CPA Approach Research Articles

DEVELOPMENT OF A LESSON ON PRISMS AND CYLINDERS USING THE CPA APPROACH WITH GEOGEBRA TO ENHANCE LEARNING ACHIEVEMENT FOR GRADE 8 STUDENTS

This research uses a learning management process based on Concrete-Pictorial-Abstract (CPA) approach with GeoGebra on prisms and cylinders. This pattern of learning management can help students interested in learning, supporting interaction, and having fun in the classroom because they are involved in learning from learning media that can be seen as concrete, thus stimulating learning very well. The sample group used in the research included 24 students of Grade 8, semester 1, and academic year 2023 at Huaiphung Pittaya School, which was obtained by simple random sampling using the classroom as the random unit. The tools used in this research were learning management plans, the achievement test, and a satisfaction questionnaire. Statistics used in the research include mean, standard deviation, percentage, and hypothesis testing using statistics (t-test). The results of the research found that: 1) the learning achievement on prisms and cylinders of grade 8 students after studying using the learning management process based on CPA approach with GeoGebra was higher than the 70 percent threshold with statistical significance at the .05. 2) The learning achievement on prisms and cylinders of grade 8 students after studying using the learning management process based on CPA approach with GeoGebra was significantly higher than before studying at the.05. 3) Students who received learning on prism and cylinder using the learning management process based on CPA approach with GeoGebra had a high level of satisfaction ( x̄= 4.13, SD = 0.70).

Development of Motion Graphics Video Based on CPA Approach to Enhance Elementary Students' Mathematical Creative Thinking Ability

It is important to develop the creative thinking ability of elementary school students so they can tackle the challenges of today’s world. This skill can be enhanced through learning activities at school, particularly in subjects like mathematics. This study aimed to create motion graphics video teaching materials based on the CPA approach to help improve students’ creative thinking abilities. The 4-D model was used to develop these materials, which involves defining, designing, developing, and disseminating the materials. The experts used teaching materials assessment sheets and test items to evaluate the effectiveness of the materials. The results showed that mathematics teaching materials using motion graphics video teaching based on the CPA approach were successful in improving students’ creative thinking skills. These teaching materials can be used in elementary mathematics education and for further research purposes.
 Keywords: CPA approach, mathematical creative thinking ability, motion graphics video.

Impact of Concrete-Pictorial-Abstract Approach with Collaborative Lesson Research on Year Four Pupils’ Proficiency in Volume

This study aimed to determine the impact of concrete-pictorial-abstract (CPA) approach with collaborative lesson research (CLR) on Year Four pupils’ proficiency in volume. The counterbalanced research design, which consisted of three different groups of year four pupils with three treatments applied to each group, was used with the Proficiency in Volume Test (PVT) administered before and after each of the three CLR cycles. Cluster sampling was used to select three groups of 115 Year Four pupils consisting of 59 males and 56 females. PVT consisted of five questions based on the five strands of proficiency in volume: Q1 (conceptual understanding), Q2 (procedural fluency), Q3 (strategic competence), Q4 (adaptive reasoning), and Q5 (productive disposition). It has a total score of 15 and the indicators of proficiency in volume are low proficiency (0–4), average proficiency (5–10), and high proficiency (11–15). The data were analysed using the paired-sampleCLR cycles-test and one-way ANOVA in SPSS version 24. The results of the paired-sample t-test showed that there was a significant difference between the mean scores of the pre- and post-tests for each CLR cycle. The results of the paired-sample t-test for cube in the first, second and third cycles of CLR were: t = –6.74, df = 37, p < 0.05; t = –19.82, df = 37, p < 0.05; and t = –22.10, df = 38, p < 0.05, respectively. The results of the paired-sample t-test for cuboid in the first, second and third cycles of CLR were: t = 3.15, df = 37, p < 0.05; t = 9.87, df = 38, p < 0.05; and t = 20.76, df = 37, p < 0.05, respectively. The results of oneway ANOVA showed that there was a significant in the post-test mean scores between the first, second and third CLR cycles. The result of one-way ANOVA for cube was F (2,112) = 53.32, p < 0.05, while for cuboid it was F (2,112) = 71.16, p < 0.05. The CLR cycles carried out helped teachers in developing better teaching plans based on the CPA approach as well as enhancing Year Four pupils’ proficiency in volume.

Impact of Concrete-Pictorial-Abstract Approach with Collaborative Lesson Research on Year Four Pupils’ Proficiency in Perimeter

The purpose of this study was to determine whether the concrete-pictorial-abstract (CPA) approach developed based on the Collaborative Lesson Research (CLR) cycles can positively impact Year Four pupils’ proficiency in perimeter. Counterbalanced design was used with pre- and post-test in every CLR cycle. The participants involved were three groups of pupils totaling 115 pupils and a group of three teachers. The sampling used was cluster random sampling. A paired-samples t test was used to determine whether there is a significant difference between the pre- and post-test for each CLR cycle while a one-way ANOVA test was used to analyze if there is an increase in proficiency from the first, second and third CLR cycles. The results indicated that there was an increase in the mean post-test scores compared to the mean of pre-test scores and the mean difference between the first, second and third CLR cycles. In conclusion, the CLR cycle carried out helped teachers in developing better teaching plans based on the CPA approach as well as enhancing pupils’ proficiency in the perimeter.

IMPROVEMENT OF ELEMENTARY SCHOOL STUDENTS 'SELF-CONFIDENCE DURING THE COVID-19 PANDEMIC THROUGH THE CONCRETE-PICTORIAL-ABSTRACT (CPA) APPROACH IN ONLINE LEARNING

Covid-19 changes human habits, especially the learning process. Teaching and learning activities that are usually carried out offline now must be online. The research was motivated by the students' assumptions about mathematics which were considered difficult. Students feel overwhelmed when studying mathematics. When faced with math problems, students often don't have the confidence to solve it. The purpose of this study is to determine the increase in self-confidence of students who get online learning using the CPA approach during the Covid-19 pandemic, both in terms of overall, and Initial Mathematical Ability (IMA). This research is a quasi-experimental research with a non-equivalent control group design on Mathematics subjects on the topic of data collection and presentation in fifth-grade elementary schools. The sample consisted of 56 students at one of the elementary schools in Central Jakarta, Indonesia The research instrument used a self-confidence attitude scale given at the beginning before and after the treatment ended. The learning process is carried out online through the Whatsapp Group, Youtube, and Google Form. The research findings showed that online learning using the CPA approach can increase students' self-confidence better than conventional learning, both as a whole, and IMA. Thus, the CPA approach can be used as an alternative to increasing student self-confidence during the Covid-19 pandemic

El método Singapur para el aprendizaje de las matemáticas. Enfoque y concreción de un estilo de aprendizaje

Los excelentes resultados obtenidos por Singapur en las últimas pruebas PISA 2015 y TIMMS 2015, han provocado un gran interés por el denominado Método Singapur de aprendizaje de las matemáticas. El marco curricular de Singapur tiene como centro de aprendizaje la resolución de problemas matemáticos y se basa en cuatro aspectos fundamentales: el enfoque CPA (concreto - pictórico - abstracto), el currículo en espiral, las variaciones sistemática y perceptual y la comprensión relacional. Estos aspectos se fundamentan en las ideas de Jerome Bruner, Zoltan Dienes y Richard Skemp. En este trabajo, tras presentar el sistema educativo de Singapur y el marco curricular, se estudian las aportaciones de estos autores y sus concreciones en el Método Singapur y se extraen una serie de conclusiones para su adaptación.

Study Based on the Early Mathematical Ability of Elementary Student Self-efficacy through the Concrete-Pictorial-Abstract Approach

Self-efficacy (SE) can encourage students to complete their assignments. The research intended to investigate the achievement of students' self-efficacy by guiding concrete-pictorial-abstract (CPA) based on early mathematical ability (EMA). The research utilized quasi-experimental methods in learning mathematics regarding the volume of cubes and rectangular prisms. The population were all fifth-grade students of elementary schools in Purwakarta, Subang, Karawang, and Bekasi. Samples were 119 participants in Karawang. The instruments applied were questionnaires, tests, and daily journals. The prerequisite materials related to the volume of cubes and rectangular prisms are a topic about arithmetic calculation, square root, flat area, unit length, and problem-solving. Study’s result informed that there was no significant difference in the achievement of students' self-efficacy through CPA and conventional mentoring in the high and moderate EMA groups. There was a significant difference in the achievement of students' self-efficacy in the low group given CPA and conventional guidance. This finding gave birth to a strategy of developing self-efficacy in elementary schools using the CPA approach, especially the use of concrete objects around students through mentoring activities in schools, considering that self-efficacy makes it easy to solve problems especially when it comes to students with low initial abilities.

Concrete-Pictorial-Abstract Approach on Student's Motivation and Problem Solving Performance in Algebra

This study aims to: 1) find out whether problem-solving performance in students who are subjected to the CPA approach is better than problem-solving performance in students who are subjected to conventional approaches, 2) find out whether learning motivation in students who are subjected to the CPA approach is better than learning motivation in students who are subjected to conventional approaches. The study was conducted on 7th-grade junior high school students in Purworejo Regency. This study was an experimental study involving 91 students in the experimental class and 96 students in the control class. The research instrument used observation sheets of student learning motivation and tests consisting of 20 multiple choice test items and 5 essay test items. The data analysis technique uses a paired sample T-test to see the improvement of problem-solving performance and independent sample T-test to see the difference in the influence of the CPA Approach with the conventional approach. The results showed that: 1) problem-solving performance in students who are subjected to the CPA approach is better than problem-solving performance in students who are subjected to conventional approaches, 2) motivation to learn in students who are subjected to the CPA approach is better than learning motivation in students who are subjected to conventional approaches. The results also show that the CPA Approach can encourage students to solve problems with nonstandard procedures.

Developing adaptive political capabilities for “difficult” political host markets

MNEs often follow an engaged CPA approach in developed host markets, whereby they deploy political capabilities to participate actively in governments to influence political affairs. While some “di...

Implementing the Singapore Mathematics Curriculum in South Africa: Experiences of Foundation Phase Teachers

This paper reports on the findings from individual interviews and focus group discussions involving six teachers implementing the Singapore Mathematics Curriculum (SMC) in the Foundation Phase (Grade R to Grade 3) in a school in South Africa. The interviews presented an opportunity to explore teachers’ experiences with their attempts to use the SMC approach in their classrooms. By the same token, it highlighted the challenges faced by the teachers as they implemented the curriculum, and informed recommendations for the effective implementation of the Singapore mathematics curriculum in South Africa. The SMC identifies problem solving as central to mathematics learning. It defines problem solving as the acquisition and application of mathematics concepts and skills in a wide range of situations, including non-routine, open-ended and real-world problems. Furthermore, the textbook activities are built on a progression from Concrete experience (through the use of manipulatives), to a Pictorial stage (in which learners draw models) and finally to the level (this is known as the CPA approach). This sequence allows learners to gain a concrete understanding of basic mathematical concepts and relationships before they start working at the abstract level. The teachers identified the following features of the SMC and the textbooks as having a positive impact on implementation: the teachers’ guides are user-friendly; the various representations of mathematical concepts, and the connections made between various topics in the Singapore textbooks, supported conceptual understanding; the CPA approach fostered deeper understanding of mathematics and was effective when teaching learners who have special needs and a language barrier; the Singapore framework has significantly fewer topics and follows a spiral organisation in which one layer of content is built on the next; and the use of the manipulatives offered visual and tactile stimulation for the learners and helped improve learning. One of the key challenges identified by the teachers was that they struggled to implement a problem-solving approach and that the learners struggled when engaged in problem-solving activities. The learners also found the bar model drawing challenging. The findings also highlight the problems associated with implementing the SMC simultaneously in all grades and advocate a grade-by-grade implementation strategy.

Performance Assessment of Model Predictive Control in an Anaerobic-Anoxic-Oxic Process

A cascade model predictive control (MPC) strategy is proposed to improve the control performance of the combined biological phosphorus and nitrogen removal in the anaerobic-anoxic-oxic (AAO) process. Owning the features of determining the capability of the current controller and locating the best achievable control performance, the control performance assessment technique (CPA) is used to determine the optimal tuning parameters of the cascade MPC controller. The plant performance of the proposed cascade controller is superior to the conventional decentralized controller in the AAO process. An improved performance of the suggested cascade MPC controller was obtained by using the CPA approach.

The Fe–Cr system: atomistic modelling of thermodynamics and kinetics of phase transformations

To understand the behaviour of irradiated defects and kinetic pathways of micro-structural evolution in Fe–Cr alloys, we use a combination of density functional theory with statistical approaches involving cluster expansions and Monte Carlo simulations. A lowest negative mixing enthalpy is found at 6.25% Cr that is consistent with our DFT prediction of an ordered Fe 15Cr structure. At 50% Cr, it is found that the predicted enthalpy of formation is 4 times smaller than that calculated by the CPA approach. Thermodynamic and precipitation properties are then discussed in term of segregation between the Fe 15Cr and α ′ -Cr phases and of vacancy-mediated kMC simulation. To cite this article: D. Nguyen-Manh et al., C. R. Physique 9 (2008).

Single-particle spectrum for a model of fermions interacting with two-level local excitations on a lattice: A dynamical CPA approach

The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Green's function is calculated in a single-site dynamical coherent potential approximation which is equivalent to DMFT. The picture of one-electron density of states is obtained for various values of the tunnel splitting and coupling between the electron and two-level system. The occurrence of a band splitting with increase of the coupling is demonstrated.

Transport properties of random media: An energy-density CPA approach.

We present an approach for efficient, accurate calculations of the transport properties of random media. It is based on the principle that the wave energy density should be uniform when averaged over length scales larger than the size of the scatterers. This method captures the effects of the resonant scattering of the individual scatterer exactly, and by using a coated sphere as the basic scattering unit, multiple scattering contributions may be incorporated in a mean-field sense. Its application to both ``scalar'' and ``vector'' classical waves gives exact results in the long-wavelength limit as well as excellent agreement with experiment for the mean free path, transport velocity, and the diffusion coefficient for finite frequencies. Furthermore, it qualitatively and quantitatively agrees with experiment for all densities of scatterers and contains no adjustable parameter. This approach is of general use and can be easily extended to treat different types of wave propagation in random media. \textcopyright{} 1996 The American Physical Society.

Frequency-dependent conductivity of polyacetylene

Abstract The finite-temperature frequency-dependent conductivity of a polymer chain such as trans-polyacetylene has been calculated using a two-band tight-binding model. A collective mode in the dielectric response gives rise to energy absorption below the interband threshold even when no account is taken of possible soliton modes. The effect of impurities on this mode has been included phenomenologically by introducing a collision time. The effect of impurities on the density of states has been studied with diagram techniques and the CPA approach. The contributions of these effects to the optical and electron energy loss spectra of trans-polyacetylene are discussed.

CPA approach for randomly diluted anisotropic ferromagnets: para-spin-flop critical field

The authors have extended the coherent potential approximation to describe linear spin wave in diluted uniaxial ferromagnets with random interactions in both exchange and single-ion anisotropy. The local anisotropy field in a given magnetic site is assumed to be dependent on the magnetic occupation of neighbouring sites (short-range-order effects) as well as on the magnetic concentration (long-range part). The effective medium is defined in terms of two coherent parameters which are self-consistently determined by requiring that the average T matrix arising from a pair of nearest-neighbour sites must be zero. The theory has been applied to investigate the behaviour of the critical field separating the paramagnetic (PM) and the 'spin-flop' (SF) phases, as a function of dilution in the SC and BCC lattices. The concentration dependence of the PM to SF critical field is found as a function of a local anisotropy parameter and of the relative size of the anisotropy field in the pure (undiluted) magnetic system.

A CPA approach for studying a rare-earth or actinide impurity in a disordered transition host

Two theoretical approaches using the CPA have been developed to describe either the magnetism of ternary alloys with an actinide impurity such as PdTh Pu or the change of valence in Sm 1− x Y x S alloys

Remarks on strongly correlated disordered cpa alloys

Strongly correlated disordered metallic alloys are discussed, within Roth's linerization method. We show that the inclusion of the complete Roth's band shift introduce a correlation-induced off-diagonal disorder, which may be treated within the extended CPA approach.

Generalized CPA approach to the disordered Heisenberg ferromagnet

A ferromagnetic binary alloy is considered where each component has spin SA, SB and concentration XA, XB=1-XA, respectively. The interaction is given by the Heisenberg hamiltonian with exchange constants Jalpha beta between nearest-neighbour spins Salpha , Sbeta ( alpha , beta =A or B). It is shown that neglecting fluctuations in the static field seen by a spin SA (SB), generalized CPA equations can be written for the configurational average matrix Gij, with components Gijalpha beta . The formalism is symmetric in both components and valid for arbitrary values of the exchange constants and spins. In the general case it is expected to be good only for intermediate values of the concentrations, because it fails to reproduce the known exact results in the dilute limit Xalpha <<1( alpha =A or B) due to the approximate treatment of the local field that suppresses the p and d modes and modifies the energy of the s modes. However, it is shown that the theory reproduces the exact results when the values of the impurity and host spins are restricted by the condition (Salpha Jalpha alpha /Salpha Jalpha alpha )=1, where alpha =A or B if alpha =B or A.