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| Geometric Containers can be filled with water, rice etc. |
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| Ropes and Ruler for tying knots activity |
"Math
Manipulatives" This is common vocabulary for present
day math education and at the same time it should not be unfamiliar to teachers
and students in older generations. In planning a math lesson, today's teachers are
encouraged to be thinking "manipulatives, manipulatives,
manipulatives!". Instead of having that box of tiles or cubes in the back
corner on a shelf, they are up front and centre, used in almost every lesson or
at least it is explained to the students how manipulatives could be used in the
lesson. As a student I remember having manipulatives in the classroom however
they were mostly used as an aid for learning instead of a tool to build
learning concepts. What I mean by this is teachers would not immediately
incorporate manipulatives in their lesson and when students would struggle with
concepts the teacher would refer them to the manipulatives station. This could
have been just from my own personal experience but there seemed to be some type
of stigma surrounding students who required manipulatives in math. It was
almost as if the students who understood the concepts and got the answers right
away without the use of any further visual were somehow stronger than the
others. This rationale of course is not true; manipulatives are used far beyond
the use of a visual aid. The first and most obvious use for manipulatives in
math is to engage students in their learning. There are so many forms of
manipulatives such as apps, games, and the traditional tiles or household
objects all of which make math fun and learning worthwhile for the students. In
our "Teaching Mathematics" class this week our instructor had brought
in sample activities that make use of a variety of manipulatives. One activity was
used for teacher linear relations. It involved ropes which the students had to
tie knots in order to determine the type of relationship between the length of
the rope and the number of knots. No matter what the manipulative being used
is, the teacher has to ask themselves is it useful, is it fun, is the activity
memorable enough for future student reference.
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| Algebra Tiles |
Manipulatives are also used to
develop a student's critical thinking skills similar to the skyscraper problem
in my last post you can have students at all different levels try a problem
with manipulatives and see where it takes them. For all students the
manipulatives should help to visualize their problem and where they need to go
from here. For some of the stronger math students, having the manipulative
might allow them to come to a conclusion alternate to their original thoughts
and they are able to learn there are multiple ways to facing a problem. In
class we experienced something similar when our teacher handed us each a card
with a number or word and in a group we were to create one sentence from our
cards. This activity was used as more of an icebreaker however you could repeat
this process by having different variables on the cards and asking students to
create a function or have descriptive words such as max/min and have students
describe a modeled situation.
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| Word Cards |
Another use for manipulatives in the classroom comes as an advantage
for both teacher and student. In my class we had discussed an article on the
difference between Relational vs. Instrumental understanding. In a mathematical
context instrumental understanding is following rules and applying formulas
without fully understanding the reason why and relational is the latter. In
order for students to have more of a relational understanding teachers can use
manipulatives to make that connection for students between the "what to do"
and "why are we doing it".
Below
I have attached a link to an article titled "Why Teach Mathematics with Manipulatives?". I believe the
article does an excellent job arguing why manipulatives are critical in the
classroom and it clearly explains that through the use of manipulatives
students facilitate their learning by making the strange become familiar.
Hey Stef! I liked how you touched on the fact that even the stronger math students can benefit from math manipulatives. This is very much true! By allowing all students access to math manipulatives there can be a variety of ways of learning and understanding. Math manipulatives not only act as a learning tool but they also can lead to different ways of approaching a problem that a student may not have thought of before.
ReplyDeleteI can't wait to read your next post!
Cobie
Hey Stef,
ReplyDeleteI really enjoyed reading your blog this week, as I found it to be very relatable. I liked the point you made about how math manipulatives should not be unfamiliar to teachers and students in the older grades. I completely agree with this and think that it is important for both students and teachers to be aware of the materials that are available to use. As it will enhance the learning of the students. I also like how you touched on the fact that manipulatives should be used not be used as a learning aid, but as a way to build on learning concepts. You mentioned that due to past experiences you felt that there were stigmas around math manipulatives and the people who used them, and I would agree with that. The manipulatives were something teachers would give to students who were struggling and not the class as a whole. I think this also gives the assumption that manipulatives are only for visual aid, when they can be and should be used for so much more. I hope that in my classroom I can get students to see beyond the stigmas and understand that manipulatives should be used to help enhance ones learning process, and can be used by everyone. I am looking forward to reading your post from next week’s class.
Jodi
Hi Stef,
ReplyDeleteI think you made a very valid point about the stigma around mathematics manipulatives. Have you considered how to address that in the classroom? A lot of the activities our instructor gave us required that all students work with the manipulatives, thereby removing stigma by design. One thought your article made me consider is having manipulative kits for each student, so each student could have them and access them as they please. I am excited to start working with manipulatives in the senior mathematics classroom and allow my students to discover the fun of math as well as to challenge themselves.
Kayla
Hi Kayla,
DeleteI haven't come up with many ideas to eliminate the stigma other than using the manipulatives at the beginning of a lesson in the hopes that the students are familiar with manipulatives as a tool instead of an aid. I do really like your idea of giving each individual student their own set.
Hi Stefanie,
ReplyDeleteYour post made me realize that we have come full circle in mathematics, with respect to manipulatives. (Excuse the terrible math pun.) Back in the day, before symbolic algebra took root (circa Descartes, so about 1600), mathematics was thought of in purely concrete terms: distances, areas, volumes, that sort of thing. Geometry - real, touchable objects - were of prime importance (granted, with some mathematical glossing-over of things like measurement error). Even Muhammad ibn Musa al-Khwarizmi, the 9th century Islamic mathematican who introduced our modern number system and published the first real work on Algebra, thought of numbers in this way. It is apt that you show the algebra tiles, as this is exactly how al-Khwarizmi did things, though without the huge benefit of negative numbers. (That would have to wait another few hundred years.)