Proving Abstract Algebra Skills with Problem-Based Learning Integrated with Videos and Worksheets

Mairing, Jackson Pasini

doi:10.1590/1980-4415v35n70a20

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Article • Bolema 35 (70) • Aug 2021 • https://doi.org/10.1590/1980-4415v35n70a20 copy

Proving Abstract Algebra Skills with Problem-Based Learning Integrated with Videos and Worksheets

Capacidad Demostrativa de Algebra Abstracta con Aprendizaje Basado en Problemas Integradopor Videos y Hojas de Trabajo

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Previous research showed students faced difficulties in solving the given problems in the Abstract Algebra course. The research aimed to describe the effect of the method of problem-based learning integrated with videos and worksheets to improve the proving skills of mathematics education students in one of the universities in Central Kalimantan, Indonesia. The researcher developed and uploaded the videos on YouTube. The research design was an experimental study. The researcher implemented the method in an experimental class. The control class students learned by using the usual method of the past three years that emphasized acquiring the Abstract Algebra concepts. The researcher selected the experimental class randomly. The numbers of students in the experimental and control classes were 32 and 28, respectively. The students of both classes solved the same problems in the post-test at end of the implementation. The post-test contained five problems to prove. The research results showed that the transactive reasoning activities in the experimental class enabled the students to prove at an appropriate abstraction level. The students’ scores in the Abstract Algebra for the experimental class were greater than those in the control class. Therefore, the method affected students’ ability to solve Abstract Algebra problems.

Keywords:
Abstract algebra; Problems; Problem-based learning; Videos; Worksheets; YouTube

Score	Description
0	The student does not write anything in the solution sheet.
1	The student writes a solution, but the means of proving is inappropriate or non-understandable.
2	The student writes a solution, the means of proving is not appropriate, but the solution shows some understanding of the problem or the Abstract Algebra concepts.
3	The student writes a solution, the means is appropriate, but the implementation is not fully correct.
4	The solution is correct

Variable	Groups	N	Mean	StDev	Variance	Minimum	Median	Maximum
Initial Abilities	Control	28	67.20	9.28	86.15	43.50	68.44	83.00
(scale of 0-100)	Experiment	32	67.47	6.00	36.02	56.06	67.74	83.54
Abstract Algebra	Control	28	6.21	1.97	3.88	5.00	5.00	12.00
(scale of 0-20)	Experiment	32	8.56	4.52	20.38	5.00	6.00	20.00

	DF	Adj SS	Adj MS	F-Value	P-Value
Initial Abilities	1	172.42	172.418	17.42	0.000
Groups	1	78.08	78.084	7.89	0.007
Error	57	564.17	9.898
Lack-of-Fit	55	539.67	9.812	0.80	0.705
Pure Error	2	24.50	12.250
Total	59	818.93

Groups	N	Mean	Grouping
Experiment	32	8,53395	A
Control	28	6,24691	B

UNESP - Universidade Estadual Paulista, Pró-Reitoria de Pesquisa, Programa de Pós-Graduação em Educação Matemática Avenida 24-A, 1515, Caixa Postal 178, 13506-900 Rio Claro - SP Brasil - Rio Claro - SP - Brazil
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[1] E-mail: jp-mairing@math.upr.ac.id.

H₁₀: β = 0	(There was no linear relationship between the initial abilities and the students’ scores of Abstract Algebra)
H₁₁: β ≠ 0	(There was a linear relationship between the initial abilities and the students’ scores of Abstract Algebra)

H₂₀: τ₀ = τ₁ = 0	(There was no effect of the different treatments on the students’ scores of Abstract Algebra)
H₂₁: at least a i that τ_i ≠ 0	(There was an effect of the different treatments on the students’ scores of Abstract Algebra)

In video 19:	“Can we proof H ≠ 0 by showing that H has an element but it is not the identity?”
In video 20:	“Can we prove that H is a group only by showing that H ⊆ G, because I think, based on the second axiom (associative axiom) we can prove that H is group since H ⊆ G and G is a group?”