Primary School Mathematics

Prognosis of Failure in School Math

It is obvious that for success in school mathematics it is necessary to master elementary mental computational skills at first - addition and subtraction within the limits of 20, multiplication and division within the limits of 100. Just those very pupils have considerable difficulties while learning the other basic topics of arithmetic and algebra. The sample includes 403 pupils. Standard tables including 64 elementary operations in addition, subtraction, multiplication and division were used for determination of the level of the skills. You can see specimens of the tables at my site Prevention of Failure in School Mathematics (Improvement of Elementary Computational Skills, Tables).

The pupils completed the tables in written form. 1) Pupils completed the tables quickly and made not more than 3 mistakes.

2) Pupils completed the tables significantly slower than the pupils from the first group but made not more than 1 mistake.

3) Pupils completed the tables at middle pace and made 3-6 mistakes.

Statistical analysis of the parameters of the first groups (separately for addition, subtraction, multiplication and division) confirmed (significance at 5% level) their internal uniformity: distribution in time is normal, and distribution in errors submits to Poisson's law. In different cases these groups included from 50% to 70% of corresponding samples. It means that results of testing of the skills may be used for prognosis of failure in school mathematics.

It is evident that the population of pupils with satisfactory skills may be represented only by the pupils from the first group.
The limit values were calculated for the standard tables including 64 similar elementary operations. For final-year pupils of primary school (the multiplication table had been completely learnt a year and a half ago) the next limit values had been obtained:

This level of elementary mental computational skills is a good means for determination of pupil's preparedness for successful studies. The limit values of the considered parameters define the first threshold of school math's learning ability. It must be noted in conclusion that the level of elementary mental computational skills of actively working pupils only do not decreases in due course. Taking part in a mathematics competition allows students to sharpen their problem solving skills and serves to generate interest for mathematics amongst them. The Asia Pacific Mathematical Olympiad for Primary Schools 2009 (APMOPS 2009) is organised annually in April -May by the Hwa Chong Institution-Aphelion Consortium. The contest held in Singapore is commonly known as Singapore Mathematical Olympiad for Primary Schools (SMOPS).

Awards for SMOPS
Students compete for the following awards in the SMOPS.

1) Top 10 individual prizes, awarded to the top 10 scorers.
2) 3 Honourable Mention Team Awards and 5 Honourable Mention Individual Awards.
3) Top 3 school awards, given to the three schools with the highest combined score of its top three students.

APMOPS 2009
During APMOPS, students get the opportunity to interact with other mathematically talented students from the various countries. Format of the APMOPS Contest
The APMOPS contest challenges students to complete six questions within two hours.
No mathematical tables or calculators are allowed for the contest. National Mathematical Olympiad of Singapore (NMOS)
The NMOS is a competition organised by the NUS High School of Mathematics and Science. This competition is designed to spur interest amongst students for mathematics. Various awards are given to students who managed to achieve quality scores in competition. American Mathematics Contest 8(AMC 8)
The American Mathematics Contest 8 is the first of a series of mathematics competitions organised by the Mathematical Association of America and is administered by Maths Oasis Pte Ltd in Singapore. This International competition welcomes students who are interested in mathematics and enrolled in grades 8 or Secondary 2 and below to participate.

Students get to challenge themselves with mathematics that is beyond what they usually encounter in school and they can experience a wide spectrum of topics available in Middle School Mathematics. Recent studies show that the skills of pupils are getting worse and worse. In one of the study, tested 106 Final year students of primary school? in mental addition and subtraction (within the limits of 20), multiplication and division (within the limits of 100). Standard tables including 64 elementary operations on addition, subtraction, multiplication and division were used for determination of the level of the skills.

The results turned out worrying: 52% of the sample has failed in addition and subtraction; 75% of the sample has failed in multiplication and division. The learning activities put more emphasis towards better grades, and so students try to minimize their chances of error.