Extensive evidence points to the need for mathematics instruction to tap into students’ informal understandings in order to conceptually develop formal mathematical ideas (Ahl, Moore, & Dixon, 1992; Freudenthal, 1973, 1991; Treffers, 1987). Contextual problems are a common means of helping students access their informal mathematical ideas (Lamon, 1993; Moore & Carlson, 2012). However, to successfully use context in this manner, we must ensure these problems are accessible to students and have the potential to promote connections to deeper or more formal mathematics (Jackson, Garrison, Wilson, Gibbons, & Shahan, 2013; Stein, Smith, Henningsen, & Silver, 2000). There is thus a need for research to identify what characteristics make contextual tasks accessible to students as a point of entry and useful for educators in analyzing and pressing students’ thinking.
This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Mathematics Education Research Journal, published by Springer. The final publication is available at link.springer.com. Copyright restrictions may apply. doi: 10.1007/s13394-016-0177-z
Carney, Michele B.; Smith, Everett; Hughes, Gwyneth R.; Brendefur, Jonathan L.; and Crawford, Angela. (2016). "Influence of Proportional Number Relationships on Item Accessibility and Students’ Strategies". Mathematics Education Research Journal, 28(4), 503-522. http://dx.doi.org/10.1007/s13394-016-0177-z