As I reflect on my thinking about teaching over the past year, I keep coming back to the idea of making learning meaningful. In my mind, meaningfulness comes from the confluence of other elements, such as collaboration, problem-solving, relevance, real-world application, student-centered instruction, and support. While my teaching philosophy has always included these core components, the development of my teaching philosophy shows in my deepened understanding of how those elements interact in ways that either do or do not promote meaningful learning, and the role my students’ and my actions play in that.

The beauty of math for me has always been its connection to the surrounding world. Coming into teaching math, I knew I wanted to bring as many real-world contexts into the classroom as possible to engage students and introduce problem-solving. On my first attempt in October to introduce a multi-day real-world problem to one of my mentor teacher’s classes, I pretty much left the students on their own after I hooked them into the problem. They struggled to transfer the skills they had just learned to this new context and engagement waned. In an effort to make the lesson so student-centered, I omitted all helpful scaffolds on my end. Reflecting on that experience in my journal entry on October 3, I wrote, “I realized that I got so caught up in wanting the students to figure things out for themselves and persevere through that struggle that I forgot that the proper supports need to be in place for that first.”

Figuring out the correct level of support has been challenging and varies greatly between my two classes. In a project with my integrated math class in February that asked students to create and analyze a system of equations based on a given scenario, I first went through a model scenario with them and then filled out the same template they would use for their own scenario. In that same journal entry from October, I theorized, “Modeling more for [my students] and with them doesn’t mean that they won’t still have the chance to figure things out for themselves; it might actually mean that they’ll feel better equipped and more willing to do so.” When I took my own advice with that project, I watched my students engage deeply with their classmates in math conversations about relevant, real-world scenarios. Although I had used most of the first day of the project for teacher-centered modeling, students were now positioned as constructors of knowledge and learned from each other through collaboration. Seeing results such as these has helped me understand that while a problem might seem meaningful in and of itself, my students’ interaction with that problem will only be as meaningful as my structure allows.

Working with two classes that have very different needs has helped me understand that this idea of meaning cannot be separated from the students in front of me. The students in my numeracy class overall have much more confidence in their math abilities than the students in my integrated math class, so the same modeling I needed to do to help my students feel comfortable engaging in the systems of equation project would not be necessary for my numeracy students. The subjectivity of meaningful learning at times frustrates me, for what works with one class might not work with another class. However, noticing this subjectivity has helped me appreciate my students’ diversity, for it challenges me to make authentic relationships and create activities that those specific students will find relevant, as opposed to just throwing any real-world scenario at them for the sake of saying that we looked at math applications.

Another significant part of the progression of my understanding of supporting meaningful learning has come from the realization that skills-based practice in math is not always bad. In fact, it becomes a necessary part of the learning process. Going into the school year, I told myself that I would make all math learning have a real-world purpose and vowed to focus on the conceptual understanding of math concepts rather than just number manipulation. As I have worked to help my students discover and understand the myriad of concepts the curriculum demands, I have realized that jumping from one exploration to the next does not constitute true learning. To get anywhere close to mastery of a concept, students need repetition. While at first I looked at this negatively, I now understand that without some skills-based repetition, most students will not be able to interact with a concept in any meaningful way because they will not have the math abilities necessary to do so. In my numeracy class in February and March, students spent a few weeks solving equations of varying degrees of difficulty, which necessitated a very singular approach and didn’t leave much room for creativity. Once they learned and practiced those skills, they worked to solve challenging word problems that they created using their knowledge of solving equations. Although I do not at all advocate for the exclusive use of classroom time for skills-based practice, I can now recognize that using it strategically will eventually support students in more meaningful learning.