Powers of the Universe: Empowering Primary School Students with the Powers of Ten Notation

Abstract In the modern era, extreme numbers, both large and small, have become increasingly important to our lives as public discourse comes to include terms like terahertz, nanometres, gigawatts, billions of light years or trillions of dollars. This paper describes three classroom trials with the learning sequence ‘Powers of the Universe’. It aims to explore how children respond to early introduction of arithmetic with extreme numbers (large and small) using powers-of-ten (logarithmic) notation. Typically, students are introduced to extreme numbers through a linear number line, often during the later years of schooling. In the trials, we taught students with a logarithmic number line. Each trial had a six-hour series of lessons, based on activities and group learning. Altogether, 66 students aged 7–13. years took part. In the lessons, students were asked to solve realistic problems in which they had to estimate, compare and calculate extreme numbers. Students’ knowledge of the concepts Doubling, Exponentiation, Halving, Estimation, Notation and Multiplication with powers of ten was assessed before and after the trials. The concepts, Logarithmic thinking and Proportionality, were also assessed after the trials. The data revealed that in Trial 1 a majority of 70 percent of the students demonstrated mastery of the key concepts, in Trial 2 and 3 a majority of respectively 84 percent and 90 percent of the students mastered the concepts. Statistical analysis showed that in all three trials the percentage of students who reached mastery was not below the expected proportion of 75%. There was no difference in mastery between students in 7 to 9 age range compared to students in the 10 to 13 age range. The study seems to indicate that primary school students of different age ranges can learn to calculate with powers of ten. Further research involving control groups, randomised sampling, and long-term effect investigation is needed to determine whether teaching powers of ten using the logarithmic number line is more effective than using the linear number line.