# Mnemonic Strategies: Tools to Increase Achievement in Fourth Grade Multiplication Essay Sample

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Abstract

Fourth graders of a Western state school district were evaluated to perform poorly when it came to multiplication mastery and problems. Most of them had below fourth-grade level mastery and had difficulty progressing in mastering their multiplication facts. Mnemonic strategies were presented as a solution through using flash cards, timed examinations and drills in order to enhance the memory of the students as they developed multiplication mastery skills. Mnemonic strategies were always effectively considered to employ memory enhancement as it employed recoding, relating and retrieving functions for instruction.

Chapter 1: Introduction

*Background*

* Description of Community.* Located in a high desert region of a Western state, the population of the city is approximately 85,000. The school district to be examined represented the larger employer in the area. Within the school district, a percentage of 80 % of the students receive free or reduced lunch.

The location of the school is located in an old residential neighborhood. The area experienced some significant transformations in terms of the new housing that are placed in the community. They interspersed among the older homes. There are also a number of low-income apartment complexes that were situated in the area. The mode of transportation for students was via school transport services.

Students usually belonged to lower class to middle class families. Most of their parents worked full-time jobs and some worked two shifts. Classrooms were also considered to be fully occupied throughout the year.

* Demographic Information. *The enrolment of students for 2006 to 2007 included 20 % white, 8 % African-American and the other 3 % was Asian or of other races. The staff included six males and three females. From the males, the principal was included and from the females, the assistant principal was one of them.

The school had a computer laboratory technician, a librarian, maintenance crew and food service personnel. The work setting of the research involved students from elementary school, or kindergarten through fifth grade. It had three self-contained structures and eight mobile classrooms. The school also had a soccer field as one of its numerous facilities and common areas.

The school is considered unique in terms of the staff’s cohesiveness and support for each other. Teachers and the staff work at a unified manner at school and offsite. The community by which the school was located also provided a significant role as well. The hard work of the parent-teacher conferences raised funds that exceeded the school’s expectations for the school of its size. The school’s adult literacy for English learners is also commendable. The school’s mission statement was that all students could learn.

* Instructional Information. *The school employed the traditional multiplication mastery instruction of lecture discussions. In this research, mnemonic strategies were employed as instructional approaches for the fourth grade students. Mnemonic strategies had been used to enhance people’s memories. It had been used to work with elderly people as well as students with disabilities.

* Writer’s Role. *The writer worked as elementary school teacher. The writer taught students qualified at the 4^{th} grade level. The grade level the writer handles has an average of 32 students per class. There is a consistent exposure and interaction with students of this grade level and the writer is very familiar with the subject manner of 4^{th} grade mathematics.

The writer would be the one who would employ mnemonic teaching strategies in raising 4^{th} grade multiplication capabilities of the students. The writer as well as the employment of evaluation methods would employ the actual application of the instructional methods.

* Importance of the Study. *Mathematics had been one of the most difficult areas in a students’ life. One of the most challenging areas would be multiplication. The purpose of the research would be to present alternatives to current teaching strategies when it came to the mastery of students of multiplication skills.

The study of new instructional strategies could provide itself to be instrumental in helping the students overcome multiplication mastery difficulties. Students had often been intimidated to perform more complex mathematical operations because of how they lacked skills in mastering the multiplication table. This could develop confidence in them in their skills and in turn improve their performance.

*Statement of the Problem *

The purpose of this study was to provide input in introducing and implementing mnemonic strategies to improve the multiplication mastery of the 4^{th} grade students. It would evaluate mnemonic strategies and its efficiency in increasing 4^{th} grade multiplication through pre-tests and post-test evaluations. It would show if fourth graders would develop a mastery of the multiplication table through this instruction that would gauge how much of an advantage this strategy could be as they advance into middle school.

*Research Questions *

* *This research would ask the research questions:

- How can mnemonic strategies be employed in helping fourth grade students’ mastery for multiplication?
- What is the level of effectiveness mnemonic strategies have when used as instructional modes for teaching multiplication mastery?
- Would fourth grade students be evaluated positively in gaining or improving multiplication mastery after being taught using the mnemonic

* Definition of Terms*

* Mnemonic Instruction. *Mnemonic strategies was also known as a memory-enhancing strategy that included a certain reconstruction of the specific content to relate new information to the learner’s existing knowledge base and to teach information retrieval (Fontana, et al. 2007). This instruction mode was based on the premise that concrete information was made meaningful or familiar to the individual when elaborated to something they already know. It transforms something that was abstract and seemingly unrelated information into something the individual could relate to and could value (Fontana, et al. 2007).

Chapter 2: Related Research

*Problem Statement *

The purpose of this study was to provide methods for introducing and employing mnemonic strategies to improve the multiplication mastery skills of the fourth grade students. It would evaluate the effectiveness of this instructional approach in the improvement of these multiplication mastery skills.

*Problem Description *

Like any other school district, grade school students find it hard to master the multiplication table. Students lack confidence in developing their mathematical operation skills because of their inability to perform multiplication operations. Most of the students did not had options to avail the services of tutors in order to improve their multiplication mastery. This prevented them from improving their skills in this area. The teachers needed to employ instructional strategies that provided for the students the skills to master the operation.

Since the instructional approach was relatively new, it could not be widely received at first employment. Students and other teachers could develop a certain resistance because of its novelty for grade school instruction. Teachers of these grade school students needed to look for numerous ways to develop mastery amongst the students. The limitation of approaches to traditional modes of instruction had prevented teachers from utilizing new modes of instruction.

*Problem Documentation*

The researcher had worked with 12 students who were 4^{th} graders who were placed in two groups. There were pre-tests and post-tests as instruments of evaluation to document the student’s mastery when it came to multiplication skills. The tests were informal and timed. The test scores of the students showed that they did not have mastery of multiplication. In fact, the students in this school district showed only a third grade level mastery of the mathematical operation as revealed by the previous test scores that were gathered by the researcher.

The evidence for this study was gathered using the analysis of the students’ grade records from their mathematics grades. The pre-tests and post-tests were also evaluative tools. Pre-tests showed that there was low mastery level and proved that students needed to improve their mastery skills for multiplication.

*Analysis of Problem *

*Insufficient Instructional Approach.* The most common method of instruction relied on the classroom approach of simply teaching the multiplication table. This involved slowly introducing to the students the different tables and letting them memorize it as is. This also commonly involved classroom recitation or board as well as seat exercises. Most of the time, students feel inadequate when they recite in class or do board exercise, as they had not received enough training to master the multiplication table. Often times, they end up feeling frustrated and develop a fear because of their inability to master the multiplication table.

* Lack of Instructional Variety. *Different strokes worked for different people. Not everybody could cope with what the teacher had been teaching. This problem needed the employment of different instructional approaches in order to provide the students a variety of opportunities to choose from in terms of learning the operation.

* Lack of Practice and Training. *Usually, multiplication mastery could only be developed through practice. The students’ fear and frustration of the subject would prevent them from practicing on their own. Since most students could not afford private after-school tutors, they had not found the time and method of developing skills in mastering multiplication. Instructional approaches that would offer the students’ self-study motivation as well as confidence in multiplication mastery would be beneficial to address this concern.

*Relationship of Problem to Literature*

The fourth graders in the school district displayed they had no mastery of multiplication skills at the fourth grade level. In fact, tests had shown how most of them only had third grade mastery of multiplication. This reflected how there was a need for an instructional approach that would increase their abilities to master the operation at the grade level they were in.

The mnemonic strategy was selected for this research because of the different characteristics it had in relation to providing the students with better skills for memorization for multiplication mastery. A review of literature would provide more pieces of evidence and background to show how mnemonic strategies were efficient modes of instruction to teach multiplication mastery to students.

* Memory.* Memory performance was studied to be influenced by the modality that the stimuli were presented and there was some type of encoding activity that was employed (Aleman et al., 2002). An illustration could include how mental imagery could produce a substantial increase in the amount of remembered material.

Experiments showed how subjects used presented words by vocalizing them, mouthing them silently or writing them down. An experiment made subjects list down words on a computer monitor as they were asked to read the words either aloud or silently. Results of this study showed that visual presentations were better remembered when they had been read aloud by the subject compared to when they were read silently (Aleman et al., 2002). There was also an auditory advantage when it came to memory decoding.

The temporal distinctiveness theory was attributed to enhanced memory performances from different activities used to carry out encoding. There was a scholarly suggestion that stated how memory-encoding activities gave rise to memory traces that were more easily accessible to retrieval processes. Vocalization certainly carried a strong advantage.

Mnemonic strategies were seen to play a great role in the encoding and retrieval process in terms of the “strategic selection of probes and inputs which are to be sent to memory and in terms of interpretations given to the output” (Anderson & Bower 1979, p. 140). Subjects could actually restructure and edit what they had previously encoded in their memory to make new information more meaningful under this strategy.

Mnemonic strategies had always been practiced even in the ancient times. They were strategies that were often related to paired-associate learning and serial learning as well as the use of interactive imagery (Carney et al., 1998; Pressley & Schneider 1997). Memory improvement books had provided and recommended mnemonic strategies for learners of all ages. They were also presented in self-improvement courses.

*Study Skills and Academic Performance. *Study skills were always seen to be a fundamental factor for academic competence (Gettinger & Seibert, 2002). Most of these skills were associated with positive outcomes for multiple academic content areas for diverse learners. Academic competence was also related to knowledge as well as the application of study skills. Any student could experience difficulty in school not because they did not have any intellectual abilities but it was because they lacked good study skills.

The instruction of the teacher must include the facilitation of good study skills. Students needed to know how they would comprehend and remember the lessons through the mode of instruction used by the teacher. Even if some students develop study skills on their own, most students go through schools without acquiring effective studying skills and as a result missing an opportunity to gain academic competence. Such skills were seen as “academic enablers” as they function as important tools for learning (Gettinger & Seibert, 2002). Study skills involved a range of coordinated cognitive skills and processes that enhanced effectiveness and efficiency in students’ learning.

The most common cluster of study skills involved repetition or rehearsal-based study strategies. They were considered the most basic strategy that involved repetition, rereading, or the rehearsal of information. They were seen to be most useful for storing smaller bits of information for the short term or as content used were frequently studied. They were also easy to learn and use.

Seemingly simple, these strategies could be enhanced by promoting greater elaboration and providing deeper processing of information during rehearsals. The strategy showed extensive evidence based in the creation and use of mnemonic devices (Gettinger & Seibert, 2002). Over the years, mnemonic strategies were seen to be effective study skills that had positive effects on student performance.

*Related Cases for Learner Memory Problems. *There were different groups that were expected to have poor memory skills. Mnemonic strategies were already employed as memory enhancers for adult learners as well as learners with disabilities. Older adults complain about their memories and most of the complaints were because of the heightened perception that mental abilities decline with age (Carney et al., 1998). However, studies had revealed that the employment of mnemonic strategies already showed how they could enhance memory, even if the process was more difficult and complex. It also helped to allay fears of adult and elderly learners for memory loss (Carney et al., 1998).

Middle school students with learning disabilities were also studied as they used mnemonic strategies to enhance their ability to recall information (Dela Paz & Macarthur, 2003; Allinder, 2001). It showed how these strategies were effectively used. Past experiments gauged the potential of these strategies to provide potential mnemonic maps for enhancing the recall of information.

*Mnemonic Strategies.* There were different kinds of mnemonic strategies that were available to choose from for employment. The keyword strategies utilized concrete and acoustically similar words to remember a new term (Fontana et al., 2007). These keywords were actually used to combine interactive illustrations that demonstrated the meaning of the new term. The keyword and the definition were related by a meaningful interactive scene (Carney et al., 2004)

Peg word mnemonics were used to facilitate the learning of information using numbers or order to be part of what was being recalled (Fontana et al., 2007; Pressley & Schneider 1997). One of the examples for this strategy would be the memorization of the list of the numerical order of the presidents of the United States.

Letter strategies employed acronyms and acrostics that could facilitate the recall of information (Fontana et al., 2007; Pressley & Schneider 1997). Using acronyms to recall information would make the information to be stored and retrieved faster. The most complex format of mnemonics would combine letter mnemonics, peg words and key words with symbolic illustrations.

Cognitive psychology would always point out how “learning proceeds most efficiently when to-be-acquired information can be meaningfully related to previously acquired information” (Carney et al. 1998, p. 164).

Organizational mnemonics was seen as the facilitation of the acquisition of ordered information. They included the method of loci and the peg word method. The method of loci was considered as the oldest mnemonic method as it was dated back in the ancient Greece as a memory aid for oratory (Carney et al., 1998). The strategy was employed by setting specific location or loci mentally. The to-be-remembered items were to be related to these locations by storing in the mind interactive images.

The peg word method was considered organizational in the application of technique of memorizing a set of concrete rhyming words that correspond to a number from one to ten. In this case, “1 = *bun*, 2 = *shoe*, 3 = *tree*, 4 = *door*, 5 = *hive*, and so forth, up to 10 = *hen*” (Carney et al. 1998, p. 167).

* Existing Multiplication Strategies*. Reciprocal teaching for mathematics was one of those evaluated to promote fourth graders’ response to complex two-step word problems (Cox & Taylor, 1997). The concept of this method would be for the educator to elicit solutions from students and to explore multiple solutions for seeking group agreement. In this method, students get to use mathematical operations as a group. The justification for this form of teaching was a solution to communication of difficulties wherein students could explain to their peers who could not understand what they had understood from the subject.

The distribution of associations model was also considered as an approach in multiplication (Perlmutter, 1986). The first step in this model was to examine which strategies children recently learning to multiply use. Middle school students were presented with 100 multiplication problems generated by factorial possible combinations of multiplicands and multipliers. The problems were presented orally as children wrote their answers on pieces of papers to work out the problems.

According to this experiment, it revealed that the methods used were through retrieval and other overt strategies (Perlmutter, 1986). Overt strategies included the repetition of the problem orally and the writing down of the problem on the answer sheet. Other overt strategies included repeated addition to solve multiplication problems and the other were drawing of visual representations and counting them.

*When Children Want to Remember. *Children had developed a range of techniques that were used for remembering information. Much of the literature that discussed children’s memory involved the deployment of the strategies that involved rehearsal, organization and elaboration (Folds, et al. 1990). The behavior of the children’s behavior towards information storage and retrieval had been a discussion that received significant attention for decades.

Mnemonic techniques were also seen to be applied in a range of contexts. It was also revealed how the consistent use of strategies was seen to increase the effectiveness for enhancing memory (Folds, et al. 1990).

When children between the ages of nine to 14 were given list of to-be-remembered items and asked to rehearse them aloud as they were presented, there existed age-related change in the types of rehearsal techniques that were employed (Folds et al., 1990). Children from different ages would approach the task of remembering in different ways. Nine-year olds would focus on rehearsing what was presented while 14-year olds would rehearse each word along with several previously displayed items in their memory.

There were differences presented in past studies with the organizational strategies children employed when it came to information recall. For instance, when presented with low-associated items and asked to form groups that would help them remember, young children would rarely create groupings based on semantic relationships but older children who were sixth-graders and above would do it spontaneously (Folds et al., 1990). The differences between the age group were related to differences in the recall success.

*Decreasing Information-Processing Demands*. Having memory as the explicit goal would entail information-processing requirements that were strategic (Folds et al., 1990). Visual access of to-be-remembered items must be increased in a more active manner even without providing explicit instruction for doing so. Visual access could lessen the demands for the learner’s information processing capabilities.

There would be lesser effort that would be required in the maintenance of the to-be-remembered items in the immediate memory. In this manner, there would be more effort that would be devoted to strategic behaviors to enhance recall. The simplification of memory tasks for young children was presumed to involved the reduction of the demand of information processing when it came to strategic performances (Folds et al., 1990)

*Expanding the Knowledge Base. *Another avenue by which children’s memorization skills would be enhanced with mnemonic strategies would be if the students could develop a wider knowledge base. The increase in the content and complexity of the child’s fund of knowledge or knowledge base would make any mnemonic activity more effective (Folds et al., 1990). Increased knowledge was related to corresponding changes when it came to recall performance.

* Basic Classroom Application*. Mnemonic strategy instruction had emerged as one of the most powerful instructional techniques. It improved “systematically integrating specific retrieval routes within to-be-learned content” (Masterpiori & Scruggs, 1991, p. 219).

Common classroom application of mnemonic strategies involved “reconstructive elaborations” or drill-and-practice techniques by which pictures were used for visual representations. Students who were under such condition had substantial recall of the content than that other students.

The language of mathematics had always been difficult and confusing at first (Rubenstein & Thompson, 2002). Technical terms were considered to be difficult to remember and some were even used in more ways than one. The children’s mathematical learning was also dependent on their fluency with mathematical language. Teachers must make the remembrance of these terms and languages as well as operations to be less complex for their students.

*Related Results from Mnemonic Application*. A study conducted by Masterpiori and Scruggs (1991), showed how the implementation of mnemonic strategy instruction after three weeks of training by regularly assigned teachers resulted in high performance scores. The study showed how the strategy used was also significantly correlated with the performance that showed how mnemonic strategies were relevantly effective for the students. According to this study, these strategies were successful because they provided systematic procedures for retrieval of target information (Masterpiori & Scruggs, 1991).

*Creation of Schemata for Learning*. As mentioned earlier, the expansion of the knowledge base would enhance the effectiveness of mnemonic strategies. Schemata involved this knowledge base. Memory retention was the process of remembering through the schemata of the learner. Association, clustering, imagery, location, mnemonic and visualization devices were seen to provide information recall for long-term memory (Goll, 2004; Boston, 2001).

Information, if emotionally charged, was usually easy to be remembered. The sounds, smells, tastes and movements as well as feelings were encoded in the person who had experienced them. Cognitive psychologists would move that long-term memory was organized in terms of schemata that provided expectations about objects and events (Goll, 2004).

Part of the enhancement of children’s mastery of multiplication skill involved providing memorable moments that were positive for remembering. Teachers must avoid charging multiplication mastery activities with fear and discouragement. The imagination, association and location also helped students remember what they were supposed to remember. There would be an imaginative click in the mind wherein information retrieval took place.

It was also important to consider the retrieval of information after it had been stored. There were different obstacles to retrieval, “clogging at the synapse, deterioration of the neural pathways involved and stress” (Goll 2004, p. 306). To address this, learners must use their brains and specific to-be-remembered information regularly in order to create an easy retrieval. Contiguity learning utilized drills from repeated pairings such as in multiplication tables. They were considered to be effective even if they could be tedious.

*Why Mnemonic Strategies Worked.* There were three R’s for the mnemonic techniques it included recoding, relating and retrieving (Bunnell et al., 2002). These properties had been applied to attain the effectiveness of this strategy as an instruction tool. The numerical, symbolic and procedural components of computation had be recoded into more relatable characters or visuals. In mathematical operations, instead of recalling the correct procedures for solution, they would incorporate the symbols and visuals use to retrieve information (Bunnell et al., 2002).

Chapter 3: Methodology and Data Collection

*Description of Selected Solutions*

There was a need for the instruction to require a more intimate approach to teaching because according to literature information that was more emotionally charged was easier to retrieve (Goll, 2004). A small group environment could better provide this requirement. Data needed to be presented in small group or one-to-one setting because there was success attributed with this strategy for overcoming academic learning difficulties.

Research showed how fear and the lack of confidence of the students could move them to be less participative and interested in their classes (Goll, 2004). It also followed that confidence was built with a more focused and teacher-connected development of the students’ study skills (Gettinger & Seibert, 2002). This strategy could build on the confidence of the students in their ability by working consistently with the researcher using mnemonic strategies (Masterpiori & Scruggs, 1991).

Mnemonic strategies were seen to be effective for memory retention even for elderly and adult learners as well as children with learning disabilities (Carney et al., 1998, Dela Paz & Macarthur, 2003; Allinder et al., 2001). The literature that supported mnemonic strategies as a valid instructional method that had worked for a more complex group of people held it to be a viable instructional strategy to be used for fourth graders’ mastery of multiplication.

*Sample*

There were twelve fourth grade students who participated as subjects of this study at an elementary school in the high desert region of a Western state. There were even females and five male students included. Their age ranged from nine to 10 years old. There were nine Hispanics, two African Americans and one white student. They were selected based on the multiplication assessment tests they took. The common denominator for them was their inability to excel beyond a certain level of multiplication mastery. Group one of the students remained on their table of three’s for months and group were not able to advance from their table of five’s.

*Materials*

There researcher utilized self-created pre-test and post-test forms that were timed in order to evaluate multiplication mastery of the subjects. There were worksheets that listed 50 multiplication problems randomly organized into columns. All of the problems were based on one level of mastery at a time. For example, the first column would reflect 1×1 thru 1×12. Automaticity or mastery to the next level was determined by completing 50 problems under or in two and a half minutes. There was a margin of 10 per cent error. The researcher used the whiteboard, multiplication flashcards as well as a standard electronic timer for the tests and lessons.

*Procedure for Data Collection*

The study took place over a period of four weeks. The research had worked with twelve students who were placed into two groups. The first group was described and assessed to have below automaticity level that meant there were struggling or stuck in the table of three’s and could not move beyond it. The next group was described to had below automaticity as well as they could not advanced beyond the table of five’s in their multiplication timed tests.

During the initial selection process, the research disseminated to the students a pre-test to obtain the said results. The group was divided for ten minutes of mnemonic instruction. The first group had directly worked with the researchers doing repetitive multiplication facts on the whiteboard. Group two worked with flashcards in a round robin fashion.

The other group was separated from each other but they were still under the researcher’s observation during the time this was happening. Group one worked with multiplication facts one to five and the other group worked with multiplication facts one to seven. The researcher alternated working with the groups for each sessions. The students who worked with the researcher had to verbally answer problems that were written on the whiteboard when called upon.

The researcher worked with these subjects for 20 days for over four-week period. At the end of the study, the students from both groups were given post-test to assess if there was any improvement or advancement in the levels of multiplication. The results showed that five out of six students from group one advanced at least to their focus. Group two did even better than the first. All of the subjects advanced to their six’s and two of them even completed their seven’s. Mnemonic strategies were shown to increase the student achievement in mastering multiplication facts.

Data collection was conducted through the tests that were given to the students. The data that was collected included their multiplication mastery levels as well as the change increase that occurred after the mnemonic strategies were implemented.

Chapter 4: Data Analysis

*Methods for Analyzing Data*

Testing for aspect-specific tests required further development. Different levels were supposed to received customized difficulty when it came to evaluation (Idol & Jones, 1991). The researcher took the two groups’ result from the pre-test and the post-test of the timed multiplication facts and compared the results. The researcher had ran a statistical analysis of the data. The independent samples of the t-test were compared with the scores of each students’ pre-test raw scores and the scores of their post-test. The mean scores for group two increased by twenty-two points.

The hypothesis of the research that held mnemonic strategies to increase multiplication mastery was proven to be valid.

TABLE 1

COMPARISON OF PRE-TEST AND POST-TEST RESULTS

FOR GROUPS 1 AND 2

Groups | N | Mean
Pre |
Mean
Post |
St. Error of Means | T Ratio |

Group 1 | 6 | 0.376 | 0.935 | 0.615 | 0.388 |

Group 2 | 6 | O.696 | 0.923 | 0.227 |

*Stories*

During the selection of subjects for this study, the researchers chose twelve students who struggled immensely with mathematics, specifically multiplication mastery. These students attended a remedial mathematics class in addition to their regular math subject instruction. One of these subjects, a female from group one was the most challenged in mastering her multiplication facts, yet after the study she had showed the most progress from all of the students in the two groups combined.

Moreover, the researcher fondly recalled when one of the male students told the researcher that he had enjoyed working with his multiplication facts as a result of the mnemonic instruction approach. This was very enlightening for the research because the same student displayed very low levels of self-esteem and little self-confidence in attacking any level of mathematic operations.

Students also seldom enjoyed mathematics and for a student who performed poorly to say he had enjoyed it recently was significant for the researcher. The bond that was created between the student and the researcher was also noted by the researcher’s colleagues as they marveled at this positive change.

*Unexpected Events*

The researcher made numerous journal notes regarding the discoveries that were not anticipated. There was one instance wherein during one session at the whiteboard with group two, the research realized that the time processing was a major factor in achieving multiplication mastery.

The researcher noted via the electronic timer that five out of the twelve students took on average more than 6.3 seconds to respond verbally to a random multiplication problem such as “3×7?”

There was also the impact of counting on their fingers. The researcher did not realize how this approach was still used by the students. The researcher observed that there were at least three students who consistently counted with their fingers during timed tests. Some students were even trying to be inconspicuous with this habit. Nevertheless, the researcher continued to study despite this element, but made the necessary journal entries regarding this discovery or limitation to the study. Several colleagues concurred that the study should move forward as it was but must be noted for credibility and transferability’s sake.

*Evidence of Trustworthiness *

* Credibility.* The research was conducted over a month. In the month, the researcher was able to meet and instruct the students for 20 days. There was significant time spent with the children that showed how mnemonic strategies affected them in how they addressed their problems with multiplication. The pre-tests and post-tests were also used to gauge the students according to their ability before and after mnemonic instructions were given.

Researcher also consulted colleagues in the academe when it came to decisions that would provide more credibility for the study. Other than that, a statistical tool was used with the t-test to measure the results of the evaluations.

* Transferability.* The researcher had created the pre-test and post-test used to collect data. However, the researcher had a degree in education by as an elementary school teacher that provided the qualifications to formulate such evaluation. The same evaluation could be used for future researches or more could be formulated according to this research’s format.

The teacher selected students who did poorly in their multiplication facts. The group was selected and was given pre-tests to evaluate the levels of mastery they were on. The results were used for the researcher to group them according to their abilities.

They were taught alternately using methods such as whiteboard exercises as well as flashcards. The researcher had employed problems that were orally given for the students to answer. Most of the answers given were timed and evaluated by the researcher.

At the end of the period, the researcher had given a post-test that evaluated the progress of the students’ mastery skills. Upon receiving the results for this examination, the researcher compared it with the pre-test results through correlation.

* Dependability and Confirmability. *However, the researcher noticed how students still counted with their fingers and it must be considered as another method used by the students outside of mnemonic strategies.

Chapter 5: Implications for Teaching and Research

*Discussion/Conclusions*

The study showed how the students had significant improvement in the test scores as evaluated by their post-test assessment. These twelve students had been selected because of their inactive mastery skills when it came to their multiplication facts. They had low self-esteem and self-confidence when it came to attacking multiplication problems. Half of the group could not go beyond their table of three’s and half of them could not go beyond their table of five’s.

Mnemonic strategy instruction was presented as a solution to this problem. It was an approach wherein the purpose would be to enhance the memory of the individual. This strategy employed memory storage and retrieval through relation new data information with other information that the individual already had. The key to this strategy’s success was making abstract and novel concepts more concrete and meaningful for the individual who suffered from memory retention and retrieval.

Research showed that memory had a lot to do with teacher’s instruction. Memory was also enhanced through effective study skills. Educators were held accountable by numerous literature when it came to teaching students with effective strategies to produce study skills for their students. It was also important to enhance the students’ knowledge banks or schemata in order to enrich their memory retention with mnemonic strategies.

The research employed basic mnemonic strategy approach through the use of the whiteboard drills as well as flashcards. The more the new information was used by the learner, the more the information could be retained and retrieved when the individual would desire. The drills were proposed in order to train the students with their multiplication facts.

The result of this study was positive. Students were able to advance from the levels of multiplication mastery they were stuck in. They were also able to perform with more enthusiasm for the subject because of the confidence they had gained from the mnemonic strategy after 20 days of sessions over a four-week period. They were able to perform better and feel better about themselves. It also proved how small group settings were more effective for students who had difficulties coping up in the classroom.

*Implications for Teachings*

Teachers should consider the power of small group settings when it came to their instruction. It developed a more intimate and more effective approach for the students. It helped them retain the information because of the more emotional allowance of such settings.

There was also the continued effectiveness of mnemonic strategies to enhance the students’ performance. A healthy amount of literature had already supported it to be beneficial for elderly learners as well as those with disabilities. In this research, it showed how effective it was for fourth grade students who had difficulties with multiplication.

Teachers must also be vigilant against psychological fears students have against mathematics. They must enable the students to see beyond their fear for the subjects’ difficulty and transform the subject into something more engaging and encouraging for the students.

*Limitations of the Study *

The sample size that the researcher had used was relatively small, although it focused on key students who had the least progress in the class. However, twelve students could still be considered as a small sample size. There was also the time constraint that must be considered. Twenty days in a month could also be relatively short. The gauge of development of the students was only limited to the one month the researcher had worked with them.

*Implications for Further Research*

Different methods and approaches to classroom instruction must be considered in terms of addressing the problem of multiplication mastery amongst the students. There must be more strategies that must be developed for them to inhabit the joy for the subject as well as the confidence to solving mathematic problems.

Mnemonic strategies were also very broad. Future research could establish which mnemonic strategy worked best when it came to mathematical problems and for what reasons. It must also be employed over a longer period of time to significantly gauge long-term memory retention of its learners.

References

Aleman, A., Appels, B., Haan, E.H.F., & Postma, A. (2002). Inter- and intramodal encoding of auditory and visual presentation of material: Effects on memory performance. *The Psychological Record, 50*, 577.

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