1. All children can learn
They may not learn at the same pace or in the same way. They may not need to learn the same thing at the same time. They may not have the same motivation or the same interests. But they all can learn and they all can learn math.
When I tell people I was a math teacher, they often tell me they just don’t have a brain for math. I don’t buy it. We need to rethink the messages we are sending students both in school and at home because I rarely hear anyone say they don’t have a brain for reading.
2. Things need to make sense to students.
Learning should be a way for students to make sense of the world around them. In a math classroom, that means taking everyday situations and using math to help make sense of them.
When math is disconnected from the world students live in, it is viewed as a series of random calculations that don’t make sense. As a result, students resort to tricks and memorization and then struggle when novel situations are presented. Math needs to make sense to students. It needs to be a way to organize the world around them.
3. Build on what students know.
All students bring experiences about the world to a learning situation. These intuitive strategies students already have can be built upon to learn math in a classroom. All too often there is this assumption that what students need to learn about math comes from a textbook or a teacher. It is as if they have never had any experiences in their lives that could be used to think about mathematics.
We need to think about how we build upon what students know. For example, I recently designed a lesson on inequalities. Students have an intuitive sense of whether their brother has more cookies or fewer cookies than them. They may not have the symbols or tools to represent these situations mathematically but they understand something about that relationship. This can be built upon so that math becomes a way to record that situation and to make sense of other situations like that.
4. There is not a single “best way” to foster learning
Some methods may be better than others but there is no one prescription for how to teach. It would be much easier if there was and I see the temptation for schools or districts to mandate one way of doing things. However, all students are unique and there can’t possibly be one right way for a variety of individuals to learn. We need to question policies that demand one way of teaching.
That’s not to say that I don’t think that we need to radically change the way we approach or evaluate good teaching. We do and we can talk more about what that looks like in later conversations. But I am nervous when people prescribe one way to teach children. I always remember someone telling me during my first year of teaching: “There is more than one way to skin a cat.” Now I’m not sure why you would want to skin a cat to begin with, but the sentiment stands.
5. What students understand is not the same as what they are able to do.
Learning is about understanding. Understanding is sometimes confused with what students can do. If students can choose the correct answer on a standardized test, we sometimes say they understand a particular mathematical concept. But all they might know is how to follow a procedure for a particular type of question.
Really thinking about what we want students to understand about a concept is an important step in designing tasks for students that will foster their learning. It is also an important step in thinking about how we want to assess them.
So there you have it. Those are the ideas that guide my work as a teacher and as a researcher. For me, it’s important to be transparent about what my beliefs are. It allows me to clear about what I value and it allows others to understand my perspective when I talk about teaching and learning. Being explicit about these ideas also helps me decide who I want to collaborate with, where I want to work and what projects I want to take on. In future posts, I’ll talk in more detail about some of the ideas and discuss the research that supports them.
What about you? What are your core beliefs?