Philosophy of Inquiry Maths

What is inquiry-based learning?

An old adage states: “Tell me and I forget, show me and I remember, involve me and I understand.” The last part of this statement is the essence of inquiry-based learning, says our workshop author Joe Exline 1. Inquiry implies involvement that leads to understanding. Furthermore, involvement in learning implies possessing skills and attitudes that permit you to seek resolutions to questions and issues while you construct new knowledge.


Part 1 of 2

Part 2 of 2

Tim O’Keefe, a teacher at the Center for Inquiry elementary school in Columbia, South Carolina, explains why he thinks inquiry is a much more effective teaching strategy than traditional chalk-and-talk.

“Inquiry” is defined as “a seeking for truth, information, or knowledge — seeking information by questioning.” Individuals carry on the process of inquiry from the time they are born until they die. This is true even though they might not reflect upon the process. Infants begin to make sense of the world by inquiring. From birth, babies observe faces that come near, they grasp objects, they put things in their mouths, and they turn toward voices. The process of inquiring begins with gathering information and data through applying the human senses — seeing, hearing, touching, tasting, and smelling.

A Context for Inquiry

Unfortunately, our traditional educational system has worked in a way that discourages the natural process of inquiry. Students become less prone to ask questions as they move through the grade levels. In traditional schools, students learn not to ask too many questions, instead to listen and repeat the expected answers.

Some of the discouragement of our natural inquiry process may come from a lack of understanding about the deeper nature of inquiry-based learning. There is even a tendency to view it as “fluff” learning. Effective inquiry is more than just asking questions. A complex process is involved when individuals attempt to convert information and data into useful knowledge. Useful application of inquiry learning involves several factors: a context for questions, a framework for questions, a focus for questions, and different levels of questions. Well-designed inquiry learning produces knowledge formation that can be widely applied.

Importance of Inquiry

Memorizing facts and information is not the most important skill in today’s world. Facts change, and information is readily available — what’s needed is an understanding of how to get and make sense of the mass of data.

Educators must understand that schools need to go beyond data and information accumulation and move toward the generation of useful and applicable knowledge . . . a process supported by inquiry learning. In the past, our country’s success depended on our supply of natural resources. Today, it depends upon a workforce that “works smarter.”

Through the process of inquiry, individuals construct much of their understanding of the natural and human-designed worlds. Inquiry implies a “need or want to know” premise. Inquiry is not so much seeking the right answer — because often there is none — but rather seeking appropriate resolutions to questions and issues. For educators, inquiry implies emphasis on the development of inquiry skills and the nurturing of inquiring attitudes or habits of mind that will enable individuals to continue the quest for knowledge throughout life.

Content of disciplines is very important, but as a means to an end, not as an end in itself. The knowledge base for disciplines is constantly expanding and changing. No one can ever learn everything, but everyone can better develop their skills and nurture the inquiring attitudes necessary to continue the generation and examination of knowledge throughout their lives. For modern education, the skills and the ability to continue learning should be the most important outcomes. The rationale for why this is necessary is explained in the following diagrams.

Illustration developed by Joe Exline

This figure illustrates how human society and individuals within society constantly generate and transmit the fund of knowledge 2.


Human society and individuals within society constantly generate and transmit this fund of knowledge. Experts, working at the boundary between the known and the unknown, constantly add to the fund of knowledge.

It is very important that knowledge be transmitted to all the members of society. This transmission takes place through structures like schools, families, and training courses.

Certain attributes are necessary for both generating and effectively transmitting the fund of knowledge. The attributes that experts use to generate new knowledge are very similar to the qualities essential for the effective transmission of knowledge within the learners’ environment. These are the essential elements of effective inquiry learning:

. Experts see patterns and meanings not apparent to novices.
. Experts have in-depth knowledge of their fields, structured so that it is most useful.
. Experts’ knowledge is not just a set of facts — it is structured to be accessible, transferable, and applicable to a variety of situations.
. Experts can easily retrieve their knowledge and learn new information in their fields with little effort.

(The list above was adapted from “How People Learn,” published by the National Research Council in 1999.)

Illustration developed by Joe Exline

This figure illustrates the attributes necessary for both generating and effectively transmitting the fund of knowledge.

We propose that the attributes experts use to generate new knowledge are very similar to the attributes essential for the effective transmission of knowledge within the learner’s environment — the essentials of effective inquiry learning.

Inquiry is important in the generation and transmission of knowledge. It is also an essential for education, because the fund of knowledge is constantly increasing. The figure below illustrates why trying to transmit “what we know,” even if it were possible, is counterproductive in the long run. This is why schools must change from a focus on “what we know” to an emphasis on “how we come to know.”

Published by makingpi

Our interest is to create a brilliant practical applied maths programme for teaching students who struggle with engaging in Maths. Our interests range from building bridges to making beautiful silver objects.

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