Design, analysis and reformulation of a didactic sequence for teaching the special theory of relativity in high school

Otero, María Rita; Arlego, Marcelo; Prodanoff, Fabiana

doi:10.1590/S1806-11173731891

Acessibilidade / Reportar erro

Brasil

Revista Brasileira de Ensino de Física

Español English

Brasil

Español English

sumário « anterior atual seguinte »

Sumário

Pesquisa em Ensino de Física • Rev. Bras. Ens. Fis. 37 (3) • Sept 2015 • https://doi.org/10.1590/S1806-11173731891 copy

Design, analysis and reformulation of a didactic sequence for teaching the special theory of relativity in high school

(Proposta, análise e reformulação de uma sequência didática para o ensino da teoria da relatividade especial no Nível Médio)

Authorship SCIMAGO INSTITUTIONS RANKINGS

In this work, we design, implement and analyze a didactic sequence for the teaching of the basic topics of special relativity theory in high school. The sequence proposes a series of situations, specially designed to allow the emergence of the central aspects of special relativity. The conceptualization process is investigated from the point of view of the theory of conceptual fields of Vergnaud. By means of a careful analysis of classroom student productions we detect the key theorems-in-action they use, evidencing that most of conceptual errors are of pre-relativistic nature. This leads us to a reformulation of the sequence, which promotes the conceptualization of Galilean relativity and the principles of the special relativity. This previous step aims at bringing to students a firm basis to address the more complex aspects of the subject.

Keywords:
physics didactics; special relativity; theory of conceptual fields; high school teaching

Theorems in action related to the principle of relativity identified in S4
The pendulum accompanies the motion	The pendulum moving with constant speed is the same that at rest	If the pendulum moves with constant speed, it does not move respect to me
38	41	23

Theorems in action related to the principle of relativity identified in S5
I only realize if the train stops or turns	I do not distinguish if the train is at rest or moves with constant speed
33	14

Observer inside the trailer
Rubber bullets		Beams of Light
They arrive together	It comes first the one that is going to behind	It comes first the beam of light that is going to behind	Both beams come together
15	27	2	37

Observer outside the trailer
Rubber bullets		Beams of Light
They arrive together	It comes first the one that is going to behind	Both beams come together
16	21	36

Observer inside the trailer			Observer outside the trailer
$V_{t} (m/s)$	$υ_{b r} (m/s)$	$υ_{b l} (m/s)$	$υ_{b r} (m/s)$	$υ_{b l} (m/s)$	$V_{t} (m/s)$


	$V_{b}$	$- V_{b}$	$V_{t} + V_{b}$	$V_{t} - V_{b}$	$V_{t}$

Observer on the trailer		Observer on the road
Left	Right	Left	Right
$x_{w l} = - L$	$x_{w r} = L$	$x_{w l} = - L + v_{c} t_{l}$	$x_{w r} = L + v_{t} t_{r}$
$x_{b l} = - υ_{b} t_{l}$	$x_{b r} = υ_{b} t_{r}$	$x_{b l} = (υ_{t} - υ_{b}) t_{l}$	$x_{b r} = (υ_{t} + υ_{b}) t_{r}$
$x_{w l} = x_{b l}$	$x_{wr} = x_{br}$	$x_{w l} = x_{b l}$	$x_{w r} = x_{b r}$
		$- L + υ_{t} t_{l} = (υ_{t} - υ_{b}) t_{l}$	$L + υ_{t} t_{r} = (υ_{t} + υ_{b}) t_{r}$
		$- L + υ_{t} t_{l} = υ_{t} t_{l} - υ_{b} t_{l}$	$L + υ_{t} t_{r} = υ_{t} t_{r} + υ_{b} t_{r}$
		$- L = - υ_{b} t_{l}$	$L = υ_{b} t_{r}$
$t_{l} = \frac{- L}{- υ_{b}} = \frac{L}{υ_{b}}$	$t_{r} = \frac{L}{υ_{b}}$	$t_{l} = \frac{- L}{- υ_{b}} = \frac{L}{υ_{b}}$	$t_{r} = \frac{L}{υ_{b}}$

Observer inside the trailer			Observer outside the trailer
$V_{t}$	$V_{L l}$	$V_{L r}$	$V_{t}$	$V_{L l}$	$V_{L r}$

Observer inside the trailer			Observer outside the trailer
Left	Right	Left	Right
$x_{w l} = - L_{0}$	$x_{w r} = L_{0}$	$x_{w l} = - L + v_{t} t_{l}$	$x_{w r} = L + v_{t} t_{r}$
$x_{L l} = - c t_{l}$	$x_{L r} = c t_{r}$	$x_{L l} = - c t_{l}$	$x_{L r} = c t_{r}$
$x_{w l} = x_{L l}$	$x_{w r} = x_{L r}$	$x_{w l} = x_{L l}$	$x_{w r} = x_{L r}$
		$- L + v_{t} t_{l} = - c t_{l}$	$L + v_{t} t_{r} = c t_{r}$
			$L = (c - v_{t}) t_{r}$
$t_{l} = \frac{- L_{0}}{- c} = \frac{L_{0}}{c}$	$t_{r} = \frac{L_{0}}{c}$	$t_{l} = \frac{- L}{- (c + v_{t})} = \frac{L}{(c + v_{t})}$	$t_{r} = \frac{L}{(c - v_{t})}$

Sociedade Brasileira de Física Caixa Postal 66328, 05389-970 São Paulo SP - Brazil - São Paulo - SP - Brazil
E-mail: marcio@sbfisica.org.br

Acompanhe os números deste periódico no seu leitor de RSS

[1] 1 E-mail: rotero@exa.unicen.edu.ar.