Out of
all the math units, algebra has always been the hardest for me to complete. Algebraic
equations appeared to be strange foreign language to me, and still do to some degree
today. So when I realized that this week in our math class we started our conversation
about teaching algebra after I completed the reading, I half excited to find
out how our instructor was going to approach it through the new math lens we
have been practicing but I was still nervous.
“Algebra
is just patterns”, is something that I have heard my instructor say many times
already, but I did not really think about how true it way. The notion of taking
a simple patter, such as number starting at 3 and increasing by 4 can be
translated into a linear equation, is something that is relatively new to me.
Sadly, I do not think my math teachers in the past ever taught me this way, and
if they did, it certainly did not stick. We began the class by performing a “mix-and-match”
exercise where we had to identify what graph, table and visual aid matched with
each equation that we were given. This activity was phenomenal at illustrating how
linear algebraic equations are able to be compared and visually shown in
different ways.
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| Matching Algebra Activity |
One aspect of this activity that stuck out to me the most was the tangible use of manipulatives. I do not recall using manipulatives at all to demonstrate algebraic patterns. The use of the connect cubes allowed me to really be able to visualize how the equations we were using change as they continue through the pattern. The idea of using two different colours of cubes would really allow students to visualize the patterns they are dealing with. The image below illustrates how the equation (Number of Tiles =2s + 2. Providing manipulatives for the students to be able use the hands to actually build a model of how the values increase would help provide background for the student when dealing with missing variables in the future.
I never
specifically associated algebraic equations with patterns, but even that simple
idea has improved my understanding of the subject. Our text book states that one of the most
common mistakes students make is misinterpreting equations, specifically when
dealing with equations that use “x” as a variable, students commonly see “x” as
the multiplicative process when first exposed to equations. It is important to
combat this by not using the letter in equations or by italicizing the parts of the equation, they would appear like this
for example T = ab X f.
I think there is a general consensus
in regards to students having negative views toward algebra. I think through proper planning and
structure, educators are able to remove the intimidating vail that comes with algebra
by focusing on committing to the use of manipulatives and open questions. Of course,
the same notion can be said with any strand of math, and it should be. However,
with algebra being the foundation to higher levels of math, slow introductions
that really focus on getting students to realize the pattern aspects would
result in the building of a better foundation for them to better understand more
complex algebraic equations in the future.
Keep on keepin’ on
Great blog post. I also had trouble as student with algebraic equations and was always nervous when it was time for that unit in math. Likewise I never associated algebra with patterns and can not remember if this was because of the way I was taught or just something that I believed on my own. I really like the idea of not using the letter x as the variable in equations. You explain why 'x' can cause confusion and offer great alternatives for this variable. The concept of proper planning and structure along with the use of manipulatives should be an integral part to teaching any mat lesson. Great blog post on patterning and algebra!
ReplyDeleteHi Joey,
ReplyDeleteI can too relate to the value of using other letters in making our algorithms. This will assure that students understand what they mean and where to input certain values they have to determine other answers. The example where students see “x” as the multiplication symbol is like a flashback to my own childhood experience with this content and the worst part was is that I was not allowed to change it according to my teachers. My discomfort with not being able to personalize my learning was one of the starting points where I began to not understand math. And once you don’t know one step, the rest don’t follow without it. The text does a really good job at identifying many of the misconceptions but also how to manage those within our own placements. This was a really enjoyable blog post to read and the visuals were great too!
A very well written blog post. I liked how you related your own personal experiences to what you are learning in the class. I found that my education was very similar to your experience where I memorized the rules of algebra to solve it, but never really understood it. I also had an aha moment when algebras were related to patterns in class because I never looked at it that way before. I think that connection could help students understand algebra in a different and better way.
ReplyDeleteJoey, I am enjoying the wonderful insight you use to create your blog each week. Your engaging posts weave assigned readings/viewings with inclass activities and some activity presentations. I can see your growth in skill and philosophy of teaching math each week as you think deeply and relate all of these to share your personal experiences. Be sure to proof read carefully.
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