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
indicated that a substantial portion of preservice teachers
(1989)
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 longterm 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 faceto-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, reallife 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 problemsolving and computational skills.
Yang (2005) concluded that 6th graders inclinations to use paper-andpencil 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 reformbased 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 selfefficacy.
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)
learning combined with metacognitive
concluded that the cooperative
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.
39
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.
41
(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.