Questioning in College Algebra
College Algebra courses serve as gatekeepers to higher mathematics courses in universities, as well as to many technical and science-intensive college majors (Small, 2002). More students enroll in College Algebra and similar courses than in all Calculus courses (Lutzer, Maxwell, & Rodi, 2007). Despite high enrollments, Small quotes a Dean of Science and Mathematics as stating, “Traditional College Algebra is a boring, archaic, torturous course that … turns off students and discourages them from seeking more mathematics learning” (Small, 2002). Small’s recommendations include a more student-centered College Algebra.
One way for teaching to be more student-centered is through focusing on types of questioning to become more intentional in using questions to support student learning. Driscoll (1999) presented a framework for questioning fostering algebraic thinking.
Driscoll (1999) recommended teachers use variety in questioning to support development of algebraic habits of mind. Driscoll organized five categories of teacher intentions: (a) Managing, (b) Clarifying, (c) Orienting, (d) Prompting Mathematical Reflection, and (e) Eliciting Algebraic Thinking, as described in Table 1 below (examples are from my observations). Note that I am not including the first category (Managing) since the course I observed is lecture-based.
My research question is: How does questioning by college algebra instructors to questioning intentions recommended by Driscoll (1999) for fostering algebraic thinking in grades 6-10?
I observed three 80-minutes class sessions for a small-lecture College Algebra section at Michigan State University that meets on Tuesday and Thursday evenings. The department provides class notes to instructors and this instructor emailed them to his students. Notes include definitions and examples with space provided to write additional notes and solutions. The instructor is in his final semester of a mathematics master’s program and intends to not continue teaching mathematics.
I wrote field notes focused on instructor questions and their context. I spent an hour after each session writing my impressions. I coded instructor questions were according to Driscoll’s (1999) four categories of teacher intentions, described in Table 1 with examples of questions from my observations.
I recorded 182 instructor questions across the three observed sessions. Table 2 below shows the results of coding each session according to four categories of Driscoll’s (1999) framework for intentions.
For the most part, each of the questions asked by the instructor did fall into one of the four categories. Most of the questions that did not fall into one of these categories were of the type: “Any questions?”
The instructor asked a variety of questions, and most questions fit into one of Driscoll’s (1999) five categories. The majority of questions fell into the Orienting category. Almost half of the Orienting questions were “Doing” questions, that is, they ask about how to do the next step of the problem. For example, “So what’s first?” or “Okay, and we have one step left, now what do we want to do?” These questions fit in the first half of Driscoll’s description: “Intended to get students started, or to keep them thinking about the particular problem they are solving…” (Driscoll, 1999, p. 6). The remainder of the questions coded as Orienting fall into the second half of Driscoll’s description (see Table 1). For example, [finding a radius] “Okay, and what does the square root of 40 simplify to?” or “I want you to write this formula in standard form. So what does it look like? Start with x – so what goes right there?” I felt in my coding that these types of questions were different enough that the Orienting category might be more usefully broken into smaller categories such as “Doing” as opposed to “Leading to Correct Answer.”
Questioning frameworks are useful focusing devices to help instructors reflect on their teaching. The questioning framework developed by Driscoll (1999) is intended to help secondary mathematics teachers focus on developing students’ algebraic habits of mind. I would argue that this framework would also be useful for College Algebra instructors and that the instructor I observed uses questions from this framework (whether consciously or not) to support students’ development of algebraic habits of mind. Using this framework to track questions types over time could help a College Algebra instructor become more planful about question use in support of students’ learning.
Driscoll (1999). Fostering Algebraic Thinking: A Guide for Teachers Grades 6-10. Westport, CT: Heinemann.
Lutzer, D. J., Maxwell, J.W., and Rodi, S. B. (2007) Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States: Fall 2005 CBMS Survey. American Mathematical Society: Providence, RI. Retrieved from http://www.ams.org/cbms/cbms2005.html
Small, D. (2002) An urgent call to improve traditional college algebra programs. Focus: The newsletter of the mathematical Association of America, 12-13.