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PUBLISHED DATE: - 14-06-2024
https://doi.org/10.37547/tajas/Volume06Issue06-06
PAGE NO.: - 28-38
STUDENTS’ PRACTICE OF MATHEMATICS
AND ITS EFFECT ON THEIR NUMERICAL
SKILLS IN PROBLEM-SOLVING IN
SECONDARY SCHOOLS IN FAKO DIVISION,
SOUTH WEST REGION OF CAMEROON
Enow William Atem
Department Of Curriculum Studies And Teaching, Faculty Of Education Of
The University Of Buea Cameroon
Dr. Nekang Fabian Nfon (Ap)
Department Of Curriculum Studies And Teaching, Faculty Of Education Of
The University Of Buea Cameroon
Dr. Nguéhan Siméon Boris
Institute Of Fisheries And Aquatic Sciences, University Of Douala
–
Cameroon
RESEARCH ARTICLE
Open Access
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INTRODUCTION
Attitude towards mathematics is defined as a
general emotional disposition toward the school
subject of mathematics. This is not to be confused
with attitude towards the field of mathematics,
towards one’s ability to perform in the field of
mathematics or toward some specific area within
mathematics (e.g., geometry, word problems).
Generally, a positive attitude towards mathematics
(as well as any other subject) is valued for the
following reasons: a positive attitude is an
important school outcome in and of itself, attitude
is often positively, although slightly, related to
achievement, a positive attitude towards
mathematics may increase o
ne’s tendency to select
mathematics courses in high school and college and
possibly one’s tendency to select careers in
mathematics or mathematics related fields.
In every mathematics lesson, the teacher is
conveying, even if consciously, a message about
mathematics which would influence this attitude.
Once attitudes have been formed, they can be very
persistent and difficult to change. Positive attitudes
assist the learning of mathematics; negative
attitudes not only inhibit learning but, very often
persist into adult life and affect the choice of Job.
Learning mathematics does not only involve
thinking and reasoning, it is dependent on the
attitudes of the learners towards learning and
mathematics (Kele & Sharma, 2014). A student
with a positive attitude towards mathematics is
more confident when learning mathematics, enjoys
mathematics, is motivated to do more, actively
engages during mathematics lessons, gets more
Abstract
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practice and achieves more. When students display
a positive attitude towards mathematics,
improvements can be seen in: emotions,
motivation, confidence, engagement, working
memory, numerical processing. According to the
American Psychological Association (APA), feelings
that impact a persons’ mood and emotional
reaction can be referred to as affect, and character
towards mathematics is an example of affective
state. Research considers affect to exist on a sliding
scale
–
ranging from positive to negative. Naturally,
this means in a school full of students, you will see
a huge range of different affective states related to
mathematics learning (Laney, 2019). He went on to
say, for every student who looks forward to the
next mathematics lesson, there is another who
feels confused and defeated. One student might not
like mathematics because they think the subject is
not useful and may not devote time to practice it,
while another dislikes it because they doubt their
own ability to succeed. Practice of mathematics is a
student attitudinal construct.
Chubb (2018) asserts, if we were to consider
reading instruction for a moment, everyone would
agree that it would be important to practice
reading. Most of us will likely think of picture books
for the children to read and not reading pages of
random words in a page. Pictures might help give
clues to difficult words, the storyline offers interest
and motivation to continue and the messages
within the book might bring about rich discussions
related to the purpose of the book. This kind of
practice both encourages students to continue
reading, and helps them continue to get better at
the same time. However, this is very different from
what we view as “practice” of mathematics. He
went further to say that, to many, “practice” of
mathematics brings about childhood memories of
completing pages of repeated random questions, or
drill sheets where the same algorithm is used over
and over again. Students who successfully
completed the first few questions typically had no
issues completing each and every question. For
those who were successful, the belief is that the
repetition helped. For those who were not
successful, the belief is that repeating an algorithm
that did not make sense in the first place was not
helpful
–
even if they can get an answer, they might
still not understand. In Dan Finkel’s Ted Talk (5
principles of extraordinary Math Teaching) he had
attempted to help teachers and parents see the
equivalent kind of practice of mathematics. Below
is a table explaining the role of practice as it relates
to what Dan Finkel calls play.
Table 1: Table explaining the role of practice as it relates to what Dan Finkel calls play.
“Practice”
Rote Practice
Dynamic Practice
Goal
-Mastery of basic skills
-Memorizing rules, formulae and
algorithms
-Understanding of facts, rules, formulae and algorithms
-Applying facts, rules, formulae and algorithms
Focus
-Following procedures
-Paper – and - pencil
-Relationships between concepts and procedures
-Sense – making
Roles
-Student passive (little or no thinking/
decision making)
-Student active (thinking and decision making are required to be
successful)
Process
-Drill
-Repetition
-Physical experiences
-Games, Puzzles
-Elements of choice is a feature
Source: https//buildingmathematicians.wordpress.com
When practice involves active thinking and
reasoning, our students get the practice they need
and the motivation to sustain learning! When
practice allows students to gain a deeper
understanding or make connections between
concepts, our students are doing more than passive
rule following. They are engaged in thinking
mathematically. If students only practice recall,
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they would not develop a full understanding of
mathematical concepts or be able to build on these
concepts moving forward. It is also unlikely they
will perform well on high stakes assessments
(Spalding, 2023).
Mathematics games and mathematics in everyday
situation are two sub indicators for students’
practice of mathematics. Play games that involve
numbers and calculation. We all love playing one
game or another in our free time. Students can pick
a fun game or app and utilize their leisure time to
polish their mathematical skills. Brown, Lewis and
Harcleroad (1977) cited in Nekang (2016) defined
instructional game as a structured activity with set
rules for play in which two or more students
interact under clearly designed instructional
objectives. In a typical game, participants make
decisions as if they are in actual situation. Games
require strategies, tactics and initiative from
players (students). There must be a winner. The
greatest strength of games in mathematics
teaching/learning is in the ability of a game to
provide drill and practical application.
Statement of the problem
Anything in the world can be perfected with
practice, and more so when it is mathematics. All
pupils need opportunities to practice skills and
routines which have been acquired recently, as to
consolidate those which they already possess, so
that there may be available for use in problem-
solving and investigational work. The amount of
practice which is required varies from pupil to
pupil, as does the level of fluency which is
appropriate at any given stage. When students do
not practice mathematics, they may develop
negative attitude towards the subject. Negative
attitude from students towards mathematics could
lead to low intake/dwindling enrolment of
students in mathematics or mathematics related
disciplines in tertiary education. This may also lead
to fewer professional mathematicians. There are
far too many schools than teachers with a degree/
diploma in mathematics. Thus, those who teach
mathematics in our schools especially lay-private
schools may not have a qualification in
mathematics. Such teachers may not have a
mastery of what they teach and in the long run can
cause potential mathematics majors to fall off from
the mathematics train. The implication is that there
will be a “swing away from science” caused by a
“drift away from mathematics”. Worse s
till, the
country in the near future will have a dearth of
qualified personnel in the critical skills area of the
country. Cameroon needs graduates with advanced
mathematical skills to promote innovation, data
synthesis and technology if it is to solve challenging
problems and be competitive in the global scenario
by 2035. But this cannot be the case if students
have questionable problem-solving skills as a
result of lack of enough practice of mathematics.
This study attempts to provide a solution.
Objective(s) of the study
The study sought to find out whether students’
practice of mathematics has any influence on their
numerical skills in problem-solving.
Review of Related Literature
Problems represent gaps between where one is
and where one wishes to be, or between what one
knows and what one wishes to know. Problem-
solving is thus the process of closing these gaps by
finding missing information, re-evaluating what is
already known or, in some cases redefining the
problem (McGraw Hill, 1997 as cited in Nekang,
2016). Problem-solving skills are skills students
need to function properly in and beyond the
mathematics classroom. Students “need to develop
a sense of number that enables them to recognize
relationships between quantities, to use the
operations of addition, subtraction, multiplication
and division to obtain numerical information, to
understand how the operations are related to one
another, to be able to approximate and estimate
when appropriate and to be able to apply their
understanding to problem
situations” (Burns 2007,
p.157) in (Switzer, 2010). Numerical skills
encompass perceiving, processing, and calculating
numbers and symbols, crucial for problem-solving
and organizational success. These skills involve
numerical perception, control, rapid calculations,
estimation, mathematical logic, percentages,
dividends and more. Employers value numeracy
for reasoning with data, often assessing it through
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online tests and interviews. Developing these skills
through practice, understanding mathematical
concepts, and embracing mistakes is key to
enhancing numeracy. In fields like accounting,
basic mathematics operations, decimals, fractions
and percentages are fundamental in understanding
concepts and solving problems. A good problem-
solving programme must include appropriate
content. The content must be of suitable difficulty
and must include at least 3 types of experiences
designed
to
improve
problem-solving
performance: Regular sessions devoted to solving a
variety of kinds of problems; Instruction in the use
of various problem-solving strategies; Practice
aimed at the development of specific problem-
solving thinking procedure and skills.
In 2022, Wongupparaj and Kadosh published a
paper online on relating mathematical abilities to
numerical skills and executive functions (EF) in
informal and formal schooling. The study was
carried out in Chonburi province in Thailand and
included 505 children (6-to 7- year old
preschoolers and first graders). 50.2% of the
participants were female. All participants were
native of Thai and attended 12 public schools. The
domain specific early mathematics is composed of
eight paper
–
and pencil tests (the dot-dot
comparison test, the dot-number comparison test,
the number comparison test, the mental number
line, the numerical strop test, the numerical
shifting test, the number sets test the numerical
operations test. The dot
–
dot comparison was used
to assess the enumerating ability by comparing 2
sets of data that reflect subitizing and counting
systems of children’s early nu
merical abilities. All
children were instructed to circle which set of dots
contained more dots without counting as
accurately and quickly as possible in 2.5 minutes.
The results showed using Multiple Analysis of
Variance (MANOVA) that primary school children
were superior to preschool children over more
complex tests of domain specific early
mathematics; number specific executive functions;
mathematical abilities, particularly for more
sophisticated numerical knowledge; and number
specific EF components. Mathematical skills are
regarded as an important tool and an integral part
of effective functioning in everyday life. These skills
are the keys to analyzing and interpreting
information and also making basic or complex
decisions (Reyna VF et al as cited in Wongupparaj
& Kadosh, 2022). Our study focused on secondary
school students and we used Pearson Product
Moment Correlation as our statistical tool.
Nazari et al. (2019) published an article titled
‘Distributed
practice
in
mathematics:
Recommendable especially for students on a
medium performance level?’ The study was carried
out in Germany. They investigated the effect of
distributed practice on the mathematics
performance of 7th graders. The initial sample
included 142 7th graders of four schools located in
and around a middle-sized German City in
neighbourhoods with a medium socio-economic
status. All students attended higher level courses
aiming at the German higher education entrance
qualification “Ahitur. Before the students were
assigned to one of the two practice condition, they
were ranked by their mathematics grade of their
last school certificate, and then, within each grade
group, they were randomly assigned to one of the
two conditions, ensuring that the overall
mathematics performance was roughly equal in
both conditions before manipulation. After a
stochastic lesson, one group of students worked
three sets of exercises massed on one day, while the
other group of students worked the same exercises
distributed over three days. Bayesian analyses of
the performance two weeks after the last practice
revealed no evidence for an effect of practice
condition. However, in a test after six weeks, strong
evidence for a positive effect of distributed practice
was revealed. Exploratory analyses indicated that
especially students in the medium performance
range benefited from distributed practice. Their
study contributes to answer the questions of why
and under which circumstances distributed
practice proves a useful learning strategy in
realistic learning contexts, even beyond learning of
rather simple verbal content.
Cao Thi et al. (2023) carried out a cross-sectional
study in Vietnam on factors affecting the numeracy
skills of students from mountainous ethnic
minority regions in Vietnam. The study was crucial
for the staff and policy-makers to narrow the gap in
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quality of mathematics education between the
mountainous and developed regions and to create
human resource strategies for minority regions in
Vietnam. There has been many efforts to improve
mathematics
education
in
the
northern
mountainous regions of Vietnam, however, the
results are not as expected. The sample was made
up of 755 middle school students (410 girls, 345
boys) from grades 6 to 8 in 8 provinces in northern
Vietnam. In each province, one school was chosen
using the convenience sampling method where 30
to 35 students were randomly selected for each
grade. Using factor analysis, they discovered the
impact of the 8 independent variables on the
dependent variable. Students’ efforts (practic
e of)
and language skills were most influential, and
teachers did not have a substantial effect. Thus,
their study demonstrated that students’ practice of
mathematics has an effect on their numerical skills.
In this paper, we use the mixed research method
with convergent parallel research design.
The National Council of Teachers of Mathematics
(NCTM) argued that problem-solving should
become the “the focus of mathematics in school”
(1989, p.6). According to NCTM (1989, 1991),
centering
mathematics
instruction
around
problem-solving can help all students learn key
concepts and skills within motivating contexts. The
use of open, contextualized problems seems
sensible at many levels. Instead of having students
complete meaningless exercises and memorize
what the teacher tells them, why not have students
learn key mathematical ideas while solving
interesting problems? Any good mathematics
teacher would be quick to point out that student’s
success or failure in solving a problem often is as
much a matter of self-confidence, motivation,
perseverance and many other non-cognitive traits,
as the mathematical knowledge they possess. An
individual’s failure to solve a problem successfully
when the individual possesses the necessary
knowledge stems from the presence of non-
cognitive and meta cognitive factors that inhibit the
appropriate utilization of this knowledge. These
factors are of at least four types: affects and
attitudes, beliefs, control and contextual factors
(Garfola et al., 1985). Classroom activities designed
to develop problem-solving ability include:
Teacher-student planning; effective discussion
procedures; effective procedures for presenting
data for group consideration; and cooperative
organization for group activity. However, a
classroom that is organized around significant
problems cannot limit its activities to studying the
textbook and listening to lectures. Its source of
information must include whatever will lead to the
understanding of current problems. Peer
interaction can foster cognitive development by
allowing children to acquire new skills and
restructure their ideas through discussion. Having
a partner can increase the amount of time students’
work on a task. However, collaborative contexts
can facilitate children’s acquisition of skills bec
ause
partners often bring different skills to the task.
Gerald and Denis (2023) carried out a study in
Philippines on students’ achievement and
problem-solving skills in mathematics through
Open-Ended Approach (OEA). Open-Ended
Approach is one of the instructional approaches
that have the potential to help students develop
their problem-solving skills. OEA focuses on
finding correct response rather than offering a
single solution to a problem at hand. The study
investigated the achievement and problem-solving
skills in mathematics of the grade 8 students in
Binuangan National High School through OEA. It
sought to identify the levels of achievement in
mathematics of students who were exposed to OEA
and those exposed to non-OEA, determine the
problem-solving skills of students who were
exposed to OEA and those exposed to non-OEA in
terms of a) self-confidence in solving problems; b)
putting effort in solving problems; and c)
procedure followed to solve problems; compare
the levels of achievement in mathematics of
students were exposed to OEA and those exposed
to non-OEA; and find out the difference on
problem-solving skills of students who were
exposed to OEA and those exposed to non-OEA.
The researchers adopted the quasi-experimental
research design in the study. The experimental
group and the control group pre-test results
showed very poor student achievement; however,
after exposure to OEA, the experimental group’s
post test results showed great student
achievement. Compared to OEA and non-OEA,
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students exposed to OEA demonstrated greater
problem-solving skills. Between the pre-test and
posttest, OEA considerably raised students’
achievement levels. Additional findings showed
that students exposed to OEA had significantly
better problem-solving skills than those exposed to
non-OEA
Materials and method
The researcher used the mixed-research method
that involves both quantitative and qualitative
research methods. We made use of the convergent
parallel design. This design is used when the
researcher collects and analyzes both quantitative
and qualitative data simultaneously during the
same phase of research process, keeping the
methods independent and then merging the results
into an overall interpretation. The accessible
population was made up of 1036 students and the
sample size of the study was made of 512 form five
students from six colleges using the random
sampling technique. There were also 26 teachers
and 6 Heads of Mathematics Department. The
questionnaire was administered to 512 form five
students of the six selected secondary schools in
Fako Division. Simple random sampling technique
was used to select the respondents who took part
in the research from the six schools. A
questionnaire was constructed based on the
objective(s) of the study. The 4-point Likert scale
type scale was used to construct the questionnaire
items with each item having four options (Strongly
Agree, SA = 4; Agree, A=3; Disagree, D=2; and
Strongly Disagree, SD=1). The questionnaire was
validated both face wise and content wise. The
direct delivery technique was used to administer
the questionnaire. In each school, permission was
obtained from the Vice Principal who delegated the
Dean of Studies or the Head of Mathematics
Department
to
assist
in
the
effective
administration of the instrument. Students were
met in class and were reminded of the anonymity
of their responses, the objectivity and sincerity
while filling the questionnaires. They were also
advised to work independently. All the necessary
explanations concerning the questionnaire were
made to the respondents at the beginning of the
exercise. The respondents were then given enough
time to fill their copies, after which they were
collected, giving a return rate of 100%. The
statistical method that was used to analyze the data
for the study was descriptive statistics and Pearson
Product Moment Correlation to test the
Hypothesis.
Findings and Discussion
Research Question: What effect does students’
practice of mathematics have on their numerical
skills in problem-solving?
Table 2: Thematic Presentation of Students’ Responses to Open Ended Questionnaire Questions
on What They do When Stuck on Something in Mathematics in Relation to their practice of
Mathematics
Code
Code Description
Grounding Sample Quotations
Groups
Study groups created by teachers in
class or by students out of class
5
“ He puts us in groups and
encourage us to work harder”.
Chalk-board
Calls students to solve more questions
on the chalk-board
35
“The teacher sends us to the board
to solve and explain to the class
how we got our answer”.
Persistence
Working harder than before
6
“I
solve
many
more
questions/exercises similar to
those given in class”.
Extra classes
Home teacher or organising more
classes outside normal time
5
“The teacher organizes extra
classes with students”.
Remedial
teaching
Additional teaching for weak students
2
“He/she knows some students are
slow learners”. “Students who
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perform poorly are supervised by
the teacher for them to sit up”.
Time constraint
Teachers creating time to attend to
students and students making time to
meet teachers with their difficulties
18
“The teacher is always busy”. “He
does not care”. “He has no
concern for us”.
Both students and teachers revealed what many students do when stuck on something in mathematics in
relation to practice of mathematics. The following were very recurrent amongst them. They include
calling students to solve questions on the chalk-board, working harder than before, time constraint and
extra time spent out of normal school hours. The fact that the teacher has to finish the syllabus and the
high student/teacher ratio in some schools has an impact on the time he gives students to effectively
practice mathematics.
Table 3: Thematic Presentation of Teachers’ Responses to Open Ended Questionnaire Questions
on What Students do When Stuck on Something in Mathematics in Relation to their practice of
Mathematics
Code
Code Description
Grounding Sample Quotations
Chalk-board
Calls students to solve more
questions on the chalk-board
3
“The teacher sends students to the board
to solve and explain to the class how we
got our answer”.
Persistence
Working harder than before
1
“They try basic examples to relate to the
question”.
Extra in-put
Extra hour out of normal school
hours
5
“The
teacher
gives
take-home
assignments”. “we take it home for
research”.
Time
constraint
Teachers creating time to attend to
students and students making time
to meet teachers with their
difficulties
3
“The student/teacher ratio is very
high”.“ The teacher has to finish the
syllabus”.
Views obtained from interviews with Head of
Mathematics Department on Students’ practice of
Mathematics
4 out of the 6 Head of Department pointed out that
it is a departmental policy that a day does not pass
without the teacher giving take home assignments
to the students in all the classes. This policy is
implemented and the class teacher devises ways to
correct these assignments. However, one of them
disagreed with the fact that if students are having
difficulty, an effective approach is to give them
more practice by themselves during the class. He
proposed that a better thing to do is to repeat the
lesson and when you see interest you can then give
them more practice. Giving the students more
practice when they have a difficulty is just making
the situation frustrating, he concluded.
Inferential Statistics for students’ practice of
Mathematics
The independent variable for research hypothesis
two is students’ practice of mathematics, while the
dependent variable is numerical skills in problem-
solving in secondary schools of the South West
Region. The scores of the independent variable
were obtained from the responses recorded from
the eight items of a four-point Likert scale
questionnaire that measured students’ practice of
mathematics. The scores of the dependent variable
were got from the eight items of a four-point Likert
scale questionnaire that measured the numerical
skills in problem-solving in secondary schools of
the South West Region. The statistical analysis
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technique used in this analysis is the Pearson
Product Moment Correlation. The result of the
analysis is presented on table 4.
Table 4: Pearson Product Moment Correlation Analysis of the Relationship Between Students’
Practice of Mathematics and their Numerical Skills in Problem-Solving
Problem-solving skills “ numerical”
Students’ practice of
mathematics
Pearson’s Correlation
.230
**
Sig,(2-tailed)
.000
N
512
**. Correlation is significant at the 0.01 level (2-tailed).
The result of the analysis reveals a positive
correlation between students’ practice of
mathematics and numerical skills in problem-
solving, which was statistically significant (r =
0.230, p < 0.001, n = 512). An r value of 0.230**
indicates a linear relationship between the two
variables being analyzed and also a slight positive
trend betwee
n students’ practice of mathematics
and their numerical skills in problem-solving. A
positive correlation (r > 0) signifies that as one
variable increases, the other tends to increase as
well, showing a direct relationship. Thus, as
students’ practice of m
athematics increases, their
numerical skills in problem-solving get better.
To determine whether there is a significant
influence of practice of mathematics on numerical
skills in problem-solving, we perform a testing of
statistical hypothesis as follows:
H0: ρ = 0 and H
a
: ρ ≠ 0
A test carried out using SPSS 23.0 with the testing
criteria as follows:
Ho2 is rejected if sig.(2-tailed) < 0.05 or if sig.(2-
tailed) ≥ 0.05. In table 4 above, it is shown that a
sig.(2-tailed) value of the Pearson correlation
coefficient is equal to 0.230** and based on the
testing Ho is rejected. We retain Ha and conclude
that there is a significant correlation between
students’ practice of mathematics and their
numerical skills in problem-solving.
The findin
gs show that students’ practice of
mathematics has a direct positive effect on their
numerical skills in problem-solving. This implies
that the more students practice mathematics, the
better their numerical skills in problem-solving
becomes. Higher numerical skills can provide the
capacity to make informed decisions based on
numerical data. Numerical skills are essential for
success in mathematics and can be beneficial in
various aspects of life, including personal finance,
scientific
investigation,
technology
and
engineering and even in the military field.
These findings are in line with Gerald and Denis
(2023) who studied students’ achievement and
problem-solving skills in mathematics through
Open-ended-Approach (OEA) and concluded that
students exposed to OEA had significant better
problem-solving skills than those exposed to non-
OEA. The findings strengthens that of Wongupparaj
and Kadosh (2022) whose study on relating
mathematical abilities to numerical skills and
executive functions in informal and formal
schooling found out that primary school children
were superior to pre-school children over complex
tests of domain specific early mathematics, number
specific executive functions and mathematical
abilities particularly for more sophisticated
numerical knowledge. Also, our findings support
that of Nazari et al. (2019) who investigated the
effect of distributed practice on the mathematics
performance of 7th graders and found strong
evidence for a positive effect of distributed
practice, especially students in the medium
performance range. These findings align with
Rheta (1985) who explored a variety of
computational estimation in relation to other
mathematical skills and sex differences. He found
that verbal tasks were not more difficult than
numerical tasks, but decimals were more difficult
than whole numbers and quotients were more than
products, which in turn were more difficult than
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sums and differences. Estimation performance was
best predicted by skill in operating with tens. Our
research indicates the relevancy of the findings of
Cao Thi et al. (2023). Their study on factors
affecting the numeracy skills of students from
mountainous ethnic minority regions in Vietnam
found out that students’ effort (practice of) and
language skills were the most influential factors
that impact the numeracy levels of students in
mountainous regions.
RECOMMENDATIONS
The teacher/student ratio in most of our
institutions of learning is low and, in some cases,
those who teach mathematics are more concerned
with syllabus coverage. The implication is that
there is lack of time/opportunity to practice / do
problem-solving in the classroom. The teacher
may not have time to attend to the students like
hold individual meetings with students to track
progress and set goals because, if he does, he may
not complete the syllabus. He may as well not do
problem-solving in the classroom because he lacks
the skills to prepare problems and use them in
whole-class situations, assist students in
monitoring and reflecting on the problem-solving
process, expose students to multiple problem-
solving strategies amongst others. Students who
develop proficiency in mathematical problem-
solving early are better prepared for advanced
mathematics and other complex problem-solving
tasks. We recommend that (1) problem-solving
should be part of each curricular unit and begin in
kindergarten. For this to be effective, the teaching
of problem-solving should not be isolated, instead,
it can serve to support and enrich the learning of
mathematics concept and notation. Schoenfeld
(1980) opines that a course in problem-solving
requires a substantial commitment from all
concerned. The teacher has to be especially flexible
because it is the process of problem-solving that
counts and the teacher is essentially serving as a
“coach” to the students. The students are being
asked to think, and to create, rather than to “recite”
subject matter. That is not an easy task but it is a
critically important one
–
and ultimately a very
rewarding one, well worth the effort on the part of
the students. It is also, of course, a source of
tremendous gratification for the teacher. (2)
teachers should cultivate students’ interest in
mathematics as early as possible. Varying
classroom instruction practices could be a remedy
to enhance
students’ understanding, achievement,
and motivation in learning mathematics.
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