Authentic Inquiry in the Mathematics Classroom

Many of the science teachers and scientists probably are unclear how inquiry learning can be implemented in a mathematics classroom.

Culling through Google, though time consuming, can often find gems.

A web site of a math teacher's professional development program out of University of Rochester, in upstate New York, does a nice job of describe the characteristics and implementation of inquiry in the math classroom.

In particular, there are a number of examples that are well described, including activities on tesellation and the calculation of area.

Here is an excellent paper on-line from the Math Forum at Drexel.
Encouraging Mathematical Thinking, Discourse around a Rich Problem

Modeling in Authentic Inquiry

Focusing inquiry activities on the development of conceptual models can be a very powerful technique to foster learning in students.

Conceptual models or mental models is a mental construct of reality or imaginary worlds. People use conceptual models to reason about the world around them.

Consider thinking about driving a car. Since it is likely you are an expert in this activity, your metal model not only includes an image of your car, including the spatial arrangement of you in relation to the interior and exterior of your car, but you models also includes of the actions of the car as a function of how you drive and the environment.

So, you likely have a pretty good mental model of how you car responds as a function of how much you depress the accelerator or the brake. This is an example of a casual relationship. You are likely also able to develop fairly accurate predictions concerning what would happen in different senarios, such as driving fast on a wet road.

• See examples of classroom activities that develop middle school student understanding of cause and effect
  
• See an example of an online tool for mapping cause and effect relationships that can help student analyze complex situations.
  

Now consider a young student being asked to use their conceptual model to make a prediction about driving a car. It is unlikely that their model would be as accurate and complex, and predictive as your model. (In fact, poor models due to inexperience are likely a major factor in the high rates of accidents involving teen drivers).

The strategy of focusing on student conceptual models rests on using exercises that alow students to test and revise their models against various types of evidence and using assessment techniques, such as concept maps, that make student models visible.