Trends in Mathematics 1
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Trends in Mathematics 2
Running head: Trends in Mathematics
Trends in Mathematics
Trends in Mathematics 3
Competence in mathematics is crucial for functioning in everyday life.
This important skill development begins in the primary elementary grades.
Educators are aware of the importance math education holds for our students. In
order to best serve our students and find the most effective methods to transmit
the essential math concepts to children, we must become familiar with the
implications of past, present, and possible future of math instruction techniques.
This can be accomplished by an examination of teaching methods used in the
past and how they have changed over time, analysis of our current mathematics
education situation, and development of a firm understanding of how essential it
is for students to master the fundamental math concepts.
Over the past 100 years of mathematical education, there have been three
main approaches to teaching students. In the early 1900s, the focus was on
traditional math, which was simply the continuous practice of basic algorithms.
There were teacher-directed lessons, followed by students working
independently to practice the topics covered in the lesson. Tests were standard
paper and pencil examinations. This form of math came to end in 1957 when
Sputnik was launched. There was an outcry in the United States, declaring, “our
students are behind in math and science” (Mathnasium, 2007, p.1).
At this point, new math was put into action. Rather than continuous
practice of basic math skills, students worked on applying new skills. There was
a newly-found focus on application and practical understanding of mathematics.
Methods continued in the same teacher-directed format with students primarily
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In the mid-seventies reform math began to be practiced. The major change made in this transition was to steer away from teacher-directed learning
and begin to combine that with student-directed self-discovery. Another
significant change was that evaluation is based on more than just tests; projects,
porfolios, journals, etc., were also taken into account. Students work in groups
more frequently and are encouraged to interact as a learning source. Learning of
basic skills is encouraged, yet critics will say that “there is a lack of emphasis in
developing basic skills in a timely fashion” (Mathnasium, 2006, p.3).
By 1989, The National Council of Teachers of Mathematics (NCTM) put
out a new document entitled Curriculum and Evaluation Standards of School
Mathematics. This manuscript calls for, “abandoning curricula that promote thinking about mathematics as a rigid system of externally dictated rules
governed by standards of accuracy, speed, and memory.” Battista states in his article, “A mathematics curriculum that emphasizes computation and rules is like
a writing curriculum that emphasizes grammar and spelling; both put the cart
before the horse” (Battista, 1994, p. 1).
The commonality that has occurred since the early 1900s is that we are
continuously searching for new methods of teaching math. We are yet to find the
method that will achieve 100% success. Does that one method exist? When referring to higher achievement in all areas of education, the phrase back to
basics is commonly mentioned. However, this insinuates that there was a time
period in the past where we found ideal balance that taught all students math to
their fullest potential. It infers that there was a time that we were completely
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satisfied with the achievement our students in mathematics. I find it perplexing
that math has had this stigma attached to it for over 100 years! Although
education is always a topic of debate, math protrudes with debate. Perhaps it is
this perceptible dispute and constant discussion of how our students are behind
in math that gives many students a downbeat attitude regarding the subject.
Throughout history, including the present, there is a disagreement
between proponents of traditional math and reform math. A suggested solution
is that the best option is a combination of these theories. A mixture of the ideas
that have found success over time, implemented on individual bases with
different students, may be key to finding improved accomplishment in the future
of mathematics. In my future classroom, I look forward to utilizing a combination
of both these methods of teaching mathematics. Although I disagree with the
strict, rote memorization of traditional math, I believe that some skills in math
require memorization. In order for students to learn the basic math facts, they
simply have to practice until the answers are automatically stored in their
memories. However, just because memorization is sometimes required in math,
I do not believe it should be a substituted for valid understanding of the concepts.
There are also aspects of reform math I am not at ease with. While I believe that
students should have the opportunity to learn math in various ways, and be given
multiple forms of evaluation, I believe the initial focus should be in assisting
students in gaining the essential skills they will need to use as building blocks
while they continue gaining their mathematics educations in elementary school.
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In agreement with new math, I believe students should not only being learning
the skills, but understanding how to apply them to actual situations.
It seems the question, “How are American students doing in
mathematics?” is continually being posed. However, finding an answer to this
question is less than straightforward. Most commonly, educators and law-
makers determine an answer to this question by examining the scores of
standardized tests. Patterns exhibited by two major math tests conducted by the
National Assessment of Educational Progress (NAEP) have indicated there is
some improvement in math; however, improvement is decreasing in basic math
skills, such as computation.
About one-half of U.S. 9-year-olds cannot multiply or
divide whole numbers accurately, and half of 13- and
17-year-olds cannot compute correctly with fractions.
These deficiencies mean that large numbers of
American elementary students are ill prepared to
study algebra in middle school, large numbers of
middle school students are inadequately prepared to
take advanced mathematics courses in high school,
and large numbers of high school students have not
mastered the rudimentary skills required for entering
college or gaining middle-class employment
(Loveless, 2003, p.3).
Educators, policy-makers, and reform activists are actively testing and examining
these results. However, these test conclusions hold no relevance if we are
unable to find the changes needed to formulate the necessary improvements.
No Child Left Behind (NCLB) is the current plan of action for ensuring all
students are functioning sufficiently not only in math, but the entire spectrum of
subjects being taught in schools. The issues related to NCLB, standards,
accommodations, and teaching to the test are never-ending; all the minute
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details are not pertinent for this focus. The relevant question is whether or not
NCLB is working. Is this government-funded program teaching our children the
skills they need to successfully carry on through school? Although there are
many ways to evaluate that question, various forms of research appear to reach
the same conclusion: NCLB has done little to improve math skills.
Results from the National Assessment of Educational
Progress (NAEP) Trial Urban District Assessment
(TUDA) show little overall improvement in math and
reading since No Child Left Behind became law, and
no closing of score gaps between racial minorities
and whites. This parallels state and national results
on the same tests. Two international reports also
demonstrate no change in U.S. scores since
enactment of NCLB (Fair Test, 2008, p.1).
These discouraging results regarding testing do not mean that NCLB is a lost
cause, but it does show us that the methods used to enact the law are ineffective.
Each and every educator I have discussed NCLB with, agrees that while it has
reasonable intentions, its plan of implementation is not effective. Also,
undoubtedly every teacher has told me that NCLB has in no way made their
students more efficient or competent in the basic subjects.
There are as many suggestions for reform as there are supporters and
detractors. However, it does not seem sensible for lawmakers to be in charge of
reform. No one can know the changes that need to be made in the educational
world better than the educators. Vicky Coy, a first grade teacher in Powell, WY,
and the woman who mentored me through my Elementary Math Methods course
explained this exact concept to me. With years of experience, she told me that
no one knows what the students need to achieve academic success like their
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classroom teacher. Each student learns differently, and each teacher finds ways
of reaching students differently. Vicky explained to me that the methods she
taught me are simply the way she teaches math; the methods that work for her.
Some of them may work for me in the future, others may not. It all develops on
an individual basis, and depending on the students one is working with (Personal
communication, April 2008).
The reasonable goal to achieve now seems to be getting input from the
teachers about NCLB. Is it effective? What works? What does not work? The
reform needs to come straight from the experience of our educators. This is
what will have the most positive effect on the students and the educational world
as a whole.
Throughout the studies of student achievement, evaluating the methods of
math instruction and finding just the right combination of all these elements, it is
most important to remember exactly why it is necessary for students to acquire a
solid understanding of mathematical concepts and processes. There are multiple
reasons why it is beneficial for students to begin learning basic math skills early.
Primarily, children need to learn the mathematics fundamentals, so they are able
to continue to build upon that learning as they progress through elementary
school math classes. Many math concepts require previous knowledge of other
math skills to be absorbed. For example, in order for students to understand and
solve the multiplication problem 3x7, they must be able to understand the
concept of addition (7+7+7 or 3+3+3+3+3+3+3). If a student is yet to master
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addition, multiplication will not only be difficult to teach a student, but he or she is likely to not understand what multiplying means.
I have had a considerable amount of time to work with students in the
primary grades (mostly first and second). Often viewed as an “extra” in the
classroom, I have frequently been given the opportunity to work with students
one-on-one with a subject they need extra help with. It seems more often than
not, it is mathematics that students are struggling to comprehend. Within the first
few minutes of working with students, I am usually able to determine that their
lack of understanding is not a lack of ability to learn, but a missing link somewhere in their math understanding up to that point. An instance in which I
have seen this is when a student is not able to comprehend addition with a trade
because he or she does not understand the idea of ones and tens, but has
simply memorized addition facts. Memorization of addition is necessary;
however, a genuine understanding of how these numbers come together should be obtained initially. There are other numerous examples such as these that
illustrate why math education is a chronological learning process.
In addition to this, as students get older they begin forming beliefs or
opinions about school and their strengths and weaknesses in certain school
subjects. Unfortunately, students often develop the I can’t or It’s too hard attitude
in math. Therefore, getting students involved and excited about math at a young
age will leave them with positive benefits as they progress through the school
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Most students enter school confident in their own
abilities; they are curious and eager to learn more.
They make sense of the world by reasoning and
problem solving. Young students are active,
resourceful individuals who construct, modify, and
integrate ideas by interacting with the physical world
as well as with peers and adults. Young students are
building beliefs about what mathematics is, about
what it means to know and do mathematics, and
about themselves as mathematical learners (Paulson,
Although it is not true for all students, it appears that often students are more
open-minded toward learning new ideas at a younger age. These earlier years
are the prime time to make our students life-long math enthusiasts!
Often times, especially in the subjects that are harder for students to grasp,
it is difficult to get them genuinely excited about a topic. However, it is evident for
anyone who has spent any amount of time in an elementary classroom, that
students will be more involved and learn considerably more if they have found an
excitement about the subject. The most effective way I have observed and
personally utilized to get children excited and interested is conducting hands-on
activities. Math Their Way, which is a teacher’s guide to teaching math, is full of
lessons in which students use manipulatives to grasp new concepts (Baretta-
Lorton, 1994). I believe it is guides like these that provide teachers with the most
realistic suggestions for helping their students learn.
When teaching a first grade class mathematics this past school year, I
introduced addition and making a trade. My first step was to explain the
procedure, and go through the process together using overhead manipulatives.