Should math be applied?
By Murray Bourne, 30 Apr 2008
In a recent New York Times article, Study Suggests Math Teachers Scrap Balls and Slices, Kenneth Chang says:
...many educators in recent years have incorporated more and more examples from the real world to teach abstract concepts. The idea is that making math more relevant makes it easier to learn.
He goes on to report that researchers at Ohio State University have conducted research that purport to refute that claim:
An experiment by the researchers suggests that it might be better to let the apples, oranges and locomotives stay in the real world and, in the classroom, to focus on abstract equations.
Better? Better for whom? In what sense better? For the learning of algebra only? And what good is that for most of the population?
Jennifer A. Kaminski, a research scientist at the Center for Cognitive Science at Ohio State is quoted as saying:
“The motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning. It was really just that, a belief.”
Chang then writes that the researchers "performed a randomized, controlled experiment" which he says is "relatively rare in education research". Really?
I started to lose it with this article when I got to the next bit:
Though the experiment tested college students, the researchers suggested that their findings might also be true for math education in elementary through high school.
There is a big difference between the abstraction skills of college students and those of elementary students. Haven’t these people heard of Piaget's developmental levels? (The final sentence from that resource says "Abstract reasoning is simply not universal." Indeed, many adults do not even reach Piaget's formal operations stage. Most elementary students are at concrete operations stage. Get that - concrete operations.)
Back to this questionable experiment:
In the experiment, the college students learned a simple but unfamiliar mathematical system, essentially a set of rules. Some learned the system through purely abstract symbols, and others learned it through concrete examples like combining liquids in measuring cups and tennis balls in a container.
Those who learned it abstractly did better than those who had experience with the concrete examples.
There could be so many other things going on here. If an elementary teacher just gets students to play with blocks, the students are unlikely to progress very far mathematically. If there is a proper design to the lesson and the students are given opportunities to make the appropriate connections, then there is a better chance that abstract thought could be triggered.
In the experiment, it is quite possible the students randomly combined liquids with no notion of why. No wonder they had trouble learning anything from it.
Another key consideration that is missing in this research is that the human brain will only remember things that have meaning and emotional significance. The whole idea of including "real life examples" is so that students will connect those experiences with the algebra (or process, or graph, or whatever) that is currently being studied.
In fact, one of the main reasons that the majority of the population (well, it always seems like the majority) don't like math and believe that it has no use in the real world is precisely because they have never seen how it is used in the real world.
Enough from me on this awful article. Go have a read and tell me what you think.
See the 8 Comments below.
7 May 2008 at 10:30 pm [Comment permalink]
i thought real-life examples are actually important. like u said, kids these days dont fancy maths because they have no idea of how it is related to the real world.
however, on the other hand, some people who has less imaginative mind would find such real-life example too much to grasp. it needs a bit of imagination. and apart from that, the conditioning of studying maths back in elementary somewhat does not help children to imagine maths in the real world.
i wish my teachers would have exposed me with real-life examples earlier, not that they dont, but i wish they had done more in order to help me and everyone else to actually love maths. (but anyway, i am a maths graduate. so my teachers have succeeded on that part. yay!)
15 May 2008 at 10:19 pm [Comment permalink]
I'm reminded of my daughter's time in early elementary school, where we (she and I) struggled with the concepts of multiplication and division. As I remember it, what worked best for her was the two pronged approach. 1) learn the tables. Ya just got to, to do math efficiently and 2) Here's what it means... divide by six means cutting the pizza in to six pieces... see how 1/3 is the same as 2/6 ?
I'm sure that post had no real value to anyone here, but I just found this blog and really want to contribute 😀
16 May 2008 at 7:48 am [Comment permalink]
Hi Stutty and welcome to squareCircleZ
Thanks for your comment. A lot of people lose sight of the fact that you just have to learn certain things in mathematics. Those who refuse to learn tables have a lot of trouble later because they just don't recognise patterns.
21 Apr 2011 at 5:37 pm [Comment permalink]
I think whether real examples should be used depends on the field of study. If you are learning basic arithmetic, real examples should be used because arithmetic is invented for practical usages. Whereas, is you are learning something like abstract algebra, it is difficult to find real world examples and if you force yourself to make some far-fetched examples, it would probably confuse people.
21 Apr 2011 at 8:27 pm [Comment permalink]
@Dalcde: I agree with you there - bad, unrealistic examples are worse than no examples at all.
12 Apr 2017 at 7:53 pm [Comment permalink]
Hi all, I struggled with math when we got to algebra bc no one ever explained the process and what it was used for. An example is rise over run. I was so focused on the immediate formulation that it was difficult to see the purpose. Then one day I finally asked, what's the point to this. Oh the teacher replied think about if you're building a ramp, stairs or a roof. Applying the concepts to real life makes all the difference. Otherwise your just moving formulas around. You may get the understanding of it but won't know how to use it. Like if you figured out how to use a blender but never had anything to use it for. Applied get math to real life made a huge difference for me.
12 Apr 2017 at 8:20 pm [Comment permalink]
@Shirley: Sadly, too many math teachers don't know how it's used either - mostly because that's how they were taught.
Thanks for sharing your story.
12 Mar 2018 at 11:41 pm [Comment permalink]
Teachers are facilitators that make learners to relate the theoretical facts to real world life. Math is not only abstractions, math is for solving, predict and model real life facts. Learner observes and discover patterns of the nature and compare with the theory to establish a math model.
Actually, we have two mathematical operations add and subtract. Multiplication follow the sum's properties because multiplication is a repeated addition of the same quantity. Division is to break a total in equal parts and if we have a remainder is because we have a difference between the quantities are dividing. Those are theoretical fundamentals that learners need to know in order to discover patterns. Calculus is divided in differential and integral (difference and sum) the rest are approaches of the phenomenon.
We have to make students to interact with Theory and facts absolutely. In the work placement individuals solve problems applying mathematics in any field.
without math is like car without gasoline.