Diagnostic mathematics assessment in the third grade

Jorine Adinda Vermeulen

Research output: ThesisPhD Thesis - Research UT, graduation UT

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This dissertation provides knowledge that can be used to educate teachers how to analyse students’ response behaviour on the ENL and how to diagnose and remediate bridging errors. The focus was on studying students’ written response behaviour and associated mathematical thinking in third grade subtraction and addition. In Chapters 2, 3, and 4 the diagnostic value of response behaviour captured with the empty number line (ENL) was evaluated. Diagnosing students’ bridging errors in subtraction was the focus of Chapters 5 and 6. The studies in this dissertation contributed to the following research questions:
1. What kind of response behaviour is considered diagnostically relevant for formative decision making in third grade mathematics?
2. What features should diagnostic tasks have to obtain response behaviour that is considered relevant for teachers’ formative decision making in third grade mathematics?
A diagnostic framework for multi-digit subtraction with the ENL was developed. The ENL is particularly effective for diagnosing self-regulatory errors (Chapter 2). Moreover, students’ response behaviour on the ENL is affected by tablet technology (Chapter 3) and their task beliefs about the ENL (Chapter 4). Furthermore, it was found that the number of digits (n) in the subtrahend and minuend influenced the diagnostic capacity of the items. Items from the category 3/4n-3n, like 1000-680, had the highest diagnostic capacity, whereas items characterized as 3/4n-2n, such as 1000-20, had the lowest diagnostic capacity (Chapter 5). Finally, it was found that students who had a high proportion of bridging errors within the total number of errors, had a relatively higher mathematical ability compared to the students who had a low proportion of bridging errors (Chapter 6). In conclusion, diagnostic tasks are not suitable for every student. What diagnostic task should be used, depends on the gap between students’ observed and intended learning. Pre-service teacher training should focus on more general knowledge about what task and student characteristics could affect students’ response behaviour and what tasks are suitable for assessing students’ mathematical thinking.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Twente
  • Eggen, Theo J.H.M., Supervisor
  • Beguin, A., Co-Supervisor
Award date6 Oct 2021
Place of PublicationEnschede
Print ISBNs978-90-365-5229-5
Publication statusPublished - 6 Oct 2021


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