# A Study On Three Hypothetical Designs

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Achievement in mathematics is often a prerequisite to higher levels of learning and without it; students cannot gain access to a large range of disciplines. Computer technology is among the cognitive technologies which helps transcend the limitations of the mind in thinking activities. The computer can be seen as able to play the role of a particularly potent mediator with the ability to restructure the thinking process, as well as its ability to make existing structures more efficient. The purpose of this survey is to assess the potential for computer-assisted instruction (CAI) to enhance math skills among learners with concurrent risk for math disability.

As children advance in counting, they begin to obtain mathematical skills or number combination skills (Gersten, Jordan, & Flojo, 2005). However, increased complexity in counting along with heightened failure to make the shift to memory-based retrieval of number combination answers are displayed by learners with math disability (Fleishner, 2002). When students with math disability retrieve answers from their memory, they differ from their academically non-at-risk peers because they tend to have increased errors and show evidence of unsystematic retrieval speeds (Ostad, 2007). The basic role of mathematical skill plays a huge part in the advancement of other math skills and given the intricacy related to the remediation at higher-grade levels, prevention is crucial among students who enter first grade with low math performance (Jordan, Hanich, & Kaplan, 2003). The objective is to develop mathematical skills with number combinations ahead of time and in so doing help prevent later problems in relation to areas of number skills. One approach for enhancing the advancement of mathematical skills involves computer-assisted instruction, which offers routine and strategically designed exercises in a logistically practical style.

Quantitative Design of Study

A survey design gives a quantitative or numeric account of trends, positions, or viewpoints of people by studying a sample of that population. From the sample outcomes, the researcher generalizes or formulates assertions about the population (Creswell, 2009). The objective of an experimental design is to examine the effect of a treatment or an intervention on an outcome, calculating for all other factors that may possibly have an effect on that result. One method of control is by arbitrarily appointing individuals to groups. When one group is given an intervention and the other group is not, the researcher can segregate whether it is the intervention and not the factors that persuaded the result (Creswell, p. 146).

Participants

The participants in this study will be drawn from 12 first grade classrooms in four Title 1 schools from Los Angeles Unified School District (LAUSD). Potential subjects will be approached at the beginning of the school year; the students will be asked for their acquiescence to participate in the study, and their guardians will be asked to give a formal consent for their child's participation. Eight weeks into the school year, educators will be asked to consider the performance of each student in their respective class in relation to the entire class and with respect to the school's curriculum standards in order to rate each student's mathematical competence using a Likert numerical scale. Participants in this research will be the subset of students who are rated low in math and will be identified as learners with concurrent difficulty in mathematics as prior work (Geary, 2005) has recommended. Children with such difficulties are especially susceptible to deficits in number combination skill. These subsets of students will be assigned randomly in blocks within classrooms to receive math remediation (CAI).

Program

Mad Dog Math-at Home - a systematic software program for teaching students their addition, subtraction, multiplication, and division facts in a fun, challenging, motivating, and exciting way; supplements any curriculum in any classroom from kindergarten through fifth grade; may be used remedially with middle and high school students (Mad Dog Math, 2007).

Methodology

The CAI software design will be based on the subsequent assumption: mastery of the basic math facts in both processes of addition and subtraction and is the solid foundation for student success in math. If learners are not competent in their memorization of these basic facts, they stagger through math at best from about third grade on (Jordan, et al., 2003). Once out of third grade and into fourth grade when long division and fractions are taught, students are at a disadvantage if their addition, subtraction, multiplication, and division facts are not readily accessible from their memory (Tournaki, 2003) Understanding this notion, the computer-mediated treatment referred to as Mad Dog Math-at Home is utilized.

The Mad Dog Math system takes the daunting body of knowledge (there are 171 fact combinations for addition and subtraction) known as the "basic facts" and breaks them down into bite-sized pieces that any student can master. A learner progresses through a series of timed exercises systematically grouped in number families known as "fact families." There are 20 problems with which first graders answer in two minutes with 90% accuracy. Once the student attains that score (minus two or better), he moves on to the next drill and the next until the student completes all the drills in two minutes. Once the student goes through all the two-minute drills, he earns a virtual "Two-minute Club Sticker" and he goes back and repeats the process again in one minute and in 30 seconds. Since repetition is the key to retention, children now have the facts embedded deeply into their memories and have easy access to them whenever they are needed.

In the process of learning their facts, students are gaining self-confidence with each victory, which, in turn, breeds more confidence (Mad Dog Math, 2007). Students for the first time will feel empowered by their gained knowledge and not intimated by mathematical problems set before them by their teacher. Research assistants will oversee the Mad Dog Math-at Home sessions three times per week, 10 minutes per session. Fifty 10-min Mad Dog Math sessions will be carried out over 18 weeks.

Procedure

All research assistants will receive pre-training in-service on the effective use of Mad Dog Math instrumentation and all students will strive for 90% to100% accuracy on all measures. Students will be pre tested within two weeks before starting intervention and post tested within two weeks after the intervention ends. For pretest and posttest levels, Mad Dog Math addition fact fluency and Mad Dog Math subtraction fact fluency will be administered in groups.

Data Analysis

Data will be analyzed using one-way analyses of variance. To compute effect sizes (ESs) when comparing post treatment scores for the treatment conditions, subtract the difference between means and divide the pooled (Standard Deviation) SD (Hedges & Olkin, 2003). To compute the ESs when comparing improvement scores for the treatment conditions, correct the correlation between the pretest and the posttest by finding the difference between improvement means and dividing by the pooled SD of improvement/square root of two (Fuchs, et al., 2006, p.42).

Discussion

Based on the findings reported by Roberts (2009) and Dynarski (2007), regarding the effectiveness of the computer-assisted instructional programs in K-12 education, it is safe to assume that when designed appropriately and executed accordingly, considering all related factors, computer-assisted instructional programs are invaluable to the teaching and learning venture in the classroom. It also confirmed the belief that the implementation of a well-designed Computer-Assisted Instructional program such as Mad Dog Math-at Home can provide the opportunity to utilize the instructional models for mathematics in other educational settings. Furthermore, an evaluative study can be designed to test the reliability and validity of the models. Such a contribution is invaluable to the teaching and learning venture in incorporating research-based CAI programs into the classroom (Roberts, p.231).

Qualitative Design Study

The goal of qualitative research is to understand a specific social position, occurrence, role, group, or interaction (Creswell, 2009). It is a process of investigation where the experimenter slowly makes sense of a social trend by comparing, contrasting, reproducing, cataloging, and categorizing the object of study (Creswell, p. 194). As suggested by Marshall and Rossman (1989), qualitative research design involves engagement in the daily event of the selected venue for the study and the experimenter penetrates the participants' world and during the continuing interface, inquires about the participants' standpoint and values.

Purpose

The primary goal of this research is to integrate the use of computer-assisted instruction in the curriculum to enhance learning and use computer software programs to support learning opportunities. The purpose of this research is to identify the learners' perceptions about utilizing computers in fifth grade math. The following questions will be adopted to achieve this goal:

1. How are the computers used in a fifth grade math classroom?

2. What are the learners' and the teacher's perceptions about the advantages of using computers?

3. What are the learners' and teacher's perceptions about the hindrances of using computers?

Participants

This study will be conducted in a local elementary school in a Western state. The school has 40 fifth grade students. The chosen classroom has 20 students and one teacher with 20 computers available in the computer lab. Most of the students are upper middle class African-Americans. One student is Japanese American. Potential participants will be contacted at the commencement of the school year; the students will be asked for their consent to participate in the study, and their guardians will be asked to give a formal acceptance in agreement for their child's participation.

Data Collection

The primary sources of data will be observations/field notes and interviews.

Observation/Field Notes: The researcher will observe the classroom during math class three times a week, Monday, Wednesday, and Friday as a non-participant observer. In total, there will be 12 observation days and each observation will be 45 minutes long. Extensive field notes will be taken primarily concerning how students use computers, which kinds of hindrances and benefits they have when utilizing the computers, and software programs used by the instructor to teach the subject.

Interviews: The teacher and the learners will be interviewed to find out if they have different perceptions regarding the use of computers during math class. According to Merriam (2005), the key to understanding, qualitative research lies with the idea that meaning is socially constructed by individuals in interaction with their world. The world or reality is not the fixed, single, agreed upon, or measurable phenomenon. Instead, there are multiple constructions and interpretations of reality that are in flux and that change over time (Merriam, p.3).

Asking questions prepared in advance is helpful but using semi-structured questions allow for more open-ended, flexible answers that may offer a richer source of data.

Questions for students:

1. How do you use computers in your math class?

2. Which computer applications and software programs are used the most during math class? Are the applications and software programs easy to use?

3. How do you feel in general about using computer-assisted instruction in math class?

4. Have you noticed any improvement in your learning as a result of using the computer?

5. What are the major problems with using computers to learn?

6. In what ways do computers help you the most in learning mathematics?

Questions for the teacher:

1. How many years have you been teaching?

2. How do you use computers in math class?

3. Which computer applications and software programs do you use the most in math class?

4. How do you feel in general about using computers in math class?

5. How would you describe your students' ability to use computers during math class?

6. Have you noticed any changes in your students' learning as a result of using computers in math class? If yes, how?

7. What are the major problems about using computers to teach?

8. What are the most important benefits about using computers to teach?

A focus group interview will be conducted with 10 students to obtain in-depth information about the interview questions. According to Russ-Eft (2001), focus group interviews offer an opening for participants to interrelate with one another in a manner that may improve the intensity and value of the data. Participants usually inspire each other in ways that conclude in innovative concepts and insights (Russ-Eft and Preskill, p.272). The following are open-ended questions that embody the research questions:

1. How do you use computers in math class?

2. What are the benefits of using computers in math class?

3. What are the problems of using computers in math class?

Data Analysis

Triangulation of data analysis will be used to analyze the data, which will compare and crosscheck the reliability of information obtained at various times and by different means within qualitative methods (Patton, 2002). Primarily, field notes with interviews will be compared and checked for reliability based on what the students and teacher will say over time as well as the perspectives of people from different viewpoints. The use of peer debriefing to share interview results and field notes with at least two individuals who have excellent training in utilizing technology in the classroom environment will be employed.

To continue analyzing the data, pattern codes, which are explanatory or inferential codes that recognize a growing theme, model, or rationalization that the site recommends to the researcher will be used (Miles & Huberman, 2004). Data will be summarized into minor segments and two categories will be determined. These categories are Advantages (A) and Problems (P). The categories will then be divided into two sub categories. They are students' opinions about advantages (SA), teacher's opinions about advantages (TA), students' opinions about problem (SP), and teacher's opinions about the problems (TP).

Discussion

The approaches of investigation chosen in the qualitative research study have a dramatic impact on the procedures, which even within strategies are anything but consistent. All perspectives contend for the spotlight in the unfolding model inquiry of qualitative research design (Creswell, 2009). In the new millennium, educators are becoming progressively sophisticated users of computer-assisted instruction (Braun, 2005). The ways that computers are utilized in the classroom to enhance instruction has expanded as the number of computers in schools has escalated (Nickell, Field, & Roach, 2001). Computer-assisted instruction has the potential to assist the expansion of the students' decision-making and problem solving skills, data processing, and communication capabilities. By employing computers, learners can obtain access to extensive knowledge links and develop their experience with diverse people and perspectives (Berson, 2006).

Action Research Design

According to Mills (2003), action research is described as any methodical examination conducted by educators, administrators, counselors, or others with increased concentration in teaching and learning development. It is used with the intention of collecting data and information about how specific schools function, how educators teach, and how students learn. Developing the concept, Sutter (2006) successfully asserted the possible contribution of action research by educators and affirmed that educators who carry out such research are "reflective practitioners" able to assemble excellent contributions to the education system.

Countless students fail to keep their motivation in learning, demonstrate low aptitude in testing, and eventually most of them give up and quit school. Therefore, the American education system is searching for a resolution. Some have claimed that the television is the cause and others asserted that the computer might be the solution (Calvert, 2004). Today's generation of children are being raised in a technological world with iPods, laptops, cellular phones, Flip videos, electronic toys, and more. They are certainly familiar with obtaining, sorting, and dispensing information through multiple sensory sources.

The study

In this study, the effect of technology on students' interest in learning mathematics, both at school and away from school, will be examined. Investigation on how the integration of technology in two third grade classes will influence the students' interest in learning mathematics will be assessed. Interest in learning mathematics can be characterized as the student's eagerness to participate in math activities in the classroom, as well as away from school. The participants in this study will include two third grade classes from a private school in Los Angeles, California. There are 21 above average and average students from each class with a total of 42 learners all together. The data will be generated by comparing the two classes concerning their attitudes toward learning math at the commencement of the school year 2010-2011, during the research study, and at the conclusion of the study period. The learners' attitudes and responses will be recorded by the students themselves, by their parents or guardians, and by the researcher's observations. Gathering data from these sources will allow for triangulation of the findings in this study. It will assist in diminishing the probability of errors in the results in the event that similar outcomes account for two or more of the sources.

Questionnaires

To establish each student's level of interest for learning mathematics, a survey containing the following questions will be provided: How do you like learning math? Have you enjoyed learning math so far this year? How interested are you about learning math at home? Students will be asked to rate their responses to each question using a scale of 1 to 5. The scale will be represented by (1) very uninterested response, (2) an uninterested response, (3) indifference, (4) an interested response, (5) a very interested response. In addition, parent surveys will be sent home with each learner to inquire and document the parents' opinions regarding their child's interest for learning mathematics. The survey will include two questions: How interested is your child about learning math? How eagerly does your child perform math activities at home? The rating scale for parents' surveys will be the same rating scale used in the students' surveys.

Procedure

At the beginning of the second four-week period, division will be introduced as a unit in mathematics. Division will be used as the unit of study primarily because addition, subtraction, and multiplication have all been introduced and studied in the previous grade levels. Although simple division problems were introduced at the end of the second grade level, the process of long division and word problems involving the concept of division were not studied. It is during this unit that technology integration will be included into the curriculum with the help of the computer lab teacher. During this period, the Mad Dog Math-at Home software program will be presented to the students. Mad Dog Math-at Home is a systematic software program for teaching students their addition, subtraction, multiplication, and division facts in a fun, challenging, motivating, and exciting way. It supplements any curriculum in any classroom from kindergarten through fifth grade; and may be used remedially with middle and high school students (Mad Dog Math, 2007). Throughout the research study, observations will be noted as to how students are learning and their reactions during math class will be sighted. The observations will be guided by the following inquiries: Are the students having difficulties using the computer? Are the students having problems using the Mad Dog Math program? Are the learners having struggles with the content? The notes will be beneficial should there be any fluctuations found in the end-of-study student survey.

At the end of six weeks, each child will be asked to write a short paragraph with a simple illustration about what he liked the most concerning the technology integration and Mad Dog Math program. After the writing exercises, each one will be asked to present their sentences and illustration to the class. The researcher will take notes on the students' remarks presented to the class. Once again, parent surveys will be solicited to obtain information about their child's interest in learning mathematics. The following questions will be asked: Is your child talking about math at home? Is your child excited to discuss and share what the class is doing and learning in math class? Do you think that your child is learning math? Why or why not? How interested is your child about learning mathematics? How interested is your child in doing math activities at home?

Discussion

The use of multimedia computer technology in the classroom can heighten all of the core curricula. Increasing enthusiasm to learning in any subject matter by incorporating technology is restricted only by the school's ability to supply the equipment, appropriate software, and teacher training. It is crucial that the necessary equipment be available for the students and teachers to work with when incorporating technology into any curriculum. If possible, computer and software should be made accessible to students and teachers for checkout to use at home as well as school through the school's learning resource center.