sarju82

Sara Julsgård

PhD student

I am interested in how the concept of logarithm is introduced in upper secondary school mathematics teaching, taking into account both mathematical and didactic aspects.

Studying the teaching of logarithms in upper secondary school

Logarithms often pose challenges for students due to their complex nature and varied representations. My research focuses on how logarithms are taught and understood in secondary education.

Since its 17th-century origin, logarithms have significantly advanced fields like astronomy, engineering, and medicine. Their power lies in connecting arithmetic and geometric patterns, transforming products into sums and quotients into differences. They are non-trivial mathematical objects, represented by a notation (logab) which does not reveal any intrinsic properties, i.e. what happens within the function to the input b. They often pose challenges for students, as reflected in errors and misconceptions.

The logarithm can be defined and introduced in various ways: as a function, an inverse, an area, a tool to simplify expressions, an exponent, to name a few. Mathematically, all these definitions lead to the same theorems and applications. However, when teaching about the logarithm, the instructor usually picks one representation to begin with, that is, one answer to “What is the logarithm?”, whereafter others may be added and explained. The question is, which way of presenting the logarithm do teachers choose? Are there motivations for and reflections of this choice? How does the chosen representation influence the narrative taught, and does it impact learning?

In my dissertation, I will explore how logarithms are taught, focusing on the definitions given and how the narrative evolves, including connections to other mathematical topics.

Teaching

Teaching future mathematics teachers

I teach students enrolled in teacher education aimed at primary as well as secondary school.

In the primary school teacher program I teach mathematics, more specifically arithmetic and algebra. The course provides an opportunity for in-depth study of basic mathematical ideas and the key features that need to be made visible throughout the school system’s mathematics teaching, starting in the preschool class.

In the secondary school teacher program, I teach didactics of mathematics, in courses where students are (initially) introduced to and (later) deepen their understanding of the teaching and learning of mathematics.

CV

Academic Degrees

  • 2022 – Bachelor of Science in Biology
  • 2023 – Secondary School Teacher Programme with a specialization in Teaching in Mathematics and Biology

Assignments

2024 – present: PhD student representative (deputy), Board of the Faculty of Educational Sciences

Current teaching

  • Mathematics 1 for the Primary School Teacher Programme with a specialisation in Teaching in Early Years Classes and Grades 1-3 of the Compulsory School 
    Course 972G10
  • Mathematics: Mathematics Education 1 for
    - Secondary School Teacher Programme - Grades 7-9 of the Compulsory School, Subject Mathematics
    - Secondary School Teacher Programme - Upper-Secondary, School Subject Mathematics
    Course 91/92MA16
  • Mathematics: Mathematics Education 2 for
    - Secondary School Teacher Programme - Grades 7-9 of the Compulsory School, Subject Mathematics
    - Secondary School Teacher Programme - Upper-Secondary, School Subject Mathematics
    Course 91/92MA33

Organisation