I just got through reading "Inevitable". This is a great book that HOPEFULLY will help us, Educators, get back to the real reason why we're here. The bureaucracy we call education has lost it's focus. It's not our fault, we are not really in control of what we teach and students aren't in control of what they learn. The book asks a great question, What's our purpose? Are we here to prepare our students for more education or prepare them for life? Unfortunately, I think my focus, as a Math teacher, has always been to prepare them for more Math! I'm not talking about preparing them for using Math. I'm saying I have always focused on teaching Math so Students can be ready for the next Math Class. I taught Pre-Algebra to get them ready for Algebra. I taught Algebra to get them ready to take Geometry. I taught Geometry to get them ready for Algebra II, then Pre-Calculus, and then Calculus. The only reason Calculus was the last class is we ran out of time. But, is that our real goal? Is it our only goal? Or can we do both? Can I prepare students for higher math AND teach them REAL LIFE MATH at the same time?
Do you know the most popular student question in High School Math??????? "When am I ever going to use this?" I can't remember where, but some blog I read the other day addressed this very question. Do you know what most teachers answered? "Because you need it to pass the test." How sad! Do you know MY most frequent answer? -- "It teaches you critical thinking skills." Great answer, right? Well, not really. Most brain research shows the pathways created during "Math Education" is only good for specifically doing "Math Education". I thought I had a great response, when in fact my response was no better than "You need it for the test." We need to make Math real for our students. We need to strip down what we teach so we can focus on it's real life applications. We can't do that in the present system. That's where the book "Inevitable" and Mass Customized Learning (MCL) comes in to play.
The other day I was going through the Common Core Standards and one topic struck me as "Why do we teach this?" -- Complex Numbers. When I taught students about complex numbers, students hated it. They certainly had no idea where we would ever use this. (To be honest - neither did I.) They would say, "Mr. Rhoades, why do I need to know this? When I put the square root of -1 in my calculator it just gives me an error." But, I always trudged forward. Do you know where you use complex numbers in real life? Google it, I did. I actually learned something. The University of Toronto has a question corner / discussion area that answers the question:
"In electronics, the state of a circuit element is described by two real numbers (the voltage V across it and the current I flowing through it). A circuit element also may possess a capacitance C and an inductance L that (in simplistic terms) describe its tendency to resist changes in voltage and current respectively.
These are much better described by complex numbers."
I think complex numbers are fun to teach, but if we're going to teach it, why don't we teach it with the application in mind? I know why. We don't teach it, in depth, because we don't have time. We also don't apply complex numbers because MOST of our students WILL NEVER USE IT. If we go to a MCL (Mass Customized Learning) system, this topic (complex numbers) would still be taught. But those students interested in Electrical Engineering could CHOOSE to explore it with other students who are also interested in it. They also might CHOOSE to do it on their own or with a REAL ELECTRICAL ENGINEER. Our current system just doesn't allow for that type of IN DEPTH learning. We just touch things on the surface and move on. In our current system, we rarely address the question, when am I ever going to use this because that answer doesn't apply to ALL our STUDENTS and it takes time.
With MCL , we can change our Math Curriculum to meet the needs of the learner not force the learner to fit into the curriculum.
Do you know the most popular student question in High School Math??????? "When am I ever going to use this?" I can't remember where, but some blog I read the other day addressed this very question. Do you know what most teachers answered? "Because you need it to pass the test." How sad! Do you know MY most frequent answer? -- "It teaches you critical thinking skills." Great answer, right? Well, not really. Most brain research shows the pathways created during "Math Education" is only good for specifically doing "Math Education". I thought I had a great response, when in fact my response was no better than "You need it for the test." We need to make Math real for our students. We need to strip down what we teach so we can focus on it's real life applications. We can't do that in the present system. That's where the book "Inevitable" and Mass Customized Learning (MCL) comes in to play.
The other day I was going through the Common Core Standards and one topic struck me as "Why do we teach this?" -- Complex Numbers. When I taught students about complex numbers, students hated it. They certainly had no idea where we would ever use this. (To be honest - neither did I.) They would say, "Mr. Rhoades, why do I need to know this? When I put the square root of -1 in my calculator it just gives me an error." But, I always trudged forward. Do you know where you use complex numbers in real life? Google it, I did. I actually learned something. The University of Toronto has a question corner / discussion area that answers the question:
"In electronics, the state of a circuit element is described by two real numbers (the voltage V across it and the current I flowing through it). A circuit element also may possess a capacitance C and an inductance L that (in simplistic terms) describe its tendency to resist changes in voltage and current respectively.
These are much better described by complex numbers."
I think complex numbers are fun to teach, but if we're going to teach it, why don't we teach it with the application in mind? I know why. We don't teach it, in depth, because we don't have time. We also don't apply complex numbers because MOST of our students WILL NEVER USE IT. If we go to a MCL (Mass Customized Learning) system, this topic (complex numbers) would still be taught. But those students interested in Electrical Engineering could CHOOSE to explore it with other students who are also interested in it. They also might CHOOSE to do it on their own or with a REAL ELECTRICAL ENGINEER. Our current system just doesn't allow for that type of IN DEPTH learning. We just touch things on the surface and move on. In our current system, we rarely address the question, when am I ever going to use this because that answer doesn't apply to ALL our STUDENTS and it takes time.
With MCL , we can change our Math Curriculum to meet the needs of the learner not force the learner to fit into the curriculum.
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