CHAPTER II

REVIEW OF RELATED LITERATURE

2.1 Studies Related to ‘Division’

2.2 Studies Related to Difficulties in Learning Mathematics

2.3 Studies Related to ‘Mathematics Learning’ Except

Experimental

2.4 Experimental Studies Related to Mathematics Showing

Effectiveness of Different Strategies on Learning

Mathematics

20

REVIEW OF RELATED LITERATURE

Every piece of ongoing research needs to be connected with the work

already done, to attain an overall relevance and purpose. The review of literature

thus becomes a link between the research proposed and the studies already done.

It tells the reader about aspects that have been already established or concluded

by other authors, and is giving a chance to the reader to appreciate the evidence

that has already been collected by previous research , and thus projects the

current research work in the proper perspective.

Here the investigator had collected a lot of studies related to different

aspects of mathematics teaching and had arranged in the following sections

(i) Studies related to ‘Division’

(ii) Studies related to difficulties in Learning Mathematics

(iii) Studies related to ‘Mathematics Learning’ except Experimental

(iv) Experimental studies related to Mathematics Showing Effectiveness of

Different Strategies on Learning Mathematics.

2.1 Studies Related to “Division”

Brauwer and Wim (2009) observed strong developmental paralles

between multiplication and division among 8-years old children. The results are in

line with strongly interconnected memory network for multiplication and division

facts, at least in young children.

Cavagnino and Werbrouck (2008) presented a complete analysis of the

integer division of a single unsigned divided word by a single unsigned divisor

word based on double word multiplication of the dividend by an inverse of the

divisor.

Imbo and Vandierendonck (2007) showed that executive working

memory resources were involved in direct memory retrieval of both multiplication

and division facts.

21

Putten (2007) found that since 1987 the Dutch primary school children’s

arithmetic skills have been shown to be declining. They are making an increasing

number of mistakes with written addition, subtraction, multiplication and division.

Lautert and Spinillo (2006) concluded that the understanding of the

remainder plays an important part in the understanding of ‘division’.

Okazaki and Koyam (2005) suggested that children’s explanation based

on two kinds of reversibility (inversion or reciprocity) are effective in overcoming

the difficulties/ misconceptions related to division with decimals.

Son (2005) found that there is a gap between learning goal (intended

curriculum) and problem presented in text books (potentially intended

curriculum).

Mattanah et al. (2004) discussed the role of authoritative parenting,

parental scaffolding of long division maths problems as a tutoring strategy that

may promote academic competence in school-aged children.

Booker et al. (2004) suggested that in some classrooms, the formal

teaching of the ‘division’ concept and ‘algorithm’ is based on memorized rules.

Lautert and Spinillo (2004), Spinillo and Lautert (2002), Squire (2002),

Correa, Nunes and Bryant (1998), Nunes and Bryant (1996) and Silver

Shapiro and Deutsch (1993) revealed that

(i) Children ignore the reminder or suggested that it be removed from the process

of resolution, in the belief that the remaining elements are not part of divison.

(ii) Children try to distribute the remainder among some of the part or include it in

one of the parts in which the whole has been divided into ; or

(iii) They try to include the remainder in a new part

Anghileri (2001) identified that increase in the use of the standard

algorithm of division led to many errors and only half of the attempts to use this

strategy in the second test were successful.

Tirosh (2000) concluded that teacher education programmes should

attempt to familiarize prospective teachers within common, some times erroneous,

22

cognite processes used by students in dividing fractions and the affects of use of

such process.

Anne (2000) discussed the role of measurement (quotient) in division in

justifying divisibility results and demonstrates one way that this connection can be

exploited to strengthen student understanding of multiplication and division

Neuman (1999) concluded that formal division, understood as related to

every day situations, only develops in interplay with informal knowledge.

Kate and Judy (1998) revealed that students who are encouraged to use

invented strategies for multiplication and division based on number relationships

have a better understanding of the meaning of those operations and more

successful in extending their knowledge proportional reasoning tasks than are

those students who are taught conventional procedures exclusively .

Mulligan and Mitchelmore (1997) found that the students used 3 main

intuitive models: direct counting, repeated addition, and multiplicative operation.

A fourth model, repeated subtraction, only occurred in division problems. Results

showed that children acquire an expanding repertoire of intuitive models and that

the model they employ to solve any particular problem reflects the mathematical

structure they impose on it.

Alexander (1997) revealed that students concepts of rational number

operations of multiplication and division are enriched by participating in a 5

week teaching experiment

Mulligan and Mitchelmore (1997); Tirosh, Graeber and Glover (1990),

Booker et al. (2004) suggested that inappropriate language confuses learners and

strongly hinders their understanding of the division concept.

Subramanian and Singh (1996) found that the students committed six

types of mistakes in addition, eight types of mistakes in multiplication and six

types of mistakes in division. It was found that the poor concept of carrying over,

poor concept of zero, poor concept of multiplication, introvert behaviour and lack

of writing skills etc were observed as possible cause of mistakes committed by

the students.

23

Dash (1996) found that the remedial intervention in solving different types

of problems on multiplication and division was more effective, the average

performance of children after remedial instruction was significantly higher than

the same before the instruction.

Silver and Mary Lee (1994) concluded that although, some aspects of

division, such as its connection to different types of problem, its relationship to

multiplication, were fairly well understood by most of the subject in the study,

limited or flawed understanding was also noted in many different areas.

Simon (1993) indicated that the prospective teachers’ conceptual

knowledge was weak in a number of areas including the conceptual underpinnings

of familiar algorithms, the relationship between partitive and quotitive division,

the relationship between symbolic division and real-word problems and

identification of the units of quantities encountered in division computations.

Ball (1990) reported that the prospective teachers’ knowledge was

generally fragmented and each case of division was held as a separate bit of

knowledge.

Graeber and Tirosh (1990) indicated that students of fourth and fifth

graders hold the misconceptions such as ‘multiplication always makes bigger’.

Tirosh and Graeber (1989) argued that one of the misconception that a

majority of pre-service teachers appear to hold explicitly is that in division the

quotient must be less than the dividend.

Silver (1986, 1988) and Silver, Mukhopadhyay and Gabriele (1992)

investigated that students’ failure to solve division problems with remainders can

be attributed, at least in part, to their failure to relate computational results to the

situations described in the problem.

Carpenter et al. (1988); and Hart (1981) argued that children’s success

rates on various task related to such division are usually very low.

Fendel (1987) and Payne (1976) opined that Division of fraction is often

considered the most mechanical and least understood topic in elementary school.

24

Greer and Magan (1986) and Graeber, Tirosh and Glover (1989)

indicated that a substantial portion of preservice teachers have difficulty in

selecting the operation needed to solve multiplication and division problem

involving decimals.

Silver (1986) revealed that only about 35% of the sixth graders in

California was able to answer correctly to a division problem appeared on the

1983 version of the California Assessment Programme (CAP)

Fischbein et al. (1985) confirmed the impact of the repeated addition

model on multiplication and of the partitive model on division.

National Assessment of Educational Progress (NAEP) (1983) has been

documented the failure of American students to succeed in solving problems

involving whole number division with remainders.

Bigalke, and Haseman (1978) and Padbery (1978) argued that for the

arithmetic of fractions there exists many ruels and these are more complicated

than those for natural numbers. If these rules are introduced too early, there is a

danger of their being used mechanically and without thought.

Grouws and Good (1976) suggested that the factors associated with third

and fourth grade children’s performance in solving multiplication and Division

sentences are place holder position and other aspects of sentence writing.

2.2 Studies Related to Difficulties in Learning Mathematics

Pal (2009) concluded that many difficulties that children face in leaning

are rooted in the lack of understanding of lower level concepts and lack of clarity

about different ruels that are often conflicting can lead to misconceptions and

affect mathematical learning.

Wang, Du and Liu (2009) identified two types of learning difficulties:

learned helplessness and defensive attribution. The students enhanced their

learning in mathematics with the use of appropriate strategies in the interventions.

Acha (2009) concluded that children’s learning processes are hindered by

limited working memory.

25

Morgan, Farkas and Wu (2009) indicated that the children persistently

displaying mathematics difficulty (MD) (i.e. those experiencing MD in both fall

and spring of Kindergarten ) had the lowest subsequent growth rates, children

with MD in spring only had the second –lowest growth rates and children with

MD in the fall only (and who had thus recovered form their MD by the spring of

Kindergarten) had the next lowest growth rates. The children who did not have

MD in either fall or spring of Kindergarten had highest growth rates.

Yang and Li (2008) indicated that 3rd

grades in Taiwan did not perform

well on each of the five number sense components and they appeared worst on

the performance of ‘Judging the reasonableness of computational results.’

Olive and Caglayan (2007) examined 8th

grade students’ coordination of

quantitative units arising from word problems and results indicated that the

identification and coordination of the units involved in the problem situation are

critical aspects of quantitative reasoning and need to be emphasized in the

teaching-learning process.

Blanco and Garrote (2007) concluded that students find two types of

difficulty in dealing with inequalities. On the one hand, arithmetic is still the

fundamental referent for those students who make errors in the algebraic

procedures and, on the other, the absence of meaning is the underlying cause of

the failure to understand the concepts and the algebraic process.

Petrill and Plomin (2007) revealed that approximately 6 to 10% of

individuals in general population have a persistent mathematical learning

disability (MLD) or dyscalculia. There is evidence that MLD is biologically

based and has genetic influences.

Voutsina and Ismail (2007) provided evidence of the nature of

understanding of selected concepts of single-digit addition held by young children

(of primary school age) who have difficulties in mathematics or are identified by

a computer based standardized test as being at risk of dyscalculia.

Dowker (2004) strongly supports the view that children’s arithmetical

difficulties are highly susceptible to intervention and concluded that

26

individualized work with children who are falling behind in arithmetic has a

significant impact on their performance.

Dowker (2004) found out some children could remember many number

facts, but seemed to lack strategies (including suitable counting strategies) for

working out sums when they did not know the answer and some other children

could deal with single-digit arithmetic but had serious difficulty in achieving even

limited understanding of tens, units and place value.

Stewart et al. (2003) have developed strategies for dealing with classes

that include a significant number of children with mathematical difficulties and

techniques that she has used include multi-sensory teaching of mathematics,

involving motor activities.

Koy and Yeo (2003), Miles and Miles (1992), Chinn and Ashcroft (1998)

and Yeo (2003) pointed out that most dyslexic pupils have difficulty with long-

term memory for facts, working memory difficulties, sequencing difficulties and

difficulties with language, including mathematical language.

Jordan, Hanich and Kaplan (2003) concluded that the children with poor

fact mastery showed little improvement on timed number fact test in over a year,

but showed normal progress in other aspects of mathematics.

Kroes Bergen and Van Luit (2002) reported that both the math

intervention, guided versus structured instruction, improved more than the

students of the regular instruction and guided instruction appeared to be more

effective for low performing students than structured instruction and especially

for those students in regular education.

Poustie (2001) discussed ways of helping pupils with mathematical

difficulties, which can be applied within classroom, in the context of

individualized or small group tuition and /or by parents helping their children at

home.

Yeo (2001) reported that while many dyslexic children have difficulties

only with those aspects of arithmetic that involves verbal memory, some dyslexic

children have more fundamental difficulties with ‘number sense’.

27

Mukherjee (2001) argued that failure to take into account the children’s

intuitive, informally learned pre-school mathematics. Knowledge is likely to result

in confusion and fear in learning mathematics.

Potari and Georgiadu (2000) revealed that a mathematical task that was

considered by an adult as easy, could also be easily understood by children and

children learn mathematics through their actual involvement in variety of teaching

activities.

Jordan and Hanich (2000) found out that children with MD/RD

(Difficulties in both reading and mathematics) performed worse than NA (normal

achievement) children on all aspects of mathematics; those with MD performed

worse than NA children only on story problems.

Fei (2000), Russell and Ginsburg (1984), Siegler (1988), Geary and

Brown (1991), Ostad (1997) and Cumming and Elkins (1999) showed children

with mathematical difficulties to be more consistently weak at retrieving

arithmetical from memory than at other aspects at arithmetic.

Paria (1999) found that the main errors identified were conceptual and

computational difficulty in selected topics.

Gonzalez and Espinel (1999) revealed that children whose arithmetical

achievement was much more worse than would be predicted from their IQ.

Jordan and her colleagues and Geary et al. (1999) suggested that

children with combined mathematical and reading disabilities tend to perform

badly on more aspects of mathematics than children who only have mathematical

difficulties.

Ash Craft and Hopko (1998), Fennema (1989) and Hembree (1990)

opined that many people develop anxiety about mathematics, which can be

distressing problem itself and also inhibits further progress in the subject. This is

rare in young children and become more common in adolescence.

Macaruso and Sokol (1998) found that the arithmetical difficulties were

very heterogeneous, and that factual, procedural and conceptual difficulties were

all represented.

28

Grauberg (1998) noted that pupils with language difficulties tend to have

difficulties in particular with (i) symbolic understanding (ii) organization (iii)

memory and in addition, language difficulties will directly affect the child’s

ability to benefit from oral or written instruction and to understand the language

of mathematics.

Szanto (1998) found that adults with arithmetical difficulties performed in

a similar fashion on both computational skills and arithmetical reasoning to

normally achieving adolescents and children who were at a similar overall

arithmetical level.

Pal et al. (1997) were found that most of the errors committed by primary

school students were due to a process of dualism.

Swarnalekha (1997) revealed that learning through games gives

remarkable improvement in the area of problem-solving and area of mathematics

learning were attained by paying attention to the language comprehension skills

and other non-scholastic areas.

Miller and Mercer (1997) discussed the need to take mathematical

difficulties into account, even while attempting to raise overall standards and

they emphasize the importance of accommodating diversity, and adopting

teaching to individual strengths and weakness.

Ostad (1997) concluded that at all ages, children without mathematical

difficulties used a far wider variety of strategies than those with mathematical

difficulties, and the differences increased with age.

Jordan and Montani (1997) opined that if there are differences between

specific and non-specific mathematical difficulties, they are probably in the

direction of specific difficulties being milder and less pervasive than non-specific

ones.

Shalev, Manor, Amir, Weirtman and Gross-Tsur (1997) found no

difference in the types of mathematical difficulty demonstrated by dyscalculic

children with higher verbal versus higher non-verbal IQ.

29

Fazio (1994) argued that the children with spoken languages and

communication difficulties usually have some weakness in arithmetic, but once

again some components tend to be affected much more than others

Rourke (1993) proposed that verbal weakness lead to memory difficulties

and non-verbal weakness lead to logical difficulties.

Tall and Mohamad (1993) illustrated the difference in qualitative thinking

between those who succeeded and those who fail in mathematics, illustrating a

theory that those who fail are performing a more difficult type of mathematics

(coordinating procedures) than those who succeeded (manipulating concepts).

Wong and Lai (1993) concluded that pedagogical content knowledge is

the crucial factor leads to effective mathematics teaching.

Sinha (1993) found out that the angular method was more effective than

traditional method in improving VI class students. Skill in simple addition and it

also was helpful in developing favorable attitudes towards learning mathematics.

Swan (1993) reported on a conflict teaching approach to involve students

in discussion of and reflection on their errors and misconceptions.

Temple (1991) reported that one child who could carry out arithmetical

calculation procedures correctly but could not remember number facts and another

child who could remember the facts but not carryout the procedures.

Russell and Ginsburg (1984) found that the difficulties with word

problem solving, as well as with memory for facts of 9 year old children who were

described by their teachers as weak at arithmetic.

Hart (1981) and her team revealed that secondary school pupils have

many difficulties, both procedural and conceptual, with many mathematical

topics, including ratio and proportion; fraction and decimals; algebra and

problems involving area and volume.

Ginsburg (1977) examined children who were failing in school

mathematics and found out (i) some had a good informal understanding of number

concepts, but had trouble in using written symbolism and standard school

methods. (ii) Some had particular difficulties with the language of mathematics

30

(iii) some children appeared to have very limited understanding at first sight, but

still had a good understanding of counting techniques and principles.

Weaver (1954) argued that interventions that focus on the particular

components with which an individual child has difficulty are likely to be more

effective than those which assume that all children’s arithmetical difficulties are

similar.

2.3 Studies Related to Mathematics Learning Except Experimental

Venkat and Brown (2009) examined the implementation of the

mathematics strand of the key stage 3 strategy and revealed that both setting and

whole–class teaching and mixed ability grouping and individualized learning

school achieved highly in relation to similar schools.

Kramarski and Mizrachi (2008) showed that the online discussion

embedded within metacognitive students significantly outer performed the face-

to-face discussion without metacognitive guidance students, who in turn

significantly outer performed the online and face to face discussion without

metacognitive guidance students on mathematical, literacy of standard tasks, real-

life tasks and various aspects of self –regulated learning.

Griffin and Jitendra (2008) concluded that both SBI (Scheme Based

Instruction) and GSI (general strategy instruction) improved word problem-

solving and computational skills.

Yang (2005) concluded that 6th

graders inclinations to use paper-and-

pencil procedures narrowed their thinking and reasoning powers: this heavy

reliance on written algorithms seemed to be a major impediment to development

of number sense.

Xinma (2005) indicated that age was critically important for fast growth

in mathematics achievement.

Son (2005) found that there is a gap between learning good (intended

curriculum) and problems presented in textbooks (potentially intended

curriculum) of mathematics.

31

Chill et al. (2005) explored and found that teachers’ mathematical

knowledge was significantly related to student achievement gain.

Arbaugh and Brown (2005) indicated that the high school mathematics

teachers showed growth in the way that they consider tasks and that some of the

teachers changed their pattern of task choice.

Muijs and Reynolds (2003) examined the effects of the use of learning

support assistants and results did not provide much support for he use of

classroom support assistants as a way of improving the achievement of low

achieving students, or as a means of increasing child-adult contact without

employing more teachers, and it would seem ill-advised to seek to solve teacher

shortage by replacing them with an army of learning assistants.

Baxter et al. (2001) suggested that both the organizations and task

demands of the reform classrooms presented verbal and social challenges to low

achievers that need to be addressed if those students are to benefit from reform-

based mathematics instruction.

Manouchehri and Goodman (2000) proposed that teachers’ mathematical

knowledge was the greatest influence on how they evaluated and implemented

the textbook.

King (1999) exposed that class size has an impact on the use of class

time, both instructional and non-instructional .

Fuchs et al. (1997) argued TFG (task focused goal treatment) students

were enjoying and benefitting from TFG, chose more challenging and a greater

variety of learning topics, and increased their effort differently.

Patel (1996) argued that the lesson idea programme in mathematics could

influence the affective behaviour of the experimental group, while it did not have

significant impact upon the behaviour of boys and girls.

Kumar (1996) concluded that less than 20% of the teachers held

positive attitude towards mathematics.

Goel (1996) found that the total no. of errors committed by children in

different grades (Class I to IV) varied significantly.

32

Mayer et al (1995) compared the lesson on addition and subtraction of

signed whole numbers in three seventh-grade Japanese mathematics text books

with the corresponding lesson in four US mathematics textbooks. The results

indicated that Japanese books contained many more worked-out examples and

relevant illustrations than did the US books, whereas the US books contained

roughly as many exercises and many more irrelevant illustrations than did the

Japanese books.

Confrey and Scarano (1995) showed that 10 and 11 years old exceeded

the comparative performance of 14 and 15 years old on ratio and proportion test

items.

Hoffer (1992) revealed that Ability grouping appears to benefit advanced

students, to harm slower students and to have a negligible over all effect as the

benefits and liabilities cancel each other out.

Christensen and Cooper (1991) indicted that practice produced more

effective learning and more effective strategy use.

Sowell (1989) showed that mathematics achievement is increased through

the long-term use of concrete instructional materials and that student’s attitudes

towards mathematics are improved when they have instruction with concrete

materials provided by teachers knowledge about the use.

Freeman and Porter (1989) revealed that there were important

differences between the curriculum of the text and teachers’ topic selection,

content emphasis and sequence of instruction.

Athappilly et al. (1983) concluded that there have not been many

detrimental effects of ‘new mathematics’ either on achievement or on attitude.

2.4 Experimental Studies Related to Mathematics showing

Effectiveness of Different Strategies on Learning Mathematics

Paksu and Ubuz (2009) found that drama-based instruction had a

significant effect on student’s achievement and make learning easy and

understand better by providing the opportunity to contextualize geometry concept

and problems.

33

Thangarajathi (2008) revealed that the mind mapping technique is more

effective than the conventional method in teaching mathematics at high school

level.

Singh (2008) indicated that jurisprudential inquiry model group students

were attaining significantly higher mean scores than conventional groups students

for verbal fluency as well as its four areas.

Sharma and Sharma (2008) revealed that STAD (student teams

achievement division) approach has greater effect.

Oyesoji and Taiwao (2008) concluded that participants in the

experimental conditions performed better than their counterparts in the control

group on the measure of academic achievement and vicarious reinforcement was

found to be more effective than contingency contracting in enhancing academic

achievement of impulsive participants.

Kumar and Sini (2008) showed that brain compatible learning is more

effective than the existing method of teaching.

Jain and Castro (2008) investigated the robustness of strategies

intervention model accompanied with mediated learning experience with students

who have poor mathematical achievement and indicated that the intervention

significantly enhanced the mathematical achievement of participants in the

treatment group.

Hoffman et al. (2008) concluded that the standardized test results

indicated superior performance for co-educational students.

Chiou (2008) revealed that (i) adopting a concept mapping strategy can

significantly improve students’ learning achievement compared to using a

traditional expository teaching method and (ii) most of the students were satisfied

with using concept mapping in an advanced accounting course.

Thangarajathi and Viola (2007) concluded that there is significant

difference between the post-test scores of students in cooperative learning method

group and conventional method group in learning mathematics at high school

level.

34

Mary and Raj (2007) found that the concept mapping method and

traditional lecture method did not make any qualitative difference.

Hanock (2007) revealed that students exposed to performance assessment

achieved some what higher scores on the final examination and demonstrated

significantly higher levels of motivation to learn than the students evaluated by

traditional paper-and-pencil tests.

Ayodhya (2007) disclosed that the polya’s heuristic approach is more

effective than the conventional method in developing problem-solving skills.

Wolgemuth and Leech (2006) showed that FDK (Full day Kindergarten)

students demonstrated significantly higher achievements on mathematics and

reading. At the end of kindergarten than did their HDK (Half-day kindergarten)

counterparts, but that advantage disappeared quickly by the end of first grade.

Wighting (2006) concluded that using computers in the classroom

positively affects students’ sense of learning in a community.

Sungur and Thekkaya (2006) revealed that PBL (problem based learning)

students had higher levels of intrinsic goal orientation, task value, use of

elaboration learning strategies, critical thinking, meta cognitive self-regulation,

effort regulation, and peer learning compared with control-group students.

Veeman et al. (2005) examined the effects of a teacher-training

programme on the elaborations and affective –motivational resources and the

programme showed moderately positive effects on use of elaborations among the

treatment dyads. Dyads with experience in cooperative learning achieved more

than dyads without such experience.

Kaufmann et al. (2005) revealed significant learning effects in the

children who participated in the numercacy program particularly for counting

sequences and mental calculation.

Isiksal and Askar (2005) concluded that the Autograph group had

significantly greater mean scores than the Traditional group, while no significant

mean difference was found between the Autograph and Excels groups, and

between the Excel and Traditional groups with respect to mathematics self-

efficacy.

35

Desimone et al. (2005) suggested that most of the perceived barriers

related to teachers autonomy, trade-offs with computational strategies, student

achievement, class size and teacher qualification are not impediments to the use of

conceptual teaching strategies in other countries and the comparative findings

hold promise for alternative paradigms for organizing better mathematics

instruction in the United States.

Nye et al. (2004) found larger effects on mathematics achievement than on

reading achievement.

Kroesbergen et al. (2004) showed that the math performance of students

in the explicit instruction condition improved significantly more than that of

students in the constructivist condition, and the performance of students in both

experimental conditions improved significantly more than that of students in the

control condition.

Fuchs et al. (2004) examined the effects of a dyadic peer-mediated

treatment on kindergarten children’s mathematics development and result indicted

that treatment implementation was strong for most, but not all.

Kramarski and Mevarech (2003) concluded that the cooperative

learning combined with metacognitive training group significantly outer

performed the individualized learning combined with meta cognitive training

group and which in turn significantly outer performed the cooperative leaning and

individualized learning groups on graph interpretation and various aspects of

mathematical explanation.

Scott Baker et al. (2002) indicated that different types of interventions

led to improvements in the mathematics achievement of students experiencing

mathematics difficulty including the following (a) providing teachers and students

with data on students performance; (b) using peers as tutors or instructional

guides; (c) providing clear specific feed back to parents on their children’s

mathematics success; and (d) using principles of explicit instruction in teaching

maths concepts and procedures.

Sahlberg and Berry (2002) concluded that there is no unanimity about the

effects of small group learning on student achievement in school mathematics; it

36

seems that it produces at least equal academic outcomes among all students

compared to more traditional methods of instruction.

Desimone et al. (2002) found that professional development focused on

specific instructional practices increases teacher’s use of practices in the

classroom.

Sivan et al. (2000) disclosed that active learning made a valuable

contribution to the development of independent learning skills and the ability to

apply knowledge.

Molia (1999) found that inductive thinking model is to be effective in

improving the achievement in mathematics.

Kumudha (1999) found that the concept mapping methods is very

effective in the achievement of standard XII students.

Bala Subramanian (1999) concluded that cognitive modeling on learning

of mathematics is to be effective in enhancing achievement in mathematics at

under graduate level.

Orman (1998) suggested that proper development and application of

educational multimedia computer programmes may benefit instrumental

education.

Ben et al. (1998) revealed that after instruction on spatial visualization

skills, fifth through eighth grade students profited considerably form instruction

and the gain was similar for boys and girls despite of initial sex differences.

Nalage (1997) explored that teaching of mathematics became more

effective when it was done with the help of teachers handbook.

Mevarech and Kramarski (1997) focused on (i) in-depth analysis of

students information processing under different leaning conditions and (ii) the

development of students’ mathematical reasoning over a full academic year.

Results of both studies showed that improve students significantly outer

performed the non treatment control groups on various measures of mathematics

achievement.

37

Fuchs et al. (1997) indicated that irrespective of type of measure and type

of learner, students in peer tutoring classrooms demonstrated greater reading

progress.

Chel (1997) tried out ‘seeing is believing’ principles in teaching

mathematics at the secondary level and found it to be more effective than the

conventional method.

Goel (1996) revealed that the performance of students at representational

level was better than their performance at abstract level.

Reddy and Ramar (1995) proved that the multimedia modular approach

did help the poor achievers in doing better in mathematics.

Bussama (1993) has studied the effect of simulation technique in teaching

mathematics and found that it is more effective than traditional method of

teaching mathematics.

Singh (1992) concluded that computer-assisted instruction was always

found superior, but the gain were more in the case of good students and there was

a definite positive change of attitude towards learning mathematics on the part of

both boys and girls due to the use of computers.

Prabha (1992) has found that programmed learning of mathematics is

superior to conventional learning of mathematics and that mother’s and father’s

education significantly affect programmed learning. Even parents’ income and

cast effects significantly the learning of mathematics.

Kulik et al. (1990) showed that mastery learning programmes have

positive effects on the examination performance of students in colleges, high

schools and the upper grades in elementary schools.

Spencer (1989) revealed that programmed instruction as a classroom

method of teaching and learning in Ibadan is likely to have a more facilitating

effect on student’s achievement.

Peterson et al. (1987) examined the long-term impact of retention/

promotion decision on the academic achievement of primary grade students and

results of same year comparisons indicated that retained students significantly

38

improve their relative class standing by the end of the retained year and in some

cases they maintain this advantage over a 2-year period. However, after 3 years

there are no differences between retained and promoted students.

Sqrensen and Hallinan (1986) showed that (a) ability grouping provided

fewer opportunities for learning than whole class instruction but greater utilization

of these opportunities (b) high ability groups provide more opportunities than low

group.

Kallison (1986) indicated no significant effect for sequence and the study

yielded a significant effect for explicit organization.

Osborne (1985) suggested that experienced teachers tended to take a more

‘task oriented’ approach providing more instruction and structure and less tasks

irrelevant conversation than did inexperienced teachers.

Hendel (1985) compared the effect of individualized and structured

curricula on the academic performance and results indicated that the two groups

were indistinguishable in persistence, graduation rate, academic success and

overall course selection patterns, but that they differed significantly in their

evaluation at follow-up of their under graduate education.

Fuchs et al. (1984) revealed that experimental teachers effected greater

students achievement and (a) experimental teachers’ decision reflected greater

realism about and responsiveness to student progress (b) their instructional

structure demonstrated greater increase and (c ) their students were more aware

of goal and progress.

Coladarci and Gage (1984) indicated that the intervention did not effect

significant change in training –related teaching practices or end-of year student

achievement.

Sharpley et al. (1983) revealed that the fifth and sixth grade tutors

effectively increased the operational mathematics achievements of their tutees, the

increase in tutors’ and tutees mathematics achievements being significantly

greater than those of the control children.

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Saracho (1982) argued that students who used CAI (Computer Assisted

Instruction) programme had greater achievement gains than did students who

participated in the regular classroom programme.

Lysakowski and Walberg (1982) estimated the instructional effects of

cues, participation and corrective feedback on learning. Strong effects appeared

constant form elementary level through college and across socioeconomic levels,

races, private and public schools and community types.

Kulik and Kulik (1982) reported results from a meta-analysis of findings

from 52 studies of ability grouping carried out in secondary schools. In the

typical study the benefits from grouping were small but significant on

achievement examination.

Peterson et al. (1981) indicated that high and low-ability students

benefited from peer tutoring processes that occurred in the small groups.

Sefkow and Myers (1980) suggested that the backward review effect

cannot be attributed solely, or even substantially, to a cueing or retrieval

phenomena but rather to a strengthening or integration of the memory traces at the

time of the probe.

Luiten et al. (1980) showed that advance organizers have a facilitative

effect on both learning and retention.

Ebmeie R and Good (1979) proved instructional model based upon

previous naturalistic research was effective and the nature of the interaction

between student aptitudes, teacher style and instructional model helps to interpret

the influences on students’ mathematics achievement.

Good and Beckerman (1978) examined the functional relationship of

teacher effectiveness and the achievement of high, middle and low attitude third

and fourth grade students. Significant main effects were found for both teacher

competence and student aptitude with no significant interaction between the two

variables.

Wilmut (1973) shown that attitudes have some effect in determining the

outcome of the project and that in a few cases the project affects the attitudes held

by the pupil.

40

MCG (1971) studied two groups of secondary school boys of below

average academic ability. The control groups received traditional English

teaching; the experimental group had experience of SRA Reading Laboratory 2a

included in their English lessons. After nine weeks, no differences were shown in

the reading performance of the two groups.

Reflection on the Review of Related Studies

Putten (2007), Lautert and Spinello (2006), Booker et al. (2004),

Lautert and Spinello (2004), Correa, Nunes and Bryant (1998) Silver Shapiro

and Deutsch (1993), Anghileri (2001), Subramanian and Singh (1996), Dash

(1996) and Tirosh and Graeber (1989) concluded that

(i) Since 1987 the Dutch primary school children’s arithmetic skills have

been shown to be declining.

(ii) The understanding of the remainder plays an important part in the

understanding of ‘division’.

(iii) In some classrooms, the formal teaching of the ‘division’ concept and

algorithm is based on memorized rules.

(iv) Children ignore the remainder or suggested that is be removed from

the process of resolution, in the belief that the remaining elements are

not part of division.

(v) Children try to distribute the remainder among some of the part or

include it in one of the parts in which the whole has been divided into.

(vi) Increase in the use of the standard algorithm of division led to many

errors

(vii) The students committed six types of mistakes in addition, eight types

of mistakes in multiplication and six types of mistakes in division.

(viii) The remedial intervention in solving different types of problems on

multiplication and division was more effective, the average

performance of children after remedial instruction was significantly

higher than the same before the instruction.

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(ix) One of the misconceptions that a majority of pre-service teachers

appear to hold explicitly is that in division the quotient must be less

than the dividend.

As per the reflections of the studies cited above and as per the review of all

the other studies mentioned above the researcher planned to carry out this study

on “Developing a Strategy for Syncopating Mathematical Skills Among Primary

School Students” to see whether the new strategy developed by the researcher

significantly enhances the division skills of students in Mathematics.