Malcolm Gladwell (2008) describes the ten thousand hours that are necessary to become an expert. He looked at a range of experts in many fields and found that while many started with talent that was not always the case. What experts had in common that delineated them from others and made someone an expert was the amount of effort that the person put in en route to becoming an expert. Carol Dweck (2006) also found that if you viewed your talent as being changeable through the effort you put in, you were more likely to become an expert than those that relied on their talent alone. So what does this effort required to become an expert do to the learning process?
Often during my teaching of mathematics in a junior high classroom, I need to stop myself before I utter “it is so easy, I don’t understand why you can’t do it” to reflect on the fact that my students, unlike myself, are novices in the learning of mathematics. As an expert, I need to be mindful that how I process mathematical knowledge is different than how my students do. I have the ability to recognize patterns in the problem that allow me to link my prior knowledge to the situation to come up with a more sophisticated solution than most of my students would (Bransford, Brown, & Cocking, 2000). I need to be cognizant that my brain is able to chunk information into units so that my working memory is freed up to manipulate more information and to process it in multiple or novel ways (Bransford et al., 2000). While I am working with students the fact that my brain requires less effort to retrieve the information necessary to the question at hand (Bransford et al., 2000) necessitates me to allow more think time for students, usually more than I think would be necessary. I find that my students are more likely to just put numbers into a formula instead of taking the time to figure out what the problem is asking them to do and applying the correct numbers, operations and formulae to solve a given problem (Bransford et al., 2000). At my school, we have been exploring students’ ability to extract necessary information from written text to answer mathematical questions. The range in ability to pull numbers from a written text and apply the correct operations or formulae to solve the question asked was marked. This reinforced, for me, that the term novice is not a singular descriptor. The term novice is a large continuum that ranges from brand new beginner to almost expert and as teachers we need to be aware that this complexity (Davis, Sumara, & Luce-Kapler, 2008) exists in our classroom.
The first aspect of complexity that exists in classrooms, especially those at my school, is the range of prior knowledge. Many of the students at my school have had large gaps in their formal education. Trips back to their country of origin are frequent with little to no schooling occurring during the trips that can span several months. In addition, some have had very little formal education in their home country if at all due to living in war-torn countries, refugee camps, natural disasters, or poverty. Adding to the complexity one then needs to look at the range of prior knowledge due to the wide range of cultural and religious backgrounds of our students. Nothing can be taken as shared (Davis et al., 2008) at my school unless it is created inside the classroom or school community. The instance that highlighted for me the need to be aware of assuming prior knowledge came during the probability unit with my grade sevens. At the start of the unit I posed a question about having the cards in their suits. One of my students, a very new immigrant to Canada, asked me for some construction paper, scissors, and tape to complete the task. Flummoxed as to why he would need those supplies I handed them over and continued on with my lesson. Checking in with the student about 5 minutes later I see that a few cards were now sporting little suits. For him, suit is a cultural reference to clothes for important occasions, so trying his best to please me as the teacher he went about putting the cards into suits even though when asked later he said he felt the request was odd. Prior knowledge is watch allows the expert to recognize patterns and to chunk information to make using that information in novel setting easier (Bransford et al., 2000). Thus ensuring that the prior knowledge that is necessary for a skill is both accessible and correct becomes extremely important. Learning is easier if there is something pre-existing to connect ideas to and if the ideas that something is connected to are valid given the context at hand (Bransford et al., 2000).
In using technology, it is important to realize that good teaching practices are good teaching practices no matter the medium. It is important that we ensure that what is best for students is at the forefront of our minds as we incorporate technology into education so that the student is not overshadowed by the lure of new technology.
Bransford, J., Brown, A., & Cocking, R. (Eds.). (2000). How People Learn: Brain, Mind, Experience, and School: Expanded Edition. Washington D.C.: National Academy Press. Retrieved from http://www.nap.edu/openbook.php?isbn=0309070368
Davis, B., Sumara, D., & Luce-Kapler, R. (2008). Engaging Mind Changing Teaching in Complex Times second edition. New York: Routledge.
Dweck, C. (2006). Mindset: The New Psychology of Sucess. New York: Ballantine Books.
Gladwell, M. (2008). Outliers: The Story of Success. New York: Little, Brown and Company.