Calculating the Why
This isn’t an anti-math post.
It also isn’t meant to be anything more than an honest question that I’m trying to find an answer to. I’ve long considered not even writing it for fear that people will misunderstand or misconstrue the question.
But, my inability to find a satisfactory answer in the discussions I have with myself is finally leading me to ask.
As a working, adult professional, I use less than 10% of the math I was exposed to in high school. What does that mean?
I’m sure a similar statement can be made about other content areas, perhaps with a variation of the actual percentage, but still. We spent four years learning content in high school that most of us can no longer remember and don’t use as a part of our profession and hasn’t proved necessary for our success.
It makes me think of two pieces by Alfie Kohn. One, where he states ten truths we shouldn’t be ignoring.
In the second, he details a very interesting observation about the result of a standardized assessment question for a Massachusetts high school math exam.
His quote from Deborah Meier is compelling. “No student should be expected to meet an academic requirement that a cross section of successful adults in the community cannot.”
So, what’s the role of content as it’s presented in today’s education?
Why did I spend four years in high school, and then several more in college learning math that I’ve long since forgotten?
Think back on your high school and college courses. If you were to take the final exam today, how would you do? What does that tell us?
What should it tell us?
Aaron HayesDecember 7, 2012
Out of curiosity, when was the last time you wrote a literary analysis of a piece of fiction?
matt leddingDecember 7, 2012
I think critically analyzing a piece of fiction is something a cross section of successful adults could do.
Aaron HayesDecember 7, 2012
And if more people remembered how to use exponential equations, they could forecast their retirement savings far easier. It’s part of the reason I show my students that $2000 in an IRA early in their career is worth $250,000 in their mid-60s and how I couldn’t catch them now at age 40 even if I put $2000 in every year until my mid-60s.
Or there’s that whole “I can afford a $350,000 house on a $35,000 a year salary? Wow!” thing that got people into trouble that some math sense would help with too.
Your argument holds some water. What are the general topics in the 10% that you use?
I do tell my students that most of what they will use are basic Algebra, some Geometry and statistics. The reason we push further than what they use everyday is then what was at one point hard for them won’t seem hard. I took three years of math past calculus even though the highest I generally won’t teach anything past calc. Why? It’s easier for me to understand and explain calculus if I’ve taken further coursework. If they stopped at Algebra 1, the day-to-day stuff would tend to be even more of a chore than they think it is now. Or you use the skills in different ways. Deduce two triangles are similar lately? No. Show why two situations are similar? Probably. Much like the compare-and-contrast essay of the Communists versus the Nationalists for my Modern Asian History class doesn’t do much for me day to day but the skills I used for it are.
Some of the new Common Core movement will take some of this as are good teachers who try and show as much applications as possible.
Ben GreyDecember 10, 2012
I think a literary analysis is a bit different, but it’s a fair point. Like I said in the post, I do wonder this for any specific content area where information, formulas, or sequences of “stuff” are memorized and soon after forgotten.
Literary analyses are directly related to the act of effectively communicating and making meaning of text. That is a skill most professional adults must master in order to be successful.
Regarding your example below about exponential equations, I can easily and quickly find an online retirement calculator that will do the math for me on the equation. I, however, must understand the broader implications of retirement and investing and why one option is better than another.
A real example. A few months ago I went in to buy a new car. I had already worked out the details of the payments I wanted using an online payment calculator and the advertised interest rate. The salesman came back with the payment sheet showing a monthly payment much higher than what I had come up with. I asked him if the numbers were correct and if they were using the advertised interest rate. He said yes. I asked him to double check. He went into the back, returned, and told me the figures were correct.
I took out my phone, pulled up the website, and showed him the figures. He furrowed his brow, went into the back, and returned to apologize and say they had made a minor mistake.
I ended up paying the right amount not because I knew how to calculate compound interest, but rather, because I knew how to access a resource that did. And, because I was willing to bring that into the conversation.
I think most of the calculations we use in our lives are available at our fingertips. The more abstract concepts that we never again use outside of math class (or abstract facts we never access outside of any given subject area) are what I’m wondering about.
See my response to Jim below for more on why I wonder about the “because you learn bigger thinking skills through certain content areas” response.
Matt TownsleyDecember 7, 2012
Great questions, Ben. As a former high school math teacher, I’ve thought along the same lines for hours on end. It seems that folks in math education circles can’t all agree on the purpose of K-12 math. Perhaps this is the same in other content areas as well?
Some math folks assume K-12 should prepare students for what I’ll call the “math careers” that require a working knowledge of advanced math in which symbolic manipulation (a la “Algebra”) is important. Engineers, physicists, mathematicians, and…well, the list is fairly short. We’ll call this the “math careers” rationale.
Then there are those that trump the “higher education” card. These are the folks that acknowledge slope-intercept form and polynomial division aren’t really valuable tasks, but they’re needed to pass the typical credit bearing college algebra course. That credit bearing course is important for anyone who is pursuing a bachelors’ degree. Ask your local community college instructor and he/she can likely tell you about the remedial math course market. I often told my unmotivated students it was in their best interest to learn math in high school on the public’s dime than it would be to pay for the exact same classes for no credit at college, just so they could eventually take a credit-bearing math course that met graduation requirements. We’ll call this rationale”delayed meaning.”
The third camp of folks I encountered were those who thought symbolic manipulation was not needed at all for the masses. “If they want to become a mathematician, they can learn that stuff after high school.” Instead, the purpose of K-12 math should be overly practical. Financial literacy, career and technical measurements and math formulas form the foundation of this mindset. These people think every student should learn about loans, mortgages, how to balance a check book, converting various measurements needed in technical jobs, etc. We’ll call this the “application rationale.”
A few other folks I knew claimed that math taught students how to think. Completing the square or using Pythagorean’s Theorem to “solve for x” were two ways students could stretch their brains. If a student can stretch his/her brain in math class, it could surely be used in other contexts, too. I call this the “math as a way of thinking” rationale.
I do not have any solid sources to back up the categories I just described, but instead they come from my own experiences and discourse with other secondary math educators. From my perspective, the current educational system attempts to balance (perhaps not equally) all of these rationales. The state I live in requires financial literacy in its content standards as well as a fairly deep coverage of symbolic manipulation. The result appears to be your question/experience: “Why did I spend four years in high school, and then several more in college learning math that I’ve long since forgotten?”
What should this tell us? I think it tells us that we are currently unable to agree on the purpose of math education. Any of this make sense?
Ben GreyDecember 10, 2012
Yes, Matt. It makes perfect sense as you’ve written it. From a learning sense, it makes little sense.
I think you’ve said it very well. We’ve not agreed on why, but we keep moving forward with the teaching of it anyway.
I hope for our students that we’re all able to step back and really look hard at what we’re teaching and how we’re teaching it to make sure we give them every opportunity to embrace and enjoy the prospect of learning throughout their lives.
I think too often we aren’t able to do that in education. I’d love it if we could change that.
JimDecember 7, 2012
Because it’s fun.
Because using your brain is fun.
Ben GreyDecember 10, 2012
I’d love to give students in high school a survey to ask them how much fun they find each of their classes.
Learning and using your brain can be, and hopefully is, fun. However, learning bits of information that are placed in a silo apart from a broader context of understanding why it is needed and important throughout life is not.
If we find value in the exercise of thinking as we work through content, then the goal is the process of thinking and the skills associated with learning. Not the content.
If we accept that as true, than why can’t we turn the content portion over to the students for their own ownership? Allow them greater choice in what they learn as we guide them through the how.
I could have certainly learned the math that I use today in the context of learning how to do carpentry. Had I done so, I would have likely enjoyed the journey more, and also been more useful around my house today. Certainly something my wife would be grateful for as well.
Steve RansomDecember 13, 2012
Maybe a related idea here is, If we can’t make the learning of information/ideas/concepts both meaningful, relevant, and satisfying to the learners, and, as David Perkins writes, learners never get to “play the game” that they have prepared for, then the problem may be more related to pedagogy/context/experience over content.
If there are some concepts that are very difficult to make relevant to the learner, especially in relation to abstract mathematical ones, then perhaps they don’t need to be introduced… yet.
Armando PerezDecember 10, 2012
I read this and thought of a TED talk by Conrad Wolfram…passing it on…
Ben GreyDecember 18, 2012
Thanks for the link, Armando. That’s exactly the kind of approach I’ve been thinking about. It seems we’re more interested in continuing the way it’s always been done because it’s the way it’s always been done. I think we can do better, and in the process, get more kids to genuinely appreciate and enjoy math.
Diana LaufenbergDecember 11, 2012
I think that there is value in bringing up something here that may be off on a bit of a tangent, but always occurs to me as I think about such things.
We don’t know who is going to be an engineer, or a scientist or a mathematician or an economist or an accountant … There are moments when I believe we take everyone down the road with different types of specific learning long enough for students to find their path. To only have those students that want it, pursue upper level math, will yield what we already know happens in those moments – all kinds of societal factors come to bear and we end up with a majority of those students in high SES groups in those classes.
While I agree we could use a revisit of the Why? I also offer that the Why? is related to the unknown futures of the students. An agile mind is a critical piece of success moving forward. For me, one part of the explanation lies in leaving as many possible avenues open for students in the future. It isn’t a perfect explanation, but it is one I think about quite a bit.
Ben GreyDecember 18, 2012
I’m afraid the way we’ve been doing it is resulting more in what Armando linked to rather than opening the possibilities for students. Because the methods we’ve been using for high school and college math, I believe, have led more kids to abandon or resent the content rather than authentically embrace with the hope of taking on a career path embedded within mathematics.
Andrew SpinnerDecember 12, 2012
I like your post and a point I think most raised. Having been through some professional exams and the working world itself, I can say it likely comes down to a few things.
The first would be a strong foundation for further learning. Yes, none of us could pass the first week’s Calculus (or spell it?) test, but we did learn it years back in order to train our brains to think critically, an essential skill in becoming professionals.
The second I would say is work ethic. These days I read the odd article about the relevancy of homework for students. Although interesting arguments from both sides, homework begins an essential phase of life that trains us to have a strong work ethic. Many times in my life, a person will not be the smartest person a group. However, if he/she has a stronger work ethic, I would likely put my money on them.
I feel like I could go on and on, but anyways….great post!
Ben GreyDecember 18, 2012
Thanks for the comment. I think you raise an issue that is part of my curiosity on this subject. Because I think there are much better ways to teach critical thinking and work ethic than having students work through content, be it math or any other content area, that they can’t connect to a purpose for their lives.
We could allow them much greater choice and areas of interest that would keep them engaged and increase their chances of engaging in deep learning rather than memorizing formulas or trivia that they’ll soon forget and won’t find occasion to use again the rest of their lives.
Susan WhitedDecember 18, 2012
I think some very important ideas have been overlooked in your discussion. An article, “Rigor Redefined” by Tony Wagner in the October 2008 Educational Leadership journal may give you some other food for thought. In the article, he states that after many interviews with leading employers he has outlined seven skills employers want in employees.
1. Ability to think critically and problem solve.
2. Collaboration and leadership skills.
3. Agility and Adaptability
4. Initiative and Entrepreneurialism
5. Effective oral and written communication skills
6. Ability to access and analyze information
7. Curiosity and Imagination.
These are things young mathematicians learn from well-crafted, deliberate, thoughtful teaching. Yes, they are also learned through the ELA curriculum, but is it not important to develop young minds fully from many different perspectives.
I think, Yes.
Ben GreyDecember 18, 2012
Thanks for the comment, Susan. You raise an excellent point, and it actually wasn’t overlooked, but rather one of the main points of the post.
The skills you listed are critical for success in the modern workplace. Yet, when we look at curriculum for a tradition high school or college, those are rarely included in the specified learning outcomes. It’s rather driven by content.
I absolutely believe building a math foundation through elementary school and even middle school is critical for students. They will use that math for the rest of their lives.
My bigger concern is when we start getting into far more advanced and abstract math like calculus or trig or the like. I took those courses in high school and in college, and as I look back, I really wish I could say I have used or have benefited greatly from the experience.
Read numbers 46, 113, and 132 here http://www.sethgodin.com/sg/docs/stopstealingdreamsscreen.pdf
Dean ShareskiDecember 27, 2012
I don’t buy the whole “habits of mind” argument. That’s simply our current rationalization for bloating the curriculum with math because we believe we need more scientists and engineers. Sure, as Diana says, we don’t know who’s going to need what but I believe our current exit strategy for kids is still college prep. Thus, our curriculum is skewed towards Math. Most of which is useless. The same might be said for other subjects outside the Humanities which have a much easier time finding relevance.
Scott MeechDecember 28, 2012
Have you asked members of the math community directly? Engineers? Construction? What does the http://www.nctm.org/ have to say about it?