How to develop modelling competence for Vietnamese students

Developing modeling competence is an educational objective in many countries such as “SEP 2: Developing and Using Models” in Next Generation Science Standards (NGSS). In Vietnam, the new physics-education curriculum has clearly defined the key learning outcomes, including modeling-competence elements as well. Experiencing modelling cycle is an effective way to develop modelling competence for students. Our recent work studies which tool is suitable for students and how to integrate this tool in modelling activities. This paper presents the use of Coach 7 modelling software to investigate common physics phenomenon of oscillations, shows feasibility and effectiveness of these activities via tryout.


Introduction
Development of modeling competence is an educational goal in many countries, for example "SEP 2: Developing and Using Models" in Next Generation Science Standards (NGSS).In Vietnam, the new physics-education curriculum has clearly defined the key learning outcomes which include modelingcompetence elements such as understanding model/modelling, developing model, and using model in reasoning and predicting real-life phenomenon (Table 1).Modeling cycle is a cognitive method used by scientists in many fields to describe, explain, and predict about systems, phenomena, complex process.Experiencing modelling cycle is an effective way to develop modelling competence in students.Currently, edtech researchers have developed modeling software to support the process of "modeling" phenomena and processes in real life.In Which, teachers and students can assign parameters and variables to physical quantities and constants; establish algebraic relations between parameters based on physics laws.The software helps to solve differential equations automatically by numerical method.The model's results are quickly displayed on data tables, graphs and verified by doing experiments connected to computer (desktop, laptop, tablet or smartphone).
Experiencing modelling cycle is an effective way to develop modelling competence for students.This study focus on which tool is suitable for Vietnamese students and how to integrate this tool in modelling activities in schools.Doerr and Pratt (2008) pointed out the collective epistemological perspective is that modelling is driven by the need to describe, explain, and/or predict some particular phenomena of interest to the modeller.We can be mapped onto a model world based on elements from the real world of the experienced phenomena are selected and structured.In other words, the model is separate from the world to be modelled.In this view, a model is a constructed system of objects, relationships, and rules whose behavior resembles that of some other system in the real world of phenomena.The rules of the model world come in our type of modelling from mathematics and physics.
Fig. 1 The cyclic nature of the modeling process in a nutshell (Heck, 2008) Based on a scientific perspective, modelling begins with asking a question about a situation in a certain context; this question is defined and specified to a problem definition that guides further model development; learning to use a modelling tool and to represent data and results in tables and graphs.The problem definition is visualized through a schematic drawing or a concept map; relevant variables in the system and their relations are identified.Data are collected and processed, preferably on the basis of own research, like an experiment or research of a phenomenon via a simulation or an online database.Translation of the conceptual model in mathematical terms; the problem is analysed and reduced; relevant equations are derived or graphically represented in an appropriate modelling environment.
Solution of the mathematical model and generation of outcomes.The results are computed with appropriate initial values of variables and parameters in the model.One iteratively tests whether the model works as meant.Retranslation of model outcomes to the problem situation; investigation whether the model fits the data and can reasonably explain observations; if needed, the accuracy of the model is determined, taking into account the uncertainties in the model parameters and numerical approximations.Reflection on the model and the modelling process; checking whether the original problem has indeed been solved and which insight in the explored system or phenomenon has been gained; what are limitations of the model and what extensions can be thought of?If desired, the cycle is repeated until the model gives a satisfying solution to the problem posed.
In general, modelling is describing a situation in reality for solving a problem.Modelling includes a way of working and thinking.It is an iterative process in which mathematical, scientific and technical knowledge is applied to describe new situations.This includes determining nature of the phenomenon, the real-life process, deploying mathematical and computational tools in creating, running, revising models and using model to explain and predict phenomenon.The approach depends on the objective, the question, or the problem to be solved.The objective may be a better understanding of the problem situation itself, but also the development of new conceptual knowledge.Modern computer technology and advanced digital applications play a central role in complex problems.Modelling used to study for a long tradition in physics, but in recent years model-based research is more and more applied in various fields such as climate and ecological models.
This research focus on graphical modelling created by modeling software, which is also rooted in theories of cognition and instructional design, and in research on systems thinking.According to this thinking, student can perceive a system as something consisting of many elements that interact with each other, understand that a change of one element in a system may lead to changes in the whole system to explain the system at the collective level.System thinkers claim that this approach promotes and supports the causal reasoning skills of students.From a mathematical perspective, the elements of a system are variables that are related either by semi quantitative relationships (e.g. as variable t increases, variable x decreases) or by quantitative relationships, i.e. mathematical equations (e.g.difference equations and direct relations).In a graphical model1 , the variables and relationships between variables are visually represented as a system of icons in a diagram (Van Buuren, Heck, Ellermeijer, 2016).
The Coach program automatically generates the corresponding difference equations based on the graphical model.However, the equations for the auxiliary variables and flow variables must be entered manually.Because the number of building blocks is limited, it is easier for students to construct a model.It is also easier to see at a glance how various variables are interrelated.The state variables and the processes of change are clearly recognizable, and for each quantity it is indicated what it depends on.Based on building blocks, students can quickly get started and after a short learning time they can even construct and interpret relatively advanced models in some cases.On the other hand, it also appears that a group of students does not see through the formal meaning of the model symbols, partly because the metaphor of stock-and-flows offers an insufficient conceptual basis.It is therefore important that the relationship between the equations and the corresponding graphical structures is made clear in the initial phase.

Integrating of Coach in Modeling activities in schools
Consider friction, energy loss, and change of influential factors such as the oscillation of spring pendulum can be damped by fluid resistance.Regarding theoretical deduction, this consideration often yields to differential equations which school students cannot solve with their current mathematics knowledge.Modeling by Coach 7 (Ellermeijer, Tran, 2019) helps to investigate both mechanical and electrical oscillations.

Graphical modelling in mechanical oscillation
Objectives: Modeling oscillation of charge in the electric circuit.

Process:
An electric circuit consists of a capacitor with capacitance C, a coil with an inductance L attached resistance r (Fig. 2a, 2b).The capacitor discharges through the coil forming a current i.
If switch K turns from position 1 to 2, the capacitor will discharge through the coil.Initially the current increases causing induced electromotive force.This electromotive force opposes the discharge of the capacitor.
When the capacitor discharges all the charge, the induced current reaches the maximum value and recharges the capacitor, so the capacitor charged but in the opposite direction.This charging and discharging process is repeated continuously (Fig. 3).Based on the Kirchhoff's voltage law for this circuit, the voltage of capacitor will be: =  −  Creating graphical models: -Create state variables corresponding to charge q, current i. (3) Fig. 3 The changing of charge and current in electric circuit + Create and assign variable u = q/C, displaying the graph u (t).

Validating the models (Evaluating the descriptive functions of the model)
To evaluate the descriptive function of the model, it is necessary to compare the graph obtained by the model with the corresponding experimental graph.
-Choose an experimental graph after investigating the electrical oscillations.The constants related to the experimental oscillations are: r = 9.5 Ohm; L = 0.036 H; C = 10 -6 F.
-Adjust the constants L, C, r on the model (Fig. 5) to equal with the real values; The resulting graph of the model closely coincides with the experimental graph (Fig. 6).This approximation confirms the descriptive function of the model.

Investigating the electrical oscillation
Objectives: -Verify the law in changing of u(t) rule deduced by the theoretical model.

The experimental setup:
-Connect the voltage sensor in two ends of capacitors via data loggers and setting: sampling frequency 30,000 data/s; sampling time 0.01s.
-Turn the switch to the right (Fig. 7), then set the value of voltage to zero 0.

Carry out experiments:
-Charge the capacitor by turning the switch to the left, then turning back the switch to discharge.
-Display the u(t) graph in Coach 7 software.

Results:
The software records and displays the experimental graph of the damping oscillation.This experimental graph and the fit function of the graph has the form: where:  0 = 7.96 V, ω = 16804 s -1 ,  2 = 1696.The oscillation will be damped faster if the resistor of the coil is larger.

Phases of modelling method for teaching real-life phenomena
The modeling method is an approach in teaching Physics that can develop student's modeling competence, including the stages as shown in the following.In the first stage, students find out properties of real physical phenomena.Based on these features and known relationships, students create models.Through model operations, students can derive theoretical consequences.In order to validate the model, empirical data related to the phenomenon need to be collected.If the two results are not fit, the student needs to adjust the model; otherwise, students can conclude about the descriptive function of the model and use that model to describe and explain real phenomena.

Tryouts and discussions
Based on the modelling cycle (Fig. 9), the modelling method for teaching real-life phenomena with modelling tool like Coach is developed.This method is elaborated into modelling activities to investigate electrical oscillation in LC circuit and then tried out with 30 students in a gifted high school in Vietnam to evaluate if it can help to develop student's modeling competence.The list of assessment tools4 including test questionnaires, rubrics, test are used in the assessment process (Table 3).x a) Behaviour: "Identifying the nature of the phenomenon" According to the result of tests, the number of students filled correctly the words and phrases to describe the process of changing charge in the circuit accounted for a high percentage (87%), the remaining students got good points and average score due to the incorrect description (Table 4).
Based on the analysis of the students' answers in the worksheets, we see the same results, many groups of students (5/6 groups) are able to draw the oscillating circuit diagram.From that, we see that the behavioral indicator "Identifying the nature of phenomena and actual processes" was observed by most students with a high degree (level 3).The results of the questionnaire show that the number of students represents and determine correctly the initial values and the relationship between the quantities accounted for (33%), most of the remaining students lacked the relationship between the quantities (Fig. 17).
This behavioral indicator is also reflected via Rubric, creating the correct links between the quantities at the right time, corresponding to level 3 with few groups of students expressed (2/6 groups).The remaining groups of students is able to build and complete the model by the support of teachers and the sample model.
It indicates that the behavioral indicator "Creating models" is observed at a low level.
After analyzing the tests, most of students (77%) achieved the good points by selecting the right sampling frequency, display, analysis, fitting function to find the form of the q(t) graph.Some students are not able to analyze the functional form (Table 4).
The results by Rubrics also confirms the same thing, many groups of students (4/6 groups) run models at high-level (level 3) such as running the model in the first time and completed on time.So, the behavioral indicator "running models" is expressed in many students with a high degree (level 3).According to the results of tests: The number of students who can add the quantity "r" and change the values of the quantities to obtain the perfect model accounted for a high percentage (83%), (Table 4).
The results by the questionnaire also show that most of students (78%) can adjust the model by adding the resistor "r", changing the values of "L, C" according to the parameters of the model (Fig. 17 The results by Rubric also show that the behavioral indicator "Evaluating and adjusting the model" is expressed at a high level, specifically, many groups of students (5/6 groups) give accurate comments and perform additional tasks (Table 5).So, the behavioral indicator "Evaluating and adjusting the model" is expressed in most students with a high degree (level 3).e) Behaviour: "Using models to explain phenomena".
Based on the results of tests, a large number of students scored well in explaining loss of energy in electrical oscillations (73%).The remaining students scored lower for lacking in establishing the relationship between the heat energy on "r" and the other quantities (Table 4).
According to the responses in the questionnaire, many students (67%) were able to explain the loss of energy in the electrical oscillation.In detail, some students said that: "Add and display W(L), W(C), W(R), W, find the reduction of electrical and magnetic energy equal to wasted energy".(Fig. 17).
The results by Rubrics shows that many groups of students (3/6 groups) that add thermal, electrical, and magnetic energy variables to the electric oscillation to show that the wasted energy (Table 5).
So, the behavioral indicator "Using models to explain the real phenomena and processes" is observed in many students with a high level (level 3).

Conclusion
The school tryout showed that students can fulfil phases of modelling method.Modelling performance indicators: "Identifying the nature of the phenomenon, the real life process", "evaluating and revising models" were observed in most students, while other indicators were not yet.There need more modelling activities with Coach to develop in students modelling competence to larger extent.
In Vietnam, modelling cycles and ICT tools used to support in teaching are a new approach for both students and teachers.Therefore, integrating modelling activities with supporting of ICT tools such as Coach 7 in training course for teachers is a meaningful work contributing to design and build and operate learning activities based on modelling.In the future research, we will focus on solutions "How to help teachers in developing modeling competence of students based on modeling cycles with Coach 7 software.

2. 1 .
Measuring and modelling an electrical oscillation 2 a) Electric circuit b) Diagram of circuit c) Model of Damped oscillation

Fig. 2
Fig. 2 Damped oscillation of electric circuit -Create auxiliary variables corresponding to   , electromotive force e. -Create constants corresponding to inductance (L), resistance (r) and capacitance (C) (L = 3,6 mH, r = 9,5 Ω, C = 1 μF).-Set up the relation between variables, constants via connector, based on the physical relation.(1)+ Set up the equation (2) in variable . =   + Press the start button on the toolbar; the results are automatically displayed on the graph.

Fig. 4 Fig. 5
Fig. 4 Graphical model of the electrical oscillation and the corresponding result

Fig. 6
Fig. 6 Comparison the experimental and model results of the electrical oscillation

Fig. 8
Fig. 8 The damped oscillation of electric circuit

Fig. 10
Fig. 10 Teaching process in electrical oscillations based on the modeling approach

Fig. 11
Fig. 11 Analyzing the discharging and charging of capacitors

Fig. 17
Fig. 17 Behaviors in modeling competence based on the results of the questionnaire.

Table 2
Representing the relation of electrical oscillation in graphical model

Table 3
The assessment plan in teaching electrical oscillation

Table 4
Results of Tests related to modeling process in electrical oscillation

Table 5
Results of rubrics in teaching electrical oscillation