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. 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

Effects of early multilingualism on child development and implications for primary education

Linguistic diversity of the student population has been identified as one of the urgent challenges that educators of the 21st century need to respond to. As classrooms become linguistically and culturally richer, there is an evident need for increasing teacher awareness on the issues of multiculturalism and linguistic diversity. Being brought-up in a multilingual environment inevitably impacts a child’s linguistic, cognitive and socio-cultural development. Educators need to better understand the unique developmental trajectory of multilingual children to be able to leverage their strengths for academic success. This study investigates the effects of early multilingualism on different aspects of child development and examines the implications these effects have for primary education settings. A list of recommendations has been summarized towards providing higher quality and more equitable education for the linguistically diverse children. Fostering equity education for multilingual children is a step further towards our global mission of educating the full range of children to become citizens not only of their linguistic and cultural groups, but of the world at large

Designing an activity-based costing system for a specialty retail store

This study designs an activity-based costing (ABC) system for a retail store specializing in one single product line and examines the suitability of ABC for such a context. This is of interest since traditionally ABC has been believed to have high-potential applications in business contexts where product diversity is high. The underlying assumption is that when product diversity is low, traditional costing systems manage to allocate costs accurately. A prescription glasses retailer serves as a research site for this study. Eyeglasses retailers have been considered in prior research to best represent businesses that offer one single type of goods. A contingency framework is used to preliminary assess the suitability of ABC for the studied company. Then an activity-based costing system is designed for the firm using a step-by-step approach. At the end ABC product costing is compared to current product costing obtained from traditional methods to compare and analyze the differences. The study finds that the existing traditional costing system produces inaccurate product costs despite the low product diversity in the company. ABC information proves to be more accurate and more useful for customer profitability analysis, and decision-making in product pricing and capacity planning. These results entail that the relation between product-diversity and ABC adaption should be revisited. This case study might give useful insights on contingent factors that have a higher enabling potential for ABC compared to product diversity, such as cost structure