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.

Service Learning

Here is a brief backgroup description of service learning.....
THE BIG DUMMY'S GUIDE TO SERVICE-LEARNING

Web Links from Cathy's Presentations

Below are some links to online sites or software that you can explore ideas from Cathy's talk:

WISE - The Web-based Inquiry Science Environment. WISE allows you to try examples of very good, online inquiry activities. WISE is a free resource for creating and using on-line science curricula using only a web browser.

DIAGNOSER. This interactive web-based physics program provides formative assessments of student thinking (e.g., assessments to inform instruction rather than assign scores}. Students receive feedback as they work through their assignment. Teachers can view reports that detail facets of their students' thinking about the assigned topic.

Teaching With Models. An outstanding introduction to teaching with a focus on scientific models. Includes examples from the Earth sciences.

Scaffolding Website. Learning occurs when information is integrated into an individual's knowledge base. Scaffolding is the process by which a teacher provides temporary support to learners to "help bridge the gap between what [the learner] know[s] and can do and what [he or she] need[s] to accomplish in order to succeed at a particular learning task."

Identifying Misconceptions

Most effective teaching methods incorporate identifying student misconceptions or prior knowledge.

Students explaining their misconceptions have been captured in a video taken during a Havard graduation, which is available online. Take a look, it is very enlightening.

Using Blogs in a Class

My wife, Amy Earhart, has been using blogging in her technical writing class at Texas A&M, with good success. The students are engaged in a discussion of the class topics through their own blogs and leaving comments on other student's blogs.

Take a look at the blogs in the ring, if you want to see nice examples of impact on learning.

English 301 Blog Ring

Houston Air Quality - Our Next Inquiry Topic?

We are have been considering different ideas for our next inquiry topic.

Cathy Loving has suggested that we use Houston air quality as the next inquiry topic for PLC-MAP. I bring this up now because the Houston Chronicle has a related story on their web site today entitled Residents learn to utilize Internet on toxic emissions. This story is part of a very interesting series of article son the topic the Chronicle has been running.

What do you think?

If you have an opinion on this topic or others that would interest you and would link into the topiocs you are covering, leave a comment on my blog.

A Personal Story.....

I was in Washington, DC last week at a meeting organized by the National Science Foundation, the agency funding PLC-MAP. Mike Heaney, a program officer at NSF, described the importance of stories when NSF reports to Congress. Well, NSF, do I have a story for you.....

On January 28th, we held the first PLC-MAP seminar. We focused on exploring the nature of authentic inquiry learning using the recent Southeast Asia Tsunami as a theme. As I described in my last blog, the intern teachers are really much more interested in learning strategies to motivate students and manage classrooms. I tried to convince the intern teachers that engaging students in interesting, authentic inquiry really helps solve many of these issues, but I saw many dubious faces.

A mentor teacher, Liane Fleming from Klein ISD, then came to my rescue. She described her own use of the tsunami theme as the basis for inquiry learning in her 8th grade class. She told how her students were captivated when she described her own experience of the tsunami, which she experienced on the back of an elephant. You could have heard a pin drop in the seminar room as the other teachers listened to her story, a perfect example of the potential of inquiry learning.

Image courtesy of KHOU.

I don't know what we did to deserve this, but I could not have asked for a more perfect start for our program.

Motivating Math Students

Strategies to Motivate Students

While the design of PLC-MAP is focused on building the ability of the intern teachers to teach using authentic inquiry, we feel it is important to address other topics to support the new teachers. If you are planning a professional development program for alternative certification teachers, then you should know that the concerns of our teachers are focused on issues surrounding student motivation and controlling negative bahviors in their classroom.

Other links to math resource web sites, include the The Math Forum at Drexel University, which has a nice library of articles, lessons and resources that can help motivate underachieving students. Even more ideas (large list) is available at the Mathematics WWW Virtual Library.

A Serious Case of Blogging

OK, using blogs to support new teachers, such as the way we are using blogs in PLC-MAP, is serious business. On the other hand, an example of significant use of technology to hype the most important but often least exciting sporting event in history is Bill Simmon's blog direct from Jacksonville and the Super Bowl. Enquiring minds want to know....or at least live vicariously.

Speaking of the Superbowl, did you hear about the feel-good story of the year? Jeff Thomason is a retired football player who nows works for a construction firm in New Jeresey.

Jeff Thomason, one lucky guy.

Last week he got a call from the Philadelphia Eagles asking if he would play in the Superbowl, replacing another hurt player. I am awaiting my own call from the Patriots....

Many of you may not know that I am a transplanted New Yorker. One of the many things that I like about Texas is that Texans are generally civil to each other. About the only time I miss being in the land of obnoxious people, I mean the North East, is during major sports championships between regional teams like Philadelphia-New England in this Superbowl or the past New York Mets - New York Yankees World Series. Wild fans just make the show more interesting. Phili fans in particular are nasty, earning their well-deserved reputation after they booed Santa Claus in 1968. Of course, we probably should question the rationality of New England fans, who would rather embrace losing than winning, in good puritan tradition.

Enjoy the game.