Assessing and Scoring Elementary Mathematical Writing: Research and Practice Considerations

Introduction

Assessing and scoring mathematical writing can provide educators with more insight into students’ thinking than what can be inferred from a simple answer to a mathematics problem. Examining mathematical writing allows teachers and researchers to go beyond determining whether students are correct or incorrect by analyzing the depth of students’ understanding. For instance, imagine students simply wrote “5.” There are numerous questions educators might have about this answer depending on the mathematical content and the kind of knowledge they seek to have students advance. If the answer was in response to an addition problem, did one student “see” two doubles in 4 to add efficiently and accurately 4 and 1, or did they realize that 5 is one more than 4? During a geometry unit, have they come to understand that the vertex of a concave angle in a hexagon is indeed a vertex even though it does not point outwards, or did they simply miscount the six vertices? Was the student able to convince the reader that the “5” represents five equal parts of a whole that would signify that they comprehend these two foundational concepts when first learning about fractions?

Not only does writing in mathematics allow teachers and researchers to gain a more comprehensive understanding of the depth of students’ knowledge, recent meta-analyses (Bicer et al., 2018; Graham et al., 2020) indicate that doing so advances students’ learning. Despite the benefits of having students write mathematically, this discourse practice is underutilized in many classrooms (Powell et al., 2021; Kosko, 2016). One reason for this is that only slightly more than half of teachers indicate that they know how to teach or assess mathematical writing (Powell et al., 2021). Some educators may not yet see the value of having students engage in mathematical writing if limited attempts resulted in some students noting “that they are correct for other nonmathematical reasons, such as ‘I tried it, and I was right’” (Lepak & Going, 2019, p. 300). Providing teachers and researchers with details about what to assess has the potential to nurture elementary students’ ability to communicate mathematically in writing and capitalize on the affordances of this discourse practice, as simply monitoring students’ progress in writing has been shown to lead to improved outcomes (Graham et al., 2011).

Various approaches have been utilized to assess students’ writing in mathematics. This includes informal assessments (Hauth et al., 2013; Lim & Pugalee, 2004; Norton & Rutledge, 2010) as well as formal measures (Hebert & Powell, 2016). The primary aim of this chapter is to describe four approaches to scoring elementary students’ mathematical writing that two of the authors investigated with other colleagues (Namkung et al., 2020). These approaches include (a) holistic rubrics to assess the overall quality of the explanation; (b) analytic rubrics to evaluate multiple dimensions of the mathematics writing construct (e.g., mathematics content, mathematics language, writing organization, and writing grammar); (c) elements scoring to determine the quality of genre-specific components of the writing; and (d) mathematics-writing sequences to examine correct use of syntactic and semantic structures when combining words, numbers, symbols, expressions, and equations within the connected text. Engaging in mathematical writing requires a combination of mathematics content knowledge, general writing skills (Namkung et al., 2020), and skills unique to the mathematics register that “refers to the forms of meaning and styles of communication characteristic to the mathematics disciplinary community” (Herbel-Eisenmann et al., 2013, p. 613). Whether educators wish to focus on assessing students’ mathematics understanding (e.g., teachers deciding if they need to provide more time for their class to comprehend the relationship between the numerator and denominator) or their ability to communicate about mathematics (e.g., researchers realizing students’ strengths and challenges in conveying precise ideas about fractions visually), mathematical writing attends to components that can be assessed and scored for both purposes.