# The relationship between opportunities to learn algebra and students’ algebra achievement

A comparative study

The article provides a report on the comparison of Opportunities to Learn algebra and eighth grade students’ algebra achievement in three countries: Botswana, Singapore and the United States. The study used student and teacher data from the Trends in International Mathematics and Science Study (2011 and 2015). By using a multilevel regression analysis, the study presents the models within the three countries of the relationships between Opportunities to Learn algebra and eighth-grade students’ algebra achievement of the recent TIMSS cycle. The findings indicate that the Opportunities to Learn algebra are context specific and align with the expectations of the curriculum guides from the governing bodies within the countries. Also, the study shows that students who learned particular algebra topics in the early grades had significantly higher algebra scores in the TIMSS 2015 assessment. In particular, students who had been taught properties of functions and simplifying and evaluating algebraic expressions before eighth grade in the United States had significantly higher scores. Also, Singaporean students who had been taught simple linear equations and inequalities and simultaneous equations had higher algebra scores. Implications for policy and research are discussed.