Stage-Sensitive (ZPD-Correlated) Assessment of Mathematical Reasoning: A Written Proxy for Interviewing

Examine an innovative, written assessment to infer a ZPD-correlated stage in students’ multiplicative reasoning as a proxy for labor- and time-intensive cognitive interviews.


The purpose of this session is to share the recent development, validation, and use of a written assessment geared toward replacing labor- and time-intensive (cognitive) interviews as a means to obtain evidence of students’ mathematical reasoning. Specifically, Ron Tzur first depicts the provisional stage (called participatory), which correlates with Vygotsky’s ZPD, and what it entails for assessment of students’ mathematics. Using examples from a two-part assessment of multiplicative reasoning, he shares key challenges his project’s team faced in developing, validating, conducting, and analyzing data from this assessment—and how the team addressed those challenges. Working in groups of two or three), participants then engage in creating their own examples of a participatory stage of a chosen STEM concept and the word problems they may use to assess it. A whole-group discussion follows in which participants share their examples and Tzur provides feedback to further everyone’s learning. Finally, and time pending, Tzur presents highly encouraging preliminary results measured by his project’s new assessment to study the impact that a professional development program for upper-elementary teachers had on their students’ learning and outcomes (urban, low SES, largely of racial/ethnic minority). The pros of this written assessment include efficiently obtaining concept- (and stage-) sensitive evidence of students’ mathematical reasoning and, thus, tailoring instruction to this reasoning; the cons include plausible loss of richness of data obtained through interviewing (which, of course, could complement the written assessment).