Obersteiner Andreas, Hoof Jo Van, Verschaffel Lieven, Dooren Wim Van
Center for Instructional Psychology and Technology, University of Leuven, Belgium.
TUM School of Education, Technical University of Munich, Germany.
Br J Psychol. 2016 Aug;107(3):537-55. doi: 10.1111/bjop.12161. Epub 2015 Nov 14.
Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth-grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.
许多学习者在有理数任务上存在困难，因为他们持续依赖其自然数知识，而这种知识并非总是适用的。研究表明，这种自然数偏差不仅会误导儿童，还会误导受过教育的成年人。目前尚不清楚数学专业知识是否以及在何种条件下能使人们在那些专业知识较少的人明显存在偏差的任务中完全不受这种偏差的影响。我们比较了八年级学生和专业数学家在同一组涉及算术运算（乘法和除法）效果的代数式问题上的表现。通过准确性和反应时间测量，我们发现学生中存在明显的自然数偏差证据，而专家中没有偏差痕迹。数据表明，学生基于他们对自然数的直觉来回答问题，而专业数学家则依赖他们对代数式的熟练直觉。我们得出结论，当专家使用不涉及自然数的策略时，他们有可能在有理数任务上不受自然数偏差的影响。
