Achievement in mathematics

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Introduction

        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 through a process known as randomization. When one group is given an intervention and the other group is not, the researcher can segregate whether it is the intervention and not other 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 his 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 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 will be 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 a third time 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 intimidated by mathematical problems set before them by their teacher. Research assistants will oversee the Mad Dog Math-at Home sessions three times per week, 15 minutes per session. Forty-five 15-min Mad Dog Math sessions will be carried out over 20 weeks.

Procedure

        All research assistants will receive pre-training in servicing 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).

Strengths of the Method and Design

        The possibility that the school where the study will be conducted will embrace CAI as part of its literacy curriculum and in turn provide an opportunity to examine its effectiveness as an integrated element of a standard classroom procedure-escalating to a higher level of ecological validity, will definitely be one of the strong points of this study (Cassady & Smith, 2005). The incorporation of larger samples and longitudinal outcomes, particularly in number combinations, to establish how early intervention influences the development of associated math skill deficits, resonate strength in the creation of this proposed research method and design. Furthermore, the increased number of weekly sessions and the consideration in utilizing CAI software programs that incorporate well-proven instructional principles to enhance classroom instruction that will include work devised to advance number sense among first grade students will reinforce effects (Paterson, et al., 2003).

Weaknesses of the Method and Design

        By researching the effectiveness of CAI in the middle of standard classroom activities, some level of control over implementation may be sacrificed. There is a possibility of inconsistent use of patterns and the need to eliminate students from the treatment group who may not complete an adequate number of sessions due to absenteeism (Macaruso, et al., 2006). Another possible limitation of this study is the tendency for technology difficulties. Because technology can be unreliable, its inclination to become slow at times, may distract students and cause them not to perform to the best of their ability. It is also possible that a Hawthorne effect can occur, where subjects make progress merely because they know that they are being examined. Yet it may be doubtful that learners perceived that they are being investigated-at least in a way that may indicate an expectant outcome. The reality that the intervention will last for a long time will more likely decrease the influence of any Hawthorne effect.

Justification of the Method and Design

        According to Woodward and Reith (2007), researchers investigating the efficacy of computer-assisted instruction in the classroom must keep in mind that the outcome of the study will be subject to scrutiny because of the occurrence of confounding variables in carrying out research in a naturalistic atmosphere like the classroom setting. Insufficient control and contrast groups, brief periods of interventions, and neglect of single case design rules suggest weak research design. It is noted that small group sample analysis compromises generalizations about noteworthy outcomes. Moreover, it is also known that single subject design research as well as case study research design presents convincing results that are hard to refute, but the outcome may not transfer. This research, then, is aimed to design a better study, intervene with compelling pedagogy, choose participants circumspectly, and conduct a study in naturalistic environment. Improved description of participants-specifically their diagnosed disabilities, if present, will assist the experimenters in identifying and employing research outcomes.

References

Ferrance, E. (2000). Action Research. Retrieved March 10, 2010, from http://www.alliance.brown.edu/pubs/themes_ed/act_research.pdf

Fleishner, J., Garnett, K., & Shepherd, M. (2002). Proficiency in arithmetic basic fact computation of learning disabled and non-disabled children. Focus on Learning Problem in Mathematics, 4, 47-56.

Fuchs, L., Fuchs, D., Compton, D., Powell, S., Seethaler, P., Capizzi, A., Schatschneider, C., & Fletchers, J. (2006). The cognitive correlates of third grade skills in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98, 29-43.

Geary, D. (2005). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363-383.

Gersten, R., Jordan, N., & Flojo, J. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293-304.

Hedges, L. & Olkin, I. (1985). Statistical methods for meta-analysis. Orlando, Florida: Academic Press.

Johnson, B. (1995). Why conduct action research? Teaching and Change, 1, 90-105.

Jordan, N., Hanich, L., & Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85, 103-119.

Mad Dog Math-at Home (2007). Retrieved March 11, 2010, from http://www.maddogmath.com

Merriam, S. B. (2002). Introduction to qualitative research. Qualitative Research in Practice. San Francisco, CA: Jossey-Bass.

Miles, M. B., & Huberman, A. M. (1984). Qualitative data analysis : A sourcebook of new methods. California: SAGE.

Mills, G. (2003). Action research: A guide for the teacher researcher. Upper Saddle River, NJ: Merrill/Prentice Hall.

Nolen, A. and Vander Putten, J. (2007). Action research in education: Addressing gaps in ethical principles and practices. Retrieved March 9, 2010, from http://er.aera.net

Ostad, S. (2007). Developmental differences in addition strategies: A comparison of mathematically disabled and mathematically normal children. The British Journal of Educational Psychology, 67, 345-357.

Russ-Eft , D., & Preskill, H. (2001). Evaluation in organizations: A systematic approach to enhancing learning, performance, and change. Cambridge, Massachusetts: Perseus Publishing.

Sutter, W. (2006). Introduction to educational research: A critical thinking approach. Thousand Oaks, CA: Sage.

Tournaki, N. (2003). The differential effects of teaching addition through strategy instruction versus drill and practice to students with and without disabilities. Journal of Learning Disabilities, 36, 449-458.

Woodward, J & Reith, H. (2007). A historical review of technology research in special education review. Review of Educational Research, 67, 503-536.

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