Quality of Instruction

Piccolo, D.L., Harbaugh, A.P., Carter, T.A., Capraro, M.M., & Capraro, R.M. (2008). Quality of instruction: Examining discourse in middle school mathematics instruction. Journal of Advanced Academics, 19(3), 376-410.

Summary:
This research wanted to know how to provide students with skills and mathematical competence through asking and engaging in rich mathematical discourse with teachers. It is found that students who verbally elaborated their ideas, with or without guidance, outperformed students who were provided the explanation of an idea. Through questioning students thought process, this study shows that when students were asked “why” questions, learning was enhanced more so than when students were not able to successfully answer a question. This provided an opportunity for students to listen and participate during mathematical lessons rather than just memorizing concepts. It is stated that, “Rich, meaningful discourse between teacher and student in a mathematical classroom is a complex, yet important, objective for educators to understand and implement in the classroom.” The students need to be able to not only hear what the teacher is teaching, but to actually generate their own understanding of the content.

Quotes:
“Mathematics instruction has evolved into a more democratic, collaborative, and conceptually based form of learning. However, the dialogic interaction that accompanies these pedagogical changes remains relatively unexplored.”

“Teaching standards recommendation that mathematics teachers initiate and “orchestrate discourse by posing questions that elicit, engage, and challenge students’ thinking”, by “listening carefully to students’ ideas,” and by “asking students to clarify and justify their ideas orally and in writing.”

“Communicate their mathematical thinking coherently and clearly to peers, teachers, and others” and the students need to learn “what is acceptable as evidence in mathematics.”

“Because teachers ask most of the questions and do not encourage students to ask their questions, students are likely to refrain from questioning.”

“When students pose questions, they are thinking about their thinking. These metacognitive strategies can help students learn to take control of their own learning by self-defining learning goals and self-monitoring progress in achieving those goals.”

“Teachers can use open-ended questions to cue students, to improve on weak responses, to develop a discussion atmosphere, or to foster curiosity and inquiry.

“Probing questions are defined as questions that encourage students to express their knowledge or understanding and to clarify, justify, interpret, or represent their knowledge or understanding. Guiding questions are classified as questions that are related to experiences or learning with real-world examples or representations by guiding students to interpret and reason about experiences or learning with real-world examples or representations.”

Text Sources:
Carlsen, W.S. (1991). Questioning in classrooms: A sociolinguistic perspective. Review
of Educational Research, 61, 157 – 178.

Corwin, R., Storeygard,J., Prince, S., Smith, D., & Russel, S. (1995). Supporting
mathematical talk in classrooms. Hands On, 18(1). Retrieved on May 7, 2008,
from http://mercury.ornl.gov/metadata/esip/sgml/esipweb/record14996.sgm

Donovan, S.M., & Bransford, J.D. (2005). How students learn: Mathematics in the classroom. Washington, DC: The National Academies Press.

Graesser, A.C., & Person, N.K. (1994). Question asking during tutoring. American Educational Research Journal, 31, 104-137.

Kawanaka, T., & Strigler, J.W. (1999). Teachers’ use of questions by eighth-grade
mathematics classrooms in Germany, Japan, and the United States. Mathematical Thinking & Learning, 1, 255-278.

Lampert, M. (1990). When the problem is not the question and the solution is not the
answer: Mathematical Knowing and teaching. American Educational Research Journal, 27, 29-63.

Mason, J. (2000). Asking mathematical questions mathematically. International Journal
of Mathematics Education in Science and Technology, 31, 91-111.

Nelson, G.D., Kulm, G., & Manon, J.R. (2000). Improving mathematics teacher practice and student learning through professional development. Proposal to the Interagency Educational Research Initiative, American Association for the Advancement of Science, Washington, DC.

van Zee, E., & Minstrell, J. (1997). Using questioning to guide student thinking. The Journal of the Learning Sciendce, 6, 227-269.