Diagnostic assessment in third-grade subtraction: the relation between bridging errors, number of errors and mathematical ability

ABSTRACT

Learning to solve subtraction problems that require borrowing (e.g., 83–57=) is challenging, and these problems often cause ‘bridging’ errors, such as the smaller-from-larger error. This study explores how bridging errors in subtraction are related to students’ mathematical ability. The study involved 694 third-grade students and 35 teachers from 25 Dutch schools. Multilevel regression analyses showed that the number of bridging errors was positively related to the students’ mathematical ability, after controlling for the total number of errors in subtraction. Thus, the 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. This result implies that diagnosing bridging errors may help to identify where students’ stand within their mathematical development. The practical implications of this result for the design of diagnostic instruments are addressed in the discussion section.

KEYWORDS:

• Diagnostic assessment
• formative assessment
• subtraction errors
• subtraction
• decomposition strategy
• primary school mathematics

Acknowledgments

We are very grateful for all the work that was done by research assistants Marjolein Nieuwenhuizen and Patricia Gillet especially regarding the organisation of the data collection and data entry.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The initial sample included 757 students, 36 teachers, and 26 schools. After removing cases with missing E3scores, 708 cases, 35 teachers, and 25 schools remained. In a final selection, cases with three or more missing values on the DI were also excluded from the analysis. This resulted in a final sample of 694 students.

2. Students could make errors in bridging the tens (3 types of BE), in bridging the hundreds (3 types of BE), or every possible combination of BE in the tens and hundreds (3 x 3 = 9). So, for items types 3 and 4 there are 15 possible BE: 3 + 3 + 9 = 15. Item 1000 – 540 = is an exception because some of the BE types lead to the same answer.

3. In total, there were 25 schools, of which there were six with two classes and two with three classes.

Additional information

Funding

This work was supported by the Netherlands Organisation for Scientific Research (NWO) under Grant [MaGW/PROO: Project 411-10-750].

Notes on contributors

Jorine A. Vermeulen

Jorine A. Vermeulen, Faculty of Education and Innovation, Teacher Training in Primary Education, Inholland University of Applied Sciences, Rotterdam, Netherlands; Anton Béguin, Cito Institute for Educational Measurement; Floor Scheltens, Cito Institute for Educational Measurement; Theo J. H. M. Eggen, Cito Institute for Educational Measurement and University of Twente, Faculty of Behavioural Science, Department of Research Methodology, Measurement, and Data-Analysis.