Hello and welcome once again to my math
blog. What is the difference between ‘knowing’ math and ‘understanding’ math? This question was mentioned in class briefly
however I would like to reflect a little more on exactly what the difference is. I believe that the most effective and
powerful learning comes when a student truly understands the knowledge that is
being shared with them. Unfortunately,
based on the way math is taught in ‘classic’ classrooms, the assumption has
been that once a student is told how to do something they ‘understand’ how to
do it. In my opinion this is a very wrong assumption to make. Knowing that the
power button will turn on your computer does not necessarily mean that you know
how the electronics in your computer works. This to me is what the difference
is between ‘knowing’ and ‘understanding’ something. It’s a
superficial/procedural knowledge (i.e knowing that the equation P=4s will give
you the perimeter of a square) versus a deeper conceptual understanding (if you
are looking for a perimeter you are looking for the length of all four sides of
the square :. s+s+s+s or simply 4 X S which is also written as 4S). Check out
this video on the difference between knowing and understanding:
I think teaching
for understanding is an important step in the 21 Century classroom and our
students should be encouraged to further their understanding rather than parrot
the equations that they see in the classroom. I think some of the math teaching
methods that we saw in class this week can be used as a way to teach math for
understanding. Math Daily 3 allows students to work on their own to resolve
math problems, with another to discuss/share and further their understanding,
and later reflect on what they have learned. Math congress is also a method
that requires students to resolve math problems through first working by
themselves, with a partner then sharing with a larger group. I believe these
methods can be used for conceptual understanding because rather than use the
tradition teacher-centered method of sharing knowledge it requires students to
be their own teachers. In other words, students are put in charge of their own
understanding, this can be used to further conceptual understanding because
students can be allowed to trial and error, to discover what methods work and
to share their discovered understanding with their peers.
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| Whitfield, Jordan. (unknown) Work Harder. Retrieved from https://bit.ly/2JSbYal |
Thank you all for reading and see you all
next week!
Hey Nadine, I really enjoyed your post where you explained the difference between knowing math and understanding it. I totally agree with you and think that most people think they know math but don't quite understand it. There are a lot of things that I may know but if I haven't applied it for myself then I don't actually understand it. I believe as future educators we should monitor our students and look out for these sorts of signs so that we can actually help them understand the material rather than them just knowing it.
ReplyDeleteHi,
ReplyDeleteI enjoyed reading the points you made between teacher centered and student centered learning. I feel that student centered learning can be more impactful and lead to better retention and understanding especially with the teacher monitoring and giving helpful nudges when required.
My concern is how the student centered model holds up as class sizes increase and less teacher attention can be given to each individual group of students. I wonder if there has been any research done that shows any insights between teacher and student centered learning in an environment with 5 to 10 students compared to 25 or more students.
Hi Nadine!
ReplyDeleteKnowing vs. Understanding is so important to learn as educators. Traditionally, we are given a method, an algorithm, a set route, and we're told to pump out an answer as fast as we can... Those math speed tests, for example. However, how many of us can actually say we understood what we were writing? I think we end up memorizing or falling into habits when answering questions instead of taking the time to really look at what the questions are asking for. We never really used to consider secondary options for answering something, nor could we ever fathom a potential third way. But, this class is beginning to show us that we are all mathematically unique and can be good students and teachers if we take the time to understand and appreciate what we are doing.
Great post!