Essays on Adaptivity and Flexibility in Multidigit Arithmetic

Publikation: Bog/antologi/rapport/Ph.d. afhandlingPh.d. afhandlingForskningpeer review

Abstract

This dissertation addresses the topic of adaptivity and flexibility in arithmetic strategies with multidigit numbers. The five chapters each contribute to answering different questions that together aim to extend our understanding and knowledge of adaptivity and flexibility in mathematics education, with a specific focus on arithmetic strategies in grade 3, 6 and 8.
In the first chapter, Tri-phase Flexibility Assessment (TriFA) is introduced as a measurement tool for students' use of different arithmetic strategies. Results show that most students in the grade 6 exhibit low levels or no adaptivity, meaning they rarely or never use the number related taskcharacteristics when solving multidigit addition, subtraction, and multiplication tasks. About half
of the students rarely or never solve problems using more than one arithmetic strategy, indicating low level or no flexibility. The TriFA is evaluated as a simple-to-use tool which can measure students' adaptivity and flexibility related to the task related characteristic (numbers and operations) in a known classroom setting.
In chapter two, results from the TriFA are compared across the three participating grade levels and operations. The results show that students in grade 6 exhibit significantly more adaptivity than students from both grade 3 and grade 8. The students in grade 6 show more flexibility than students in grade 3 but similar to students in the grade 8. At all grade levels, students exhibit the least adaptivity and flexibility in subtraction compared to addition and multiplication."
In chapter three, a specific focus is on the highest performing students, measured by accuracy in solved arithmetic tasks, referred to as experts. Individual characteristics that distinguish adaptive experts from routine experts are further examined. The results show that both groups are high achieving in mathematics, but adaptive experts perform about 0.5 standard deviation higher than routine experts do. The adaptive experts are also more flexible, meaning they can often find multiple strategies. There is also a significant difference between genders, where girls constitute a majority of the routine expert group, but boys constitute 75% of the group of adaptive experts.
In chapter four, there is a special focus on the lowest achieving students in grade 6 and their use of number-based strategies and standard algorithm. Results show that there is a clear relationship between the use of number-based methods as preferred strategies and students' achievement level, the higher achieving, the more frequent use of number-based strategies. At the same time, there is no relationship between achievement level and use of the standard algorithm. For the total group of all students, number-based strategies more often lead to correct answers than the standard algorithm. This difference is significant for all achievement levels except for the lowest performing students where there is no significant difference.
In chapter five, the influence of the teacher's adaptive beliefs in relation to teaching focus on developing flexibility/adaptivity in arithmetic is examined in more detail, with a special focus on the gender gap. The results show that the adaptive-oriented mathematics teacher affects the gender gap in the grade 3 in terms of both general mathematics achievement and adaptivity, by improving
the boys' results. In grade 6, the gender-gap in adaptivity also increases, in favor of the boys. The results do not show a significant effect of the teacher's beliefs in the grade 8.
OriginalsprogEngelsk
UdgivelsesstedAarhus
ForlagAarhus Universitet
Vol/bind2023-7
Antal sider206
StatusUdgivet - 26 apr. 2023
Udgivet eksterntJa

Emneord

  • Læring, pædagogik og undervisning
  • Arithmetic strategies
  • Flexibility
  • Mathematics

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