Targeted teaching works!

The case studies and descriptions of misconceptions about decimal notation show that there are many difficulties that students encounter when trying to understand decimals. Decimals are sometimes thought to be easier than fractions, because the operations are closer to the whole number operations and therefore easier. However, as the research data shows, understanding of decimals is too often missing.

This need not be the case. The substantial variations from class to class, school to school and country to country in levels of expertise in decimal understanding show that good teaching will pay dividends.

Here is a brief report of one of our experiments.

We identified four schools where the Year 5 and 6 children had low achievement on our decimal comparison test, over several years.

We invited them to undertake a one-hour professional development activity on this topic, to demonstrate LAB and some targeted lesson plans, similar to those on this CD.

Three schools were too busy - we know this feeling! One school with four Year 5 and 6 teachers took up our offer and attended the short in-service activity and received sets of LAB and booklets.

All the Year 5 and 6 students were tested on the Decimal Comparison Test in June. Their results were reasonably consistent with previous results from the school.

The teachers of two classes were too busy with other topics to do any work on decimals over the next four months.

One teacher used LAB and some other lesson ideas on three or four occasions in August. The other teacher used it on one occasion.

At the end of October, long after the teaching, we retested all the students.

In the classes which had done no work on decimals, there was no change - the students' ideas were unchanged.

In the 2 classes which had done some work on decimals, about one half of the children who had a misconception moved to expertise and all the experts stayed as experts. (The others obviously need further help.)

Just a little bit of targeted teaching can make a difference!
This experiment is reported in the article by Helme, S. & Stacey, K. (2000).

Other researchers have also found that targeted teaching works. Peled and Shahbari (2003) tested 261 students in 7th and 8th Grade in Israel and found that 59 (23%) were denominator focussed. Of these, 46 (78%) were unable to correctly compare common fractions. After a 3-session intervention which focussed on co-ordinating the number of parts and the size of the parts in common fractions, they found a significant improvement in the ability of these students to not only compare common fractions but also to compare decimals.