Given the prominence of group work in mathematics education policy and curricular materials, it is important to understand how students make sense of mathematics during group work. We applied techniques from Systemic Functional Linguistics to examine how students positioned themselves during group work on a novel task in Algebra II classes. We examined the patterns of positioning that students demonstrated during group work and how students' positioning moves related to the ways they established the resources, operations, and product of a task. Students who frequently repositioned themselves created opportunities for mathematical reasoning by attending to the resources and operations necessary for completing the task. The findings of this study suggest how students' positioning and mathematical reasoning are intertwined and jointly support collaborative learning through work on novel tasks.

### Anna F. DeJarnette and Gloriana González

### Sandra L. Laursen, Marja-Liisa Hassi, Marina Kogan, and Timothy J. Weston

Slow faculty uptake of research-based, student-centered teaching and learning approaches limits the advancement of U.S. undergraduate mathematics education. A study of inquiry-based learning (IBL) as implemented in over 100 course sections at 4 universities provides an example of such multicourse, multi-institution uptake. The study suggests the real-world promise of broad uptake of student-centered teaching methods that improve learning outcomes and, ultimately, student retention in college mathematics.

Have you ever noticed a gap between research and practice? How can research effect change in the classroom? The Connecting Research to Teaching department of Mathematics Teacher (MT) invites classroom teachers to explore research findings in relation to their practice. MT also invites education researchers to demonstrate how results from their studies shape classroom practice. Findings from collaborative action research projects are also encouraged. Evidence of connections from research to practice commonly includes student work and brief transcripts from interviews or classroom videos.

The Editorial Panel of Mathematics Teaching in the Middle School is seeking submissions for a department titled Informing Practice. The articles written for this section should entice and invite classroom teachers to learn about aspects of research that are closely related to their classroom practice.

### Peter Kloosterman and Tracey L. J. Warren

*Computer Aided Assessment of Mathematics* focuses on assessment in college mathematics courses with a special focus on computer-based assessment as a means of providing partial credit and immediate feedback on student work. Written by Chris Sangwin, a senior lecturer in mathematics at the University of Birmingham in the United Kingdom, the book is an important resource for mathematicians or software developers interested in understanding the promise and the pitfalls of using computers to assess student work in college courses. Each chapter of the book addresses a different issue so readers have the option of reading most of them out of order or selecting the chapters that are most valuable to them. Thus, in addition to describing Sangwin's perspectives on teaching and assessing mathematics, this review is designed to help readers decide which chapters in the book will be useful to them.

### Nerida F. Ellerton

Research journals like *JRME* play key roles through the publication of peerreviewed research, and it is through such publications that the field has the potential to grow. The metaphor of a growing tree is a useful one to explore in the context of mathematics education research. Growth in the natural world is generally multidimensional. A tree's growth is measured not only in terms of its height but also in terms of the girth of its trunk, the spread of its branches, and the development of a substantial root system, all of which are essential for the tree's continued growth and survival. Soil nutrients need to be replenished, and without sufficient moisture, growth is arrested, and the tree becomes stunted. Many of the most interesting natural landscapes include a range of tree species as well as supporting undergrowth.

### Patricia F. Campbell, Masako Nishio, Toni M. Smith, Lawrence M. Clark, Darcy L. Conant, Amber H. Rust, Jill Neumayer DePiper, Toya Jones Frank, Matthew J. Griffin, and Youyoung Choi

This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for teacher preparation and professional development programs.

### Katherine E. Lewis

Mathematical learning disability (MLD) research often conflates low achievement with disabilities and focuses exclusively on deficits of students with MLDs. In this study, the author adopts an alternative approach using a response-to-intervention MLD classification model to identify the resources students draw on rather than the skills they lack. Detailed diagnostic analyses of the sessions revealed that the students understood mathematical representations in atypical ways and that this directly contributed to the persistent difficulties they experienced. Implications for screening and remediation approaches are discussed.

## Informing Practice: A Hybrid Perspective on Functions

### research matters for teachers

### Eric Weber

Formal notions of function, which appear in middle school, are discussed in light of how teachers might complement the input-output notion with a covariation perspective.

### Anita A. Wager

This article describes how teachers in a professional development course responded to what they noticed about children's participation in elementary mathematics classrooms and how what they noticed was connected to the teachers' positionality toward equitable mathematics pedagogy. Findings suggest that a lens of participation supported teachers as they considered how to provide more equitable mathematics instruction. Further, the depth to which teachers noticed children's participation was connected to their positionality as equitable mathematics educators.