What an incredibly short-sighted sentence: "Sorry, education reformers, it’s still memorization and repetition we need.".
I could not disagree more with this article. Memorization helps, but MAKING CONNECTIONS between concepts is _HOW YOU MEMORIZE EFFECTIVELY_.
Memorizing is great for learning different languages. NOT MATH.
Sure, maybe students are bullshitting in understanding concepts, and forgot quickly since they didn't learn anything. However, just memorizing shit doesn't do anything. So many students in other cultures are being forced to memorize everything, and since they don't understand the connections, they cannot come up with the answer on their own. There was a piece on HN about a math teacher that was amazed by how little students knew: They memorized how to solve a particular problem instead of actually knowing why something was true, and therefore couldn't work through basic proofs and stupidly basic, foundational stuff.
Did you even read the article, or did you read the subheading, which I will admit is a stretch, and immediately cast judgement? You used the strawman of a k-12/college student who learns something and quickly by practicing a particular method then forgets it. What about those who actually do learn this way? There are most certainly visual learners who can see concepts in their head -- a trait I admire personally.
>So many students in other cultures
Do you know every student? Every culture? Again, nothing but over-generalizations here. The article actually referenced the afterschool programs in Japan that had success.
Yes at some point you have to back and understand the why and the how, but solving equations and crafting proofs are actually two different skills in my opinion and I have met mathematicians that were stronger in either or both.
In any case, I think you are missing the point of this author. I think the authors strongest argument which is building that foundation, or "innate ability" and he argues that comes through memorization and rote learning. Quoting, "building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success" I don't think he just pulled that out of his butt. If you take the time to practice like the author did where it becomes engrained into your mind, you are in fact learning effectively.
Besides all this, what is mathematics anyways? Is it not a language? Does it not have "letters" (variables, operators, symbols), does it not have a grammar? Does it not have "parts of speech?" (an equation must have a left side, and a right side), Is it not used to communicate to others?
In any case, certainly not a terrible read in any way.
As a CPGE student I must say that memorization IS key to solving problems (the essence of learning maths); it's not a traditional "dumb" memorization of proofs however.
The whole assertion of "understanding how a proof is done rather than memorizing it is how maths should be done" holds true, BUT only when you are not bound by time or a deadline, which is not the case most of time, whether you are working through a test, an exam or even on a PhD, you cannot afford losing time "reinventing the wheel"; working on proving theorems that have already been proven rather than using them directly.
The factor of time forces you to "memorize" certain concepts/theorems/facts so that you can use them directly as tools.
Personally, my approach consists in working on proving these "tools" at a first stage; understanding why they are true, then, I simply go past that and simply "memorize" them in order to boost my workflow.
In a nutshell, in order to be productive (doing maths or even physics), you must memorize shit, just don't do it blindly.
"In a nutshell, in order to be productive (doing maths or even physics), you must memorize shit, just don't do it blindly."
And voilà, you put it much better than I did in 5 rambling paragraphs. Memorization is key (at least for some learners), but only as one part of a process.
This is why the education system will never ever change. Too many people learn too many different ways. Some people can read a formula and instantly memorize it. Other's need a connection to that formula. Some need to figure out how that formula was derived in order to understand and memorize it. And some know the formula before you even show it too them.
Not to rehash what you hashed, but it depends who you are. If you are really good at memorizing, you may not need to make connections. You may just be able to memorize everything. Some people can.
This is very true. A corporate trainer once told me there's specific kinds of learners. They've actually identified each type, and which specific methodologies you need to reach each one. The best teachers find a way to synthesize it all into an effective single presentation. (This may also be why tutors are so helpful -- they can customize their material to the audience...)
Although there is ample evidence that individuals express preferences for how they prefer to receive information, few studies have found any validity in using learning styles in education.[2] Critics say there is no evidence that identifying an individual student's learning style produces better outcomes. There is evidence of empirical and pedagogical problems related to the use of learning tasks to "correspond to differences in a one-to-one fashion".[3] Well-designed studies contradict the widespread "meshing hypothesis", that a student will learn best if taught in a method deemed appropriate for the student's learning style.[2]
Heh. Okay, that's good to know. These comments prompted me to look up "Learning Styles" on Wikipedia, which confirms that scientific studies have not confirmed the validity of the "different learning styles" theory.
That probably says something about corporate trainers. I still remember the HR department at one company where I worked that insisted on giving the Myers-Briggs personality test to every employee. So maybe this also says something about junk science and the way it lingers on in our workplaces...
A corporate trainer once told me there's specific kinds of learners.
I don't believe there is compelling evidence that this is the case.
Instead, different people have different backgrounds and experiences. Learning requires making connections. Depending on what you have in your head already to which you can connect, you may respond differently about a particular topic than someone else.
This is a good point. It's important not to overgeneralize. At the same time, for those students who learn best by memorizing, it's best not to completely discard rote learning.
I could not disagree more with this article. Memorization helps, but MAKING CONNECTIONS between concepts is _HOW YOU MEMORIZE EFFECTIVELY_.
Memorizing is great for learning different languages. NOT MATH.
Sure, maybe students are bullshitting in understanding concepts, and forgot quickly since they didn't learn anything. However, just memorizing shit doesn't do anything. So many students in other cultures are being forced to memorize everything, and since they don't understand the connections, they cannot come up with the answer on their own. There was a piece on HN about a math teacher that was amazed by how little students knew: They memorized how to solve a particular problem instead of actually knowing why something was true, and therefore couldn't work through basic proofs and stupidly basic, foundational stuff.
A terrible article!