Graphical calculator

TI-89 , graphing calculator with CAS

A graphical pocket calculator ( graphic calculator or GTR for short ) is a portable calculating machine that usually has a higher-resolution display than conventional pocket calculators and supports multi-line inputs and outputs as well as the display of simple graphics (e.g. function graphs or diagrams). Some models are now equipped with a backlit color display. As a rule, graphics computers can also be programmed . For some years now, higher quality models have been equipped with Flash ROM memories, which means that their operating system can be updated and additional software can be installed.

Categories

Graphics calculators are usually, i. H. by the manufacturers and, with regard to test regulations, by the ministries of education, divided into the following groups:

• Numerical- graphic pocket calculators or graphic calculators in the narrower sense (GTR for short) work purely numerically, i. That is, the solutions of equations, derivatives of functions, etc. are determined solely with numerical methods and output as approximate values ​​within the computational accuracy of the computer.
• Symbolic- graphic pocket calculators (short: SGTR) or computer algebra- pocket computers (short: CA-TC), on the other hand , calculate symbolically , so they can algebraically solve equations, determine derivative functions, determine antiderivatives, etc. Classic example: TI-92 .
• Latest models such as B. TI-Nspire CAS offers in addition to the computer algebra functionality also dynamic geometry , spreadsheets , dynamic statistics, mathematically active worksheets and interfaces to data acquisition systems.

Manufacturers and well-known models

Manufacturer	Models without CAS (GTR)	Models with CAS (SGTR)
Casio	Casio CG 20, Casio 9860G II , Casio 9750 G II	Classpad 330 Plus , Casio FX 2.0 Plus
Hewlett-Packard	HP 39GII	HP Prime
Sharp	EL-9900G SII	no
Texas Instruments	TI-Nspire (CX) , TI-84 Plus	TI-89 Titanium , Voyage 200 , TI-Nspire (CX) CAS

Graphing calculator in school

Evaluations

The first graphing calculator, the Casio fx-7000G, was produced in 1985. In Germany, various aspects of the use of graphics computers in teaching have been evaluated since 1991. A first major evaluation was carried out in Saxony-Anhalt from 1991 to 1996 . Current model tests, which are significant due to the large number of participating students (over 1,000) and the long duration (over five years), are e.g. B. CALiMERO in Lower Saxony or M3 model test media integration in mathematics lessons in Bavaria .

Curricular situation and admission in lessons and exams in Germany

As part of the educational freedom, it is up to the respective teacher to decide on the use of graphics computers in the classroom. In the curricula of many federal states, graphic calculators are explicitly mentioned as aids; in some cases, their use is mandatory, e.g. B. in Baden-Württemberg , Lower Saxony or Saxony. In North Rhine-Westphalia, the use of graphics computers is compulsory from the 2014/15 school year in the upper secondary school.

With regard to the use in exams, there are at least for centrally placed examinations, e.g. B. Abitur, state-specific regulations.

In Baden-Württemberg, the use of graphics computers is prohibited from high school graduation 2017 (vocational high schools) or 2019 (general high schools).

Didactic and methodological considerations

In numerous national and international studies, the influence of graphics computers with or without computer algebra on the learning success of students was examined. In these studies, various conditions of success for the use of GTR in lessons and exams were named.

In addition to the possibilities of illustrating mathematical relationships (keyword: The Power of Visualization), the literature u. a. discussed the following didactic ideas:

• Whitebox-blackbox principle and blackbox-whitebox principle : In the classroom, phases of using an aid alternate. In the black box phase, a given function of the aid is used without questioning it. This specific function is examined in the whitebox phase. Example: Whitebox phase = development of a concept or algorithm; Black box phase = application of the previously developed concepts and algorithms to practical problems or to develop higher mathematical skills.
• Scaffolding method : Pupils can concentrate on learning advanced mathematical skills, especially if some of the prerequisite skills are not yet or not sufficiently mastered.
• Module principle or building block principle : combining knowledge units for cognitive relief e.g. B. of routine tasks.
• Window shuttle technology : Achieving a deeper understanding by switching between different prototypical representations.
• Rule of the Three : Every mathematical problem should be viewed graphically, numerically and analytically on an equal footing.
• Multiple representations : Extension of the Rule of the Three and merging with the window shuttle technology to include geometric, linguistic and possibly other dimensions.
• Three-pillar model : the graphic calculator as a calculation, teaching and learning tool.

Controversial discussion about the mandatory introduction of the GTR in NRW

In North Rhine-Westphalia, the decree “Use of graphical pocket calculators in mathematics lessons in upper secondary school and vocational high school” of June 27, 2012 led to a controversial discussion.

In response to the multiple criticism of the decree, a supplementary decree “Use of a computer algebra system (CAS) on tablets, laptops and computers in mathematics lessons and in examinations for upper secondary school and vocational high school” was published on April 10, 2014.

Currently (as of February 2015), since the supplementary decree of April 10, 2014, the paradoxical situation has existed in North Rhine-Westphalia that, under the conditions specified in the supplementary decree, tablets with CAS software are allowed in schools in schools, but tablets that are similar to the classic GTR are not permitted. Tablets with both CAS and GTR software are permitted at advanced training and vocational colleges, provided that the provisions of the supplementary decree are complied with.

Web links

• Michael Fothe (Ed.): Mathematics lessons and computers - inventory and outlook (PDF; 277 kB) - conference report (24/25 September 2004) in the series of Jenaer Schriften zu Mathematik und Informatik .
• Marco Haase: Graphics calculator in school - model overview, comparison test and use in mathematics lessons at secondary level II.
• Heinz-Jürgen Harder: How the TI-92 can change mathematics lessons in lower secondary level (PDF; 665 kB) - Conference contribution from May 24, 2002 (University of Münster).
• Hildegard Urban-Woldron: GTR and CAS change mathematics lessons (PDF; 519 kB).

Individual evidence

1. ↑ Journal für Mathematikdidaktik , 1995, pp. 193–232
2. ↑ CALiMERO ( Memento of the original from April 1, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Website of the accompanying university 
3. ↑ M3 model experiment media integration in mathematics lessons Website of the accompanying university
4. ↑ M3 model experiment with media integration in math lessons  ( page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. Website of the project  
5. ↑ Binding introduction of graphical pocket calculators ( memento of the original from June 14, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. Website for the introduction of GTR in NRW  
6. ↑ Central high school diploma with CAS - status and perspectives ( Memento of the original from January 28, 2016 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , T3 Germany , 2008  
7. ↑ Renate Allgöwer: Abitur ban remains , Stuttgarter Zeitung, August 31, 2016, accessed on February 9, 2017
8. ↑ B. Barzel: Expertise on the use of computer algebra systems (CAS) in mathematics lessons in Thuringia . (PDF; 1.16 MB) pp. 22–49
9. ↑ B. Barzel: Expertise on the use of computer algebra systems (CAS) in mathematics lessons in Thuringia . (PDF; 1.16 MB) pp. 50–59
10. ↑ B. Waits, F. Demana: Graphing Calculator Intensive Calculus: A First Step in Calculus Reform for All Students . ( Memento of the original from July 20, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 99 kB) 
11. ^ B. Buchberger: Why Should Students Learn Integration Rules? RISC-Linz Technical Report no.89-7.0. Linz, Austria: University of Linz
12. ↑ B. Kutzler: Technology and the Yin & Yang of teaching and learning mathematics . ISBN 978-3-901769-84-9
13. ↑ Heugl, Klinger, Lechner: mathematics teaching and learning with computer algebra systems . (PDF; 2.43 MB) p. 148 ff.
14. ↑ Heugl, Klinger, Lechner: mathematics teaching and learning with computer algebra systems . (PDF; 2.43 MB) p. 162 ff.
15. ↑ H. Knechtel, W. Weiskirch et al: Computer algebra systems in mathematics lessons in upper secondary education . (PDF; 5.71 MB) NLI reports 64
16. ↑ K.Stacey: Didactic map for the description of technology-based teaching .  ( Page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice. (PDF; 692.4 kB)  
17. ↑ E. Bichler: Exploratory study on long-term use of pocket computers in mathematics classes . Publishing house Dr. Kovač, Hamburg 2010, ISBN 978-3-8300-5306-4 .
18. ↑ New round in the NRW noble computer dispute . news4teachers.de
19. ↑ Supplementary decree on the binding introduction of graphical pocket calculators with regard to the use of computer algebra systems. ( Memento of the original from April 2, 2015 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. school ministry.nrw.de