Featured Research

from universities, journals, and other organizations

The importance of clarifying language in mathematics education

Date:
March 23, 2011
Source:
University of Gothenburg
Summary:
The way in which teachers and textbooks use language and different metaphors in mathematics education determines how pupils develop their number sense, according to new research from Sweden.

The way in which teachers and textbooks use language and different metaphors in mathematics education determines how pupils develop their number sense, according to a recent 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.

"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.

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."

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.


Story Source:

The above story is based on materials provided by University of Gothenburg. Note: Materials may be edited for content and length.


Cite This Page:

University of Gothenburg. "The importance of clarifying language in mathematics education." ScienceDaily. ScienceDaily, 23 March 2011. <www.sciencedaily.com/releases/2011/03/110321183013.htm>.
University of Gothenburg. (2011, March 23). The importance of clarifying language in mathematics education. ScienceDaily. Retrieved September 18, 2014 from www.sciencedaily.com/releases/2011/03/110321183013.htm
University of Gothenburg. "The importance of clarifying language in mathematics education." ScienceDaily. www.sciencedaily.com/releases/2011/03/110321183013.htm (accessed September 18, 2014).

Share This



More Computers & Math News

Thursday, September 18, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Virtual Reality Headsets Unveiled at Tokyo Game Show

Virtual Reality Headsets Unveiled at Tokyo Game Show

AFP (Sep. 18, 2014) Several companies unveiled virtual reality headsets at the Tokyo Game Show, Asia's largest digital entertainment exhibition. Duration: 00:48 Video provided by AFP
Powered by NewsLook.com
What HealthKit Bug Means For Your iOS Fitness Apps

What HealthKit Bug Means For Your iOS Fitness Apps

Newsy (Sep. 18, 2014) Apple has delayed the launch of the HealthKit app platform, citing a bug. Video provided by Newsy
Powered by NewsLook.com
Apple's iOS8 Includes New 'Killswitch' To Curb Theft

Apple's iOS8 Includes New 'Killswitch' To Curb Theft

Newsy (Sep. 18, 2014) Apple's new operating system, iOS 8, comes with Apple's killswitch feature already activated, unlike all the models before it. Video provided by Newsy
Powered by NewsLook.com
Let's Review Apple's Latest iPhone Reviews

Let's Review Apple's Latest iPhone Reviews

Newsy (Sep. 17, 2014) The tech press has shared its thoughts on the latest iterations of Apple's iPhone. We summarize the reactions to help you decide: iPhone 6 or 6 Plus? Video provided by Newsy
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins