This study was conducted to determine the effect of conceptual approach on solving word problems involving multiplication of whole numbers as well as addition and subtraction. The study was carried out in Tambongon Elementary School to Fourty-one Grade Two students. Descriptive statistics (mean & SD), paired-sample T-test and ETA2 were used as tools in the analysis of data. Results revealed that there was a significant difference on the pretest and post test scores of conceptual approach. Further, conceptual approach has large effect.

1. CONCEPTUAL APPROACH AND SOLVING WORD PROBLEM INVOLVING
MULTIPLICATION OF WHOLE NUMBERS AS WELL AS ADDITION
WENEFREDO S. HIFARVA JR.
Abstract
This study was conducted to determine the effect of conceptual approach on solving
word problems involving multiplication of whole numbers as well as addition and subtraction.
The study was carried out in Tambongon Elementary School to Fourty-one Grade Two
students. Descriptive statistics (mean & SD), paired-sample T-test and ETA2 were used as tools
in the analysis of data. Results revealed that there was a significant difference on the pretest
and post test scores of conceptual approach. Further, conceptual approach has large effect.
Introduction
Conceptual is a form of analysis, an approach that studies a complex
problem and determines its basic concepts. The problem is analyzed to identify
the basic domain concepts and laws as well as the tools and skills that are
essential for solving the problem. By reducing the problem’s structure or
mechanism and eliminating some of its components, the number of concepts of
the problem is reduced. Thus, the level of problem solving complexity decreases.
The advantage of this approach is the flexibility of choosing the level of problem
difficulty that suits the individual student’s cognitive level.
Students remember learning that makes sense to them. If they understand
a concept, they can solve problems with or without memory of the related
procedure. Students do not have the conceptual understanding may flounder
with a vaguely remembered and incorrect answer and not have the
understanding to recognize that their answer is incorrect. Conceptual
understanding occurs when students recognize meaningful relationships in
numbers and make connections between mathematics. Hiebert & Wearne (1993)

2. indicated that, problems can promote student’s conceptual understanding foster
their ability to reason and communicate mathematically, and capture their interest
and curiosity. In addition, students should be exposed to truly problematic task so
that mathematical sense making is practiced (Marcus & Feg, 2003:NCTM, 1991;
Van de Walle, 2003).
The theoretical underpinning of the study is anchored from brain-based
learning theory of Jensen (1998) that a solid conceptual understanding of
numeracy by the age of seven is a strong indicator of strength in this area is very
difficult to overcome later on. In addition, Hiebert and Carpenter (1992) state that
conceptual knowledge that is understood. On the other hand, conceptual
understanding helps students with long term understanding.
In other countries, Lappan and Philips (1998) developed a set of criteria
for a good problem that they used to developed their middle school mathematics
curriculum (connected mathematics), and their has been some research
supporting the effectiveness of this curriculum for fostering students conceptual
understanding and problem solving (Cai, et. al).
The study aimed to answer the following statements; 1. What is the pre
test scores of pupils in analyzing and solving word problems involving
multiplication of whole numbers as well as addition and subtraction? 2. What is
the post test scores of pupils in analyzing and solving word problems involving
multiplication of whole numbers as well as addition and subtraction? 3. Is there a
significant difference in the pre-test and post-test scores of pupils? 4. What is the
effect size of conceptual approach to the solving word problems involving
multiplication of whole numbers as well as addition and subtraction?
Conceptual Approach – is an approach that helps student with long term
understandings. In this approach allow the pupils to generate their own problem
representation. Children ability to represent problem correctly is assessed by
means of their explanation of the correct answer.

3. Performance of pupils in solving word problem is refers to mathematical
tasks that have the potential to provide intellectual challenges for enhancing
students mathematical understanding and development.
Method
This study made use of the Descriptive-Comparative research design
using paired sample T-test. The respondent of this study were the 41 pupils of
Grade Two. The researcher made use of purposive sampling technique. The
study was conducted at Tambongon Elementary School, Paquibato District
Davao City. The researcher made use of secondary data, specifically the scores
in pre test and post test. The statistical tools use were Descriptive Statistics
(mean & SD), paired-sample T-test and ETA2. In this study, the learning
conceptual approach will be examined. The data were collated and analyzed
using SPSS IBM statistics.
Results and Discussion
Table 1. Pre-Test Scores
Test n sd m Descriptive Interpretation
Pre-Test 41 1.62 5.93 Low
Table 1 shows the pre-test scores of pupils. It shows a mean of 5.93 with
a descriptive interpretation of low.
Table 2. Post Test Scores
Test n sd m Descriptive Interpretation
Post-Test 41 1.45 10.29 High
Table 2 shows the post test scores of pupils. It shows a mean of
10.29 with a descriptive interpretation high.
Table 3. Paired Sample T-test on Conceptual Approach
Test n df t-value p-value Remarks
Pre Test -
Post Test 41 40 -32.545 .000 Significant

4. Table 3 shows the Paired Sample T-Test on Conceptual Approach. It
shows that the pre-test and post-test scores generated a T-value of -32.545 with
a p-value of .000 which is interpreted as significant.
The result of the study corroborates with Yasin Soylu Ahmet Işık (2008)
that conceptual approach is an effective tool in the improvement of pupils skills in
solving word problems involving multiplication of whole numbers.
Table 4. Effect Size of Conceptual Approach in Solving Word Problem
N or n t-value Eta2 Remarks
41 -32.545 0.964 Large Effect
Table 4 shows the Effect size of Conceptual Approach. It generated an
ETA2 value of 0.964 which signifies large effect, thus the conceptual approach is
effective in improving solving word problems in involving multiplication of whole
numbers as well as addition and subtraction.
Conclusion
The pre test result of grade II pupils in analyzing and solving word
problems involving multiplication of whole numbers as well as addition and
subtraction is low. The post test result of Grade II pupils in analyzing and solving
word problems involving multiplication of whole numbers as well as addition and
subtraction is high. There is significant difference on the pretest and post test
scores of conceptual approach. The conceptual approach has large effect on the
solving word problems involving multiplication of whole numbers as well as
addition and subtraction.
Recommendation
Students should be taught mathematics in a way that fosters
understanding of mathematics concepts and procedures and solving problems.
Engage pupils in solving word problem through understanding approach in which
they can refine and comprehend. Teachers need to be strategic in selecting
appropriate tasks and orchestrating classroom discourse to maximize learning
opportunities. Teachers should engage students in a variety of problem-solving

5. activities and provide children with opportunities to develop their conceptions of
relational structures by creating lessons that incorporate various representations.
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