Error analysis is the process of analyzing student work to determine why students solved a problem incorrectly (Ashlock, 2010). Many errors can easily be detected—for example, regrouping ones instead of tens or adding denominators rather than finding common denominators. Other errors that are specific to an individual student’s understanding of a process are more difficult to identify. Even more confusing, some errors lead to the correct answer, and, in turn, students develop misconceptions. These errors require more careful examination, and often, students need to explain their thinking before the errors can be identified. Developing a step-by-step task analysis for some skills may help the instructor identify where in the process a student is having difficulty. Once errors have been identified, instructors should quickly address them so that the student does not continue to practice incorrectly, and educators should adjust their instruction to facilitate student understanding (Archer & Hughes, 2011; Stein et al., 2005).
(National Center on Intensive Instruction, 2016)
The following text is adapted from: Herholdt, Roelien, & Sapire, Ingrid. (2014). An error analysis in the early grades mathematics – A learning opportunity?. South African Journal of Childhood Education, 4(1), 43-60. Retrieved September 13, 2019, from. CC-BY
Error analysis, also referred to as error pattern analysis, is the study of errors in learners’ work with a view to finding explanations for these reasoning errors. This multifaceted activity can be traced back to the work of Radatz in 1979. Not all errors can be attributed to reasoning faults; some are simply careless errors (Yang, Sherman & Murdick 2011), identified as “slips” (Olivier 1996:3), which can easily be corrected if the faulty process is pointed out to the learner. Slips are random errors in declarative or procedural knowledge, which do not indicate systematic misconceptions or conceptual problems (Ketterlin-Geller & Yovanoff 2009). Error analysis is concerned with the pervasive errors (or ‘bugs’) which learners make, based on their lack of conceptual or procedural understanding (Ketterlin-Geller & Yovanoff 2009). These authors explain that such mathematical errors occur when someone who makes this type of error believes that what has been done is correct – thus indicating faulty reasoning. Such errors are systematic (Allsopp, Kuger & Lovitt 2007) and persistent and occur across a range of school contexts (Nesher 1987). Yang et al (2011) point out that systematic errors might be the result of the use of algorithms that lead to incorrect answers or the use of procedures that have not been fully understood.
Error analysis, however, does not just involve analysis of learners’ correct, partially correct and incorrect steps towards finding a solution, but also implies the study of best practices for remediation (McGuire 2013). This would require of the teacher a good knowledge of mathematical content, as well as a good grasp of learners’ levels of mathematical understanding (McGuire 2013). McGuire (2013) argues that the ability of teachers to remediate common learner errors and misconceptions underlies Shulman’s (1986) definition of pedagogical content knowledge. Hill, Ball and Schilling (2008) further includes the ability to anticipate learner errors and misconceptions in their understanding of pedagogical content knowledge. Hill et al’s (2008) explains that activities such as error analysis, which require pedagogical content knowledge, involve more than just pedagogy; they involve a well-grounded understanding of the learner and how a learner learns.
Resource on Error Analysis in Mathematics instruction