Applications of Research Methodologies in Educational Practice

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Secondary Mathematics Comprehensive Exam

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According to Lai, the modern secondary mathematics classroom is a complex ecosystem,

shaped by diverse student backgrounds, varied learning needs, and persistent educational

challenges (Lai, 2024). The educator must take on the role of a teacher and researcher, carefully

looking into practice-related issues to go beyond informal observation and bring about

significant change. This essay examines my experience applying research approaches to pinpoint

and resolve essential problems in my classroom. I went from recognizing a problem—an

ongoing achievement gap in Algebra I connected with student background—to comprehending

its underlying causes and putting specific, evidence-based solutions into place by combining

quantitative, qualitative, and mixed-methods strategies. The particular techniques used, the

framework of my research on math mindsets, the ethical measures taken, and the significant

ramifications of these findings for establishing a more equal learning environment for all

students will all be covered in detail in this reflective analysis.

While teaching, I have realized that research could be used to improve my teaching and

enhance student learning. I have used qualitative, quantitative, and mixed methods, offering a

different perspective on my classroom. According to Williams, quantitative research concerns

numerical data and statistical analysis. Its strength lies in its ability to identify broad patterns,

measure change, and provide objective, generalizable results on a larger scale (Williams, 2021).

For example, administrators at my current school have recently started requiring all core subject

teachers to administer a pre-test before each unit and a post-test after the unit. The administrators

are trying to measure the learning that is happening within the classrooms. This is a strength

because it helps teachers identify which students are constantly struggling from unit to unit.

However, just by looking at the score, it is difficult to determine the “why” or “how” the students

are not progressing. Qualitative research focuses on non-numerical, descriptive data, seeking to
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understand experiences, beliefs, and context (National University). It uses interviews,

observations, and surveys to get a deeper understanding. I administer a brief informal interview

to my class almost at the end of every lesson, asking questions like “What did you understand

about today’s topic?” or “What are you still confused about?” I like doing this because it

provides the “why” behind test scores. However, it is difficult to get 100% participation, so I

cannot determine the “why” behind some students. Mixing both of these methods, not only am I

able to see which students are consistently struggling, but I can also get a better understanding of

the reasoning behind it.

The issue I chose to address was the achievement gap between students from lower and

higher socioeconomic backgrounds. This social and economic issue has been ongoing in

education for many years. Just from my Algebra I class, I have noticed that students who receive

free and reduced lunch, usually lower socioeconomic students, typically struggle to learn new

concepts. They also tend to be less attentive during class discussions and are quicker to give up

on challenging problems. I constructed a research project involving quantitative and qualitative

methods to go beyond this simple observation and get a deeper understanding. I wanted to

identify if there was a statistically significant correlation between a student’s socioeconomic

status and their prior knowledge in mathematics, and how students from lower socioeconomic

backgrounds describe their experiences within a mathematics classroom. Using a mix method

was the best option because it allowed me to grasp the baseline of the issue, but also helped me

go deeper into understanding the “why”. I began by getting student volunteers to take a survey

asking about their social and economic demographics, and then a mini math test to evaluate their

current math knowledge. After reviewing the results, I selected approximately 10 students who

identified as lower socioeconomic students based on their responses to the survey. The 10
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students’ scores on the math test ranged from low to high. I then interviewed them and asked

questions like “How do you feel when you are faced with a math problem you don’t know how

to solve?” and “Tell me about a time you felt successful in a math class.” This method revealed

answers that aligned with the initial problem. Students expressed how they felt “out of place”

and lacked specific resources as their peers, causing their math ability to be limited.

The findings in this research impacted my teaching methods drastically. I discovered that

teaching high-quality content was not enough for some students. I needed to prepare a growth

mindset and create a safe classroom for students to struggle and celebrate their perseverance. I

began giving students motivational feedback like “I like the effort you put into solving this

problem”. I also began assigning more group work to build that sense of belonging. I shared my

findings with my colleagues, ensuring that students were anonymous. The focus was more on

strategies they could implement in their classrooms.

Conducting research with students I was familiar with made me feel as if I was walking

on thin ice. My main goal was to ensure they were comfortable, and no judgment came their way

because of their participation and, more specifically, their answers. Before conducting my

research, I spoke with all the parents and guardians of students who volunteered. I explained to

them the purpose of the project and the type of data that will be collected. I also informed them

that it was completely optional, and it would not impact their grades. I made sure that all

documentation was communicated through email. Most importantly, I made sure all students’

answers were confidential, and I was the only one who knew who said what.

The journey from being a teacher who observes problems within the classroom to a

teacher who researches the problem and systematically solves them has been transformative. I
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could identify a complicated issue with equality and attitude in my classroom, comprehend its

human aspects, and carry out focused, significant changes by embracing mixed research

methodologies. This process underscores the idea that our classrooms are not just places of

instruction but living laboratories where thoughtful inquiry can lead to profound and positive

change. Continuing this inquiry, action, and reflection cycle is essential for creating truly

equitable and empowering mathematics classrooms for every student.

Lai, C. (2024, June 17). Nurturing student agency in Secondary Mathematics: Challenges and
opportunities. ECIS. https://ecis.org/student-agency-secondary-mathematics/

National University. (2025, March 24). What is qualitative vs. Quantitative Study?
https://www.nu.edu/blog/qualitative-vs-quantitative-
study/#:~:text=These%20examples%20illustrate%20how%20qualitative,quantitative%20re
search%20focuses%20on%20measurable

Williams, T. (2021, June 14). Why is quantitative research important?. GCU.