Teaching by Genre: Embracing a Diversity of Practices in Mathematics

Neither back-to-basics nor reform-oriented practices are sufficient by themselves for successful learning in math. Incorporating both approaches presents richer options for student learning. For some time now, the math wars have pitted back-to-basics educators against those promoting reform-oriented practices. Some mathematicians and educators have argued that children need to practice time-tested algorithms in classrooms that use worksheets and have teachers who provide positive feedback for right answers and corrective feedback for wrong ones. Others have argued that children need to engage in meaningful discussions about problems that encourage invented algorithms or multiple solution paths (O'Brien 2007). One result of this debate is the emergence of two mutually exclusive images of ideal classroom practice. In one, children sit in orderly rows, repeatedly computing the answers to similar problems until they achieve mastery. In the other, children engage in lively conversations over unusual bits of mathematics and concern themselves more with their own thinking and that of their classmates than with the production of right answers. In reality, most teachers' practices fall somewhere between these two extremes, including both episodes of shared problem solving and computational practice. [ILLUSTRATION OMITTED] The mathematics education research community has tended to portray this diversity of practice as a problem to be corrected (Boaler 1998; Spillane 1999). However, including both reform-oriented and traditional teaching can be seen as a good thing - allowing more students to be successful and offering a broader image of mathematics in our world. TEACHING GENRES If we think of teaching strategies like genres of books, the need for variety becomes more apparent. You might love to read mysteries in bed before falling asleep, but if you want to impress your neighbors with your chocolate souffle, you need to turn to another genre. Just as genres of books have different styles, different purposes, and different attractions for readers, so do genres ofteaching (Bakhtin 1986). A classroom that offers students only discussions or only worksheets is shortchanging students who might be drawn to other genres and is presenting a narrow view of mathematics. I saw the power of drawing on diverse genres of teaching during the year I spent observing Diana (a pseudonym), an experienced 3rd-grade teacher in an urban school. Diana, who has engaged in many professional development activities in mathematics, routinely draws from multiple genres in her classroom because she believes that these diverse experiences allow her children to engage with mathematics in multiple ways. During the year I spent in her classroom, I saw students tackle problems in groups, explain their own invented algorithms, take timed tests on multiplication facts, answer fact-based questions in quick succession, chronicle multiple solution paths in their journals, work series of similar problems in the math books, and engage in mathematical debates. Because Diana saw me as a representative of the university, she sometimes apologized when I visited during a more traditional activity, but I soon recognized that during these activities, different student voices dominated the classroom than those heard most frequently during more reform-oriented activities. As a result, I became interested in the different portrayals of mathematics in each of the genres present in Diana's classroom as well as the different opportunities available for student participation and success. MATH GENRES One of the most common genres in Diana's classroom was Mathematical Discussions. During these conversations, the object of discussion was generally a mathematical idea or process, rather than an answer. Diana frequently challenged students' answers by asking them to explain or by presenting counterexamples; and many students participated, sometimes talking to each other. …