Basic Arithmetic 2
Running head: BASIC ARITHMETIC IS AT THE HEART
Basic Arithmetic is at the Heart of Mathematics:
Students must be Independently Capable
Dustin Sharpe
Wright State University
Abstract
In the earliest years of education students learn how to perform basic arithmetic operations in mathematics, such as addition, subtraction, multiplication, and division. These basic math skills are the basis and foundation for every math topic, which is why students must be fully capable and competent to perform each operation. In the age of technology calculators have come to the forefront and provided assistance to allow students to carry out such operations with ease. While students progress through school, emphasis on such basic skills should not be diminished and replaced with sole dependency on a calculator. The purpose of this paper is to explore the ability levels involving basic math skills of higher educated students with and without the assistance of a calculator.
Table of Contents
I. Chapter I……………………………………………………………………………………...4
Background Literature……………………………………………………...... 4
Purpose of Study……………………………………………………………………..6
Problem Statement…………………………………………………………………...6
Research Questions…………………………………………………………………..7
Definition of Terms…………………………………………………………………..7
Pilot Study…………………………………………………………………………....7
Data Collection Methods……………………………………………………………..9
Data Analysis Methods……………………………………………………………...10
Significance of the Study….………………………………………………………...11
Limitations of the Study……….……………………………………………………12
Chapter Summary……………….…………………………………………………..13
II. Chapter II……………………………………………………………………………………14
Literature Review…………………………………………………………………...14
Relevance to Study………………………………………………………………….21
Chapter Summary…………………………………………………………………...21
III. Chapter III…………………………………………………………………………………..22
Research Ethic………………………………………………………………………22
Research Setting and People………………………………………………………..22
Data Collection Methods……………………………………………………………24
Data Analysis Methods……………………………………………………………..25
Chapter Summary…………………………………………………………………..26
IV. Chapter IV………………………………………………………………………………….28
Research Findings………………………………………………………………….28
Literature Relevant to Findings……………………………………………………31
Chapter Summary………………………………………………………………….32
V. Chapter V…………………………………………………………………………………..33
Summary of Study…………………………………………………………………33
Recommendations…………………………………………………………………33
Personal Plan of Action……………………………………………………………34
Chapter Summary………………………………………………………………….34
VI. Selected Bibliography……………………………………………………………………...35
VII. Appendices………………………………………………………………………………38
Appendix A: Pilot Study…………………………………………………………….38
Appendix B: Data Analysis Matrix…………………………………………………56
Appendix C: Positive/Negative Survey……………………………………………..57
Chapter One
Introduction
In this chapter I will introduce the reader to a few sources which express relevant groundwork to the study, the purpose of the study, the problem that I have chosen to study, and my related research questions. I will review selected literature associated with views and opinions on calculator use in today’s school classrooms and why non-calculator computations are still important in incorporate in such a technology driven society. Along with this I will also include brief descriptions of the data collection methods and data analysis methods used in my study. The significance of the study and limitations of the study will also be acknowledged as well.
Background Literature
When discussing the use and role of calculators in a math classroom one will more than likely receive mixed opinions from educators. So far literature themes include: why should we severely limit or entirely prevent the use of calculators by students; why should we encourage and promote the use of calculators by students; and what are current implications of performance pertaining to the use of calculators in classrooms.
Many teachers view a calculator as a negative object used in the classroom. Many have the opinion that calculators are used as a “crutch,” or students develop calculator dependencies. “If students are always using a calculator to compute the answers then they aren’t learning anything,” some educators may say. According to Walen, Williams, and Garner (2002):
Students viewed the calculator as a tool, a ready –to-hand tool, to help them accomplish their immediate goal, not to help them gain a deeper understanding and appreciation of mathematics. Moreover, they saw the kind of mathematics they were involved in as being mainly computational. Since they did not see that the calculator could accomplish anything other than the basics… (p.458-9).
A lot of this opinion is based on the fact that educators feel that mathematics involves memorizing arithmetic facts and procedures and calculators are just used in place of memorization. Similarly, the same case can be made against calculator use in which students may just learn keystrokes rather than concepts and have them focus more on computations (Dion, Harvey, Jackson, 2001). If calculators are apparently affecting student knowledge and understanding negatively because of some underlying factors, then should students be expected to learn mathematical processes mentally? Rubenstein (2001) argues that “one simple reason to emphasize mental math is that it is useful for workers, consumers, and citizens” (p.442). Students should be able to demonstrate that they are capable of performing the basic skills of mathematics to the general public, to show their competence as individuals.
According to Cicci (2001) calculators can enhance the learning of basic facts, not just do the memorization and computation, help students focus more on problem solving, eliminate the essence of drills, and even reduce the anxiety felt by students during math class. Calculators can greatly reduce time spent on calculations and therefore allow students to focus less time on the computations and more time on problem solving. In order for calculators to show proof of effectiveness students should be able to give support and reasoning behind his/her answers. Such answers help provide a sense of knowledge and understanding achieved. The National Council of Teachers of Mathematics (NCTM) (2000) has a strong position for the use of calculators in mathematics teaching and learning. Many classrooms have been issued a standardized calculator as evidence, so every student can have access to a calculator at any given time.
According to Klein (2001), the Third International Mathematics and Science Study have found that 6 of the top 7 scoring nations in the study reported that 85% or more of students never use a calculator in class. On the other hand, the majority of 10 of the 11 lowest scoring nations, of which include the United States, use calculators almost everyday. This clearly provides strong evidence that calculator use is connected to student performance and in this case not positively.
Purpose of Study
The purpose of my study is to determine how well students are performing using basic skills of mathematics such as addition, subtraction, multiplication, and division. I want to understand what types of basic skills students are having problems performing when they are only allowed to us mental computations. I also want to discover if students would improve their results if they were allowed to use a calculator to assist them in their computations or if the students would continue to make the same mistakes.
Problem Statement
During my observation experiences, namely Spring Quarter 2005 and Fall Quarter 2005, I noticed a developing trend that students, when given the opportunity, would always use a calculator to complete any assignment. Regardless of how simple the assignment may have been the students would always opt to use a calculator without an initial attempt at the assignment to discover if they needed to use one. There is nothing wrong with the use of calculators, to a certain extent, but I became interested in knowing if the students could have performed the simplest of assignments without the use of a calculator. This study focuses on student performance levels using basic skills of mathematics. I completed this study to observe if students could perform basic mathematical skills without the use of a calculator, with the use of a calculator, and what basic mathematical skills the students may have difficulties performing. My goal is to understand if a calculator dependency may exist, what results this may have on student performance without the use of a calculator, and what are possible interventions that can used to increase performance. There is a saying that says, “The calculator is only as smart as the person using it,” but is this statement really true?
Research Questions
Baseline Questions:
1. a. What is the students’ performance (achievement) levels using basic mathematical skills (arithmetic) without a calculator and with a calculator?
b. What basic mathematical skills (arithmetic) are students having problems with?
Definition of Terms
· Performance – the act of accomplishing or finishing; something accomplished successfully, especially by means of exertion, skill, practice, or perseverance.
· Arithmetic – the mathematics of integers, rational numbers, real numbers, or complex numbers under addition, subtraction, multiplication, and division.
Pilot Study
The role of a calculator in the classroom is a sensitive topic among mathematics educators. The role of a calculator is supposed to be as a tool for learning not as a tool to eliminate any mathematical thinking and processes that may occur otherwise. Therefore I wanted to specifically study how well students performed with a calculator and without a calculator. I chose this topic due to first hand observations of calculator dependencies among students in various school districts and grade levels. Students would continually choose to use a calculator over mental and/or paper and pencil computations. The specific types of problems that the students wouldn’t attempt without a calculator were also manageable in relevance to their grade level and abilities. Consequently I chose research questions to help guide my study to find out how well students are performing with a calculator as well as without a calculator, and what mathematical skills students are lacking sufficient performance.
One data collection method that was used for my pilot study was a test document. The test document consisted of 20 problems which involved basic mathematical skills such as addition, subtraction, multiplication, and division. There were approximately 20 students given the test document and the students were given the same test document when they were suppose to do mental/paper and pencil computations and computations with a calculator. Another data collection method was the use of a survey, which consisted of 17 questions. The survey was to be used to gain some insight as to how comfortable students felt while answering math problems like those stated in the test document without the assistance of a calculator. I also used passive observations to note the actual use of calculators in my assigned classroom.
For the data analysis of the test document I used primarily three inductive codes. These codes were computational error, sign confusion error, and did not attempt. To analyze the survey I used a modified Likert scale which labeled each response with a number: very comfortable = 5, comfortable = 4, uncomfortable = 2, very uncomfortable = 1.
The test documents where students were unable to use a calculator produced the following results of the three central tendencies.
Ø Mean – 59.12%, or a score of 11.8 correct responses out of 20
Ø Median – 12 out of 20
Ø Mode – 12 out of 20
The test documents where students were allowed to use a calculator produced the following results of the three central tendencies.
Ø Mean – 91.25%, or a score of 18.25 correct responses out of 20
Ø Median – 20 out of 20
Ø Mode – 20 out of 20
When looking at the survey responses, the feeling of the students are that they are pretty confident in their own abilities. By using the scale as stated the following percentages were recorded.
Ø Average amount of very comfortable responses per student – 5.2
Ø Average amount of comfortable responses per student – 7.6
Ø Average amount of uncomfortable responses per student – 3
Ø Average amount of very uncomfortable responses per student – 1.2
Ø Average response per question - 3.7
From these results it shows that students feel that they should get the answer correct more often than not in almost any situation.
Data Collection Methods
I used a survey/questionnaire to obtain data on how the students feel about performing certain operations within mathematics. The survey/questionnaire enabled me know what the mood of the students skills were without even attempting or seeing a problem of the nature that I will face them with. This also allowed me to see what problems the students think they will have themselves. It also let me see what the students think are the more difficult problems as well as the easier problems. Instead of labeling the answers as a specified comfortable level it may be easier to just label them as very easy, easy, difficult, and very difficult as the this language may be more comprehensible to the students.
I used a test document to evaluate the students’ performance levels of basic skills involved using mathematics. The basic skills evaluation permit myself to witness what the students are having problems with first hand. I had a well diverse set of problems that enabled me to pinpoint specific operations that the students had problems with. The test document was used to note any difference in performance of students with the use of calculators and without the use of calculators. The two documents will be very comparable and results will not be skewed due to difference in difficulty.
I used passive observations to note the use of calculators within the classroom and performance issues within the class. Students always had questions about homework problems and I noted if any of these questions pertain to my area of focus, such as addition, subtraction, multiplication, and division questions. Also sometimes students were given ample time to complete homework in class and I would note the use of calculators and also provide help and assistance to the students to see difficulties they may have had.
Data Analysis Methods
The following codes were used when assessing the test documents: Computational Error, Sign Confusion Error, and Did Not Attempt (DNA).
n Computational Error: I defined this particular type of error to include any error which occurred in the students’ calculations that involved incorrect computations of the various operations of addition, subtraction, multiplication, and division.
o Ex. 13 – (-9) = 4, this particular student failed to recognize that subtracting a negative number results in the operation of addition as well as ignoring the (-9) and just subtracted 9 from 13. Therefore, this student performed a computational error.
n Sign Confusion Error: I defined this particular type of error to include any computation performed correctly but of which the student did not label the answer correctly with a positive or negative sign.
o Ex. 11 + (-30) = 19, this particular student knew to subtract 30 from 19 because of the negative sign but failed to recognize that the answer should have been negative due to the fact that 30 is larger than 19.
n Did Not Attempt: This type of problem is simply what it says, the student left the answer blank because they didn’t know what to do or they did not have enough time to complete the test document.