Recently at the MCATA conference held in Calgary I had the opportunity to attend a keynote session by Dr. Olive Chapman. Dr. Chapman is presently Professor of Mathematics Education and Associate Dean in the Division of Teacher Preparation, Faculty of Education, University of Calgary. She is also the associate editor of the International Journal of Mathematics Teacher Education.
The topic that she chose to present was “The Joy is in the Journey when the Route is Mathematical Thinking”.
Dr. Chapman points out that “Math is a method of inquiry and a field of creative endeavor” and that “Math is fun when you understand it”.
So how can I begin to build techniques of inquiry into my existing lessons?
Dr. Chapman suggests the following: -create an atmosphere of questioning, challenging and reflecting -allow students to work on inquiry-oriented or investigative tasks, solve challenging problems, explore patterns, formulate and check conjectures, reason and communicate.
She discussed five categories of inquiry tasks that encourage concept development:
1. Classifying math objects- students devise own rules or apply ones from other students
2. Interpreting multiple representations- verbal, pictorial (graphic), symbolic (algebraic), concrete
3. Evaluating math statements- students decide with justification if something is always true, sometimes true, or never true
4. Creating problems-students write problems relating to their own personal experiences or understanding
some problem formats could include-own choice, similar to a given problem, open ended, similar solution, related to a specific concept, modifying a problem, derived from given pictures
5. Anaylzing (reasoning) solution, errors, and/or misconceptions
-Explain how something works. Make up your own examples.
Dr. Chapman discussed using careful techniques of questioning for math thinking. She suggested using a combination of formats including:
A. Comparing- same / different
C. Reversing- if this is the answer what is the question
D. Justifying- what is wrong with this answer
E. Exemplifying- to show by example
Dr. Chapman describes the focus of the mathematical journey as being very different for different types of students. The following chart is a summary of how she suggested students focus might fit into five categories..
|Student A||Happy to just arrive at the destination|
|Student B||Content to just follow directions|
|Student C||Feels the need to constantly check on directions|
|Student D||Follow directions and is a passive noticer|
|Student E||Embraces “lost” moments and is an active noticer|
When I returned from this conference I was reminded that students learn via many different learning styles and that there is no one way to present a lesson to ensure that you are capturing an active audience.
Following the inquiry based / creative thinking learning model our staff decided to focus on implementing more H.O.T.S. (Higher Order Thinking Skills) Activities this year at our school. Living just outside of Edmonton in a small hockey spirited community, I decided to do an Oilers vs Flames activity with my students while studying number concepts (whole and decimal). Using our classroom set of netbooks I set out the following task.
Number Concepts Activity (including decimals)
Oilers vs Flames
Your parents give you $150 for your birthday. You and a friend want to go to the Edmonton Oilers game March 26th, 2011 at Rexall Place with a start time of 8:00 p.m. They are playing off for the battle of Alberta against the Calgary Flames. You check ticketmaster for ticket prices and find a single seat ranges from $45 dollars in the “nose bleed” section, to $125 dollars for some better seats. Parking costs $12 if you decide to drive. The concession prices are quite high with most items averaging $5 and don’t forget they have the Oiler’s store you may want to visit.
You are quite thrifty and want to make sure that you are getting the “most for your money”.
With your budget, make a plan for your evening out.
Will you go dutch with your friend or will you treat your friend? How will you get to the game? Where will you be sitting? What (if anything) will you have to eat? Will you be purchasing any souvenirs or memorabilia?
Be prepared to share, discuss, and post your Oilers vs Flames evening plan.
Some of the sites that my students chose to search and visit via their netbooks included:
Students visited Ticketmaster or The Official Website of the Edmonton Oilers to actually price seats for the game
Rexall Place Concessions- Students who had recently visited this vendor came back with suggested retail prices on food and drink items.
Oiler’s Store at Rexall Place- students could visit the virtual on-line version of the Edmonton Oiler’s Store to view merchandise and decide if they were going to purchase any memorbalia.
Students worked within their given dollar amount (for this event $150), and devised individual budgets for their night out. They were adding, subtracting, multiplying numbers and the math talk was very rich with students explaining to peers what they were doing and why. When presenting they were justifying why they chose to buy an item, or why they decided not to buy a particular item. Students explained their thinking strategies aloud to a very captive audience. This activity allowed for success for all my students by scaffolding the assignment. In my classroom my students found this learning activity to be very rewarding and even fun. In repeating Dr. Chapman’s words…”Math is fun when you understand it!”
I am attaching a PDF copy of the activity I used in my classroom in case anyone else in interested.