Effects of integrating a brain-based teaching approach with GeoGebra on problem-solving abilities

B-Geo Module is a module that has been developed using the brain-based teaching approach (BBTA) integrated with GeoGebra Software (B-Geo Module) is expected to help students’ problem-solving abilities of the topic of Differentiation. The BBTA is a strategy that uses brain-based learning techniques. It was created to be consistent with the individual brain's tendencies and ideal functions in order to ensure that pupils can learn efficiently. Therefore, the proposed of this study is to explore the possible effects of the B-Geo Module on problem-solving abilities for the Topic of Differentiation. A quasi-design of pre-test and post-test experiments was utilized in this study, which included 118 form 4 pupils from rural secondary schools. For school selection, the researchers employed cluster sampling approaches, and for sample selection, they used an intact group. The schools were separated into two groups: experimental and control. The experimental group used the B-Geo Module, while the control group used traditional ICT modules. The instrument used was the Problem-Solving Test of Differentiation. The results of the data analysis showed the effectiveness of the B-Geo Module in the problem-solving abilities in the topic of Differentiation among rural secondary school pupils. The multimedia such as GeoGebra can be the tools for BBTA to facilitate Additional Mathematics teachers in secondary schools to help students solve problem and improved their learning in the topic of Differentiation

On the derivation of second order variable step variable order block backward differentiation formulae for solving stiff ODEs

In this paper, we derive a second order Variable Step Variable Order Block Backward Differentiation Formulae (VSVO-BBDF (2)). This method pertains to the study of solving stiff Ordinary Differential Equations (ODEs) of second order (y"). The pertinent findings in term of total number of steps, accuracy and computational time are displayed and discussed through distinct tables

An efficient solver for solving chemical kinetic equations using higher order block backward differentiation formula

In this paper, an efficient solver known as higher order block backward differentiation formula (HOBBDF) is applied to chemical kinetic equations. In order to prove the applicability of this higher order solver, the chemical kinetic ordinary differential equations (ODEs) are numerically tested. Then, a comparison of performance between HOBBDF and two ODE solvers in MATLAB, particularly ode15s and ode23, are made. Evidently, it is proven that HOBBDF method outperforms ODE solvers in terms of accuracy. Therefore, HOBBDF method can also be applied to solve chemical kinetic equations

Formulation of modified variable step block backward differentiation formulae for solving stiff ordinary differential equations

Objectives: A modified variable step block backward differentiation formulae (MVS-BBDF) method is introduced in this paper as another alternative way for solving ordinary differential equations (ODEs). Methods: We demonstrated the detailed formulation of the corrector formulae for MVS-BBDF method which is carried out using Maple software. Then, to validate the performance of the introduced method, we applied it to stiff ODEs problem. Findings: The performance of the method in terms of maximum error and number of total steps taken during the computation are compared with the performance of ode15s and ode23s solver in MATLAB. Consequently, the efficiency of MVS-BBDF shows that it is able to outperform both Matlab’s ODE solver since it produces better accuracy and manages to reduce the number of total step

Variable step variable order block backward differentiation formulae for solving stiff ordinary differential equations

Block Backward Differentiation Formulae (BBDF) method with variable step variable order approach (VSVO) for solving stiff Ordinary Differential Equations (ODEs) is described in this thesis. The research on Variable Step Variable Order Block Backward Differentiation Formulae (VSVO-BBDF) method is divided into two parts where the first part attempts to solve first order stiff ODEs, whereby second order stiff ODEs are considered subsequently. Initially, the computation of Dth-order variable step BBDF (VS-BBDF) method of order three up to five is presented. The detailed algorithms of VSVO-BBDF method is discussed to show the crucial parts of the order and stepsize selections. Prior to getting the numerical results, the MATLAB’s suite of ODEs solvers namely ode15s and ode23s is applied for the numerical comparison purposes. Meanwhile, the consistency and zero stability properties that lead to the convergence of the method are also discussed. Finally, the implementation of the VSVO-BBDF(2) method for the solution of second order stiff ODEs is analyzed. The derivation of the method of order two up to four, as well as the strategies in choosing the order and stepsize are elaborated. Similarly, numerical results are obtained after a fair comparison is made between VSVO-BBDF(2) and stiff ODEs solvers in MATLAB. In conclusion, the results display positive trends in reducing the total number of steps and increasing the accuracy of the approximations. The results also show that VSVO-BBDF method reduces the time execution for solving first and second order stiff ODEs as compared to MATLAB’s ODEs solvers. Therefore, these methods serve the purpose of significant alternatives for solving stiff ODEs

Solving directly higher order ordinary differential equations by using variable order block backward differentiation formulae

Variable order block backward differentiation formulae (VOHOBBDF) method is employed for treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) of higher order stiff ODEs directly. BBDF method is symmetrical to BDF method but it has the advantage of producing more than one solutions simultaneously. Order three, four, and five of VOHOBBDF are developed and implemented as a single code by applying adaptive order approach to enhance the computational efficiency. This approach enables the selection of the least computed LTE among the three orders of VOHOBBDF and switch the code to the method that produces the least LTE for the next step. A few numerical experiments on the focused problem were performed to investigate the numerical efficiency of implementing VOHOBBDF methods in a single code. The analysis of the experimental results reveals the numerical efficiency of this approach as it yielded better performances with less computational effort when compared with built-in stiff Matlab codes. The superior performances demonstrated by the application of adaptive orders selection in a single code thus indicate its reliability as a direct solver for higher order stiff ODEs

Effects of Brain-Based Teaching Approach Integrated with GeoGebra (BGeo Module) on Students’ Conceptual Understanding

The Brain-Based Teaching Approach is a strategy that implements methods from a brain-based learning (BBL) model. This approach was designed to be compatible with the inclinations and optimal functions of the individual brain to ensure that students can learn effectively. The module uses the Brain-Based Teaching Approach integrated with GeoGebra Software (B-Geo Module) to help students’ conceptual understanding of the topic of differentiation. Therefore, this study aims to explore the possible effects of the Brain-Based Teaching Approach with the integration of GeoGebra Software on conceptual understanding of the topic of differentiation in rural secondary schools in Malaysia. This study used a quasidesign of pre-test and post-test experiments involving 118 form 4 students from rural secondary schools. The researchers used cluster sampling techniques for school selection and intact group for sample selection. The school selection was divided into two groups, namely, the control group using conventional information and communication technology (ICT) modules and the experimental group using the B-Geo Module. The instrument used was the Conceptual Understanding Test of Differentiation. The results of the data analysis show that the conceptual understanding of the topic of differentiation amongst rural secondary school students increased when using the Brain-Based Teaching Approach with the integration of GeoGebra Software

Solving stiff ordinary differential equations using extended block backward differentiation formulae.

A comprehensive research on the existing Block Backward Differentiation Formulae (BBDF) was done. Based on the suitability in solving stiff ordinary differential equations (ODEs), BBDF of order 3 up 5 is collected using simplified strategy in controlling the step size and order of the method. Thus, Extended Block Backward Differentiation Formulae (EBBDF) is derived with the intention of optimizing the performance in terms of precision and computation time. The accuracy of the method are investigated using linear and non linear stiff initial value problems and its performance is compared with MATLAB’s suite of ODEs solvers namely ode15s and ode23s

A quantitative comparison of numerical method for solving stiff ordinary differential equations

We derive a variable step of the implicit block methods based on the backward differentiation formulae (BDF) for solving stiff initial value problems (IVPs). A simplified strategy in controlling the step size is proposed with the aim of optimizing the performance in terms of precision and computation time. The numerical results obtained support the enhancement of the method proposed as compared to MATLAB's suite of ordinary differential equations (ODEs) solvers, namely, ode15s and ode23s