Learning is the way a person collects, stores and recall information.   Learning is usually associated as being something that takes place in a classroom between a teacher and a student, but it is so much more than that.  Learning can be between two people, a group of a people, or even one’s self.  When you were a small child and you touched something that was hot, like a cup of coffee, you had that realization and you didn’t continue to touch that cup.In How People Learn, John D. Bradford discusses the difference between experts and novices and how their learning differs.  Bradford states “experts notice features and meaningful patterns of information that are not noticed by novices,” and “cannot be reduced to sets of isolated facts” (31).  This is extremely prevalent in the new 21st century classroom.  Students are no longer needed to recall facts, but instead answer higher ordered questions and problem solve.

Similarly, in Will Richardson’s article Why School?  TED ebook author rethinks education when information is everywhere, he states that “[s]chools were built upon the fundamental premise that teachers and knowledge and information were scarce. That is no longer the reality.”  With the abundant amount of information on the Internet, there’s no need for these facts to be taught—we will always have access to it whenever.

Because this, we are required as teachers to change up our teaching pedagogies.  We need to shift from teaching to facilitating learning.  Despite there being this abundance of information available at student’s fingertips, we need to guide them and constantly question them every step of the way.  We need to promote critical thinking in our classroom; we need to use the words “why” instead of “how.”   As we do this, our students will progress from novice learners to experts.

One approach that mathematics teachers can use is discovery-based learning.  For example, when you are introducing exponential growth you pose the question: “Think of the story of Alice in Wonderland.  When she was directed to go through a door that was too larger for her, she found a bottle that said DRINK ME and she would double in size.  Using any mathematical problem solving to help you.  Is there a pattern? A formula?”  Most students would create table and graph to help them with the information.  During this discovery time, you may give guiding questions or ask why they are doing what they are doing.  At the end of this time, you can meet as a class and discuss your finding and finish the discussion with information on exponential growth and the formula that is used.  This give a chance for students to think critical with the skills they are given first before providing them with sound information.  It also improves upon problem solving skills, skills which only expert learners possess.


Donovan, S., Bransford, J., & Pellegrino, J. (2000). How people learn: Brain, mind, experience and school. Washington, DC: National Academy Press. Retrieved from http://www.nap.edu/openbook.php?isbn=0309070368

Richardson, Will. “Why School? TED ebook author rethinks education when information is everywhere. | TED Blog.”TED Blog: Further reading on ideas worth spreading. TED, 14 Sept. 2012. Web. 29 June 2013. <http://blog.ted.com/2012/09/14/why-school-ted-ebook-author-rethinks-education-when-information-is-everywhere/&gt;.

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