Finnish fourth graders’ number sense and related misconceptions in mathematics learning:a study of pupils’ performance in judging the reasonableness of computational results and their reasoning strategies

Abstract

Abstract. Number sense, broadly defined as a general understanding of numbers and mathematical operations, is developed through instruction from an innate primitive ability to grasp quantity changes, into complex skills to engage with complex algorithms. The paramount importance of number sense in mathematics learning has been emphasized worldwide in mathematics education research and curricula setting since the 1980’s. One of the main identified components of number sense is the learner’s ability to judge the reasonableness of computational results. This ability is also emphasized in the recent Finnish National Core Curriculum for Basic Education 2014. The aim of this research was to investigate Finnish fourth graders’ number sense and related misconceptions they reveal in their mathematics learning. The study measured the performance of 90 fourth graders from a school in Northern Finland in judging the reasonableness of computational results and analyzed the solution strategies pupils employed when answering the questions. A web-based two-tier diagnostic test was used for such a purpose. The test was based on instruments used in similar research internationally and it was adapted in line with the curriculum and learning materials used locally. Results revealed that the study participants perform less well in identifying reasonable and meaningful answers to mathematical problems, compared to how they perform in typical pen-and-paper mathematical calculations. The average correct answer rate for all the ten questions of the test was 57%. These findings are in line with prior research, which has found pupils’ number sense ability to lag behind their mechanical computational skills. In 28% of the cases sampled pupils revealed various mathematics misconceptions due to incorrect modelling, non-mathematical prototypes, overgeneralizing of knowledge, or challenges in linking mathematical process-object linking. This thesis provides an in-depth analysis of pupils’ answers and their captured reasoning, drawing on the theoretical concepts of number sense and misconceptions in mathematics, as well as findings reported in related prior research. Several implications for developers of learning materials and teachers are discussed and a list of recommendations for further research is provided. The study adds to the international mathematics education research on number sense and contributes to the Finnish national discussion on improving curricula and instruction for higher mathematics proficiency among all learners