LO.2: Relate the microscopic electron current model, which is related to the electric
field magnitude in the conductor (i ¼ n A v d ¼ n A u E ¼ n A u ΔV/L ), with the
conventional current (I ¼ ΔQ/Δt). Knowing how to use the magnitudes of each
model in the appropriate context and field of validity (i ¼ n A u E; I ¼ ΔQ/Δt ¼ n
q A v d ¼ n q A u E).
Secondly, here is often a need to find an alternative to a purely macroscopic
description. We are often left at the macroscopic scale, with explanations such as
“this law, or this other law, tells us that things have to be this way.” These types of
explanations are insufficient to satisfy students, especially when alternative conceptions appear on the way of learning. So, it will be necessary to define the causal
mechanism that generates the electric field inside the wire:
LO.3: Knowing and applying the model of Gradient of Surface Charges (GSC) in
relation to the role played by the battery in the production of the distribution of
surface charges in the wire. This distribution of surface charges (GCS) produces
an electric field inside the wire and consequently, produces a potential difference
in the different parts of the circuit.
Thirdly, it is necessary to know how to relate the electrical current microscopic
model with the measurements of the ammeters and voltmeters in the different parts
of the circuit, for an understanding of the context in which the different laws in a DC
circuit are applied. In consequence:
LO.4: Know how to explain the conservation of charge and energy (Kirchhoff’s
laws) in a simple DC circuit, both at the microscopic level (the electric field that
drives the electron sea) and macroscopic (the potential difference between the
parts of the circuit). This implies knowing how to relate the conventional current,
the electric field inside the wire and the potential difference in different parts of
the circuit (ΔV ¼ E L; I ¼ ΔV/R; i ¼ n A u ΔV/L; ε ¼ ΔV + rI).
Once the learning indicators have been defined, it is necessary to identify the
learning demands. That is, it is necessary to know the magnitude of the gap between
the defined learning objectives and the learning difficulties that students usually have
in those objectives. This allows the teachers to get an idea of how big or small the
cognitive demand is. This will lead to justify the greater or lesser number of activities
to work the learning indicator and the process of construction of the concept,
procedure or theory. At the beginning of this section, a summary of previous studies
showing the learning difficulties on the subject has been made. However, some of
the defined indicators have not been specifically investigated and, therefore, it was
necessary to carry out a study of learning difficulties.
In a previous study (Goikoetxea 2017), we designed a questionnaire with an
emphasis on explanations. We gave 120 students at the University of the Basque
Country (Spain) a questionnaire after they had studied the topic in class. We describe
here, as an example, one of the questions completed by the students and summarize
the results. In the second question Q2 (see Fig. 13.1), the difficulty of students’
understanding on the concept of potential difference in electrostatic to electrokinetic
13 Designing Teaching Learning Sequences Based on Design-Based Research
169
field magnitude in the conductor (i ¼ n A v d ¼ n A u E ¼ n A u ΔV/L ), with the
conventional current (I ¼ ΔQ/Δt). Knowing how to use the magnitudes of each
model in the appropriate context and field of validity (i ¼ n A u E; I ¼ ΔQ/Δt ¼ n
q A v d ¼ n q A u E).
Secondly, here is often a need to find an alternative to a purely macroscopic
description. We are often left at the macroscopic scale, with explanations such as
“this law, or this other law, tells us that things have to be this way.” These types of
explanations are insufficient to satisfy students, especially when alternative conceptions appear on the way of learning. So, it will be necessary to define the causal
mechanism that generates the electric field inside the wire:
LO.3: Knowing and applying the model of Gradient of Surface Charges (GSC) in
relation to the role played by the battery in the production of the distribution of
surface charges in the wire. This distribution of surface charges (GCS) produces
an electric field inside the wire and consequently, produces a potential difference
in the different parts of the circuit.
Thirdly, it is necessary to know how to relate the electrical current microscopic
model with the measurements of the ammeters and voltmeters in the different parts
of the circuit, for an understanding of the context in which the different laws in a DC
circuit are applied. In consequence:
LO.4: Know how to explain the conservation of charge and energy (Kirchhoff’s
laws) in a simple DC circuit, both at the microscopic level (the electric field that
drives the electron sea) and macroscopic (the potential difference between the
parts of the circuit). This implies knowing how to relate the conventional current,
the electric field inside the wire and the potential difference in different parts of
the circuit (ΔV ¼ E L; I ¼ ΔV/R; i ¼ n A u ΔV/L; ε ¼ ΔV + rI).
Once the learning indicators have been defined, it is necessary to identify the
learning demands. That is, it is necessary to know the magnitude of the gap between
the defined learning objectives and the learning difficulties that students usually have
in those objectives. This allows the teachers to get an idea of how big or small the
cognitive demand is. This will lead to justify the greater or lesser number of activities
to work the learning indicator and the process of construction of the concept,
procedure or theory. At the beginning of this section, a summary of previous studies
showing the learning difficulties on the subject has been made. However, some of
the defined indicators have not been specifically investigated and, therefore, it was
necessary to carry out a study of learning difficulties.
In a previous study (Goikoetxea 2017), we designed a questionnaire with an
emphasis on explanations. We gave 120 students at the University of the Basque
Country (Spain) a questionnaire after they had studied the topic in class. We describe
here, as an example, one of the questions completed by the students and summarize
the results. In the second question Q2 (see Fig. 13.1), the difficulty of students’
understanding on the concept of potential difference in electrostatic to electrokinetic
13 Designing Teaching Learning Sequences Based on Design-Based Research
169