In support of efforts to foreground functions as central objects of study in algebra, this study provides evidence of how secondary students use trigonometric functions in contextual tasks. The author examined secondary students' work on a problem involving modeling the periodic motion of a Ferris wheel through the use of a visual programming environment. This study illustrates the range of prior knowledge and resources that students may draw on in their use of trigonometric functions as well as how the goals of students' work inform their reasoning about trigonometric functions.

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### Gloriana González and Anna F. DeJarnette

Students develop ownership and increase their understanding of mathematics when they are allowed to discuss alternative perspectives.

### Gloriana González and Anna F. DeJarnette

An open-ended problem about a circle illustrates how problem-based instruction can enable students to develop reasoning and sense-making skills.

### Anna F. DeJarnette and Gloriana González

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.

### Edited by Anna F. DeJarnette and Stephen Phelps

A monthly set of problems is aimed at a variety of ability levels.

### Edited by Anna F. DeJarnette and Stephen Phelps

A monthly set of problems is aimed at a variety of ability levels.

### Stephen Phelps

### Edited by Anna F. DeJarnette

A monthly set of problems is aimed at a variety of ability levels.

### Anna F. DeJarnette and Stephen Phelps

A monthly set of problems is aimed at a variety of ability levels.

### Edited by Anna F. DeJarnette and Stephen Phelps

A monthly set of problems is aimed at a variety of ability levels.

### Stephen Phelps

### Edited by Anna F. DeJarnette

A monthly set of problems is aimed at a variety of ability levels.