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Children’s Acquiring the Principles of Mathematics and Science

It has been pointed out that learning mathematics and science is not so much learning facts as learning ways of thinking. It has also been emphasized that in order to learn science, people often have to change the way they think in ordinary situations. These changes in ways of thinking are often referred to as “conceptual changes”. But how do “conceptual changes” happen? How do children change their ways of thinking as they learn in school?

The psychologist Piaget suggested an interesting hypothesis (假说) relating to the process of cognitive (认知的) change in children. Cognitive change was expected to result from the pupils’ own intellectual activity. When met with a result that challenges their thinking, that is when faced with conflict, pupils realize that they need to think again about their own ways of solving problems, regardless of whether the problem is one in mathematics or in science. He hypothesised that conflict brings about unbalance, and then triggers processes that ultimately produce cognitive changes. For this reason, pupils need to be actively engaged in solving problems that will challenge their current mode of reasoning. However, Piaget also pointed out that young children do not always abandon their ideas in the face of conflicting evidence. They may actually abandon the evidence and keep their theory.

Piaget’s hypothesis about how cognitive change occurs was later translated into an educational approach which is now termed “discovery learning”. Discovery learning initially took what is now considered the “lone learners” route. The role of the teacher was to select situations that challenged the pupils’ reasoning; and the pupils’ peers had no real role in this process. However, it was subsequently proposed that interpersonal conflict, especially with peers, might play an important role in promoting cognitive change. This hypothesis has been investigated in many recent studies of science teaching and learning.

Christine Howe and her colleagues, for example, have compared children’s progress in understanding several types of science concepts when they are given the opportunity to observe relevant events. In one study, Howe compared the progress of 8 to 12-year-old children in understanding what influences motion down a slope. In order to figure out the role of conflict in group work, they created two kinds of groups according to a pre-test: one in which the children had dissimilar views, and a second in which the children had similar views. They found support for the idea that children in the groups with dissimilar views progressed more after their training sessions than those who had been placed in groups with similar views. However, they found no evidence to support the idea that the children worked out their new conceptions during their group discussions, because progress was not actually observed in a post-test immediately after the sessions of group work, but rather in a second test given around four weeks after the group work.

1．Which of the following statements is in line with Piaget’s hypothesis?

A．Teachers play a big role in learning by explaining difficult concepts.

B．Teaching should be consistent in order to easily acquire knowledge.

C．Children can help each other make cognitive progress.

D．Cognitive progress mainly relies on children’s own intellectual activity.

2．The lone learner’ route is an educational approach which ________.

A．was adopted during discovery learning early on

B．requires help from the pupils’ peers

C．relies on how the teacher guides the students heavily

D．played an important role in cognitive change

3．Which statement describes Howe’s experiment with 8 to 12-year-old children correctly?

A．The most active children made the least progress according to a pre-test.

B．The children were evaluated on their abilities to understand a physics phenomenon.

C．The teacher aided the children to understand a scientific problem in group work.

D．All the children were working in mixed-ability groups to work out new conceptions.

4．It can be inferred from the last paragraph ________.

A．that children acquire more when learning in groups

B．that children opposing each other would learn slower

C．that the children were given a total of three tests, at different times

D．that there can be a satisfying result thanks to the duration of test