Thinking Loft

Aug, 2011

In my years of teaching both preschoolers and P1 children, I have found that one of the most difficult topic to teach is teach children how to analyse questions such as “ 4 is ______ less than 7” or “8 is ______ more than 5".

I know many parents who are extremely frustrated with trying to help their young ones grasp the concepts behind such questions.  I have even seen circumstances whereby parents resorted to finding the various permutations which the questions could be asked and get their children to memorise whether it should be addition or subtraction based on how the questions are phrased. 

I agree with many parents that this type of questions do test a little of English comprehension besides Mathematics understanding.  However, I do feel that it is important to provide children with a simple visual model as a heuristic to help them tackle such questions. 

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May 29, 2011

This is a great game to help preschoolers develop an understanding of the composition of numbers and to help them remember number bonds.  It is also a great game to train up their speed of respond towards number bonds.  You can start playing this finger game with your child as soon as s/he could count the number of fingers s/he has.

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May 19, 2011

As adults, when we see 5 + 3 = ?, we understand that this is a symbolic representation of a problem and we know the answer “8” is a symbolic representation of the solution to the problem.  We do but children may not necessarily understand that.  This is also one reason that contributes to many young children struggling with solving mathematical word problem questions.

In a class that I took, I got two children to act out a scenario : one child was given 3 pencils.  A second child was asked to pass 5 pencils to the first child.  When I asked the children to think of a possible question a third child could ask in this scenario, I drew blanks from almost all of the children in the class.  But when I wrote down 3 + 5, almost all the children could very quickly shout out 8.  This short little excerpt from a class I took is a good demonstration of the technical strength of many Singaporean children in applying mathematics formula.  Most, by 6 years old could do complete arithmetic sums quickly and confidently.  However, when they are required to analyze and develop their own questions and solutions, they are at a loss.

Hence, as parents, we could help our children by playing a simple game with them. 

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May 15, 2011

Here’s a question I spotted from a primary one CA test paper :

Susan and Mary have 8 chocolate cookies altogether.  Mary has 4 more cookies than Susan.  How many chocolate cookies does Susan have?

When I showed this question to fellow parents, the most common reaction I get from these parents is perplexity at solving this without having to resort to algebra. 

“Isn’t this something we learn in secondary school?”  “How can a seven year-old work out a problem sum like this?” were among some common complaints.

Well, in fact, I have proven that even 5 years old can solve problem sums like this if they have been given the right tools and foundation in learning.  In my years of studying and learning about early childhood teaching (I’m still learning every day), I have been heavily influenced by Lev Vygotsky, the revolutionary Russian thinker whose study on developmental psychology inspired generations of educationists.  It is through the study of Vygotsky’s theories and the under the mentorship of Galina Dolya, a Russian educationist currently based in UK, that helped me understand that the first step towards teaching mathematics is to help children first develop their understanding of mathematical relationships.  In other words, before we even teach children to count, we teach them algebra – mathematical relationships.

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