Reflections is a monthly column for teachers, by teachers on topics of interest to mathematics educators: reflections on classroom experiences, professional development opportunities, resource reviews, and more. If you are interested in sharing your own ideas with mathematics educators in the province (and beyond), consider contributing to this column! Contact us at firstname.lastname@example.org.
An Open Conversation About Curriculum
“When am I going to use this in the real world?”
I don’t know if it’s because I teach math, or if all teachers are asked this question, but it’s the time of year during which it comes up a lot. And this year, for the first time, I engaged in a conversation with the students instead of issuing a witty remark such as, “Well you might not, but the smart kids will,” which usually garners plenty of chuckles and allows us to move on, forgetting the question that was asked in the first place.
But students should question. Why are they learning these particular mathematical concepts, and why right now, and when are they going to be useful? We are trying each day to help students become critical thinkers and problem solvers, but too often shut them down when they inquire about the purpose of a lesson.
So here’s what I, and the students, learned from the conversation initiated by this question:
- They didn’t know what a curriculum is
- They had no idea that teachers do not just teach from a text book
- They had no idea that teachers have to plan lessons every day
- They didn’t know that sometimes, we are as frustrated as they are about what they need to learn.
So we opened a curriculum document. I projected the Aims & Goals of our Saskatchewan Mathematics Curriculum (e.g., Ministry of Education, 2010).
In our curriculum, there are four overarching goals for the teaching and learning of mathematics: Logical Thinking, Number Sense, Spatial Sense, and Mathematics as a Human Endeavor. I explained that these are what I’m trying to help students achieve, and the material is a vehicle to get them here. I asked them to try to explain if, and when, they felt they were working towards these goals.
Logical Thinking: students should develop and be able to apply mathematical reasoning processes, skills, and strategies to new situations and problems. This goal encompasses processes and strategies that are foundational to understanding mathematics as a discipline. (Ministry of Education, 2010, p. 8)
Student had very little trouble coming up with examples of when this happens. Math class is full of new situations that require previous knowledge to navigate. And as students move forward in their math education, they begin to see the importance of previous units of studies. Some also identified persistence as something they have developed and strengthened in math class as a result of having to solve new problems.
Number Sense: students should develop an understanding of the meaning of, relationships between, properties of, roles of, and representations (including symbolic) of numbers and apply this understanding to new situations and problems. (Ministry of Education, 2010, p. 9)
Again, this goal had pretty strong relevance to and was easily observable in our day-to-day work in the classroom. How many decimal places do we use? When do numbers have equivalency? At what point is it okay to use 2.83 instead of ? We had just been working on solving quadratics, so the idea of an exact value was pertinent. The more they reflected on their previous mathematical work, the more easily they were able to identify when one set of numbers was more appropriate in a given situation than another, or when they would need to move between sets of numbers.
Spatial Sense: students should develop an understanding of 2-D shapes and 3-D objects, and the relationships between geometrical shapes and objects and numbers, and apply this understanding to new situations and problems. (Ministry of Education, 2010, p. 10)
Earlier in the year, students had worked on a problem (Banting, 2016) that involved doubling the surface area of a house. Students were quick to reference this as an example of when they had to use their knowledge about 2-D shapes and 3-D objects and apply it in a new situation.
Mathematics as a Human Endeavor: students should develop an understanding of mathematics as a way of knowing the world that all humans are capable of with respect to their personal experiences and needs. (Ministry of Education, 2010, p. 10)
The students struggled with the language of this one, so we looked a little closer at the list that suggested what an understanding of mathematics as a human endeavor would result in, which includes:
- recogniz[ing] errors as stepping stones towards further learning in mathematics;
- enjoyment, curiosity, and perseverance when encountering new problems;
- self-confidence related to mathematical insights and abilities.
Students had differing reactions to this goal. They said that my classroom was a safe place to make mistakes in that they felt confident that they wouldn’t be ridiculed for making a mistake, but they weren’t sure that mistakes were used as a way to further their understanding in math. And, most discouragingly, they did not all feel confident in their mathematical abilities: by the time they had reached my classroom, they felt that they knew exactly the extent of their mathematical abilities—and some of them were under the impression that they’d never be any good at it. Those same students also said they didn’t believe that I could change this—but I’m surely going to work on trying!
As a result of this conversation, my course outlines have changed for next year. These goals are highlighted as the focus of math class. I hope to use this language often in my classes and remind students that all of them are capable of achieving these goals… And that logarithms, even if we hate them, can help to strengthen our persistence!
So, my recommendation to you: Rather than trying to explain when students might use polynomials in the future (they won’t), focus on the skills that learning, and mastering, a new concept helps to develop, and how those skills are critical to future success. And lastly, please stop telling students that the world they live in isn’t real. So often, students hear that we are “preparing them for the real world,” or “when you get to the real world…”, insinuating that the work they do every day isn’t as valuable or as important as the work they will do in the future, or outside the walls of the school. But school is real. The work they do every day is real. Their world is very real—and it’s the world that you’ve chosen to make a career in.
Banting, N. (2016, February 23). My favourite surface area question [Blog post]. Retrieved from http://musingmathematically.blogspot.ca/2016/02/my-favourite-surface-area-question.html
Ministry of Education. (2010). Foundations of Mathematics 20. Regina, SK: Author. Available at https://www.edonline.sk.ca/bbcswebdav/library/curricula/English/Mathematics/Mathematics_Foundations_Of_20_2010.pdf
Sharon Harvey has been a teacher within the Saskatoon Public School Division for eight years. She has taught all secondary levels of mathematics, as well as within the resource program. She strives to create an inclusive and safe environment for her students.