Math in the Real World:
Teaching math to enhance understanding
EDCP 340 110
Teala Mackowetsky
January 24, 2014
UBC
Math in the Real World: teaching math to enhance understanding
Teala Mackowetsky
The goal I have for my long-term practicum math class is to ignite a spark in my students
that will help them understand and enjoy math. As Ms. Toliver did in her classroom, I want to
find innovative ways to engage students and to relate the course material to practical, “real
world” scenarios. Too often throughout my education I was asked to do what seemed like
meaningless tasks that had no relevance to the real world or my lived experiences; for me this
experience happened most frequently in math. I almost felt as if everything I did was just to
appease the teacher and I never understood why. Additionally, if I did not understand ‘the why’
or the practical significance the material could have in my life, I simply could not grasp the
concept. In my elementary math class for example, adding, subtracting, multiplying and dividing
fractions seemed impossible; in my mind, this process was simply a task we were required to do;
the figures were simply figures, and they did not apply to a real world scenario. It was not until I
was baking with my grandmother that the information finally clicked; in order to double a batch
of 2 ¼ cups, you would have to add an additional 2 ¼ cups; in turn this would equal 4 ½ cups.
Prior to this baking experience, the game of numbers did not add up and just resulted in
confusion. In Erlwanger’s article (1973), Benny’s Conception of Rules and Answers in IPI
Mathematics, discussed in class, Benny experienced the same problem as I did because he was
relying primarily on playing a game with numbers rather than comprehending the concept
(Erlwanger, 1973).
After doing some research on different approaches of teaching math, I have discovered
that my personal experiences surrounding learning math is not much different then what Douglas
Clements and Michael Battista call traditional learning or transmission/ absorption”. They state
that this approach involves the students passively “‘absorbing’ mathematical structures invented
by others and recorded in texts or known by authoritative adults” (Erlwanger, 1973, p. 34). As
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Math in the Real World: teaching math to enhance understanding
Teala Mackowetsky
the name ‘traditional’ suggests, this type of teaching is what used to be, and can still be found in
schools.
Given my experiences, I am interested in teaching through real life examples in order to
contrast the traditional method that I experienced. From what I have read there are several
different ways in which you can incorporate real world problems into your math class. For the
purpose of this paper, I will consider what I have self-labeled as: play before you learn and label,
use real life lessons, and relate content to the students personal history and interest.
In the first example, play before you learn and label, the teacher is required to create a
lesson that will allow the students to interact with the concept or play first before the teacher
introduces the concept and labels. What I have discovered in my practicum so far, as well as
what I am learning in various classes at UBC is if students have time to play, and an opportunity
to figure out information on their own, then they are more likely to understand a concept. A
constructivist perspective explains, “People construct their own understanding and knowledge of
the world, through experiencing things and reflecting on those experiences. When we encounter
something new, we have to reconcile it with our previous ideas and experience, maybe changing
what we believe, or maybe discarding the new information as irrelevant” (Exline & Costa, 2004).
In other words, information is easier to retain if it relates to experience. In addition, in Dan
Meyer’s Ted talk Math class needs a makeover, he considers the advantages of students getting
the visual first so they can create their own understanding, connect this understanding with their
previous knowledge, and then receive the information or labels (Meyer, 2010). By giving the
students the time to play or to think for themselves, they are able to actively think about what is
happening rather than passively absorbing information and computing numbers as a game. Judy
Willis (2010) also agrees that there is merit in “developing the concept before giving it a label”
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Math in the Real World: teaching math to enhance understanding
Teala Mackowetsky
(Willis, 2010, p. 122). To summarize, it is better if the teacher presents the student with the
experience first, and labels second; then the students can reflect on their lived experience once
they discuss the labels and make connections. These experiences can be generated through
interactive hooks; examples I have found include manipulatives, interactive questions, games,
and so on. Throughout my research, I have discovered several resources, mostly websites and
blogs, that offer good interactive hooks and lessons for teachers to incorporate these interactive
scaffolding experiences. The two most helpful sites I found include Dan Meyer’s blog DyDan
(Meyer, 2011), and the website doingmath.com (Reid, 2012). Both of these sources provide
examples of lessons and ways of teaching students through real world scenarios.
Another method is bringing real life examples into the content, or into the lessons taught.
A great example of this is in Jana Dean’s article Living Algebra Living Wage. In Jana’s article
she describes how she teaches algebra through jobs and the Socio-Economic Status of the people
in the neighborhood. In her article, she describes her success with teaching algebra in this way;
after the unit was over the students reflected positively on the process. Many students discussed
how the algebra unit she taught made them reflect on different aspects of their own lives or the
world around them, which created a concrete understanding of the material. Dean (2007) states
that “their responses let me know that I had met my goals of building a bridge between algebra
and the world of wages and work, and of showing them that math can be a tool for reading their
world” (Dean, 2007, p. 35). What I concluded from her study was that the students learned the
content because the material was rooted in something practical and relevant; as a result, the class
became something they wanted to do rather than had to do.
Finally, a teacher can relate information to the real world through their student’s funds of
knowledge and personal interests. By presenting students with tasks they have a personal interest
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Math in the Real World: teaching math to enhance understanding
Teala Mackowetsky
in, and/ or connect the material to real world examples they already have, the kids are much
more likely to be motivated to learn. Willis (2010) suggests that there is a connection or
correlation ‘between people’s driving interest in a particular topic and high success”. She also
mentions that by getting to know your students personally, you are allowing to relate to the
“here-me-now” in the students learning; she calls this “kid watching” (Willis, 2010, p. 116). As I
mentioned earlier, if a learner can connect what they are learning with something they have
already experienced, we can reconcile it with what we already know and in turn facilitate and
increase understanding.
After considering this research and discussing this topic with colleagues and the teachers
in my practicum, in conjunction with my own personal experience, I have concluded that through
teaching math in an interactive/ practical way, it will not only facilitate understanding of
concepts, but will also increase interest and the desire to learn. As the illustration below suggests,
we must eliminate the current gap between the math that we teach in class and the math we
experience in the real world. Based on my research, if we as teachers employ the correct
techniques, we can narrow the gap between the two mountains and ultimately improve the
quality of math taught in schools.
(Screenshot, Meyer, 2010)
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Math in the Real World: teaching math to enhance understanding
Teala Mackowetsky
References
Clements, D. H., & Battista, M. T. (1990). Constructivist learning and teaching. The Arithmetic
Teacher, 38(1), 34.
Dean, J. (2007). Living algebra, living wage: 8th graders learn from real-world
math lessons. Rethinking Schools, 21(4)
Erlwanger, S.H. (1973). Classics in mathematics education research: Benny’s Conception of
Rules and Answers in IPI Mathematics. In Journal of children’s mathematical Behavior 1
(pp. 49-58). Reston, VA: National Council of Teachers of Mathematics.
Exline, J., Costa, A. (2004). Concept to Classroom. In thirteen ed online. Retrieved Dec 3, 2013,
from http://www.thirteen.org/edonline/concept2class/constructivism/index.html.
Meyer, D. (2010, May). Dan Meyer: Math class needs a makeover. Retrieved from
http://new.ted.com/talks/dan_meyer_math_curriculum_makeover
Meyer, D. (2011, July 8). Dy/dan: Pyramid Of Pennies . Retrieved from
http://blog.mrmeyer.com/?p=10919
Reid, L. (2012). Real World Math. Retrieved Jan 23, 2014, from http://www.realworldmath.org
Willis, J. (2010). Learning to love math: Teaching strategies that change student attitudes and get
results., Alexandria, Va: ASCD
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