Hartwig Meissner (July 2007)

 
Calculators
in  Mathematics  Education
 Investigations with Simple Calculators
Summaries and References		 International
Survey

We invite you to study this web page though the page still is under construction.

Basically we will give a small international survey about the actual use of calculators in primary schools. There also is another web site which reports from TIM projects with calculators in Germany.

We also refer to and reflect on mental processes of learning and understanding mathematics when using calculators and we touch the delicate question about the future of paper & pencil skills. Thus we recommend also to study the separate web site

Discussion Forum on the Future of Paper & Pencil Skills



1. Calculators everywhere   -   also in schools?

It is impossible to give an international survey. On this web page we just will try to summarize some experiences from different countries. Most of the information was collected by Christina Ebbing-Rupieper and Hartwig Meissner on international conferences, through personal communication and via correspondence. Additional comments are welcome, they will be added here whenever possible. We also recommend to study the references added at the end.

In 1986 - 1989 there was an important Calculator-Aware-Number (CAN) Project in England and Wales, “a curriculum development project  …  the aim of which was to study effects that the availability of calculators would have on the mathematics curriculum of primary schools” (Shuard, H. et al., 1991). Ruthven (1999, 2001a) analyzed some of the complexities of developing such a curriculum. But “During the 1990's, [the] curriculum and assessment system [became] much more 'calculator beware' as a result of opinionated criticism of calculator use by mathematicians and politicians which received wide publicity. This climate, and the circumstances it has produced in schools, have made developmental research on calculator integration virtually impossible” (Ruthven 2007, personal communication).

In Germany there is no federal curriculum, each Land (= state) is responsible for itself in education. Regarding the syllabuses for mathematics education in primary schools from the 16 German Laender we must summarize that paper & pencil algorithms still play the dominant role and, that calculators are not mentioned at all to replace them in any kind of activities. There are only a few investigations in primary schools by individuals or small research groups how calculators could be or should be used in the future in mathematics education.

In Sweden calculators are allowed in each grade. It depends on the teacher how and how often the calculator is used. Swedish school books touch the topic calculator quite differently. Some offer many exercises to use calculators and others do not. According to the syllabus the children must have learnt till the end of grade 5 to compute mentally, to compute by the use of (reduced) paper & pencil algorithms and to compute with calculators (Hedren 2001).

In Norway the situation is similar. Starting with grade 2 (age 7) “pupils should have the opportunity to  …  experiment with large numbers and symbols, examine arithmetic operations and use calculators and computers” (http://Skolenettet3.1s.no/97_eng/Curriculum, 13.11.2002). The use of  calculators is  included in school books, but “many decisions related to the use of calculators in primary schools are left to the teacher” (Brekke 2001).

In the Netherlands officially the use of calculators starts in grade 7 (age 11), but it is allowed to work earlier with calculators. Many textbooks contain activities for calculator mathematics, but many teachers will deny these activities or exercises. “On the other hand in Dutch mathematics education for primary schools there is a strong movement – an intention – to reduce paper-and-pencil maths, especially the traditional algorithms. In the place of these algorithms mental arithmetic is introduced as an alternative, and calculator math as well (ter Heege 2001).

There are also many calculator investigations in North America. In a meta-analysis Hembree and Dessart evaluated 79 studies (grades K – 12) and got the conclusion that calculators should be used in all grades: “It no longer seems a question of whether calculators should be used along with basic skill instruction, but how” (Hembree and Dessart 1986, p. 97). But in reality also in the US this research result is not accepted unanimously. Ralston analyzes and refutes (in Ralston 1999) the arguments made by "back-to-basics" proponents against the use of calculators And on the web site http://www.doc.ic.ac.uk/~ar9/LDApaper2.html he argues: “The truth is that few can be expected to make sense of arithmetic if  …  teachers are supposed to act as if the calculator and computer had never been invented.”
 

2. Mental Processes
(still under construction)

We will summarize aspects of  Tools, Artefact and Instrument. (See also the TIM references related to Mental Processes on the TIM web page.)


3. Topic "Calculator" at ICME conferences
(still under construction)

There will be reports from the conferences in Karlsruhe, Berkley, Adelaide, Budapest and following. (See also the TIM papers # 48, # 63, # 70 and # 71 in List 1 of References)

4.  References

Arens, E.; Meissner, H.; Vogt, C. (1978): Taschenrechner in der Grundschule? Der Mathematikunterricht. Jg. 24, Heft 1, pp. 7-21. Klett Verlag, Stuttgart.

Battista, M. (1994): Calculators and Computers: Tools for Mathematical Exploration and Empowerment. Aritmetic Teacher, Vol. 41, no. 7, pp. 412-417.NCTM, Reston VA, USA.

Brekke, G. (August 2001), Personal Communication.

De Moor, E.; van den Brink, J. (2001): Calculator. In: Van den Heuvel-Panhuizen, M., Buys, K. (Eds.): Children Learn Mathematics. A Learning-Teaching Trajectory with Intermediate Attainment targets for calculation with whole numbers in primary school, pp. 203-226. Groningen.

Department for Education and Employment (1998) The Implementation of the National Numeracy Strategy. London

Duffin, J. (1991): Mathematics for the nineties: A calculator-aware number curriculum. Mathematics Teaching, H. 136, pp. 56-62.

Duffin, J. (1992): CAN we change. Micromath, Vol. 8, no. 1, pp. 23-25.

Floer, J. (1990): Taschenrechner in der Grundschule? In: Die Grundschulzeitschrift, 4. Jg., Heft 31, S. 26-28 und S. 50-54. Friedrich Verlag, Velber.

Gur, H.; Ersoy, Y. (2001): Reflections from a two days seminar/workshop on using calculators in teaching of elementary school mathematics. Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, p. 311. Utrecht.

Groves, S. & Stacey, K. (1998). Calculators in primary mathematics: Exploring number before teaching algorithms. In L.J. Morrow (Ed.): The teaching and learning of algorithms in school mathematics, 1998 Yearbook. Reston VA: National Council of Teachers of Mathematics.

Hedren, R. (1985): The Hand-Held-Calculator at the Intermediate Level. Educational Studies in Mathematics, Vol. 16, no. 2, pp. 163-179.

Hedren, R. (August 2001), Personal communication.

Hembree, R. & Dessart, D. (1986). Effects of hand-held calculators in precollege mathematics: A meta-analysis, Journal for Research in Mathematics Education, 17 (2), 83-99.

Hembree, R. & Dessart, D. (1992). Research on calculators in mathematics education. In J. Fey & C. Hirsch (Eds.), Calculators in Mathematics Education, 1992 Yearbook (pp. 23-32). Reston VA: National Council of Teachers of Mathematics.

Jianpan, W. (2002): The Reform of Mathematics Curriculum for Compulsory Education in China. Proceedings of ICM-2002, Satellite Conference on Mathematics Education, pp. 8-16. Lhasa, Tibet.

Lange, B. (1979): Schneller Kopfrechnen mit dem Taschenrechner. In: Sachunterricht und Mathematik in der Primarstufe, 7. Jg., Heft 11, pp. 430-441. Aulis Verlag Deubner & Co KG, Köln.

Lange, B. (1984): Zahlbegriff und Zahlgefühl. Lit Verlag, Münster.

Lange, B.; Meissner, H. (1983): Zum Lernprozess im Bereich Arithmetik. In: Zentralblatt für Didaktik der Mathematik, Jg. 15, Heft 2, pp. 92-101. Klett Verlag, Stuttgart.

MAA Online (2007): Finding Common Ground in K-12 Mathematics Education. See: http://www.maa.org/common-ground/

Meissner, H. (1984): Zum Einfluss des Taschenrechners auf den Mathematikunterricht. In: Walsch, W.: Taschenrechner in der Schule, pp. 52-60. Halle (Saale).

Meissner, H. (2006): Taschenrechner in der Grundschule. mathematica didactica, 29. Jg., Heft 1, pp. 5-25. Franzbecker Verlag Hildesheim, Germany.

NCTM (2000): Principles and Standards for School Mathematics. NCTM, Reston VA, USA.

NCTM (2005): Computation, Calculators, and Common Sense. Position Statement May 2005. NCTM, Reston VA, USA.

Ralston, A. (2006):  K-12 Mathematics Education: How Much Common Ground Is There? MAA Online: http://www.maa.org/common-ground/ralston-focus-jan06.html

Ruthven, K. (1999): Constructing a calculator-aware number curriculum. The challenges of systematic design and systematic reform. In: Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, pp. 56-74. Haifa, Israel.

Ruthven, K. (2001a) Towards a new numeracy: the English experience of a ‘calculator-aware’ number curriculum. Edited version appears in J. Anghileri (ed.) Principles and Practice in Arithmetic Teaching (Open University Press, Buckingham).

Ruthven, K. (2001b). British research on developing numeracy with technology. In M. Askew & M. Brown (Eds.) Teaching and Learning Primary Numeracy: Policy, Practice and Effectiveness (British Educational Research Association, Southwell) pp. 28-32.

Ruthven, K. (2003). Creating a calculator-aware number curriculum. Canadian Journal of Science, Mathematics and Technology Education  3 (4) 437-450.

Ruthven, K. (June 2007), Personal Communication.

Shuard, H.; Walsh, A.; Goodwin, J.; Worcester, V. (1991). Calculators, Children and Mathematics. London UK: Simon & Schuster.

Shuard, H., Walsh, A., Goodwin, J. & Worcester, V. (1991) Calculators, Children and Mathematics (London: Simon and Schuster).

Shuard, H. (1992). CAN: Calculator use in the primary grades in England and Wales. In J. Fey and C. Hirsch (Eds.), Calculators in Mathematics Education, 1992 Yearbook (pp. 33-45). Reston VA: National Council of Teachers of Mathematics.

Sparrow, L.; Swan, P. (1997): Calculator use in primary schools: A survey, Perth: Mathematics, Science and Technology Centre.

Sparrow, L.; Swan, P. (2001): Learning Math With Calculators. Math Solutions Publications.

ter Heege, H. (Sept. 2001), Personal communication.


See also the references on two other web pages:

(1)    Discussion Forum on the Future of Paper & Pencil Skills?
(http://wwwmath1.uni-muenster.de/didaktik/u/meissne/WWW/Forum-P&P.htm)
(2)   Summary report on TIM Calculator Projects in Germany
(http://wwwmath1.uni-muenster.de/didaktik/u/meissne/WWW/TR.htm)