An investigation of patterns in the sequence and emphasis of mathematical topics in the times data

Data from the 1995 Third International Mathematics and Science Study (TIMSS) were analyzed to determine if patterns exist in the sequence and emphasis of mathematics topics in K--8 grade curricula. 34 of the countries participating in TIMSS, the first large-scale international study undertaken to provide a comparative international assessment of educational achievement in mathematics and science, were subdivided into three tiers according to achievement. Precedence and emphasis matrices were constructed for each country in each tier and analysis of these matrices was carried out. The results of the data analysis suggest that there is no great difference in the sequence of the 43 TIMSS mathematics content topics across the top tier, the middle tier, and the bottom tier countries in K--8 grade curricula. The analysis of the data leads one to conclude that the top tier countries are more homogeneous in the sequencing of the 43 content topics as well as the 17 pivotal topics into their K--8 grade mathematics curriculum than are the countries in the other two tiers. It appears that the bottom tier countries are the least homogeneous in doing this. The analysis of the data leads one to conclude that in the top tier countries it is at age 12 that most topics are emphasized while most topics in the middle and bottom tier countries are emphasized at age 13. On average, the most emphasized topic in the top tier countries is topic 121 (measurement units), the topic being emphasized 3.7 times. In the middle tier countries the most emphasized topic is topic 1112 (whole number operations), this topic being emphasized 3.3125 times and in the bottom tier countries, the most emphasized topic is topic 121, this being emphasized 4.75 times