Introduction to Modeling Technology Enhanced Inquiry Based Science Education

Scientific Model A Model in science is a conceptual representation of a “real thing” - an object, phenomena, process or system. Its purpose is to explain how real things work and behave. Often in a model abstract and complex things are represented in a simplified way. A model allows to predict a behaviour in response to some change.

Scientific model Plays a crucial role in the practice of science and science education.

Computer Model Computer (numerical) model is a computer program that attempts to simulate a real-life system and to give an accurate prediction. Today used in every area of research and industry.

Computer Models in Science Education With software, specially designed for education, powerful but not too difficult to use. Students can: –Test hypothesis by running computer simulations. –Adapt and create models to make predictions. –Compare model data with experimental results.

Modeling Modeling is the process by which a model is constructed. Step1: Identify and define the real world problem Step 2: Decide the scope boundaries and purpose of the model Step 3: Create the (mathematical) modelStep 4: Test the modelStep 5: Evaluate the model The Real World “Models and modelling”, ASE, Hatfield

Modeling cycle Modeling Cycle by Blum & Leiß (2005), the cycle jumps between the reality and model (mathematical) world.

Dynamic Modeling Modeling of situations where quantities change over time. Relationships between variables are expressed by mathematical functions. The evolution of a system is computed step by step with a constant time step. Can be applied to a wide range of systems such as population systems, ecological systems, mechanical systems, chemical reactions, radioactive decay and many, many more.

System Dynamic Modeling in Coach Dynamic behavior is based on the principle of accumulation – flows accumulate in stocks (state variables in Coach). State variables are core elements of the model and change in time through physical Inflows and Outflows. Furthermore dependencies between variables determine the system behavior over time. These relations are made explicit in the form of mathematical relationships.

Graphical representation Graphical representation provide a visual overview of the model variables and their interactions. Model variables are represented by graphical symbols. Relationships are denoted as arrows between variables. After the graphical representation is drawn, mathematical relationships are specified as properties of the variables.

Equations representation Equations representation provides the set of equations of the underlying mathematical relations. The Graphical representation has a one-to-one connection to the Equations representation: each variable is described by a mathematical equation. State variables are represented by algebraic differential (or difference) equations.

Textual representation Textual representation provides a computer program that implements the iterative numerical solution of the differential equations. Three numerical integration methods are provided: Euler, 2 nd and 4 th order Runge-Kutta methods. Executing the model means executing this program and calculating values of model variables.

Model - Bathtub A simple bathtub model. The state variable Bathtub represents the amount of water in the bathtub. Inflow Fill represents a faucet that fills, outflow Drain represents a pipe that drains.

Bathtub improved Modifying the model to better simulate a real system – an improved Bathtub model. Now Drain depends on Bathtub, the more water in the bathtub the greater the rate of outflow.

Biology Trees A simple model for tree growth. Growth is limited by cutting trees.

Biology Predator – Prey model A predator-prey model. Upper diagram: the variation of the fox and hare populations vs. time. Lower diagram: Foxes vs. Hares.

Chemistry Non-reversible reactions Modelling the general non-reversible chemical reaction A  B. Note the use of the special Process variable controlled by the reaction - rate constant k.

Chemistry Reversible reactions Modelling the equilibrium reaction N 2 O 4 ↔ 2 NO 2. Note the use of two Process variables for the forward and backward reaction.

Physics Free fall Model of a free fall. A constant gravity force is acting on a falling body. The body falls with constant acceleration g.

Physics Parachute jumper Model of a parachute jump. The free fall model is extended with the air resistance force acting when the parachute is opened. The air resistance force depends on the velocity, and finally balances the gravity, resulting in a constant terminal speed.

Physics Cooling a cup of coffee Model of a cooling process. The heat loss of the coffee (Qc) to the surroundings is proportional to the difference in temperature of the coffee (T c ) and the temperature of surroundings (T 0 ).

Modeling and Measuring Models often follow experiments. Students build models of the phenomenon and compare results produced by the model with those collected during the experiment. When model and experiment diverge then the model needs to be modified to match as closely as possible with the experimental results. Both ways of looking at a physical phenomenon - theoretically by modeling as well as experimentally by measuring - profit from each other.

Physics Discharging a capacitor Comparing the model data with the experimental data.

Modeling is different than simulation! Any model when it is run with a particular set of data becomes a simulation. The model behind a simulation is usually invisible and inaccessible. Users are often not even aware of the limitations of the underlying model. By using a simulation students can solve problems, devise and test hypotheses. They are usually led to believe that the simulation behaves in a similar way to the real world.

Educational benefits Computer modeling is an important process in scientific research and therefore students should develop understanding of the process as well as acquiring modeling skills. Computer modeling allows to solve complex and realistic problems not just limited to ideal laboratory phenomena. Such realistic problems are normally too difficult to solve analytically at the school level.

Educational benefits Computer modeling encourages students to think, to discuss their ideas and to clarify their understanding. Graphical representation forces the students to engage in a qualitative analysis of the problem. The structure and the relevant quantities have to be defined. Theoretical assumptions become visualized by iconic representations.

Educational benefits Students can experiment with ideas. The model structure is easy to modify allowing trying different modeling ideas. The model results can be compared with experimental data. The model can be modified to match the data from the real experiment and the theoretical model.

Educational benefits Formulating the (difference) equations becomes the main tasks of students instead of solving them. Different model representations (graphical, equations and textual) can constrain interpretation, construct deeper understanding or complement each other.

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