Teaching, Learning, and Understanding

            It is often common practice for parents to ask their children “so what did you learn today?” which is often followed up with a response such as “nothing much.”  However, when a student performs an activity during their day, a student’s response is much more elaborate, such as “I know how the Earth revolves around the sun!”  These students’ responses are the difference between learning or understanding and experts or novices.

When I attended middle school, teachers would model one or two problems and students would work individually.  Explanations of “why” were never needed because students were to memorize and repeat steps for a similar problem.  The importance of understanding was not emphasized because as long as you could follow the steps, you could pass the test.  With the creation of Common Core and Next Generation, students are forced to ask themselves “why” to understand concepts with deeper meaning.  At the University of Michigan – Dearborn, we were taught to use hands-on, inquiry, and project-based lessons.  During one math course, we used materials to find a definition for pi.  Through this activity, I began to understand instead of memorize the formula for the circumference of a circle.  We also used inquiry lessons to dispel misconceptions such as the idea that the Earth gets closer to the sun.  Our professors performed an experiment with us where one student was holding a tilted 23 degrees Earth and walked around a Sun.  Students participated in discussion and noticed that the Earth stayed the same distance from the sun while the tilt of the Earth changed.

In my own classroom, I have adopted the use of hands-on and project-based lessons, which has forced students to understand their own thinking.  I have found that students are more likely to remember an inquiry lesson than a day full of taking notes and memorizing.  Bransford, Brown, and Cocking (2000) described Alan Schoenfeld’s classroom as very similar to my own as he includes “elements of modeling, coaching, and scaffolding, as well as collective problem solving and whole-class and small group discussions.”  Units begin with a day of introduction where a math problem is modeled in different contexts and shown through problem demonstrations.  Students work collaboratively in groups and are required to present their problem solving and explain why each step was important before giving the answer.  “At the end of each of the problem-solving sessions, students and teacher alternate in characterizing major themes by analyzing what they did and why” (Bransford, et al, 2000). Students begin to understand a concept more clearly and answer “why” when they are able to perform hands-on activities, participate in collaboration, and use metacognition to verbalize their reasoning and thinking.

Experts and novices can be seen all around the world:  a mathematician versus a high school math student, or professional athletes versus high school football players.  In the classroom, students can be seen as “novices” and teachers as “experts.”  Experts’ “knowledge is not simply a list of facts and formulas that are relevant to their domain, instead, their knowledge is organized around core concepts” (Bransford, et al, 2000).  Novices are being exposed to new facts and need experiences to build up to the skill level of an expert.  “Research on expertise suggests the importance of providing students with learning experiences that specifically enhance their abilities to recognize meaningful patterns of information” (Bransford, et al, 2000).  Students need direction and instruction on how to organize their knowledge and make it easily retrievable in contexts.  Students or novices must be taught to understand problems rather than jump to conclusions.  Practicing this skill will make retrieval of information automatic and fluent which is an important characteristic of being an expert.

It is important for teachers to consider different metacognitive methods while teaching.  This gives the students a chance to understand a concept because they are answering “why” and required to explain their reasoning.  Teachers also have to remember that being an expert in their field “can sometimes hurt teaching because many forget what is easy and what is difficult for students” (Bransford, et al, 2000).  Working with other teachers and creating lists of misconceptions or difficulties for students can improve instruction.  “Expert teachers know the kinds of difficulties that students are likely to face” (Bransford, et al, 2000) and know how to connect new concepts to prior knowledge.


Bransford, J., Brown, A.L. & Cocking, R. R. (Eds.), How people learn: Brain, mind, experience and school (pp. 3-27). Washington, D.C.: National Academy Press.

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