irThe whirlwind that was my first two semesters of teaching daily in a classroom is almost over. Just one week remains in what has been a dynamic, bouncy, and transformative journey! I am looking forward to a calm summer after what has felt like a tornado for me personally. With all that said, I truly believe that I have learned a lot about the nature of mathematics teaching, and about how much I still have to learn.
Teacher Assisting and Student Teaching came and went so fast.
From my time at a small charter school at the middle school level on the north side of Holland, to today finishing up at a large high school on the Northwest side of Holland, I have seen a great shift in my development as an educator. I began the final semester of my senior year thinking that I could model a mathematical process and students would just understand. Like osmosis or diffusion the high concentration of mathematical thinking in my mind would diffuse into the lower concentration of their minds. I quickly learned that whether at the middle school level or the high school level students develop most mathematically by working on problems and developing their thinking. Don’t get me wrong, some students will pick up perfectly well when I show a problem and present a procedure, but a majority need something more. My thinking is not good enough for most students because mathematics has its own language. Often times I fail to translate math well enough, and a great number of students are not translating the language of math on their own. Over hours and hours of examples, and seeing students watch the method, and attempt to repeat the method taught. I have come to the realization that this is often times not the best way to go. I am excited to share my reflections from my year teacher assisting at a middle school and student teaching at the high school level.
A few key things I learned I believe will begin to combat the issues I faced in my teacher assisting and student teaching semester. Number one…
Engaging Student’s Minds
I must activate and encourage student thinking about mathematics because students are not made like robots to have the information that I know directly passed on to them.
Psychologically students learn best when they are actively associating, making connections to previous things they have learned and have experience with. The process of making memories begins with encoding where students construct memories from their perceptions of events. A mathematics teacher lecturing at a board may seem fascinating to some students and thus it will be perceived as interesting and encoding will occur on an acoustic and visual level, but many students crave something more and their attention is just not gained through direct instruction. Better than visual or acoustic encoding, semantic encoding is said to be most effective for long term storage most of the time. So what is semantic encoding and why should a math teacher care about it?
Semantic encoding is the process of converting to a construct something that has a particular meaning or can be applied to a specific context. I care about semantic encoding because in today’s mathematical landscape student’s understanding of mathematical concepts depends on applying meaning to mathematical symbols and numbers.
Therefore, I want to focus on giving students rich open ended tasks which as much as possible have a real context. These tasks will engage students and allow them to make their thinking visible to their classmates through small group collaboration and sharing out to the class. One activity where I successfully engaged student’s minds was in a Clinometer Activity where they measured the height of very tall objects using trigonometry. To do this I need to create a classroom culture where students feel safe to share and are willing to make mistakes. This is not an easy task, but through persistence and clear classroom norms I believe that this is possible.
Make Sense of Problems & Possible Solutions
Second, I learned that in math class it is very important to emphasize making sense of a problem before diving into solving it. If students have no clue what they are doing they give up or come out with inaccurate answers. Making sense of a problem eliminates answers that are way off in many problems. Instilling student confidence in making sense of problems expands their critical thinking skills and prepares them for the real world.
Valuing Student Thinking
Lastly, I have learned that even struggling students appreciate it when teachers really are interested in what they are thinking and respond with thankfulness. I can value student thinking by creating a classroom culture which sees mistakes as an opportunity to grow and participation as a necessity to personal learning. Also, I can provide a variety of means for students to share their thinking through questioning, writing to explain their reasoning, having respectful arguments, and encouraging students to share their thoughts with their classmates on a consistent basis! Talking out your thoughts cannot be merely something that is asked, but something that is expected from every student from early on in the year.
In the end, I had an outstanding year of learning as a mathematics teacher that will stick with me and serve me well for the rest of my teaching career. I have been able to build a foundation for future success. Day by day through reflection and gradual transformation I have the opportunity to become an excelling teacher!
A few other key areas of more general growth for me as a teacher that I want to represent.

I have expanded greatly my knowledge of how to work well with ESL students. I had to explain geometric vocabulary and analyze their formative assessments in effective manners. I learned to provide resources to ESL and English Language Learning students early and often to allow them to have the most possible academic success. I used my Spanish speaking skills to connect with the students and describe concepts like enlargement and reduction. When speaking skills were not enough I used hand gestures, pictures, and other means to teach these students.

Each semester I improved my unit plans by becoming better at forming clear objectives from the Common Core State Standards. I analyzed the standards to decide on the best organization of objectives for my units.

I have learned that grading formative assessments quickly is very beneficial for student growth, and can allow students to improve their skills quickly. By returning graded papers quickly, I gave students plenty of time to consider their mistakes, and to improve upon those mistakes to prepare for a summative assessment.

Also, I have seen the value of developing relationships beyond mathematics curriculum by talking to students about their lives on a regular basis. I try to keep this focus in order to encourage students to grow in character and integrity before growing more as mathematicians.
What a year a tornado indeed, but I have learned so much!
Kevin, thanks for sharing your reflections on a year’s worth of field experiences at both middle and high school levels. Two things that stood out to me: your comments about valuing student thinking, and your growth in the area of supporting ESL students. Lots of other good stuff here too! Congrats on finishing up.
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