Classroom Practice

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Ambiguity is a natural part of communication in a mathematics classroom. In this paper, a particular subset of ambiguity is characterized as clarifiable. Clarifiable ambiguity in classroom mathematics discourse is common, frequently goes unaddressed, and unnecessarily hinders in-the-moment communication because it likely could be made more clear in a relatively straightforward way if it were attended to. We argue for deliberate attention to clarifiable ambiguity as a critical aspect of attending to meaning and as a necessary precursor to productive use of student mathematical thinking.

Think alouds are valuable tools for academicians, test developers, and practitioners as they provide a unique window into a respondent’s thinking during an assessment. The purpose of this special issue is to highlight novel ways to use think alouds as a means to gather evidence about respondents’ thinking. An intended outcome from this special issue is that readers may better understand think alouds and feel better equipped to use them in practical and research settings.

Response process validity evidence provides a window into a respondent’s cognitive processing. The purpose of this study is to describe a new data collection tool called a whole-class think aloud (WCTA). This work is performed as part of test development for a series of problem-solving measures to be used in elementary and middle grades. Data from third-grade students were collected in a 1–1 think-aloud setting and compared to data from similar students as part of WCTAs. Findings indicated that students performed similarly on the items when the two think-aloud settings were compared.

Response process validity evidence provides a window into a respondent’s cognitive processing. The purpose of this study is to describe a new data collection tool called a whole-class think aloud (WCTA). This work is performed as part of test development for a series of problem-solving measures to be used in elementary and middle grades. Data from third-grade students were collected in a 1–1 think-aloud setting and compared to data from similar students as part of WCTAs. Findings indicated that students performed similarly on the items when the two think-aloud settings were compared.

Learning goals differ from performance goals. We elaborate on their function and importance as the guiding force behind maintaining cognitive rigor during mathematics learning.

Hunt, J. & Stein, M. K. (2020). Constructing goals for student learning through conversation. Mathematics Teacher: Learning and Teaching PK-12, 113(11), 904-909.

One of the most relentless areas of difficulty in mathematics for children with learning disabilities (LDs) and difficulties is fractions. We report the development and initial testing of an intervention designed to increase access to and advancement in conceptual understanding. Our asset-based theory of change—a tested and confirmed learning trajectory of fraction concepts of students with LDs grounded in student-centered instruction—served as the basis for our multistage scientific design process.