After a given lesson, each student's understanding of the material is unique; thus, each student represents a point on what could be called the "Spectrum of Confidence" related to the taught material.
 |
| The "Spectrum of Connnnfidennncee" according to Spongebob |
Let Spongebob's right hand represent no confidence in understanding a given concept, his left hand represent complete confidence in understanding a given concept, and each "star" represent an arbitrary student in the classroom (sound like the start of a proof anyone?). From my experience of serving a SLA Facilitator (for those unfamiliar with the role, a description can be found
here), I can tell you that it is not hard to find two points along the spectrum: complete confidence and complete lack of confidence. To visualize what is going on internally with these types of students, I call upon my friends Robin Hood (complete confidence)
 |
| Oh please, I got this concept. |
and Harry the hedgehog (complete lack of confidence).
 |
| If I can't see you, you can't see my lack of understanding. |
As teachers, we need to identify if our students fall into either of these levels of confidence especially. First, we will discuss what it means to look like Harry the hedgehog. While going over a topic with my SLA class, I can often identify these students by looking for the face depicted below.
 |
| I look like I got it, right? |
This blank stare signals to me that I am speaking what sounds like a foreign language to these students. For most students, it is very difficult to be honest with themselves and admit that they need help with understanding the material. Often, they choose to give up because they believe will never understand it since, as some of them say in frustration, "math is stupid and too hard for me to understand."
 |
| Did you really just say that? |
I believe that every student has the capability to not only understand the material, but also should feel confident that he/she can learn and understand anything presented to them Thus, in my future classroom and currently as an SLA Facilitator, I want to instill self-efficacy into each each student, especially those who utter that dreaded phrase that sounds like nails on a chalkboard. However, I must be cautious in doing so as it is important they do not lose the ability to think critically. In other words, a student should not be so confident as to think their initial understanding will always be the correct one. An example of a student who is confident in his understanding, but not have an accurate understanding of the material is Colin from "
Quadratic Functions: Students' Graphic and Analytic Representations." In the article, Colin, a tenth grade honors student, is interviewed on his knowledge of quadratics. He confidently completes each task presented to him without questioning his answers, since he believes the connections he has made are correct. However, his understanding of quadratics is very flawed. Whether going from an equation to the graph or vice versa, he made connections that he believes are mathematically sound, but are actually completely false. As teachers, we must also pay attention to the students who seem to understand the lesson because they could be just like Colin. These students will probably look like Lea Michele below, but without further investigation, there would be no way of discovering this false sense of confidence and severe misunderstanding of the concept.
 |
| See Mr. Schweitzer, I understand the material! |
In other words, I want to prevent myself from finding out that a student has a severe misunderstanding of a concept before a summative assessment, and looking like this guy when seeing their test or quiz.
 |
| But it seemed like you were getting it!?! |
Therefore, on my quest to instill self-efficacy into my students, I must use an abundance of formative assessment and check-in with each student. In doing so, I hope that when my students leave my classroom, they will be ready to take on not only the material in their other courses, but also everything they encounter during their lifelong learning.
I think you're going in a healthy direction here. Formative assessment, and understanding that it goes past "I could see it in their eyes." Good example from the article. I think you might want to consider getting the students in on the game in self-assessment. Do they know what they're looking for or are they relying on you for the thumb's up? (Related old post of mine: http://mathhombre.blogspot.com/2010/12/self-assessment-for-teachers.html)
ReplyDeletecomplete: maybe an idea of how you are going to check competence as well as confidence?
clear, coherent, consolidated, content +
I really enjoyed your post, Nick! I also know what it's like to receive those blank stares from a classroom of students, but I also know that I too have been a culprit of giving it. From being on both the receiving and sending ends of the blank-stare-of-low-confidence, I have three observations: case 1) students (or I) really don't understand the material very well; case 2) I asked the question in a confusing way, in which case revision is needed on my part; and case 3) wait time. In my personal experience, if I can't respond to a question, I usually just need more time to think. Simple. But, student teaching I've found that it takes a lot conscious and intentional effort to provide adequate wait time (which is important because we don't want to mistake lack of understanding for lack of time to process).
ReplyDeleteThis makes a lot of sense to me. Confidence is a key in anything. Something as important as a job interview requires confidence. Someone who is confident gives off a better vibe to an employer. The only problem is, as you said, someone who has no reason to be confident. If you don't know what you are talking about, your confidence level doesn't matter. I wonder how you could gauge a student's confidence accurately though. Student's will often lie whether in public or private because they don't want to admit that they have no clue what is going on in the classroom. I really like this post though.
ReplyDelete