1.A.1: Subject Matter Knowledge
About the Element
The teacher candidate must be well-versed in the subject matter, including knowledge, understanding, and the pedagogy needed to consistently and effectively engage students in learning the content and subject-specific skills.
This element is important as it assesses whether the teacher candidate has the knowledge and understanding in teaching the specific content. One cannot teach what one does not know and understand. In combination, this element also assesses whether the teacher candidate has the pedagogical methods in conveying the subject matter to the students they are teaching. Being able to demonstrate and explain what you know and understand to others in order to teach them material, such that they are able to advance with those concepts in the field, is the baseline of teaching and the true test to fully understanding a topic.
It is necessary for a teacher to constantly be able to provide information to the students in varying ways, as not all learners learn the same way. Teachers also have to be able to listen and be well-versed enough in the subject matter, such that if a student proposes a certain approach to a problem, the teacher can help determine if that is a viable method of reaching the solution.
My Subject Matter Knowledge
As a WPI student, my middle school mathematics skills have only strengthened, especially as middle school mathematics forms the groundwork for a lot of future mathematics courses. The number of WPI mathematics and engineering sciences courses that I have taken have continually tested my strong foundation of basic math skills learned from my middle school years, in areas such as algebra, geometry, statistics, etc.
My coursework at WPI has prepared me for the pedagogy that is involved in transferring my skills and ideas to my students as well. I learned different methods in teaching mathematics in the classroom setting. From my student teaching experience, I further developed my skills by learning how to adjust to what and how students were learning from the material and strategies I was utilizing. I needed to be flexible in my understanding of the content, especially since in math, there are often multiple ways to get to the same answer. Being able to recognize when and how students were thinking differently about the concepts was key to knowing my strengths in the Subject Matter Knowledge category.
Element Artifacts
The sample videos to the right are a demonstration of my subject matter knowledge, understanding, and pedagogy in explaining the information. I would film 1-3 brief videos for almost every lesson through the recording program, Screencastify, and we would post these videos on my Supervising Practitioner's YouTube channel, to ensure that all students could access viewing the videos.
In the videos, my voice is heard as I bring in material to show the individual steps in solving problems. I utilized the multi-media principles of temporal contiguity and the signaling principle to enhance the videos. Temporal contiguity was used as I added transitions to allow my text to fly in as I was speaking. This allowed the viewer to follow the steps that I was verbalizing. For the signaling principle, I highlighted key words and steps in order to draw attention and focus to specific content.
During class, students were asked to view the videos independently for a time before we moved into practicing example problems. The videos were also helpful as students were able to review the videos as many times as they needed to, during class and outside of class. Students who missed class were still able to access the content they missed too. Any additional videos from other people, were used as extra resources to extend students' learning.
Description of videos on the right, from top to bottom:
How to solve a multiplication and addition equation: subtraction then division
This was one of the first videos I created for my classes. It was part of a series of solving equations videos. This video broke down the steps in solving an equation, where we see multiplication and addition. For each step, a written description of the step is included to align with what I am saying in the video. This helps to account for differences in learning styles, as some students are stronger in reading the example, some are stronger in listening to the example, some are stronger in modeling the example, and this helps to strengthen their organization in approaching a problem.
How to solve a 2-step equation when there are infinite solutions - Extended
This video was filmed towards the middle of my student teaching practicum. By this time, my skills in creating the videos were continually improving. Also, I was able to adjust my videos based off of how students had learned from previous videos. This video covered solving an equation that has infinite solutions, and included the sentence frame that students would be able to use in the following examples. In this video, we brought in previous concepts that had been discussed, such as the Distributive Property and combining like terms. This video was an extension to the first "How to solve a 2-step equation when there are infinite solutions."
Divide in Scientific Notation
This was one of the last videos I filmed during my student teaching experience. It brings my knowledge, understanding, and pedagogy in a slightly new context of dividing in Scientific Notation. The same techniques in the general structure of the video have remained. As I filmed more videos though, I became more comfortable and stronger in my delivery. Even my voice and tone in the later videos has changed and grown with more confidence and enthusiasm.
Word Problems with Scientific Notation and Standard Form 2
This also was one of the final videos for my student teaching. It built on the previous "Divide in Scientific Notation" video and the first "Word Problems with Scientific Notation and Standard Form 1" video, to demonstrate how we can approach solving word problems involving Scientific Notation and Standard Form. I revisit concepts that we have already learned to reinforce ideas and strengthen students' understandings, while introducing new techniques to approaching a given example problem.
Anna Eng
WPI Teacher Preparation Program
aeeng@wpi.edu