Saturday, September 29, 2012

"Playing the Game" of Algebra Story Problems- Coordinating Reasoning and Representation

The importance of mathematics instruction including "real life" contexts relevant to students' experiences is widely acknowledged (Common Core State Standards Initiative, 2010; NCTM, 2000; 2006; 2009). Common justifications for contextualized mathematics include the idea that relevant contexts may help students to apply what they learn in school to out-of-school situations, and that relevant contexts may scaffold learning by providing a bridge between what students understand and the content they are trying to learn. 

The study reported here investigates these justifications using story problems on linear functions. A situated cognition theoretical framework is used to interpret student behavior in the complex, social system of "school mathematics." In a series of interviews, students from a low-performing school were presented with algebra problems, some of which were personalized to the ways in which they described using mathematics in their everyday lives. Results showed that students rarely explicitly used situational knowledge when solving story problems, had consistent issues with verbal interpretation, and engaged in non-coordinative reasoning where they bypassed the intermediate step of understanding the given situation before trying to solve the problem. Problems with the same mathematical structure with different amounts of verbal and symbolic support elicited different strategies from students, with personalized problems having high response rates and high use of informal strategies. This suggests that students can use sophisticated, situation-based reasoning on contextualized problems, and that different problem framings may scaffold learning. However, results also demonstrated that the culture of schooling, and story problems as an artifact of this culture, undermines many of the justifications for contextualizing mathematics. -Dr. Petrosino

PlayingThe Game

Picture: Hoboken's own Cake Boss (Buddy Valastro) created a special cake to celebrate Hoboken High School's 50th Anniversary. Pictured from (L-R) are: Hoboken teacher and 50th Anniversary Coordinator Mr. Chris Munoz, Board of Education Trustee Carmelo Garcia, and Ms. Nina Delia.