Note: I am currently unable to access my lap top/ ipad or wifi. I have attempted to complete the readings and blog post on my phone using my data plan. It hasn’t been the easiest thing to accomplish. When life returns to normal I will fix up the errors and properly cite material. Sorry for the inconvenience.
This unit on Conceptual Challenges really synthesized for me my role not only as a teacher but also as a student. Until recently I believe I have been the antithesis of Piaget’s statement “Not how fast but how far”. Educationally I believe I have always been on the fast track, not in terms of being educationally superior but rather looking at a volume of work I needed to conquer and setting about conquering it, not learning it. Homework and assignments were a check list of activities that I tackled and prided myself if I got through it (honestly never considering if I understood it or could explain it but rather could I do what was asked as a robot would).
Reflecting over the past few days on Heathers experience and the other students, as well as, Harvard Grads and Faculty, I realized that early on in my education I was considered ahead of my peers. By the time I was in grade 5 I was two years younger than my peers. It was around this time also I began to feel like a fraud. My confidence slipped and I would say I became a very average student until grade 11. In grade 11 something finally clicked. Did my brain catch up with the material? Did I become more confident? Did I just learn how to play the system and know what I needed to do to get good grades?
From grade 11 through until about eight years ago, I kept on that track I learned how to do what needed to be done to get a job done “well”. At least in the eyes of others. I taught curriculum, got through units, students produced work that they could be proud of. But what were they really learning? Had I really not just taught them how to play the system the same way I had.
I probably would have continued right on that path if a slap in the face moment had not occurred. I had to face my misconceptions head on. LIke Heather’s teacher in the video I believed that students arrived at my door with the background knowledge to proceed from where their last curriculum left off. Never once did I question the teaching that was going on in those rooms, rather if the students arrived not knowing something they just were not good at it.
I would review if needed (lecture style), and dispense new information (lecture style and perhaps with a model I demonstrated with) and often found myself thinking, that went really well, these kids have to understand this I did a great job. What a fantastic sage on the stage I was (notice I did not say teacher).
The slap in the face moment came when the first week of classes with grade sevens they were struggling with the most basic of concepts. Frustrated and decidedly sarcastically, at the time, I reverted to a primary teacher reviewing math concepts. It was then I became dumbfounded. None of the students had any understanding of WHY they did things in math. They perhaps knew the how’s of computation but application and understanding were sorely lacking. Later that day, to make myself feel better I walked in to the class that my students from the previous year were in. I asked the same question, and I got the same dumbfounding answers. They had no clue. HOw could this be?
If this was true in Mathematics it had to be true in other subjects as well. I sat down that night deciding how to map out my future as a teacher. My plan was to change my lessons from students listening to a chalk and talk to me listening to what they knew, talking to them about why they did something and trying to get them to apply that knowledge to new situations in whatever way possible.
Goal setting became important. As Blanchett (1977) stated “a good experiential situation must permit the child to establish plans to reach a distant goal,while leaving him wide freedom to follow his own route (p 37).” This led to my understanding of how I was rushing through the curriculum to check off units I had completed. I needed to slow down. In 1987, Duckworth stated that “learners need time to explore phenomenon (Chapter 6).”
Exploration became a large part of my classroom time. Allowing students to manipulate and create their own models. Give them an opportunity to try ideas and learn from the results.
In the Confrey (1990) article there is a very poignant section on arithmetic that discusses the difference between rote learning and meaningful learning. The following portion stood out for me “We label students as wrong, but do not delve into the preconceptions that may have led to this”.
Fosnot’s (2013) book delves deeply into how children can benefit from constructing their knowledge. Taking what they know (or think they know) and expanding on that. Allowing this will help them see if what they previously believed was true or if they had a misconception. Without the opportunity construct their knowledge students may never understand how to move forward and deepen their knowledge base.
After reading the articles and watching the video I began to wonder how, in mathematics specifically I could improve my own understanding of what my students knew and what misconceptions they may have.
I found a very helpful article by An and Wu (2012) entitled: Enhancing Mathematics Teachers Knowledge of Student Thinking from Assessing and Analyzing Misconceptions in HOmework.
First of all I have not been a big fan of homework for about the past 8 years, as well. During my epiphany, mentioned above, I realized that homework seemed to be busy work. Also that I assigned “busy” homework and did not really use the results to any end, other than marking it as done or not done. An and Wu (2012) bring up this point as well. Their research focuses on how we can use the grading of homework as a way to understand what our students know and what misconceptions they may have. If we assign fewer, more meaningful questions and take the time to evaluate that work we will have a much better picture of that students knowledge. We will be able to identify misconceptions and have the opportunity to allow the student time (with teacher direction and assistance to understand and correct these misconceptions).
This leads directly to my thoughts about how technology can help in this area. I envision my students choosing three of their “assigned work questions” one from each of the three sections to complete “on line”. Students could access a variety of programs that would enable them to show and talk about how they solved the problem. Why they did, what they did, why it made sense to them, as well as, if they believe they have solved the problem properly. This would allow the teacher to not only see the work the student has done, but also allows them to hear the rationale. Having this valueable information to refer back to would not only aide in understanding the students misconceptions but also be an excellent marker to refer back to once the student has progressed past this problem.
References: (Not in proper citation format to be fixed later)
Confrey, et al. Article from class notes list 1990
Fosnot, C. Chapter 1 and 2 from class notes list, 2013
An,S. and Wu, Z. Enhancing Mathematics Teacher’s Knowledge of Student Thinking from Assessing and Analyzing Misconceptions in HOmework. International Journal of Science and Math Education (2012) 10: 717