Inductive Method In Mathematics Pdf
This research is experimental quantitative about quasi experiment that emphasize on improve mathematical understanding and problem solving for Junior High School students by inductive-deductive implementation. The population of this research are all of students at IX degree students in Subang 2012/2013. Two of nine classes were chosen as sample for this research. The topic which used is probability including random occurrence, basics of chance, relative frequency, calculation of probability, determining the value of probability, the expected frequency and the combined odds of two events. The instrument that was used are test and non-test. Mathematical understanding and problem solving were used as a test methods. Meanwhile questionnaire, and observation sheet were used as non-test methods. The data was analyzed by Mann-Whitney and t-test. According to whole analyze in this research, can be concluded: 1) the student improvement of mathematical understanding by using inductive-deductive approach is in middle quality, 2) there is no significant difference at improvement mathematical understanding between experimental class and control class, 3) the improvement of student's ability in mathematical problem solving that use inductive-deductive approach has a low quality, 4) there is no significant difference at mathematical problem solving between experimental class and control class, 5) most of students has positive responses to mathematic learning by inductive-deductive approach, although the students have many problems when learning takes place.
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Inductive-Deductive Approach to Improve Mathematical Problem Solving for Junior High
School
View the table of contents for this issue, or go to the journal homepage for more
2017 J. Phys.: Conf. Ser. 812 012089
(http://iopscience.iop.org/1742-6596/812/1/012089)
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Inductive-Deductive Approach to Improve Mathematical
Problem Solving for Junior High School
Mariam Ar Rahmah
Email: mariamarrahmah@gmail.com
Abstract.This research is experimental quantitative about quasi experiment that emphasize on
improve mathematical understanding and problem solving for Junior High School students by
inductive-deductive implementation. The population of this research are all of students at IX
degree students in Subang 2012/2013. Two of nine classes were chosen as sample for this research.
The topic which used is probability including random occurrence, basics of chance, relative
frequency, calculation of probability, determining the value of probability, the expected frequency
and the combined odds of two events. The instrument that was used are test and non-test.
Mathematical understanding and problem solving were used as a test methods. Meanwhile
questionnaire, and observation sheet were used as non-test methods. The data was analyzed by
Mann-Whitney and t-test. According to whole analyze in this research, can be concluded: 1) the
student improvement of mathematical understanding by using inductive-deductive approach is in
middle quality, 2) there is no significant difference at improvement mathematical understanding
between experimental class and control class, 3) the improvement of student's ability in
mathematical problem solving that use inductive-deductive approach has a low quality, 4) there is
no significant difference at mathematical problem solving between experimental class and control
class, 5) most of students has positive responses to mathematic learning by inductive-deductive
approach, although the students have many problems when learning takes place.
1. Introduction
In 21st century is a globalization era, the era of resulting technology products with abundant quantity and
quality that increasingly sophisticated and dissemination of information flow is increasingly and
unstoppable. This has led to intense competition among individuals who have skills and ability to think
critic, systematic, logic, creative, and able to communcate creative ideas that will be part of it.
To create human who meets the above characteristics, it can be achieved through education, such as
through mathematics education. By studying mathematics as a whole, the students will be able to have
ability of understanding, communicating, connecting, reasoning, problem solving, logical thinking,
systematic thinking, critical thinking, and creative thinking. This is because mathematics is a means of
thinking, so that mathematics can be regarded as a "vehicle" for developing ability to think logic and
higher cognitive skills for children [1].
Nevertheless, the research that examined on this study was on mathematical problem solving aspects.
This was because mathematical problem solving ability is an ability that considered important on learning,
MSCEIS I OP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 812 (2017) 012089 doi:10.1088/1742-6596/812 /1/012089
International Conference on Recent Trends in Physics 2016 (ICRTP2016) IOP Publishing
Journal of Physics: Conference Series 755 (2016) 011001 doi:10.1088/1742-6596/755/1/011001
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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as proposed by Sabandar [2], that is mathematical problem solving is an ability that must be achieved, and
improved mathematical thinking are the priority objectives of mathematics.
In addition to the opinion stated above, the importance of this ability can be seen from the regulation of
the Minister of National Education of the Republic of Indonesia Number 20 of 2006 on the Standards
Content [3] stated that the purpose of study mathematics is to make learners have the following
capabilities:
xUnderstanding mathematics concepts, the relationship every concepts and apply concepts or
algorithms as flexible, accurate, efficient, and precise in troubleshooting.
xUsing the reasoning in the patterns and nature, perform mathematical manipulation in making
generalizations, compile evidence, or explain mathematical ideas and statements.
xProblem solving, include the ability to understand the problem, contruct a mathematical model,
solve the model and interpret the obtained solution.
xCommunicating the ideas with symbols, tables, diagrams, or other media to clarify situation or
problem.
xHaving a good respect of the usefulness mathematics when solving the problem, also confidence
in problem solving.
But the reality has found in the field that the level of achievement of mathematical problem solving
ability is not satisfactory. It is based on research conducted by Nurhadiyati [4] to the junior high school
students in the Bandung city. Generally, the results of mathematical problem solving ability of junior high
school students is not satisfactory, around 30% - 50% from the ideal score. Similar opinion was also
expressed by Ahmad [5] that is based on case studies in mathematics subject probability and statistics
conducted on 41 students of second grade in SMP Negeri 2 Purwokerto, it was found that the students are
still experiencing difficulties in resolving problems that related with the ability of understanding
mathematical and mathematical problem solving.
The failure of students to achieve mathematical abilities above is not impossible causing the formation
to negative course. According to Suherman [6] mathematics is a formation of affectives mathematics
towards to the formation of cognitive area, although sometimes the opposite occurs. For example, a
student who often feel able to solve mathematics problems, they enjoyed and desire to get more
mathematics problems. Conversely, if they qite often can not feel disable, it will lead them to scare and
shy. This is proven on the reality that most of students have negative affectives to mathematics. As stated
by Muijis and Reynolds [1] mathematics is usually regarded as the most difficult subjects for children and
adults. At school, many students seems to be uninterest on mathematics, and often there is doubt about the
relevance of so much time spent for teaching mathematics.
These problems occur not only due to the students factors but also it could be occur because of
insufficiency facilities and infrastructures when learning takes place, the educational environment not
supporting, and also because teachers could not maximize their competency as teachers. From all factors,
a slight incompetence teacher in teaching lead to an enormous impact on the students' lack on
mathematical ability. Besides from Gage and Berliner's opinion [7], teachers should be able to play as a
role, in charge of, and responsible for: (1) Planning, which should be prepare what is needed in teaching
and learning process; (2) Implementing, which should be create a situation, leaders, stimulate, mobilize,
and direct the KBM according to plan; and (3) Assessor, who should be collect, analyze, interpret, and
make a consideration of teaching and learning process based on defined criteria.
In this condition, teacher not only prepare physical things (eg props) but also teachers have to prepare
non-physical things, like mastery material that will be delivered through learning approach. The approach
adopted is not based on self-interest, for example, practicality or the approach of "it" is the most
MSCEIS I OP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 812 (2017) 012089 doi:10.1088/1742-6596/812 /1/012089
controlled, but a teacher should use learning approaches that can stimulate interest and explore the
knowledge of students, so it will impact on the emergence of students positive affectives towards
mathematics. Such an approach is of course adapted to the material to be learned and the objectives to be
achieved.
The ideal ways of learning that was expressed in Standard Process on the National Education
Standards [8], is a process of learning in the educational unit organized in an interactive, inspiring, fun,
challenging, motivating the students to actively participate and give enough room for innovation,
creativity, and independence in accordance with their talents, interests, and physical and psychological
development of learners.
Hamzah [9] suggested that in learning, students need to be active mentally, build a knowledge based on
cognitive maturity they had. In other words, students are not expected to be like the little bottles ready to
be filled with a variety of science in accordance with the will of the teacher. Meanwhile, Dahlan [10] also
noted when the learning takes place, knowledge is not accepted passively. Knowledge gained through
active activity in solving relationships, patterns, and make generalizations that are integrated in the new
knowledge that obtained by the students, and learning is a social activity that occurs from the interaction
of students with teachers and students with their peers. Such learning can be applied with inductive-
deductive approach.
Inductive-deductive approach refers to activities undertaken by teachers so that teaching materials can
be adapted by the students. Inductive-deductive approach according Mulyana [11] is the process of
presenting a concept mathematical principle started by giving examples, followed by finding / construct
the concept, constructing a conjecture, and ends with the givingexercise correspond to the stages of the
concepts and principles that have been given. Through learning by using this approach students are trained
to make generalizations.
To reachof making generalization stages, it needs capability to understand the relationship/linkages for
given examples, problem solving plan, calculation process, and the process to re-examine the truth of the
results obtained. These elements are an indicator of the ability of mathematical problemsolving. Based on
the above, allegedly learning by using inductive-deductive approach could be improve students'
mathematical problem solving ability.
2. Problem
Based on the introduction of the problems that have been described previously, the issues examined in this
research are: (1) is the increase in mathematical problem solving ability of students to get math learning
with inductive-deductive approaches are better than students who received conventional approaches? and
(2) how is the students' affective using inductive-deductive approaches for mathematics learning?
3. Research Method
This research is a quasi-experimental research involving a group that has been formed to serve as the
object of research with research design called non-equivalent control group design [12]. The population in
this research were all students of third grade Junior High School in Subang Academic Year 2012/2013.
Two of nine existing class was selected as research sample, that is the experimental group (the group that
gets learning by using inductive-deductive approaches) and a control group (group with conventional
learning). The formation of two classes aimed to determine the effect of learning mathematical problem
solving ability. The instrument used is the ability tests, student questionnaire, and observation sheet.
MSCEIS I OP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 812 (2017) 012089 doi:10.1088/1742-6596/812 /1/012089
4. Results And Discussion
Results and Discussion in this study are based on factors that were observed and found in the research
include:
4.1 Description of Mathematical Problem Solving Ability Based on Learning (PSA)
Here are the results of descriptive statistics score students' mathematical problem solving ability.
Table 1 Descriptive statistic ofPSA score
Test Experiment Group Control Group
N
ܵ
N
ܵ %
Pre-test 35 10,11 5,465 25,28 35 7,69 4,234 19,23
Post-test 35 14,66 4,065 36,65 35 11,17 5,366 27,93
Ideal Maximum Score: 40
Based on Table 1 shows that the average score of the pre-test of mathematical problem solving ability
to the experimental class is 10.11, while for the control group was 7.69 with early abilities difference in
the second grade reached 6.05%. However, based on nonparametric statistical test Mann-U Whitne
obtained Sig. (2-tailed) is 0.055> Į = 0,05 so that H0 is accepted. This means there is no difference in the
average scores pre-test mathematical problem solving ability in the experimental class and control class.
While the average post-test score for an experimental class was 14.66 and the average for the control
group was 11.17. Differences in the average scores in both classes is 3.52% with the highest average is in
the experimental class. To prove that the mathematical problem solving ability score in experiment class is
better than the control class there is a test of difference in the average score of N-gain using independent
sample t-test, because the normal distribution of data and derived from a homogeneous variance. Here's a
summary of the results obtained.
Table 2 Difference of Average Post test
t-test for Equality of Means
T df Sig. (2-tailed)
3,152 68 0,003
Based on statistical tests above it can be concluded that there is the different mathematical problem
solving ability between the students who got a math learning with inductive - deductive approach and
conventional learning.
4.2 Enhance Mathematical Problem Solving Based Learning (PSA)
Table 3 below presents the average of mathematical problem solving abilities by learning N-gain.
Table 3 N-Gain Average and Clasification PSA
Class N-gain Average Clasification
Experiment 0,138 Low
Control 0,107 Low
From Table 3, although the classification of the enhancement in both classes is low, but the
enhancement in mathematical problem solving ability of students in the experimental class is greater when
compared with the increasing capability in the control class . To determine the significance then tested the
nonparametric Mann - Whitney U because the results of the analysis show that the data are not normally
distributed . Here's a summary of the results obtained.
MSCEIS I OP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 812 (2017) 012089 doi:10.1088/1742-6596/812 /1/012089
Table 4 Difference of N-Gain Average Test
Statistic Score Explanation Conclusion
Mann-Whitney U 521,000 Ho
Accepted Hipotesys rejected
Z -1,081
Asymp. Sig. (2-tailed) 0,280
Asymp. Sig. (1-tailed) 0,140
Thus, there are no significant differences between the average N-gain mathematical problem solving
ability of students who got the inductive-deductive learning with students getting conventional learning.
From the results, it can be concluded that there are no significant differences in mathematical problem
solving enhancement abilities between students who study with inductive-deductive approach and
conventional.
The discrepancy between the hypotheses are made with the results obtained made possible because of
the inductive-deductive approach is less suitable for use in the classroom are the reasons:
First, students still unfamiliar implementing learning by using inductive-deductive approach.
Workmanship in groups and provision of teaching materials about probability using tools to each student
(in this case the coins, dice and cards bridge) was not enough to help the students to understand the
material. Most of the students are still asking how to get a conclusion/ generalization of the examples
above. Whereas Hudojo (Dahiana, 2010) states that, think math is a mental activity, which is in the
process using generalizations. This indicates that the students thinking activity mathematically with
inductive-deductive approach to the selected sample was not going according to what is expected. The
students problems being unfamiliar with the way of learning using constructivist-based approach is
confirmed by Dharmadasa (Muijis, D. and Reynolds, D., 2008), which suggests that a number of studies
shows that many students thinks constructivist methods is quite difficult to be implemented. The same
thing also expressed by Au and Carroll (Muijis, D. and Reynolds, D., 2008) stating that the teacher sees
constructivist methods are burdensome and alarming effect on classroom discipline. They are not sure
about the provision of appropriate materials, promoting experimentation, and started constructing the
child's knowledge.
Second, there is lack of researcher that studies the class while the class is relatively large resulted not
all students can be handled optimally. As a result, the students who have not been handled by researchers,
conclusions/ formulas that have been made in the teaching materials is not based on an understanding of
the premises above, it is obtained from the copying conclusion at the end of learning.
Third, the classic problem, is the limited time. Although researchers have designed a time as possible
so that learning takes place in line with expectations, but the reality is different. Researchers do not have
enough time to discuss the problems of mathematical problem solving for probabilities material, so there
are still many students who are not accustomed to do problem solving mathematical problems contained in
the post-test. This problem is recognized by Dharmadasa (Muijis, D. and Reynolds, D., 2008) based on the
results of an informal interview to the implementation of programs designed to introducing constructivist
methods shows that teachers consider a constructivist approach as a challenge and a concept hard to
capture in a short time. These constraints may cause some differenciesof hipotesys and the result obtained.
5. Conclusions andRecommendation
Based on the results of research and discussion, it could be produced some conclusions as follows: (1)
there is no significant difference between comprehension ability of mathematical problems solving in both
of experimental group and control group; and (2) most of students have positive affective on learning
mathematics by using an inductive-deductive approaches, even though in reality students have problems
during and after the learning takes place.
MSCEIS I OP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 812 (2017) 012089 doi:10.1088/1742-6596/812 /1/012089
The conclusion has been stated above, implies that: (1) learning mathematics by using inductive-
deductive approaches could not improve mathematical problem solving skills significantly compared to
conventional learning, and (2) learning mathematics by using inductive-deductive train students to
socialize, communicate, and be unyielding before the goals are reached.
The recommendation after the course of this study are as follows: (1) Learning mathematics by using
inductive-deductive can be applied in schools with high clusters and (2) teaching mathematics using
inductive-deductive could be tested in a shorter period of time.
6. References
[1] MuijisD and Reynolds D2008Effective Teaching (TeoridanAplikasi) (Yogyakarta: PustakaPelajar)
[2] Kurniawan 2010 (Tidak ada di Referensi)
[3] RegulationNomor 22Tahun 2006tentangStandar Isi (Jakarta: Depdikbud)
[4] Anriani N2011PembelajarandenganPendekatan Resource Based Learning
untukMeningkatkanKemampuanPenalarandanPemecahanMasalahSiswa SMP Kelas
VIII(Bandung: Thesis PPS UPI)
[5] Ahmad2005KemampuanPemahamandanPemecahanMasalahMatematikaSiswa SLTP dengan
Model PembelajaranBerbasihMasalah (Bandung: Thesis PPS UPI)
[6] Suherman., et al 2003StrategiPembelajaranMatematikaKontemporer (Bandung: FPMIPA)
[7] Makmun AS2007PsikologiKependidikan (PerangkatSistemPengajaranModul) (Bandung: Rosda)
[8] National Education Standards (2009) (Tidak ada referensi)
[9] Hamzah2001PembelajaranMatematikamenurutTeoriBelajarKonstruktivisme
[Online:http://depdiknas.go.id/jurnal/40/pembelajaran]
[10] Dahlan J
A2004MeningkatkanKemampuanPenalarandanPemahamanMatematikSiswaSekolahLanjutan
Tingkat PertamamelaluiPendekatan Open Ended (Bandung: Dissertation PPS UPI)
[11] Mulyana T2005UpayaMeningkatkanKemampuanBerpikirKreatifMatematikaSiswa SMA Jurusan
IPA MelaluiPembelajarandenganPendekatanInduktif-Deduktif(Bandung: Thesis PPS UPI)
[12] RuseffendiET2005 Dasar-dasarPenelitianPendidikandanBidang Non EksaktaLainnya ( Bandung:
Tarsito)
[13] Hafriani2004MengembangkanKemampuanPemecahanMasalahMatematikamelalui Problem
Centered Learning (Bandung: Thesis PPS UPI) (Tidak ada di badan teks)
MSCEIS I OP Publishing
IOP Conf. Series: Journal of Physics: Conf. Series 812 (2017) 012089 doi:10.1088/1742-6596/812 /1/012089
... Another approach that teaches the students to learn how to learn rather than what to learn is induction. This is an effective approach for helping students to understand concepts and generalizations and for developing their higher-orderthinking skills (Rahmah, 2017). The inductive approach is a much more studentcentred approach that makes use of a strategy known as 'noticing.' ...
... To check if the arrived conclusion is correct and acceptable, the students are to test and verify the principle and concept using the examples given. Through this method, the students attain the knowledge and logical explanations (Rahmah, 2017). ...
- Jose M. Cardino
-
Ruth A. Ortega-Dela Cruz
This study was conducted to analyse the influence of learning styles and teaching strategies on academic performance in mathematics. Surveys were conducted to 277 randomly selected grade 9 students and five purposively sample mathematics teachers. Findings reveal that most of the student-respondents have a combination of dependent, collaborative and independent learning styles. Multiple regression analysis indicates that among the learning styles, only the independent style has a significant influence on the academic performance of grade 9 students. Four teaching strategies including cooperative learning, deductive approach, inductive approach, and integrative approach, were found to have a significant influence on academic performance. By understanding the learning styles of students, teachers will be guided in designing different strategies to help students enhance learning for their improved performance in mathematics.
... The lack of mathematical problem consciousness in senior high school is partly due to the long-term impact of examination-oriented education. A slight incompetence teacher in teaching lead to an enormous impact on the students' lack on mathematical ability [9]. Therefore, teachers must change the educational ideas and update the educational concepts to change this situation. ...
... According to Suherman [10] mathematics is a formation of affectives mathematics towards to the formation of cognitive area, although sometimes the opposite occurs [9]. So, teachers should fully respect students' principal status in the mathematics classroom teaching, create a harmonious, democratic and relaxing classroom atmosphere in order to eliminate students' tension and anxiety in class and cultivate students' mathematics problem consciousness. ...
... Pada tingkat SMA/MA pada pembelajaran abad ke-21 adalah era globalisasi, era dihasilkan produk teknologi dengan kuantitas yang berlimpah dan kualitas yang semakin canggih terutama dalam dunia pendidikan, Pada pembelajaran fisika dipandang penting untuk diajarkan sebagai mata pelajaran tersendiri dengan beberapa pertimbangan, pertama, selain memberikan bekal ilmu kepada peserta didik, mata pelajaran fisika dimaksudkan sebagai wahana untuk menumbuhkan kemampuan berpikir yang berguna untuk memecahkan masalah didalam kehidupan sehari-hari. Kedua, mata pelajaran fisika perlu diajarkan untuk tujuan yang lebih khusus yaitu membekali peserta didik pengetahuan, pemahaman dan sejumlah kemampuan yang dipersyaratkan untuk memasuki jenjang pendidikan yang lebih tinggi serta mengembangkan ilmu dan teknologi yang sangat diperlukan di dunia pendidikan (Mariam, 2017: 3). ...
- Nurmutmainna Ramadoan
- Dwi Suisworo
- Ishafit Jauhari
p class="AbstractEnglish"> Abstract: Deductive hypothetical thinking strategy is learning that contains an explanation of the principles of the content of the lesson explained in the form of the application of things that are general in matters that are specific. In deductive hypothetical thinking, students are required to be more critical in accepting and understanding what they have learned and experienced themselves in the 21st century. In the 21st century learning, using PhET simulations learning media to understand physics learning is better and more interesting. This study aims to determine the differences in deductive hypothetical thinking strategies with PhET simulations on critical thinking skills compared to conventional learning in Work and Energy subject. This research method is using quasi-experiment, randomized control group pre-test and post-test that is a researcher who has a randomized design with initial tests before learning and final test after learning. The subjects of this study were 10th grade level of SMAN 1 Soromandi, where the 10th grade level of MIPA1 was the experiment group with the number of students as much as 26 and 10th grade level of MIPA2 as the control group with the number of students as much as 23. The results of this study concluded that there were differences between experimental groups and control groups, deductive hypothetical thinking is more effective than conventional learning on business and energy material at SMAN 1 Soromandi. Abstrak: Strategi berpikir hipotetikal deduktif adalah suatu pembelajaran yang berisi penjelasan tentang prinsip-prinsip isi pelajaran yang dijelaskan dalam bentuk penerapan hal-hal yang bersifat umum pada hal-hal yang bersifat khusus. Pada berpikir hipotetikal dedukif peserta didik dituntut lebih kritis dalam menerima dan memahami apa yang mereka pelajari dan alami sendiri dalam pembelajaran di abad ke-21 pada kurikulum K13. Dalam pembelajaran abad ke-21 untuk lebih memahami pembelajaran fisika lebih menarik mengunakan media pembelajaran PhET simulations. Penelitian ini bertujuan untuk mengetahui perbedaan strategi berpikir hipotetikal deduktif dengan PhET Simulations terhadap keterampilan berpikir kritis dibandingkan dengan pembelajaran konvensional pada pembelajaran fisika materi Usaha dan Energi. Metode penelitian ini adalah menggunakan quasi esperiment , randomized control group pre-test dan post-test yaitu suatu penelitian yang memiliki rancangan secara acak dengan tes awal sebelum pembelajaran dan tes akhir sesudah pembelajaran. Subyek penelitian ini adalah kelas X SMAN I Soromandi, dimana kelas X<sub>1</sub> Mipa sebagai kelas eksperimen dengan jumlah peserta didik sebanyak 26 dan kelas X<sub>2</sub> Mipa sebagai kelas kontrol dengan jumlah peserta didik sebanyak 23. Hasil penelitian ini menyimpulkan ada perbedaan antara kelompok eksperimen dan kelompok kontrol, dan menggunakan berpikir hipotetikal deduktif lebih efektif dari pada pembelajaran konvensional pada materi usaha dan energi di SMAN I Soromandi.</p
Bandung: PPS UPI) Pembelajaran dengan Pendekatan Resource Based Learning untuk Meningkatkan Kemampuan Penalaran dan Pemecahan
- N Anriani
PPS UPI) Kemampuan Pemahaman dan Pemecahan
- Ahmad
PPS UPI) Meningkatkan Kemampuan Penalaran dan Pemahaman Matematik Siswa Sekolah Lanjutan Tingkat Pertama melalui Pendekatan Open Ended Dissertation
- J A Dahlan
Inductive Method In Mathematics Pdf
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