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Mathematics appears to be almost entirely neglected in early childhood learning. As both a mathematics teacher and father home-schooling his four-year-old daughter, I am particularly focused on teaching mathematical reasoning.

Consistent with the conclusions of Ginsburg et al, my daughter had a very natural grasp of number, operations, shape, space, measurement, and pattern from the time we began (age two). Imitation and rote were clearly the more natural mechanisms of learning at that age, as they remain now. And, as was discussed in another post, mathematical logic did not appear until she was approaching four years old. Now, her logic is limited more by her ability (or otherwise) to focus, and to organise her thoughts.

A lot of data exist relating age with typical cognitive abilities, but these are necessarily influenced by our collective culture of education. Has any rigorous research been done to determine when particular cognitive abilities can be developed, for example deductive as opposed to inductive reasoning? For early childhood development, can educators know what is possible or (generally/typically) impossible to teach at a certain age, or what is appropriate or inappropriate?

Thank you.

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A study (1) found that while 10% of 6-year old children used the conditional proficiently, 50% of 8-year old children not only could use it proficiently but also understood what the conditional meant. The conditional is one of the two basic verbal forms we use for expressing a logical reasoning, together with syllogisms.

It should be noted, however, that most of the time, most people don't bother articulating reasons, even when it seems that they must have reasons so say what they say.

Aristotle already discussed extensively enthymemes, i.e., implicit reasoning where part of the reasoning is clearly missing, although usually easily retrievable. The speaker may for example state one premise, leaving the audience to guess the conclusion from both the stated premise and the context of the conversation. Guessing is also usually performed intuitively, the brain somehow processing the relevant data without any conscious effort on the part of the listener.

Given this, it is debatable whether reasoning starts with verbal communication. It may come before language. However, if you define reasoning as verbally articulating reasons, then reasoning starts at least potentially around 6-8 years of age in a majority of children.


(1) Julia R. Badger, University of Oxford, and Jane Mellanby, University of Oxford, Producing and understanding conditionals: When does it happen and why does it matter? -- Journal of Child Language Acquisition and Development, Vol 6, Issue 1 21-41 (March 2018)

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  • $\begingroup$ Thank you for such an insightful reply! By extension, the research would suggest that half of eight-year-olds (third-graders) can not use a conditional proficiently, and/or do not know what it means. As an educator, that has interesting implications as to what and how we should be teaching at primary level. $\endgroup$
    – POD
    Jul 2 at 21:42
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    $\begingroup$ @POD "can not use" Maybe they could. Some kids learn faster, other may be a bit slow for all sorts of reasons. I added the reference of the study. Maybe you'll find some relevant information in it. I think it is not the only one on this topic. $\endgroup$ Jul 3 at 10:22

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