Mathematics

We share here results from a quasi-experimental study that examines growth in students’ algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3–5.

The purpose of this study was to identify affordances and limitations of using order and value comparison tasks versus number placement tasks to infer students’ negative integer understanding and growth in understanding. Data came from an experiment with kindergarteners (N = 45) and first graders (N = 48), where the experimental group played a numerical linear board game and the other group did control activities, both involving negative integers.

In this chapter we discuss some of the affordances and constraints of using online teaching simulations to support reflection on specific pedagogical actions. We share data from a research project in which we implemented multiple iterations of a set of simulated teaching experiences in an elementary mathematics methods course. In each experience, preservice teachers contrasted the consequences of different pedagogical choices in response to a particular example of student thinking.

Professional learning experiences (PLEs) provide teachers with opportunities to improve their understanding of mathematics content and teaching practices. However, PLEs are often conducted in person and in small groups—hence costly and localized. The purpose of the current study was to explore different ways for teachers to engage in PLEs and how these approaches might enable the field to scale up these efforts in a sustainable manner.

Researchers have generated a powerful framework that identifies three aspects of noticing students’ mathematical thinking: attending to, interpreting, and deciding how to respond to student thinking. Previous research has tended to focus on evaluating how well teachers engaged in noticing, and how well they connected the different aspects of noticing. We describe a complementary way of studying the connections between different aspects of noticing, one that stresses the content of teachers noticing.

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.

Test scoring procedures should align with the intended uses and interpretations of test results. In this paper, we examine three test scoring procedures for an operational assessment of early numeracy, the Early Grade Mathematics Assessment (EGMA). Current test specifications call for subscores to be reported for each of the eight subtests on the EGMA. This test scoring procedures has been criticized as being difficult for stakeholders to use and interpret, thereby impacting the overall usefulness of the EGMA for informing decisions.