A Worked Example for Creating Worked Examples

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 (Star and Rittle-Johnson 2009). Unfortunately, algebraic misconceptions that students may form or that deepen during middle school tend to follow them throughout their academic careers (Cangelosi et al. 2013). In addition, the longer that a student holds a mathematical misconception, the more difficult it is to correct (Kilpatrick, Swafford, and Findell 2009). Therefore, it is imperative that we, as teachers, attempt to address these algebraic misconceptions while our 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 (see fig. 1) (Aleven and Koedinger 2002). 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 your own students.