Running head Trends in Mathematics

By Alice Harris,2014-04-08 07:55
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There are multiple reasons why it is beneficial for students to begin learning basic math skills early. Primarily, children need to learn the mathematics

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Sample ADP Required Research Paper

    In APA Style


    Trends in Mathematics 2

    Running head: Trends in Mathematics

    Trends in Mathematics

    [Student’s name]

    Prescott College

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     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

    working independently.

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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,

    2006, p.1).

    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.

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