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.
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?
Educators, I have some bad news to give you. You aren’t going to get rich. It doesn’t matter how many of your lessons you carefully hoard, or how many great ideas you keep to yourself, none of that is going to make you rich. You will probably never publish your "book" and you aren’t going to get famous.
You could however make a difference. You could give what you’ve got away for free and help make the world a better place. The technology exists to make it relatively easy to share your project ideas, assessments, lesson plans, curriculum, thoughts, whatever you are working on with students. The problem is right now, not enough educators are sharing what they are doing.
The main reason we as educators do not share more of what we do, is that we lack time. We don’t see the value in sharing what we do because it takes effort to upload & share our ideas, and the return is not immediate obvious. Getting that test written, or deciding what you are going to cover for the next week is tedious. To this I say, let your students help you out. Instead of having your students write summaries and rewrite notes from class, have them share the great ideas you come up with collectively with the world. Enable your students to help you. Petition your administration for collaboration time to polish your ideas with your colleagues and then share the result with the world.
Another reason not to share resources is that what we do is fairly specific to our group of students. Many of us customize what we do to the particular group of students we have. To this I say, share the core of what you are doing then, and not all of the details which make it work for your specific case.
Michael Nielsen makes the case in the TED video for Open Science, but in my mind, the same should hold true for education. The resources you make for your classes should be owned by the public, since in the long run, we all benefit. We need to move toward a more open collective experience in education, an Open Education, rather than our current isolated walled garden approach.
In the video above, shared by Dan Colman this morning on the Open Culture blog, Richard Feynman makes this powerful statement.
It doesn’t make a difference how beautiful your guess is, it doesn’t make a difference how smart you are, who made the guess, or what his name is, if it disagrees with [the] experiment, it’s wrong. – Richard Feynman
How would we apply this to education?
We should look at what is working and decide our policies based on the evidence. We should be looking at data, which should have a broad spectrum of types (just like scientific data has) and use it to help determine policy. We need to hold true to Feynmann’s process as well, which is to make a guess as to what will work, decide what the consequences of those actions would be, and then find a way to determine if this is true or not.
There are a number of initiatives in education which either lack data to support their implementation, or which have contradictory evidence as to their effectiveness. For example, various influential people have been promoting the idea of merit pay for teachers, for which the evidence is inconclusive. In other words, someone had an interesting guess about how education works (teachers will work harder for the chance at more money) and drew the conclusion that student learning would improve as a result (as measured by one form of assessment, a standardized test), and the results of the experiment have not shown a result one way or the other (but have shown that when you dangle a big enough carrot in front of people, they will cheat to get it).
My guess is that the schools that work the best start with the premise that teachers should have sufficient autonomy and support to master their craft, and someone (parents, school, or teachers) provides the resources (food, clothing, shelter, safety, supplies, technology) for their children to succeed. I predict that in such schools you would see higher engagement in learning from administrators, teachers, students, parents, and the community.
Who is willing to do an experiment to see if my guess is right?
