I envision a world where the word “math” isn’t seen as a four-letter word: a world where mathematical thinking, problem solving, and mathematical connectedness are commonplace. In this vision, math would not be viewed as a challenging, anxiety building endeavor, but an exciting opportunity in problem solving.
In order to achieve this vision, it would require a shift in mindset and it starts is in the classroom. K-12 classrooms are a fertile ground where students learn to see the world with a mathematical lens. I envision K-12 mathematics similar to what Jo Boaler suggested: “What is helpful in maths is to think visually and creatively.” She continues, “Maths is about patterns, and space, seeing things differently, and making connections” (Boaler, 2015). Similarly, I also believe that students should be provided with opportunities to engage in mathematics that allows them to think creatively and use visual thinking to look at things differently.
I believe classrooms need to be an oasis of mistake making for maximum learning opportunity. Often, the unpleasant perceptions of math have come from the response to failing. As students have put their answer or thought process out there, they were told they were wrong. This formed the perception that they were not good at math and therefore stopped trying. It may have added to the belief they formed along the way that they weren’t a “math person.” Unfortunately, this deflating believe in mathematical abilities happens far too often. Mistakes are really valuable opportunities to grow and strengthen your brain. The science of learning says that when you are struggling, your brain is engaged in more than one pathway to make sense of what is happening. By working through those struggles, the brain becomes more adaptable and strong. It’s similar to lifting weights: lifting heavy weights causes micro-tears in the muscles. As the body adapts to and repairs those tears, the muscles to grow. In our brain, neurons are formed and strengthened the more electricity is fired over them. This happens through repetition and practice, positive emotions, and visualization (Hilary, 2010). Therefore, celebrating mistakes as the learning, neural pathway strengthening activities in your brain they are, the more everyone can learn mathematics to high levels. John Krumboltz put it this way, “If we could think of failing as a path towards success, then I think we would all be better off” (as cited in The Atlantic, 2014).
My vision for an effective mathematics classroom includes productive and timely feedback. This means during instruction, following practice, and following any assessment. Feedback can come from a teacher or parent with corrective information, an alternative strategy from a peer, “A teacher or parent can provide corrective information and encouragement, a peer can provide an alternative strategy, a book can provide information to clarify ideas, and a learner can look up the answer to evaluate the correctness of a response (Hattie, 2007). My experience tells me that technology provides corrective information, a format for peers to share an alternate strategy, a clarification of ideas, and encouragement all in one. Especially with mathematics, quickly having corrective information can quickly turn mistakes to learning. Technology can also quickly provide more practice for when the mistakes are learned from and the student can try again with more success. I love what Valarie Shute from Florida State University said concerning feedback: that when it “is delivered as formative guidance rather than summative evaluation, it can help students develop a learning orientation, in which they view improving their own competence as the goal of learning, as opposed to a performance orientation, in which they view being evaluated well by others (or getting a good grade) as the goal of learning” (as cited in Goodwin & Miller, 2012). That learning orientation is something every student could benefit from. Thus, technology can assist with meaningful feedback that is targeted toward the learning goals, specific, and timely (Goodwin & Miller, 2012).
Technology should play an integral part in learning as it is accompanied with strategic pedagogy, covering the content well. A teacher’s knowledge of technology integration, effective pedagogical strategies, and deep understanding of mathematics can make or break the classroom experience for students. It requires “developing sensitivity to the dynamic, transactional relationship between these components of knowledge situated in unique contexts” (Koehler, 2012). Technology in a mathematics class can be used for individualized practice and learning, as a way to differentiate instruction, as a station for practice and learning, and more. I see my role as a teacher is to know when and how to use the technology in a way to enhance learning mathematics, based on formative assessments.
I believe everyone deserves to feel the sense of accomplishment that comes from solving a difficult math problem, regardless of their previous mathematical experience. My goal is to create an environment where students come to a love of math by finding mathematical success through learning from mistakes.Through technology, students will engage in their learning and interact with math, each other, and the class in meaningful ways to deepen their understanding of mathematical problem solving skills, which will help them problem solve in other aspects of their life.
Boaler, J. (2015). Boosting math. Retrieved July 1, 2017 from Youcubed at Stanford: https://youtu.be/bxrPy1fjVU4
Boaler, J., (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages, and innovative teaching. San Francisco, CA: Jossey-Bass
Goodwin, B., & Miller, K., (2012). Research says / Good feedback is targeted, specific, timely. Feedback for Learning, 70 (1), 82-83. http://www.ascd.org/publications/educational-leadership/sept12/vol70/num01/Good-Feedback-Is-Targeted,-Specific,-Timely.aspx
Hattie, J., & Timperley, H., (2007). The power of feedback. Review of Educational Research, 77 (1), 81-112. http://www.columbia.edu/~mvp19/ETF/Feedback.pdf
Hilary, K., (2010). Neural plasticity: 4 steps to change your brain. Retrieved on July 14, 2017 from Authenticity Associates Coaching and Counseling: http://www.authenticityassociates.com/neural-plasticity-4-steps-to-change-your-brain/
Koehler, M., (2009). TPACK explained. Retrieved on July 14, 2017 from Tpack.org: http://matt-koehler.com/tpack2/tpack-explained/
The Atlantic, (2014). The power of failing (featuring John Krumboltz). Standford Graduate School of Education News, March 3, 2014. Retrieved July 14, 2017 from https://ed.stanford.edu/in-the-media/power-failing-featuring-john-krumboltz