Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

The importance of clarifying language in mathematics education

22.03.2011
The way in which teachers and textbooks use language and different metaphors in mathematics education determines how pupils develop their number sense.

This is shown in a thesis from the University of Gothenburg, Sweden.

When school pupils encounter numbers that cannot be conceptualised as quantities in an obvious way, clarity is required in terms of the language used by both teachers and textbooks. One significant risk is that the explanatory models and metaphors used by teachers are overgeneralised by pupils or create contradictions.

In her thesis, Cecilia Kilhamn shows how the difficulties experienced by pupils in understanding negative numbers – numbers that are less than zero – are similar to the difficulties that mathematicians have experienced historically. This suggests that better knowledge about the history of mathematics would provide a better understanding of pupils’ problems.

Concretising the abstract
“A reluctance to accept negative numbers is closely linked to our desire to be able to concretise that which is abstract and understand negative numbers in terms of concepts such as debts, lifts or temperatures,” explains Kilhamn.

However, many of the concrete explanatory models used in school mathematics cannot deal with subtraction, multiplication or division using negative numbers. A transition to a clearer mathematical language is therefore needed when the number domain is expanded from natural numbers to signed numbers, i.e. positive and negative numbers.

The study in question is a longitudinal case study in which pupils in a school class were followed over a period of three years. The results show that pupils’ ability to accept and make sense of negative numbers depends on how well developed their sense of natural numbers is.

Clear explanations
Insights such as being able to visualise zero as a number and not just a representation of nothing, understanding how subtraction works and being able to deal with the number line are important prerequisites for negative numbers. Another crucial factor is how clear teachers and textbooks are in their explanations. Numbers can be seen metaphorically as quantities, points, distances or operations, as constructed objects and as relations.

“But no individual metaphor for numbers can make negative numbers fully comprehensible,” continues Kilhamn. “It is therefore important that the deficiencies and limitations of these metaphors are also made clear in teaching, and that logical mathematical reasoning is used in parallel with concretised models.”

Contradictory properties.
Her study also highlights a number of problems relating to the fact that the mathematical language used in Swedish schools is a little ambiguous or inadequate. For example, no distinction is made between subtracting the number x and the negative number x if both are referred to as “minus x”. There is also no word in the Swedish language corresponding to the English term “signed number”.

“Swedish textbooks introduce negative numbers without making it clear that all the natural numbers change at the same time and become positive numbers,” she adds. “Another difficulty is the size of negative numbers, which have two contradictory properties that are distinguished in mathematics by separating absolute value (magnitude) from real value (position). A large negative number has a smaller value than a small negative number. This distinction also needs to be made clear to pupils.”

The thesis was completed within the framework of the Graduate Research School in Educational Sciences at the Centre for Educational Sciences and Teacher Research (CUL) at the University of Gothenburg.

For further information, please contact:
Cecilia Kilhamn, tel.: +46(0)31 786 2037, cecilia.kilhamn@ped.gu.se

Helena Aaberg | idw
Further information:
http://www.gu.se
http://hdl.handle.net/2077/24151

More articles from Science Education:

nachricht New Master’s programme: University of Kaiserslautern educates experts in quantum technology
15.03.2017 | Technische Universität Kaiserslautern

nachricht Decision-making research in children: Rules of thumb are learned with time
19.10.2016 | Max-Planck-Institut für Bildungsforschung

All articles from Science Education >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Making lightweight construction suitable for series production

More and more automobile companies are focusing on body parts made of carbon fiber reinforced plastics (CFRP). However, manufacturing and repair costs must be further reduced in order to make CFRP more economical in use. Together with the Volkswagen AG and five other partners in the project HolQueSt 3D, the Laser Zentrum Hannover e.V. (LZH) has developed laser processes for the automatic trimming, drilling and repair of three-dimensional components.

Automated manufacturing processes are the basis for ultimately establishing the series production of CFRP components. In the project HolQueSt 3D, the LZH has...

Im Focus: Wonder material? Novel nanotube structure strengthens thin films for flexible electronics

Reflecting the structure of composites found in nature and the ancient world, researchers at the University of Illinois at Urbana-Champaign have synthesized thin carbon nanotube (CNT) textiles that exhibit both high electrical conductivity and a level of toughness that is about fifty times higher than copper films, currently used in electronics.

"The structural robustness of thin metal films has significant importance for the reliable operation of smart skin and flexible electronics including...

Im Focus: Deep inside Galaxy M87

The nearby, giant radio galaxy M87 hosts a supermassive black hole (BH) and is well-known for its bright jet dominating the spectrum over ten orders of magnitude in frequency. Due to its proximity, jet prominence, and the large black hole mass, M87 is the best laboratory for investigating the formation, acceleration, and collimation of relativistic jets. A research team led by Silke Britzen from the Max Planck Institute for Radio Astronomy in Bonn, Germany, has found strong indication for turbulent processes connecting the accretion disk and the jet of that galaxy providing insights into the longstanding problem of the origin of astrophysical jets.

Supermassive black holes form some of the most enigmatic phenomena in astrophysics. Their enormous energy output is supposed to be generated by the...

Im Focus: A Quantum Low Pass for Photons

Physicists in Garching observe novel quantum effect that limits the number of emitted photons.

The probability to find a certain number of photons inside a laser pulse usually corresponds to a classical distribution of independent events, the so-called...

Im Focus: Microprocessors based on a layer of just three atoms

Microprocessors based on atomically thin materials hold the promise of the evolution of traditional processors as well as new applications in the field of flexible electronics. Now, a TU Wien research team led by Thomas Müller has made a breakthrough in this field as part of an ongoing research project.

Two-dimensional materials, or 2D materials for short, are extremely versatile, although – or often more precisely because – they are made up of just one or a...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Expert meeting “Health Business Connect” will connect international medical technology companies

20.04.2017 | Event News

Wenn der Computer das Gehirn austrickst

18.04.2017 | Event News

7th International Conference on Crystalline Silicon Photovoltaics in Freiburg on April 3-5, 2017

03.04.2017 | Event News

 
Latest News

NASA's Fermi catches gamma-ray flashes from tropical storms

25.04.2017 | Physics and Astronomy

Researchers invent process to make sustainable rubber, plastics

25.04.2017 | Materials Sciences

Transfecting cells gently – the LZH presents a GNOME prototype at the Labvolution 2017

25.04.2017 | Life Sciences

VideoLinks
B2B-VideoLinks
More VideoLinks >>>