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In the context of national collaborative efforts to increase the prevalence of active learning strategies in undergraduate precalculus and calculus classrooms, we discuss the context, strategy, and processes used at one university to create change within a mathematics department. We highlight the use of a unified active learning approach and the importance of collaborative practices as leverage for departmental change. We conclude with lessons learned from the first year of implementation.

Policymakers and the public are increasingly asking educators to approach instruction from a STEM perspective, integrating science, technology, engineering, and mathematics to prepare students for future careers. At the same time, administrators are directing teachers to make learning more communal and student-driven, emulating the workforce students will likely enter. Often there is no specific training or support for the teachers who lead these STEM-oriented, collaborative classrooms. A 2013 report issued by the Chicago STEM Education Consortium noted that one fundamental challenge is the absence of a clear and common definition of STEM education (C-STEMEC, 2013). This article defines the the goal of the authors as building a cohort of K-8 teachers who can engage their students as mathematical and scientific thinkers. Two questions drove their work: (1) How to get teachers to collaborate around STEM education in a meaningful way; and (2) How to create a common understanding of what science and math integration looks like in the classroom? An Illinois State Board of Education Math and Science Partnership Program grant allowed the authors to explore these questions through a Practices in Mathematics and Science: Connections and Collaboration project.

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or that deepen during middle school tend to follow them throughout their academic careers. In addition, the longer that a student holds a mathematical misconception, the more difficult it is to correct. Therefore, it is imperative that teachers attempt to address these algebraic misconceptions while students are still in middle school. One tool commonly used to do such a task is the combination of worked examples and self-explanation prompts. This article will describe not only the benefits of using this strategy but also how it connects to the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010). It will also provide instruction on creating worked-example and self-explanation problem sets for students.

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the "activity of generating explanations to oneself" (Chi 2000, p. 164), especially "in attempt to make sense of new information" (p. 163) as one reads or studies. A "worked example problem," to be differentiated from "working an example problem," shows students an already completed problem and directs their attention to certain steps of the task as the focus of questioning. Self-explanation, then, specifically encourages students to identify the reasoning behind the steps that they see carried out and to explain why these steps were completed. This strategy of providing worked example problems coupled with prompts for self-explanation has recently been shown to influence students' learning positively in both traditional (Booth, Koedinger, and Paré-Blagoev 2011) and computer-based classrooms (Booth et al. 2013). A unique and powerful aspect of using worked examples in the classroom occurs with the inclusion of examples of both correct and incorrect solutions (subsequently referred to as correct and incorrect examples). Using incorrect examples forces students to think about the steps that have been carried out and the reasons why these actions are wrong and then to confront their own possible underlying misconceptions. The desired result is a deeper understanding of mathematics for all students, regardless of prior skill level. By using probing questions that require students to explain a previously worked example, teachers can ensure that students are making sense of what solving equations really entails. Students also engage in reasoning while constructing explanations and strengthen critical thinking skills while critiquing the correct or incorrect solutions. These tasks, carried out in conjunction with the Common Core State Standards, serve to promote deeper understanding of solving equations, which will help students of all ability levels prepare for higher-level mathematics. This article explores using examples in a computer-based activity, using examples in a traditional classroom, the student experience, and targeting student misconceptions.