The Reflective Educator

Education ∪ Math ∪ Technology

Menu Close

Day: April 11, 2011

Bad calculations

Question: If you didn’t know the procedure for addition or multiplication, and lacked numeracy skills, could you catch the errors in the calculations shown here?

This is what happens when you teach computations instead of reasoning. Anyone who looks at 14 x 5 and gets 25 does not have basic numeracy and estimation skills developed, and quite possibly has never used real objects to do multiplication before. The error is not primarily in the calculations that they are doing but in the system that leads them to trust their calculations more than their common sense and intuition about the problem they are working on. This kind of error happens independently of the tool used. If you don’t believe me that students can make similar computational mistakes using a calculator, ask math teachers how often they see 4/8 = 2 and other similar mistakes.

A mathematics curriculum based on the ability to do computations and not solve problems is flawed in my mind. We should focus on mathematics as a tool, rather than mathematics as a goal.

People change (ps. kids are people)

People change.

Change

(image credit: dhammza)

I’m not talking about the obvious physical characteristics that change about people, but their inner thoughts and feelings, the cognitive abilities that make them sentient. No one is exactly the same their whole lives as no one is immune to the effect of gaining experience and wisdom from life’s experiences. It has been shown time and time again that the assumption that people are static and unchanging is false. People often change in dramatic and unexpected ways.

I have two students this year who have made leaps and bounds in their academic ability, largely because they push themselves much harder this year and generally acting more motivated and energized in class. My colleague at my last school loves to talk about a child who started in 9th grade as one of the least academically able 9th graders and ended up top of his class in Calculus AP by the end of 12th grade.

When I was in public school, I was painfully socially inept and struggled not only to make friends, but even to understand the motivations and social expectations of the people in my life. Now, I’m in an incredibly social profession as a teacher, I’m comfortable presenting to a room full of a hundred people, and I interact with thousands of people in the course of a month. I’ve changed a huge amount.

Not all change is positive growth of course , but we need to recognize that change is not only possible, it is likely. Our educational policies should reflect the ability of people to change.

Is it possible for children in your school to switch tracks? For example, can a child on a less academic path switch to a more academic path and vice versa? Can students choose to switch courses when their needs change? Can they switch what elective courses they take? Do your discipline policies reflect a student who can change, or do they apply penalties using strict criteria which allow for no opportunity for growth on the part of the student? Do you let students know that they are even capable of change?

Most importantly, what opportunities exist in your school to help kids change their own lives?