Métodos y técnicas pedagógicas en educación nutricional
2. Marco Metodológico
2.3 Formulación del esquema de trabajo
117 Interpretive analysis
The matching was correct but the descriptions were somehow vague. Translating between two different graphic registers was properly done.
Procedure for GV
The following picture was produced by a student in the category of global visual thinkers. Vignette 4.31: Matching task for GV
Interpretive analysis
The student managed well in matching the shapes, i.e. translating between symbolic to a three-dimensional graph, two-dimensional graph, and then to verbal descriptions. Some shapes were difficult to describe, especially G4 and G2.
118 4.1.12 Task 12
The task required students to solve the two subtasks. Exercise (a) could be solved by the method of double integrals or by simply visualising that the solid under consideration was a hemisphere, hence, the volume was simply half that of the sphere. Exercise (b) could be solved using double integration only if students were able to produce good and relevant diagrams of the region of integration. The task tested students’ ability to:
Visualise regions in ℝ3 from algebraic equations.
Link geometrical concepts with analytical concepts.
Extract relevant information from a diagram for the sake of problem solving. Ability to create relevant images
The students’ responses were scrutinised and grouped according to visual levels. Table 4.53 illustrates the distribution of visual levels.
Table 4.53: Visual level for Task 12
Visual levels Frequency Percentage
NV 21 42
LV 9 18
GV 1 2
Missing 19 38
TOTAL 50 100
Non-visual thinkers dominate in this exercise. Table 4.54 illustrates the competence matrix of competencies versus visual levels.
Table 4.54: Competence matrix for Task 12 (linking concepts)
Image role NV LV GV Total
Correct link 0 0 1 1
Partial correct 0 3 0 3
No link 21 6 0 27
Total 21 9 1 31
Double Integrals
(a)Find the volume of the solid bounded by the plane z = 0 and the paraboloid z
=√1 − 𝑥2− 𝑦2
(b) Find the volume of the solid that lies under the paraboloid z = x2 +y2and the
119
Global visual thinkers were able to link geometrical and analytical concepts.
Chi-square test (Task 12a)
H0: There is no association between visual levels and competencies; versus
H1: There is an association between visual levels and competencies.
Table 4.55: Chi-square test for Task 12
Value df Asymp. Sig. (2-sided)
Pearson Chi-square 39.037a 4 .000
Likelihood Ratio 16.883 4 .002
N of Valid Cases 31
Condition three of the assumptions of the Chi-square test was not satisfied . We cannot conclude that there is an association even though the significant value 0.00 was less than 0.05. A true conclusion can be obtained after further -hoc tests.
Further test
The method of combining categories was used in cases were the third assumption was violated. For this case the NV category was attached to LV category and the No Link category was attached to Partial Link category to form a 2x2 contingency table. The following results were obtained.
Table 4.56 : Chi-square test for task12 after post-test
Value df Asymp. Sig. (2- sided) Exact Sig. (2- sided) Exact Sig. (1- sided) Pearson Chi-square 31.000a 1 .000 Continuity correctionb 27.125 1 .000 Likelihood ratio 42.943 1 .000
Fisher's exact test .000 .000
N of valid casesb 31
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 7.26. b. Computed only for a 2x2 table
Results: There is an association between visual levels and competencies (α =0.00 0< 0.050). Table 4.57 illustrates the competence for ability to extract relevant information.
120
Table 4.57: Competence matrix for Task 12 (extraction of information)
Image role NV LV GV Total
Correct extraction 0 0 1 1
Partial correct 0 6 0 6
Incorrect 21 3 0 24
Total 21 9 1 31
Global visual thinkers extracted relevant information from the diagrams. Chi-square test (Task 12 b)
H0: There is no association between visual levels and competencies; versus
H1: There is an association between visual levels and competencies.
Table 4.58 Chi-square for Task 12
Value df Asymp. Sig. (2-sided)
Pearson Chi-square 49.083a 4 .000
Likelihood ratio 27.402 4 .000
N of valid cases 31
Condition three of the assumptions of the Chi-square test was not satisfied. We cannot conclude that there is an association even though the significant value 0.00 was less than 0.05. A true conclusion can be obtained after further post-hoc tests.
Further test
The method of combining categories was used in cases where the third assumption was violated. For this case the NV category was attached to LV category and the No extraction category was attached to Partial extraction category to form a 2 x 2 contingency table. The following results were obtained.
Table 4.59 : Chi-square test for task12 after post-test (extraction)
Value df Asymp. Sig. (2- sided) Exact Sig. (2- sided) Exact Sig. (1- sided) Pearson Chi-square 31.000a 1 .000 Continuity correctionb 27.029 1 .000 Likelihood ratio 42.165 1 .000
Fisher's exact test .000 .000
121
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.45. b. Computed only for a 2 x 2 table
Results: There is an association between visual levels and competencies (α = 0.00 0< 0.050).
Procedures used in solving tasks
In order to conduct an analysis of the procedures used by the students in solving this task, the researcher made use of the vignettes of students’ work related to Task 12.
Procedure for NV
The following picture was produced by a student in the category of non-visual thinkers.