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| Forgot Algebra |
As a math teacher, I can relate to the sentiment of this comic. People regularly boast to me about how bad they are at math (especially algebra), and still, they are successful in life. Much like the young woman in the comic, these people seem to believe that they were lied to about the utility of math, and they are resentful about it. Maybe lied is too strong a word, but perhaps we do misrepresent the purposes behind the math taught in schools.
Because I was teaching some algebra to middle school students twenty years ago, I remember how I responded to the question, "When will I ever use this?" Therefore, I have a theory about what might have been going on in Miss Lenhart's Algebra classes in the late 80s/early 90s. I imagine it might have looked like one of these four scenarios (depending on what she tried before).
Has much changed? I mean, besides the fact that we now add cell phone contract problems into the mix. For the most part, students remain unimpressed as we tie ourselves in knots to demonstrate how they will need the math we teach in everyday life. That is why I suggest that when asked by students, "When will we ever use this?" that teachers respond truthfully.
I don't know when or if you will ever need this particular concept. It depends on what you do with your life and what technological advances are made in the future. But you know what you will need to be able to do, regardless? You will need to problem solve. You will need to think critically (reason and prove). You will need to be able to communicate quantitative thinking to others. You will need to use representations to support your thinking and share your thinking. And you will need to make connections in order to consolidate your understanding. Mathematics is a discipline that provides opportunities to practice and strengthen all of these skills. So, as we solve for x, I want you to monitor your thinking because that's what's really important.
That is how I learned to respond to my middle school math students. The NCTM Process Standards gave purpose to my math lessons, and the students bought into it. It worked for me because I finally believed in what I was teaching.
Interestingly enough, I just watched a video a couple of nights ago which was an interview with John Sweller and he says "You can't teach general thinking skills" which would blast a hole in your argument, if it is true. I don't personally think it is true, because I think that would pretty much defeat the purpose of teaching mathematics.
ReplyDeleteJohn says that if you could prove, using somewhat stringent requirements, that one can A. Define the thinking skill you mean, B. teach it, C. Establish that students who have learnt the skill think differently, then he will accept that you can teach it.
See http://davidwees.com/content/can-you-teach-thinking for the video itself.
David,
DeleteThanks for your comment and sharing the link.
Here's an example that meets Sweller's requirements: Schoenfeld taught college students how to problem solve (A and B) and showed that they thought differently as a result (C). A PDF of the research can be found here:
http://gse.berkeley.edu/faculty/ahschoenfeld/Schoenfeld_MathThinking.pdf
But based on the portion of the video that I watched, I'm not sure if Sweller would consider the five Process Standards as "general thinking skills." If he does, there is a preponderance of research through the NCTM around the teaching and learning of the Process Standards.
This is such an interesting, perennial question. I've seen a few recent posts on this exact topic, and have been impressed by ideas from people smarter than me about the general skills developed while doing mathematics.
ReplyDeleteI like your point about "finally believing in what [you were] teaching" - I think this discussion has benefits for teachers as well as students.
Peter,
DeleteI appreciate your thoughts. Authenticity is one of the major themes in the courses I teach for preservice teachers. Some people might me able to sell the idea that everyone needs to learn a particular piece of mathematical content because it will be used in everyday life - now and forever. I am not one of them.
For all too long education in mathematics has focused on the teaching of concepts, the covering of content and moving onto the next page. We have wanted our students to "do" math. Math that serves more math the next day, the next year and into the future. But what does that future look like? As an adult the math I was taught to "do" has had little influence on my life. This is mainly because my school math did not transfer into the math off my world. The math I do now does not live in isolation of purpose. The math I do now I understand. The math I do now provides me with opportunities to problem solve, make sense of my world and be creative. My hope is that our children do not have to wait until adulthood to see this too.
ReplyDeleteThanks for your comment, Jennifer. I think we are in agreement that not all mathematics needs to have direct utility for everyday life, just that as teachers we need to be honest about the purposes associated with the topics. Sometimes practicing problem solving or making and testing conjectures is enough without it having some "manufactured, real-life" purpose (like figuring out a tip).
DeleteUltimately, the mathematical practices we learn ought to help us to understand the concrete and abstract objects inhabiting the world.
A very interesting article, but one which scarcely addresses the underlying issues inherent in teaching mathematics. As a CIS major with a horrible math handicap, I can say that I ask "why" more than any other in my classes. I'll even admit to feeling annoyed when others will not ask "why" when clearly they don't fully understand. How do I know they don't understand? Take any 4.0 Math wiz that solves quadratics in their head, and then ask them "why" they would use a quadratic in life. Do we know what their response will be? It usually goes something like, "I don't know" or "they wouldn't teach it if we didn't need it." An individual who can solve complex equations on paper without knowing what it's for is no more meaningless than a professor who teaches it and doesn't know why.
ReplyDeleteInstead of making excuses for how best to deal with the 'why issue' perhaps it's simply time fot society to admit that anything over Algebra 1 is useless.
If you think it's not... then PROVE it.
Additional Note: 80% of high-level math uses numbers to explain concepts which are not mathematical in nature. It's just laziness in my opinion.
hi,im in 8th grade, name is Ajmain
Deletehow can you say its lazy!!!!
"80% of high-level math uses numbers to explain concepts which are not mathematical in nature. It's just laziness in my opinion."
the imaginary number "i" is the square root of -1.
it is "imaginary" because there is no "negative area" (where Area=length*width and the Area part comes out negative) in real life.
so just immagine a negative square with an area of -1
Area= side^2
-1 = something*that same thing
whats that thing?
there is no "real" value for it so humans made something to represent that something which was "i"
its not lazy!!!