Overview of Inquiry/Problem Solving in Middle School Math
Although the following article, initially published in ENC Focus: A Magazine for Classroom Innovators (vol. 6, no .2, 1999), deals explicitly with inquiry as it applies to science instruction, the principles expressed in the article can be applied to mathematics teaching and learning, as well. Along with additional supporting resources, it can be accessed online at:
To read a story about how a middle school math teacher changed her teaching practice over time, see "Teaching Students to Swim in Any Pond" at:
Inquiry in the Everyday World of Schools
by Ronald D. Anderson, University of Colorado
Inquiry is a word with a long-standing place of honor in science education circles. It was the label for many of the new approaches to teaching promoted in the NSF-funded curriculum materials of the 1950s and 60s. It has a central place in the current National Science Education Standards (NSES). It is the favored word for describing the essence of good science teaching; seemingly, everyone uses it and there seems to be little disagreement about it.
But is everyone talking about the same thing when they use the word inquiry? If we got precise about its meaning, would we still be agreeing with each other? What does it look like in the classroom? What are the results?
A close look at the NSES shows inquiry is used in at least three different senses:
Scientific inquiry refers to the means scientists use to study nature and formulate explanations of what they observe. It deals with how science proceeds and can be considered independently of educational processes.
Inquiry learning refers to the active processes in which students are engaged as they pursue increased understanding of science. The writers of the NSES obviously see some relationship between scientific inquiry and inquiry learning. It is thought that student learning in a school context should reflect the nature of inquiry in the world of science. While the word "constructivism" is not used in the NSES -- possibly because its meaning varies significantly among its users -- inquiry sometimes appears to be used in the NSES in a similar way. In fact, many scholars who study human learning would argue that significant learning demands an active process for which the label of constructivism, or inquiry learning, would be appropriate. In other words, inquiry is the essence of learning.
Inquiry teaching as used in the NSES has no precise operational definition, although, however it is understood, it seems to be something that promotes inquiry learning. This lack of clarity as to what inquiry teaching entails is at the heart of many teachers' struggles to put the NSES into practice. This same lack of clarity is found in the extensive body of research studies on inquiry teaching; it is defined differently by different researchers, and often in terms that are not easy to use in talking about the everyday activities of a teacher in the classroom.
In the interest of being able to communicate in concrete terms, the rubric in the box to the right may be of help. It was developed in connection with case studies of schools from across the country that were judged to be successful in putting into practice reforms such as those advocated in the NSES and the 1989 NCTM standards for mathematics (Anderson, 1996).
Understanding what is entailed in inquiry teaching, and inquiry learning, requires close attention to three tangible aspects of the classroom--the role of teacher, the role of students, and the nature of student work--described in the rubric. The specifics listed in the rubric were observed in actual classrooms and are offered here as a beginning point for personal reflection on our own teaching.
Research has some important insights to offer as assistance in this personal reflection. Review of a large number of research studies supports the following generalizations:
Sources of information are available about how to put new forms of teaching and learning into practice (e.g., Anderson & Pratt, 1995). In addition, it is hoped that the work of such groups as the Center for Science, Mathematics and Engineering Education at the National Research Council will soon provide significant additional help in putting inquiry teaching and inquiry learning into practice in schools. It is the right direction to go, but getting there will be a big challenge.
(Note: Use "back" button and click on "References" to access the reference list for this article.)
Anderson, R.D. and Pratt, H. (1995). Local leadership for science education reform. Dubuque, IA: Kendall/Hunt.
Anderson, R.D. (1996). Study of curriculum reform. Washington, DC: U.S. Department of Education.
Anderson, R.D. (1998). The research on teaching as inquiry. A paper commissioned by the Center for Science, Mathematics and Engineering Education at the National Research Council, Washington, DC.
Web Sites of Interest: