Research in mathematics education has shown that mathematics assessments have become highly consequential for students, teachers, and educational institutions (Hamilton, Stecher, & Yuan, 2012; Swan & Burkhardt; 2012). Even so, traditional assessment methods are often lagging behind reform curriculum design and advancements in instructional methods (Shepard, 2000). One advancement in instructional practices is the promotion of mathematical habits of mind in mathematics classrooms as evidenced by various standards documents and seminal works (CCSSI, 2010; NCTM, 2000; 2014; NRC, 2001; Seeley, 2014). My study focused specifically on one aspect of the Standards for Mathematical Practice, SMP3b, “critique the reasoning of others” (CCSSI, 2010, p. 6).Extending the work of curriculum researchers studying the use of student work embedded in textbook tasks (Gilbertson et al., 2016; Going, Ray, & Edson, in preparation), tasks provided in the student textbook for classwork or homework, I explored the use of student work embedded in curriculum-based assessment tasks, tasks included in curriculum-designated assessment materials. Because curriculum-based assessments can be highly influential on the mathematics promoted in classrooms (Hunsader et al., 2013; 2014), it is important to consider what kinds of opportunities students have to make sense of, or critique, someone else’s mathematical thinking on assessment tasks and how these opportunities compare to tasks in student textbooks.The purpose of this study was to explore whether or not student work embedded in assessment tasks can be used as a mechanism for assessing SMP3b. I gathered data from text analyses of curriculum-based assessment materials from five seventh-grade, CCSSM-aligned curriculum series, interviews with students (n=6), and interviews with teachers (n=6). Using these data sources, I investigated (1) the prevalence and nature of student work assessment tasks (SWAT) as compared to student work textbook tasks (SWTT), (2) students’ experiences with SWAT, and (3) teachers’ perspectives on SWAT and students’ written work on SWAT.My text analyses findings revealed substantial differences between students’ opportunities to make sense of someone else’s mathematical thinking on curriculum-based assessments as compared to the student textbooks, reinforcing Shepard’s (2000) observations about assessment methods often lag behind instructional methods. Also, not surprisingly, my analyses of students’ written and verbal work on assessment tasks showed that students often verbally communicated more of their mathematical thinking than they included in their written responses. Even so, there were interesting differences between the types of evidence of thinking students tended to omit from their written work for SWAT and non-SWAT. Students also provided thoughtful perspectives on characteristics of SWAT as compared to non-SWAT.My analyses of teacher interviews revealed that, while student work embedded in curriculum-based assessment tasks may provide students the potential to engage in SMP3b, more assessment task design work is needed to (1) determine the types and extent of thinking students should provide on written assessment tasks to demonstrate SMP3b and (2) decide how these requirements can be explicitly communicated to students on written assessment tasks in order for students to successfully demonstrate what they know. These results suggest a need for additional attention on the design of tasks for assessing mathematical practices and other habits of mind as well as critical thinking about whether or not written assessments are the most conducive assessment formats for assessing practices which are described as dynamic processes.
Read
