Abstract
Traditionally, mathematics is taught as a subject based on algorithms and patterns that students practice until they reach a sufficient level of mastery. However, there exists a complete realm of mathematics that involves historical discoveries, real-world applications, and other ways that bring mathematics a sense of meaning. Prior research on teaching mathematics from these historical and real-world perspectives has shown that authentic teaching of the subject provides students with the space to make individual discoveries and take ownership of their learning. This ultimately helps students develop a greater understanding and appreciation for mathematics. The teaching strategy that best embodied the findings of the literature was the approach of mathematical creativity.
Mathematical creativity is defined as a teaching method through which students “approach problems in novel ways or find new solutions to existing problems through ‘engaging in a task for which the solution method is not known in advance’” (Firmender et al., 2017, p. 206). While it is encouraging to bring into the classroom, the current literature research only seemed to show evidence of mathematical creativity benefiting mathematically gifted students. This then begged the question of how mathematical creativity can be something that is attainable for all students of all ability levels and learning styles.
The following study focuses on answering this very question through a narrative analysis. The narrative analysis was done through virtual interviews of two e-board members of the International Group for Mathematical Creativity and Giftedness. After organizing the information shared from both interviews, three focus areas emerged as part of the proposed way that mathematical creativity can be attained by all students. In sum, the findings suggest that as long as a safe and secure learning environment is established, content is differentiated for every student based on their learning needs, and classroom material highlights open-ended tasks that allow students to try things on their own, mathematical creativity can reach every student. Because this combination of approaches can make this distinct form of teaching realistically possible in a classroom, it allows students to see mathematics not as a rigid subject but a malleable discipline that can be uniquely used as a tool in their own lives.
My first inklings to become a teacher have begun ever since I was in fifth grade. I remember very clearly I would be multiplying numbers by hand just as a pastime before going to bed at night. In eighth grade, I remember casually joking around with the idea of becoming a math teacher. Then in my sophomore and junior year of high school, I had the most incredible math teacher. He was different from the other math teachers that I had because he not only taught mathematics from an algorithmic perspective but also with a practical point of view. If one of his students asked a question beyond the curriculum, he would come into class the following day with the answer to that question to kick off class. His willingness to explore mathematics in an open-ended manner while showing his passion for the subject has completely strengthened my love for mathematics. Since then, I’ve wanted to be in a position to share that knowledge with other people.
Throughout my undergraduate career at Endicott College, I have slowly found my teaching identity and that is my desire to show students the purpose of mathematics in their own lives. Even if mathematics might not directly relate to students in the moment, teaching them generalized practical use is something that makes the subject matter so interesting to me. Over the course of my undergraduate, I have also had the opportunity to be in multiple classrooms and not only observe what the teacher does but also get to practice how I want to teach the subject. I got to see how many limitations that teachers had to face in education, with standardized testing and common core curriculum being two enormous barriers to creativity. Despite this though, I got to witness teachers make it work and keep the focus on purposeful learning. Seeing this helped me stay encouraged when wanting to bring authentic learning into my future math classroom one day.
Therefore, when presented with the opportunity to explore any topic of mathematics education for my senior thesis, it was clear to me that I wanted to look at different strategies of authentic teaching in math classrooms. Doing this exploration helped me find that mathematical creativity was the strategy that seemed to encapsulate all of the things that I was looking for in my teaching approach. The teaching method allows students to make their own discoveries through individual/group exploration, it engages students to think critically, and the challenges of the task can teach students resilience while bringing the classroom together. The literature also showed me some evidence of the creative math content benefiting mathematically gifted students. It was at this point that something had rubbed me the wrong way.
I was determined to look for a way to implement mathematical creativity and have it be something welcoming for all students of any level, and so making that the focus of my thesis was a necessity. By getting to interview members of the MCG and gain so much insight from them, I got to see beyond my doubts of the teaching method. President Nolte and President Elect Freiman offered so many key aspects of making mathematical creativity work in the classroom that allows me to have a plan when shaping my own classroom one day. For my classroom atmosphere, I hope to maintain a safe and secure environment by welcoming mistakes and offering encouragement to continue. This can be coupled with promoting mindfulness techniques that allow students to maintain their focus in the present moment and get the most out of their learning. For student interactions, I will not be afraid to give them honest feedback but I will always remain constructive and positive to begin with while also keeping the students in a position to succeed. For presenting math content, I will borrow from both mathematical history and real-life situations to make mathematics feel real and worth exploring beyond the surface.
While this plan sounds very encouraging now, I am very much aware that the road ahead as a teacher can be rocky at times. There will be days when I feel discouraged from teaching creative mathematics. Perhaps the core curriculum is being pushed so much to the point where there’s too little time to bring math creativity into the classroom. No matter how big or small I can bring this type of teaching into my classroom, there is no doubt that I will keep teaching in the way that I believe is right for my students. That is a mentality that I will keep as a teacher and hopefully that can propel me into a position as a content coordinator or principal one day.