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The Learner and Learning
Summarized in a single concept, I believe mathematics education should be rooted in the real-world contexts to which each skill applies. My academic background is in corporate strategy and data analytics, which are subjects that are inherently interdisciplinary and rely heavily on a strong foundation in different branches of mathematics. This has shaped the way I teach my students because I know firsthand that math doesn’t exist in a vacuum. The future engineers in my class will never be asked to complete a worksheet as a requirement of their engineering job description, so why should that be the primary deliverable in my classroom?
Whenever I can, I aim to infuse my teaching with project-based learning to develop context and provide students a structure in which they can guide their own exploration of a topic. For example, in learning right-triangle trigonometry, my students designed wheelchair ramps for different locations on our campus according to the ADA legal regulations. Students studied the laws dictating wheelchair ramp requirements, modeled their designs using CAD software, and pitched their designs using public speaking best practices. When students learn in this way, I believe that even the students who have never felt confident or successful in previous math classes can find a touchpoint that engages their curiosity in the subject.
Because of my background in data analytics, I believe that measuring progress and results in the classroom is both a quantitative and qualitative process. My students’ and my success are not dictated by a single score or number. My biggest indicator that I have succeeded as an educator is my student’s academic efficacy self-assessment. Between four and five times per year, I ask my students to rate their confidence in their ability to learn new mathematical concepts on a scale of one to five, and I track their responses over the course of the year. Last year, my students’ rating moved from an average of 2.4 out of 5 to 4.1 out of 5 by the end of the semester, and I believe this finding says more about my students’ growth and my growth than any standardized benchmark ever could. This represents only one of many ways I track data and utilize it to inform my instruction.
For many of my students, some of my teaching practices are radically different from their previous math instructors’. So, it is important to create buy-in built on a foundation of trust. Relationship-building is at the heart of successful project-based learning, which is why it is also integral to my teaching philosophy. I strive to learn details about my students’ lives so I can get to know them more holistically, rather than base all of my knowledge solely on their performance in my class. This approach aligns closely with the teachings of Fay and Fay, who advise building relationships rooted in high expectations and compassion (2016). This looks like meeting students where they are emotionally and socially, not just academically. As students today are avid social media users and have grown to prefer electronic communication over verbal communication, I provide my students many different avenues for communication, including texting, emailing, and, of course, meeting one-on-one, per the research of Carr, et. al. (2021).
My goal for all my students is for them to leave my math class feeling confident in themselves and prepared for their next stage in life, whether math is a part of that vision or not. Every decision I make is a means to this end, from how I structure my projects, to how I configure my classroom.
Classroom Community & Safety Plan
The plan detailed below identifies specific structures of classroom community, physical structure, and organization to facilitate classroom instruction. These questions are also answered in detail within each of the lesson plans linked throughout the dossier.
How will you ensure students know where to find and understand class activity instructions?
Instructions will be repeated multiple times. Written and graphic instructions will be projected on the board, and verbal instructions will be repeated throughout the activity. Additionally, during independent working time, instructions and a timer will remain on the screen as well as posted in Google Classroom for students to access.
In what ways will you respond to interruptions or disruptions?
Strategies for responding to interruptions that would be easy to integrate into the lesson include:
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Setting expectations before the lesson starts, reminding students that there will be an opportunity to talk with peers later in the class period
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Redirection during active monitoring
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Appreciating appropriate behavior and acknowledging inappropriate behavior
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Pacing the lesson to avoid passive transitions
How will you provide other additional support that may be needed (for students who are disengaged or who do not understand)?
Differentiation in the process and product of the lesson will allow students to seek the support they need. If a student has not opted to utilize these supports, it becomes the instructor’s prerogative to redirect students to these options. For example, students who are becoming distracted due to the new seating arrangement will be encouraged to fill out the guided notes, or students who need the concept reiterated after the “lecture” portion of the lesson will be encouraged to start their independent work with an EdPuzzle video.
What are your plans for transitions from one activity of the lesson to another?
The instructor will announce transitions and the expectations for the next activity before it occurs. If it appears that students are not paying attention or may misunderstand the instructions, the instructor can employ the strategy of asking a student to repeat back the instruction in their own words. This will give an opportunity for clarification.
How will you use/reinforce classroom norms?
It is important to refresh norms during every class session, which is why this discussion is part of the introduction to the lesson. These expectations can be reiterated throughout the lesson. Additionally, the instructor should praise and appreciate positive behaviors and redirect students who are engaging in negative behaviors.
How will you handle supplies needed for the lesson?
The front table of the classroom will be the home-base for student materials that are required for the lesson, with the exception of student notes and Chromebook's which students are responsible for bringing with them to class. In the event that a student is not prepared with these materials, students know where additional materials are located. Students can also opt for a hard-copy version of the independent work instead of the digital versions.
What are the physical components of the classroom, such as desk arrangement, stations, cooperative learning groups, etc. that support your learning objectives?
Desks are typically arranged in a grid. However, for lessons that hinge on student collaboration, desks will be arranged in groups of four to promote student discussion. Because of this, establishing and reinforcing classroom norms is paramount and will be prioritized throughout the lesson.
Both in teacher preparation programs and within schools, there is a consistent and steadfast push for educators to make data-informed instructional decisions. My personal belief is that this usage of the word, “data,” is vague and can mean various pieces of information from various sources. Nonetheless, I also believe that this phrase is reflective of the choices I’ve made teaching pre-calculus over the last year and a half.
Since I do not teach a course that culminates in a standardized exam, monitoring student progress depends on local definitions of success rather than global ones. Because of this, I, with the help of the leaders in my department as well as my students, developed our own benchmarks to reflect the unique learning needs of my individual students and the Frederick Douglass High School community. Out of these conversations, I developed a simple math efficacy survey, which I distribute to my students quarterly. This survey monitors students’ confidence in their ability to learn new things as well as their confidence to improve their math skills. According to Samuel and Warner, measured increases in academic efficacy in the math classroom can reduce math anxiety in the long term (2021). Coupled with formative data collected during class and students’ grades on various assignments, the results of this survey helped me assess my own effectiveness as a teacher.
Overwhelmingly, students’ confidence rose over the course of the academic year (Figure 1). During this time, and into the subsequent school year, I employed strategies that intentionally lower students’ barriers to entry for challenging mathematical concepts. I scaffolded assignment and allowed students to self-diagnose their level of need for instructor guidance to give all students the opportunity to understand a concept more deeply. Teaching abstract concepts within trigonometry was conducted through tangible tasks and projects that connected the standard to student interests like architecture, computer science, and design, in line with the principles of Culturally Responsive Pedagogy, explored by Voigt et. al. (2020). These practices were similarly guided by Muhammad’s Historically Responsive Literacy framework (2020). We explored the context of math using examples that are proximal to our class’s experiences, like partnering with local businesses and nonprofits and framing math on Frederick Douglass High School’s campus.
I know that adjusting my instructional practices will be an ongoing process throughout my teaching career. I see this process as adding tools to my teaching toolbox, and as new challenges or needs arise, I can draw the tool that fits best. Currently, I would assess that I need many more tools to help me differentiate. At the beginning of my teaching journey, integrating differentiation strategies feels less organic than other components of my planning. Over the next few years, this is an area of my arsenal I wish to bolster to better serve the different needs of my students in both pre-planned and spontaneous ways.