## Personal Teaching and Learning Trajectory

At the end of the Fall 2018 semester, I sat in my advising meeting with Professor Jack Dougherty. I needed to select just one class to fill my schedule and put towards my Ed studies major. And on top of that, with the classes I had selected thus far, I had no Friday classes at all, which was an exciting prospect for me. Jack proceeded to pitch Educ 350: Teaching and Learning to me. He explained that it was being taught for the first time in many years, and would involve the opportunity for me to be in a real classroom again, like I had done in Educ 200, but this time with a more central role directly teaching lessons I would be planning. I thought it sounded like a great opportunity for me to get hands on teaching experience which is something I am passionate about new teachers doing before starting their careers. I asked Jack if the course would fit into my current proposed schedule, and he excitedly told me it would perfectly- it met for 3 hours on Friday afternoons. I reluctantly agreed to give up my day off and signed up for the course.

I underestimated the value of experience I would get to prepare me for the world of education. Our first couple sessions about inquiry based learning and types of assessment enlightened the way I looked at teaching. I would say my own education growing up was very typical. I remember of receiving a lot of “teaching to the test” and having work in my math and science curriculum that was very much geared towards “just getting it right”. In our first few classes I was challenged to write my own definition of inquiry based learning, which I defined as: Learning in which students are challenged to learn about a topic through a process of generating questions about it and coming up with solutions. I think that this approach to learning was one I gradually implemented as I went on through my lessons.

As much as I learned in our classroom sessions, the real learning happened outside the walls of our classroom and in the walls of another one. I was placed at the Environmental Sciences Magnet School, in the 6th grade math class of Mr. Adam Smith. I planned my first lesson with my classmate Lexi Zanger. The learning objectives of my first lesson were:

“Write, read, and evaluate expressions in which letters stand for numbers; Use variables to represent numbers and write expressions when solving a real world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specific set”

This lesson ended up being somewhat stressful to carry out, because my plan was to just do an introduction to the topic, followed by completing the practice problems in the student workbook and having an extension activity available in case there was some extra time at the end of the lesson. However, I found out just before going to my first lesson that Mr. Smith had already completed the lesson I was to teach, including the practice problems from the student workbook. My lesson was actually supposed to be a review of solving equations with variables, rather than an introduction as I had planned it. I think that reflecting on this lesson again after all of my experiences, I could have better adapted it based on the students already having some experience with the topic. However I still kept my original launch with which I opened the lesson explaining the lesson in likely too simplified of terms because it appeared to be too easy for the students. Then, I skipped completing the practice problems and went straight to the challenge activity, which involved students writing their own word problems. It was a bit of a stretch to make this activity fill the majority of the class time and I ended up having kids copy their word problems onto posters and hang them on the walls.

As one might expect, my first lesson was definitely my least successful. Though my plan met the objectives, and was also equitable and had appropriate assessment, it could have been more engaging and creative. This area was something I think I improved upon a lot in my second lesson.

My second lesson felt more like a game than a typical math class, and I think engagement from the students was highest on this lesson, which immediately after made it feel like a big success to me. The objective of my second lesson was

“Find the area of right triangles, other triangles, special quadrilaterals, and polygons, by composing into rectangles or decomposing into triangles and other shapes: apply these techniques in the context of solving real-world and mathematical problems.”

This idea for a lesson actually just popped into my head when I was trying to think of a situation where area is used in real life. All of a sudden my mind just went to my when I was 10 years old and would drag my stylus across the screen of my Nintendo DS screen to draw the area of the animal enclosures in my favorite game, Zoo Tycoon. I was thus inspired to create a similar game involving drawing animal enclosures in the shapes of triangles and parallelograms. I added an element of their being a minimum amount of space each animal needed in order for an enclosure to meet regulations. So, students had to correctly solve the area of each of the shapes they drew in order to have the quantity and type of animal they wanted to place in their zoo. Once they did, I had paper cutouts of different animals which I handed out to students to glue to their zoo maps. As you can imagine, the students seemed to have a lot of fun making decisions about their zoo designs and finding area as they went.

While I made great strides in the level of engagement this lesson generated, I think it caused me to overlook other important areas of the lessons’ design. In terms of equity, I had initially thought that the topic of my lesson was appropriate under the assumption that most of the students had been to the zoo before. In fact, some students had not when I asked at the beginning of the lesson, and on top of this I had nothing in place to ensure inclusion of all the students while working in groups. My assessment methods were also not as thorough as possible, as this consisted only of me checking students’ work for correctness in order to determine if they met the requirements for any given animal they were asking for. This didn’t allow me to really see the learning but more the end result.

I had a hard time feeling great about my third lesson because I wasn’t able to top the level of engagement of my second lesson. However, I think that I made great improvements in my final visit to Mr. Smith’s classroom. The learning objective this time was

“Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V= lwh and V= bh to find volumes of right rectangular prisms with fractional edge lengths in the context in the context of solving real-world and mathematical problems.”

I adopted the lesson structure of the Three-Act Task, which was first introduced to me by Georgina Rivera when she guest spoke during our class session on March 29th. The students definitely were uncomfortable with this type of lesson which was novel to them, but did a good job discovering the question themselves, which was “How many Rubik’s cubes will it take to fill this cardboard box?”. There was a lot of frustration from students during this lesson. While this meant that I had finally come up with something that was challenging enough for students, I think there was also difficulty for them coming from not having the steps they must take to answer the question outlined for them, but rather being told to get from the question to the solution in their own way. That being said, I think this structure of lesson was actually optimal for making it “real world” as the objective says. My lesson was also more equitable and had better assessment than any prior. I got much better at being mindful in terms of including all students by not only answering questions for students who asked them, but also asking questions of students who weren’t to try and get them on the right track to understanding the problem. I captured and individualized my assessment better than before as well, by sending students to my camera in the back of the room to explain how they found their answer. Despite many students being frustrated with the Three-Act task, I think this stemmed more from them not being comfortable with this style, however I think it was actually a great example of inquiry-based learning.

I think just looking at my experience across the three lessons I can see a lot of growth in myself. I was able to take into account more factors to make my lesson well rounded and optimal for learning. These are things I will take into account when designing my own lessons in my future teaching career.

Taking this course actually inspired the design of an independent study I have proposed to do in Fall 2019. I really liked the experience of being hands on in a classroom, and since my focus in education is on special education, I decided to design an independent study to combine these things and design curriculum for students in special education. I am currently in communications with the special education coordinator at HMTCA investigating the potential of collaborating for this project, and from there will seek out readings to do in order to educate myself on features of curriculum design for students in special education, in collaboration with the components focused on in Teaching and Learning. In the future, my hope is to work with students in special education as a future career, as there is a major issue in the quality of education these students receive, and I hope to have a role in changing this.