Josh Rendall
2/26/13
EDCI 534
Measurement: What’s the Big Struggle?
The Standard
The National Council of Teachers of Mathematics (NCTM) has created
standards and expectations that serve as the guidelines of what is important in the
realm of teaching and learning mathematics. Of course there are the obvious topics
of algebra, geometry, and probability, among numerous others, that most people
would recognize because secondary school classes are dedicated to them. In
addition, there is so much publicity about algebra specifically because of
standardized tests and the fact that it is considered a gateway for high school
graduation. However, there is another standard that may not be easily recognized
by most people when they think of mathematics: Measurement (National Council of
Teachers of Mathematics, 2013).
Students, as they journey through school from kindergarten to the 12th grade,
should be able to meet certain expectations in the measurement standard.
According to NCTM, one of the overall goals of this standard is to “understand
measurable attributes of objects and the unit, systems, and processes of
measurement” (National Council of Teachers of Mathematics, 2013). Specifically,
students in elementary grades should begin to understand how to measure standard
units and select an appropriate tool and unit when measuring an object. Students
also should be able to approximate measurements and perform simple unit
conversions, such as feet to inches. As students move into middle school, NCTM’s
standards progress not just to knowing both the metric and customary systems of
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measurement, but students should be able to easily convert between units within
the same system. Students also begin to look at measuring angles, perimeter, areas,
surface area, and volume. Finally, high school students should be able to problem
solve and think critically when looking at different scenarios that incorporate
measurement to them.
The second overall goal of NCTM’s measurement standard is to “apply
appropriate techniques, tools, and formulas to determine measurements” (National
Council of Teachers of Mathematics, 2013). In the elementary years, students are
expected to learn how repeat the length of a smaller unit to measure a larger unit
and select and apply the standard units of measurements to objects. This could be
done with something small like a paper clip and figuring how long a piece of paper is
in terms of the length of one paper clip. Middle school students should be able to
apply and develop formulas for areas of different polygons and volumes and surface
area formulas to prisms, pyramids, and cylinders. Scale factors, in concurrence with
ratios and proportions, also are learned during middle school years where more
higher-level thinking about math begins to take place. Finally, high school students
are expected to be able to find approximate error and analyze how precise
measurements are. Students should also be able to understand more abstract
objects (cones, spheres, etc.) and how to find their volumes and measurements.
The new Common Core Mathematics Standards students will be subjected to
in the near future emulate what NCTM says. The measurement standards are
completed mainly by 5th Grade in terms learning what the standard units of
measurement are and recognizing how to solve problems with measurement. The
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terminology of length, area, volume, and mass are all supposed to be taught in the
elementary years, along with the conversions between units of measurement within
the same system (Common Core Standards Writing Team, 2012). Students then
work on apply measurement to more complex ideas, such as ratios and proportions,
in middle school and move away from only physically looking at measurement.
There is more abstraction and problem solving involved. In high school, much of the
focus of the Common Core looks at probability and calculating expected values using
the measurement knowledge that has been learned in prior grade levels (Common
Core State Standards Initiative, 2012).
These standards from NCTM and the Common Core are vast. They are taught
from when a student begins in elementary school until he or she graduates from
high school. Multiple facets of measurement need to be taught – area, length,
volume, surface area, mass, boundaries, and perimeter. The list grows and grows. It
has to be a group effort from all teachers from all grade levels in order for a student
to succeed in the measurement standard. That being said, it would be naïve to think
that every standard of measurement could be synthesized and analyzed together.
There is just too much information and research to try and do that. Instead, the
focus of this paper will look at topics that occur more during the middle school
years. What does the research say about what is happening to students during their
6th – 8th grade years concerning the measurement standard? What can be improved
to help students meet the standards and expectations NCTM and the Common Core
have made?
Measurement: What’s the Big Struggle?
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The Struggle
Measurement is the topic of mathematics that all students, not just middle
school, seem to have the most trouble with during the course of their math
education. It is often not given enough attention in textbooks, in schools, and by
teachers (Lewis & Schad, 2006). At times, it could be considered forgotten among all
of the other parts of mathematics that are taught (Foley, 2010). When teachers
themselves were asked, they overwhelming said that measurement is the section
where their middle school students are the weakest. It is also interesting to note
that these same teachers, along with other adults, view measurement as the most
applicable to a student’s life (Preston & Thompson, 2004). Every student will be
affected by measurement during their life, whether it is dealing with a car,
measuring furniture for a room, or cooking in the kitchen. The same probably
cannot be said about the other subjects in mathematics.
Students consistently perform low on standardized testing, according to the
National Assessment of Educational Progress, in measurement, where the topic of
length is a struggle even though it is taught beginning in kindergarten (Kamii, 2006).
Trends in International Mathematics and Science Study (TIMSS) and Programme for
International Student Assessment (PISA) also show that U.S. students’ performance
on measurement problems were significantly lower than in other math categories
(Driscoll, 2007). The question then becomes - Why is measurement so hard for
students?
One overlying factor in why students struggle learning measurement is how
it is taught currently in schools today. Students like procedures. They make sense,
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do not require much thinking, and can produce the correct answer. Mathematics in
general could be viewed in this light. It should not be a surprise, then, that
measurement is often taught as a procedure. However, because of this, students
have no actual concept of what they are really looking at (Gray, 2001). For example,
students will just memorize how to convert from one unit to another, without really
understanding what they are doing or why they are doing it. Often, when converting
units, students do not know when to multiply or divide. They are “not able to
visualize the problem or [do] not have efficient strategies for solving the problems”
(Klamik, 2006, p. 188). Everything a student focuses on is just memorizing the
procedure, insteading of being able to understand what the measurements
physically mean.
Along with the prodecural nature of measurements, students do not see the
value of it outside of the classroom walls. To a student, measurement can be as
simple as finding one unit of measurement, following an empirical procedure, and
writing a numeric answer. Rarely are students asked to think logically about
measurement. They are not even asked to compare two objects, via their
measurements, in most classrooms (Kamii, 2006). It is a procedure of finding a
measurement and writing it down. In learning length, for example, students are
often given a pages with objects where a ruler is already drawn out for them
(Martinie, 2004). There is no real world application or high level thinking involved
for students to see the value of measurement.
Perhaps the biggest struggle students have with measurement, espeically in
the United States, is the fact that there are two entirely different systems to learn –
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metric and customary. Currently, the United States is one of a handful of countries
still using the customary system (Monroe & Nelson, 2000). The rest of the world has
adopted the metric system. Because of this, students are bombarded with units,
from meter to inch to liter to ounce to pound – the list goes on and on. There is so
much information and different units of measurement for students to keep track of,
and not only do they have to keep track of it, the two systems of measurement do
not correlate well together (Preston & Thompson, 2004). It is clear that some of the
struggles students have about measurement stems from the fact that two systems
are taught simultaneously. Another important observation about the two systems is
the amount of time spent in a classroom on them. Often, there is a week’s
(sometimes longer) worth of lessons dedicated to the customary system, whereas
only a few days focused on the metric system (Taylor, Simms, Kim, & Reys, 2001). It
is important to note that students in the United States perform better on items using
the metric system rather than the customary system (Preston & Thompson, 2004).
However, they are lagging behind significantly internationally and still have a
difficult time learning measurement.
The Change
The research about the measurement standard is clear – students are not
getting it! What then can be done to improve it? There is not a single, one size fits all
solution to this dilemma. It will require a revamp in how educators teach
measurement and how students view it. There is an inexhaustible list of plans and
ideas of how to improve students’ comprehension of measurement. For the purpose
of this paper, only a few can be highlighted. The ideas featured were chosen because
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of how they correlate to the struggles and challenges students face currently in the
classroom when learning measurement.
When it comes to the classroom lessons, most research says teachers should
look at changing how measurement is taught. Lessons cannot be just memorizing
facts and procedures. Instead, students should learn through practice and problem
solving. Rather than just having students work on unit conversion over and over,
students could create their own word problems. These could then be exchanged
between students and solved (Klamik, 2006). It allows the students to take
onwership of what they are learning and make their lesson unique to their interests.
This is just a small example of the problem solving type questions and lessons that
could be implemented into the classroom. Middle school students, especially, are
missing out on the problem solving nature of measurement (Driscoll, 2007). Instead,
they are learning formulas and memorizing the information; there is little meaning
to what they are learning. In order to help these students improve their
comprehension of measurement, a change is the classroom is clearly necessary.
Relating measurement to other parts of mathematics and the real world is
another way to help students improve. Measurement is not a single, isolated topic. It
can be integrated into all the other parts of mathematics in some way. It makes
measurement more accessible and meaning to the student (Martinie, 2004).
Relating measurement to other parts of mathematics is important because time is at
a premium in a classroom. There is not enough time to add more lessons to a school
calendar (Preston & Thompson, 2004). A teacher needs to find ways to incorporate
Measurement: What’s the Big Struggle?
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this into their other lessons. Even an algebra lesson can have measurement
interwoven into it (Foley, 2010).
Relating measurement to the other strands of mathematics is not enough to
improve student performance, though. Problems that are applicable to the real
world are essential for students to truly understand measurement. The subject
becomes tangible to students, and they can begin to understand that measurement
occurs everywhere (Pumala & Klabunde, 2005). They can also begin to see the value
of knowing measurement in their lives after graduation. Sometimes, estimates of
measurement can be used in the classroom. It show they can understand mentally
what units represent and the relationships among them without being bogged down
in the number calculations (Preston & Thompson, 2004).
If teachers are going to change how they teach their measurement lessons,
assessment changes may also be needed. A traditional test at the end of the unit
where students are asked mundane, lower-level thinking questions is not
appropriate for checking student comprehension. Instead, “formative assessment,
continual feedback, and tracking of progress” (Pumala & Klabunde, 2005, p. 453)
should be used. Journal entries, group work, open-ended questions, and problem
solving activities should be integral pieces to a measurement curriculum. Students
should find their own measurements empirically and actually experience visually
what they are measuring (Kamii, 2006). It will be messy to teach in this style.
Students will resist the open-ended questions and the lack of guidance from the
teacher (Foley, 2010). However, it is a necessary change if educators are going to
help students improve in the standard of measurement.
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The metric system is an important key to success for students when it comes
to mastering measurement. NCTM (2006) has the following position statement
about teaching measurement:
To equip students to deal with diverse situations in science and other subject
areas, and to prepare them for life in a global society, schools should provide
students with rich experiences in working with both the metric and the
customary systems of measurement while developing their ability to solve
problems in either system.
NCTM understands that students cannot just learn the customary system, which is
commonplace in the United States. The metric system must be learned as well.
Students need to see the relationships and estimate conversions between the two
systems. Teachers also need to work to incorporate the metric system more (Taylor,
Simms, Kim, & Reys, 2001). The habit of teachers is to only look at the customary
system, but there needs to be a larger focus on implementing the metric system in
the math classroom.
It would be difficult for United States to make a complete switch to the metric
system because of the engrained nature that the customary system has in the
country. It would also be difficult and costly for many businesses to make the switch
(Monroe & Nelson, 2000). The world is getting smaller and smaller because of
technology and increased means of communication. The United States’ economy is
international, and for businesses to be successful, the metric system must be used
(Taylor, Simms, Kim, & Reys, 2001). Because of this, students need to be adequately
prepared in school to meet the world and the metric system.
Measurement: What’s the Big Struggle?
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Conclusion
Measurement is one of the fundamental building blocks of mathematics. Its
importance is being overlooked compared to some of its counterparts – algebra,
probability, and geometry. It cannot be overlooked anymore. Measurement cannot
be viewed as the last section in the book that is only covered if there is extra time. It
cannot just be a few lessons of unit conversions where students are not required to
think and just perform procedures. It needs to be problem solving and hand’s-on
activities where students can begin to actually comprehend how measurement
works, see it visually, and effectively use the tools necessary to find measurements.
Measurement should not just be a bunch of number crunching, but a mixture of
lessons where students can do everything from figuring out the width of a fingernail
to estimating the mass of the earth.
Students need to understand the intricacies of measurement to be ready for
the world around them. Measurement is a part of everyday life. Students need to see
the value in learning and comprehending it. If the purpose of school is to prepare
students for the real world and life after graduation, measurement needs to have a
larger focus in the math classroom. Students deserve it, and they need teachers who
are willing to take the risk and incorporate all forms of measurement, metric and
customary, into the classroom.
Measurement: What’s the Big Struggle?
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References
Common Core Standards Writing Team. (2012, June 23). Progressions Documents
for the Common Core Math Standards.
Common Core State Standards Initiative. (2012). Mathematics - Content Measurement and Data. Retrieved from Common Core State Standards
Initiative: http://www.corestandards.org/Math/Content/MD
Driscoll, M. (2007). Fostering Geometric Thinking: A Guide for Teachers, Grades 5 - 10.
Portsmouth, NH: Heinemann.
Foley, G. D. (2010, September). Measurement: The Forgotten Standard. The
Mathematics Teacher, 104(2), 90-91.
Gray, E. D. (2001). Teaching Measurement in the 21st Century. Louisiana Association
of Teachers of Mathematics Journal, 2(1). Louisiana. Retrieved from Louisiana
Association of Teachers of Mathematics:
http://www.lamath.org/journal/Vol2/gray.pdf
Kamii, C. (2006, October). Measurement of Length: How Can We Teach It Better?
Teaching Children Mathematics, 13(3), 154-158.
Klamik, A. (2006, October). Converting Customary Units: Multiply or Divide?
Teaching Children Mathematics, 13(3), 188-191.
Lewis, C., & Schad, B. (2006, October). Teaching and Learning Measurement.
Teaching Children Mathematics, 13(3), 131.
Martinie, S. (2004, April). Families Ask: Measurement: What's the Big Idea?
Mathematics Teaching in the Middle School, 9(8), 430-431.
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12
Monroe, E. E., & Nelson, M. N. (2000, October). Say "Yes" to Metric Measure. Science
and Children, 38(2), 20-23.
National Council of Teachers of Mathematics. (2006). Teaching the Metric System for
America's Future. Retrieved from National Council of Teachers of
Mathematics: http://www.nctm.org/about/content.aspx?id=6346
National Council of Teachers of Mathematics. (2013). Measurement Standard.
Retrieved from National Council of Teachers of Mathematics:
http://www.nctm.org/standards/content.aspx?id=316
Preston, R., & Thompson, T. (2004, April). Integrating Measurement across the
Curriculum. Mathematics Teaching in the MIddle School, 9(8), 436-441.
Pumala, V. A., & Klabunde, D. A. (2005, May). Learning Measurements through
Practice. Mathematics Teaching in the Middle School, 10(9), 452-460.
Taylor, P. M., Simms, K., Kim, O.-K., & Reys, R. E. (2001, January). Do Your Students
Measure Up Metrically? Teaching Children Mathematics, 7(5), 282-287.