integrated ways. This study looks into the potential of developing computational thinking skills using GC technology. The data of the study was obtained from secondary sources through a systematic review method. The study showed that GC seems to be effective tools to practice STEAM education as well as to develop students’ computational thinking through analysing and decompose real problem as well as engaging in the abstraction process and developing an algorithm using coding. The findings provides justifications on the impact of GC in developing computational thinking skills thereby maximizing the pedagogical benefits to students.

12 - The Graphics Calculator and Mathematical Modelling – Creating an Integrated Learning Environment

ABSTRACTGraphing calculators are hand-held technological tools currently used in mathematics classrooms. Teachers’ perspectives on using graphing calculators are important in terms of exploring what teachers think about using such technology in advanced mathematics courses, particularly precalculus courses. A descriptive intrinsic case study was conducted to analyse the perspectives of 11 teachers using graphing calculators with potential Computer Algebra System (CAS) capability while teaching Functions, Statistics, and Trigonometry, a precalculus course for 11th-grade students developed by the University of Chicago School Mathematics Project. Data were collected from multiple sources as part of a curriculum evaluation study conducted during the 2007–2008 school year. Although all teachers were using the same curriculum that integrated CAS into the instructional materials, teachers had mixed views about the technology. Graphing calculator features were used much more than CAS features, with many teachers concerned about the use of CAS because of pressures from external assessments. In addition, several teachers found it overwhelming to learn a new technology at the same time they were learning a new curriculum. The results have implications for curriculum developers and others working with teachers to update curriculum and the use of advanced technologies simultaneously.

The purpose of this mixed-methods study was to investigate the relationship between teachers’ conceptions of mathematics and their use of intelligent tutoring systems for mathematics instruction. Intelligent tutoring systems are adaptive computer programs which administer mathematics instruction to students based on their cognitive state. A conception is a mixture of beliefs and knowledge. The participants in this study were 93 junior high school mathematics teachers from three school districts in the Midwest. Data were gathered using a two-part online survey. The first part of the survey contained questions about their use of intelligent tutoring systems, graphing calculators, Desmos and dynamic geometry software. The second part of the survey contained Likert questions from the teachers’ version of the Conceptions of Mathematics Inventory. Desmos is a website providing interactive classroom activities and a user-friendly graphing calculator. Dynamic geometry software is a class of interactive geometry programs. The quantitative analysis revealed no statistically significant interactions between teachers’ conception scores and intelligent tutoring system use, or between teachers’ conception scores and how intelligent tutoring systems were used. There were statistically significant interactions between teachers’ conception scores and their use of graphing calculators, Desmos, and dynamic geometry software. The qualitative analysis revealed that teachers used intelligent tutoring systems for differentiation. Teachers used graphing calculators, Desmos, and dynamic geometry software for visual, computational, and exploratory purposes. Teachers exclusively using intelligent tutoring systems to incorporate technology should also incorporate technology which promotes student exploration.

This study examines African American students’ interactions with the graphing calculator as a tool to support their mathematical learning. Two participants, chosen through purposive sampling, were the focus of this study. The participants were presented with a task-based interview, and the strategies they employed in solving these tasks with the help of a graphing calculator were examined. The participants’ strategies were analyzed using Goos, Galbraith, Renshaw, and Geiger’s (2003) framework of the varying modes of sophistication with which students work and interact with technology and the ways in which technology can mediate learning. These modes include technology as master, technology as servant, technology as partner, and technology as an extension of self. In solving the mathematical tasks, the participants’ modes of interacting with the graphing calculator technology were influenced by how and when they chose to use the graphing calculator. They were also influenced by their ability to reinforce their mathematical and technological knowledge mutually. It is this ability to develop an interactive relationship between mathematical and technological knowledge that shaped the participants’ fluency in solving the mathematical tasks.

In this study, we focused on the graphing calculator to support the activity-oriented mathematics instruction with considering the accessibility of technology. The purpose of this study was to investigate the direction of the education of mathematics teachers. For this, we gave the teacher training for mathematics using graphing calculators for secondary mathematics teachers, and then examined the recognition for that of teachers. Teacher training of the graphing calculator was carried out three times in two years, we conducted a survey immediately at the time that has passed and after the 8 months or more after the training. As a result, we have obtained the suggestions of the advantages of using a graphing calculator in the learning mathematics, the difficulties of use of the graphing calculator in the classroom and the form of teacher training they want.

In a climate where the use of calculators is being criticised as one of the reasons for failure in mathematics, this paper explores how graphic calculators can be used to support students' mathematical development through the processes of visualisation, formalisation and interpretation. It explores the current research through a vignette of one student's experience and argues for a reconceptualisation of assessment procedures that makes use of the representational power of the graphic calculator.

This paper outlines an experiment in which pupils in Key Stage 2 were encouraged to use graphics calculators, in particular two simple programs, which helped them develop recall of their tables and allowed them to practise multiplication. The pupils responded very well to the calculators and seemed to have been motivated by them. The pupils did not find them difficult to operate and experienced very few technical problems. The authors concluded that the graphics calculator has considerable potential to enhance the mathematical experience and learning of pupils at this level, and that although the extent of the investigation was fairly limited the results were encouraging enough to justify further work in this area.

This study focuses on the influence of socio-contextual factors in the interrelations between teachers' perceptions of the role of graphing calculators, as mediating tools, to help facilitate mathematics instruction of students from two different SES backgrounds. The main source of data are in-depth semi-structured interviews with four teachers, two from each SES school. To better understand the role of SES socio-context, this study suggests a framework, consisting of teacher, student, subject matter, and graphing calculator use, for graphing calculator integration in the classroom. The components of the framework were taken to be continuously in interaction with one another implying that a change or perturbation in one of the components affected all the other components. As such, addressing equity issues in connection to the successful integration of graphing calculator in the classroom requires continually creating, maintaining, and re-establishing a dynamic equilibrium among all components of the framework.

The purpose of this study was to determine the effect of TI-Nspire graphing calculator use on student achievement and on teacher behavior variables of planning, teaching, and assessing. This study investigated the teaching of functions by teachers using the TI-Nspire graphing calculator versus teachers using a non-graphing scientific calculator. A review of the literature found that the emergence of calculators and computers has changed the way mathematics is both done and used (Ellington, 2006; Thorpe, 1989; & Kieran, 1992). Research also showed that students can effectively use a graphing calculator as an instructional tool to make and understand different types of representations (Choi-Koh, 2003; Colgan, 1993; and Drijvers & Doorman, 1996). Other studies have shown how graphing calculator use has engaged students in higher level thinking skills (Dessart, DeRidder, Charleen, & Ellington, 1999; Ellington, 2006; Graham & Thomas, 1998; Keller & Hirsch, 1998; Huntley, Rasmussen, Villarubi, Sangtong, & Fey, 2000; & Ronau et al., 2008). Since it is a relatively new tool, there is a limited amount of research on the classroom use of the TI-Nspire. The TI-Nspire is designed to link together multiple-representations within a single problem, so the concept of functions is an ideal context within which to study the impact of the TI-Nspire. This was a quasi-experimental study. The researcher gathered and analyzed pretest, post-test, and post post-test data on student performance on function concepts. The study included a 90 minute classroom observation of each class as well as document analysis of weekly questionnaires, daily lesson plans, and daily assessments. Vignettes employed classroom observations, document analysis, and thick description to triangulate the results of the qualitative analysis. During the summer prior to this study, all teachers attended 12 hours of training over the course of two days with a National Texas Instruments Instructor in which they were trained to use the TI-Nspire graphing calculator. Teachers were then given a TINspire, TI-Nspire emulator and access to online Atomic learning video training (Atomic Learning, 2011), to continue their exploration of the TI-Nspire. The week prior to the study, the teachers attended another day of professional development activity taught by a Texas Instruments Trained Cadre member. This "Function Focused Session" was six hours long and provided review on the TI-Nspire, specific training about teaching the function concept with the TI-Nspire, and time to create lesson plans and activities for this study. During the two weeks of treatment and two weeks

Summary statistics used to describe a data set are some of the most commonly taught statistical concepts in the secondary curriculum. Mean, median, mode, range, and standard deviation are topics that can be found in nearly every program. Technology empowers us to access these concepts and easily to create visual displays that interpret and describe the data in ways that enhance students' understanding. Many graphing calculators allow students to display nonparametric statistical information using a box-and-whiskers plot or a modified box plot showing a visual representation of the median, upper and lower quartiles, and the range of the data. But how can students visually display the mean of the data or show what it means to be within one standard deviation of the mean? One way to create this type of visual display is with a bar graph and constant functions. Unfortunately, graphing calculators, and some computer programs, only display histograms and not bar graphs. The tips in this issue focus on using graphing calculators to draw bar graphs that can help students visualize and interpret the mean and standard deviation of a data set.

This study extended through three academic semesters and involved 710 subjects. It compared the performance of college students taught precalculus using a graphing calculator and a textbook written to be used with a graphing utility, to the performance of students using the traditional approach, a regular textbook, and a scientific calculator. On a comprehensive common final exam, students who were taught precalculus using the graphing calculator had significantly higher scores than those taught by traditional methods.

Summary This article describes how a teacher changed her method of teaching after acquiring knowledge about graphing calculators in a Professional development program. It describes one particular unit on understanding variables and graph interpretation taught in a seventh-grade science and math class. The use of graphing calculators proved to be effective in increasing student understanding of relationships between variables, graphing, and experimental design. The teacher in our project also found graphing calculators to be effective tools for teaching constructively. Our study implies that math and science teaching can be improved through the use of graphing calculators.

<span>This paper reports on a case study which examined factors leading to the adoption of graphics calculators (GCs) by secondary mathematics teachers in the state of New South Wales, Australia. In total, 587 teachers of the General Mathematics Course (Years 11 and 12) participated in the study. The median teachers' stage of adoption of GCs was found to be at the "Understanding and application of the process" level, the third lowest on a six point scale. The results also indicate that competence is the most important factor in explaining stages of adoption, training the second most important, followed by personal interest in GCs as well as faculty support. Teachers' gender, teaching experience, educational qualifications and the number of GCs in schools were not found to be statistically significant. Qualitative analysis of teachers' open ended comments also shed light on the nature of the explanatory variables. The findings are relevant to curriculum development policy and the design of professional development programs, and has implications for the introduction of other technologies.</span>

This paper presents the preliminary results of a study conducted to investigate the differences in brain hemisphericity and learning styles on students' confidence in using the graphics calculator (GC) to learn mathematics. Data were collected from a sample of 44 undergraduate mathematics students in Malaysia using Brain-Dominance Questionnaire, Index of Learning Style Inventory, and Confidence in Using GC to Learn Mathematics Questionnaire. Statistical analyses revealed that the sample differ significantly in their hemispheric preference and learning styles. In addition, sequential-global and sensingintuitive learning styles were found to associate significantly with brain hemisphericity. However, there was no significant association between brain hemisphericity with gender, race, and program of study. Finally, the study also revealed that GC confidence ratings are not significantly different across brain hemisphericity as well as learning styles.