Philosophy of Mathematics Teaching
As an educator I uphold these three ideals to be prevalent in my mathematics teaching: Any student is capable of learning and doing mathematics, mathematics can be an exciting way to learn about the world around you, mathematics brings opportunity for collaborative learning which encourages deep level thinking.
In education there is an ongoing construct that math ability is either inherit for some or fixed for others. The growth mindset model for mathematics considers that through emphasis of a positive mindset over ability one can achieve mathematical understanding and skill that can be sculpted and developed over time. The fixed mindset model, however, considers that mathematical skill and understanding are innate and that there is not much that can be done to improve one’s overall math competency. According to youcubed.org, “About 40% of students have these damaging “fixed mindset” ideas”. As a teacher it is important to be aware of such popular beliefs that students take on in order to highlight and challenge them within the classroom. A fixed mindset can be remedied through giving a student who shares this mindset the opportunity to see evidence of their growth and improvement within the math class. However, transitioning a student’s belief from a fixed mindset may not always be the easiest thing to do as according to, youcubed.org, “Students with a fixed mindset are those who are more likely to give up easily, whereas students with a growth mindset are those who keep going even when work is hard, and who are persistent”. Sometimes students might not necessarily have one belief mindset over the other and may just simply lean more towards the fixed mindset because they have not been proven otherwise through experience in the math classroom. In, Make me!:Understanding Student’s and Engaging Resistance in School, Eric Toshalis (2015) states,
“As discussed, when students are choosing whether to allocate time and energy to an academic task, they need experiences of competence. These experiences need to occur regularly, not just on tests or on project presentation days. To stay motivated and reduce resistance, students need “little wins” as they go along” (pg. 115).
Some remedies of the fixed mindset may be allowing a student to retake a quiz in hopes of improving from their initial quiz or test score and posting such success on an improvement board in the classroom. Another example of this would be to allow a student to monitor their own understanding as the math progresses through a biweekly progress survey. This survey could ask the student questions like, What is one thing you learned this week in class?, What is one thing you struggled to understand this week?, What is one tool you can use to improve this particular math skill?. This survey would allow students to reflect on their learning and determine ways that they can help themselves improve throughout the year.
In any classroom, motivation is key to student involvement and effort. The more rewarding, internally and externally, a task appears to a student, the more likely they are to give effort. Additionally, Toshalis (2015) reveals, “To help students connect to the lessons they’re learning right now, not in the distant future…We need to show why the topic is relevant, why it matters, why they should care. Failing to do this is a recipe for diminished motivation and outright resistance” (pg. 115). A common question that students who do not see the relevance of certain topics learned in class might ask is, “Where am I going to see this in everyday life?” The irony in such a question is that math is used every single day both consciously and subconsciously. Although procedures that students must learn in class such as multiplication tables or order of operations are important, it is equally important for students to practice math in ways that require them to connect to and make sense of the real world. Incorporating activities that utilize student interest and connect to the real world like, estimating angles and lengths of measure for building structures, use of multiplication and percentage calculation for grocery shopping to estimate the total cost , and allotting students a set amount of pretend money individually or in groups to make financial decisions regarding saving and investing are great ways to get students intrigued. As a result of students’ peaked interest, they become more involved during lessons and classroom activities.
In the math classroom students are given tasks to work on individually and collaboratively with other students. It is important that all math teachers always consider in their minds that students do not come into their classrooms as “blank slates” who do not have any prior knowledge and experience of mathematics. And since students’ math ideas and experiences are individual, teachers should create opportunities for students to work amongst one another in group tasks. Giving students group tasks allows them to share their own experiences, make sense of each other’s prior knowledge and experience through reasoning and justification, and to create a unified understanding through a shared math experience. Ilana Horn (2012) in, Strength in Numbers: Collaborative Learning in Secondary Mathematics, shares that,
“Argumentation, justification, and generalization are thinking practices that mathematicians engage in. They also support students’ understandings of content by helping them learn not just the how of mathematics but also the why. Argumentation and Justification support the scaffolding of student thinking because asking students to justify their thinking requires engagement of their prior understandings” (pg. 37).
Students in group tasks who engage in such thinking practices as, argumentation, justification, and generalization subconsciously are exploring math meanings and relationships. These thinking practices serve as branches that connect these math meanings and relationships to students’ own math ideas and representations, enhancing students’ ability to conceptualize critical math ideas.
All three ideals are powerful and necessary tools that all math teachers should consider as primary areas of focus for their students as they engage in mathematics learning in their classrooms.
References
Growth Mindset Archives - YouCubed. (2012). Retrieved December 20, 2019, from YouCubed website: https://www.youcubed.org/resource/growth-mindset/
Horn, I. S. (2012). Strength in numbers: Collaborative learning in secondary mathematics. Reston, VA: National Council of Teachers of Mathematics.
Toshalis, E. (2015). Make Me!: Understanding and engaging student resistance in school. Cambridge, MA: Harvard Education Press.