This study demonstrates the effectiveness of Klopfer’s taxonomy and a candidate hypothetico-deductive thinking and reasoning theory of didactic transposition, in teaching critical thinking skills, analogies and transferability of knowledge for problem-solving now and for the future in the experimental sciences. It was conducted in four socio-cultural zones of Cameroon involving 307 high school students (166 English-speaking and 141 French-speaking). Four lessons on the human skeleton were used. A researcher-made Likert questionnaire to investigate the level of appropriation of the tool was administered in the pre- and post- intervention treatments. Data was analysed in SPSS v.20.0 and pair-wise t-test analysis revealed a significant difference in mean scores between pre- and post-interventions with a moderate effect size. A two-way factorial ANOVA to determine the main and combined interaction effects of distal variables, further confirmed the results. Within limits, the results led to the conclusion that Klopfer’s taxonomy and the candidate theory enhanced the development of critical thinking skills, analogical reasoning for transferability and problem-solving in novel contexts among high school students. From the results, we recommended the adoption of the candidate theory as framework guide for classroom practice in teaching the experimental sciences.
Science and technology play a fundamental role in the development of any country. On-going science and technology curriculum reforms in Cameroon secondary education prescribes a complete paradigm-shift from a purely knowledge-based to the knowledge-utilization approach commonly referred to as the competency-based approach to teaching and learning [
1) inferential thinking and creative skills;
2) the spirit of initiative and enterprise;
3) the taking of informed decisions, acting on them and tackling life problems in different contexts; and
4) self-assertion, autonomy, social and civic responsibility skills.
All of these critical thinking skills are necessary for the citizens of the rapidly changing 21st century and beyond [
The new classroom practice mandates all teachers in secondary education to introduce their lessons using real life contextual problem situations. By prescribing this, the reform in other words is calling on teachers to adopt a problem-based learning (PBL) approach to teaching. This means that scientific knowledge should be acquired for problem-solving and not for its own sake. Contextualizing brings learners face-to-face with their own local realities that favour the establishment of a concrete link between school knowledge and its utility in society [
In Cameroon schools today, the sciences are taught as packages of disjointed and isolated facts as if there were no relationship between them and other disciplines, and between them and other aspects of life [
This led to the formulation of the following research question:
Can cognitive remediation informed by Klopfer’s taxonomy and the hypothetico-deductive thinking and reasoning candidate theory for didactic transposition, teaching and learning of the experimental sciences influence high school student’s ability to learn how to think critically, reason, and transfer their knowledge to seek solutions to real life societal problems now and for the unknown future?
From this question, the following null research hypothesis was formulated to guide the investigation:
Ho: There is no significant difference in variances between summated mean scores of respondents on both the predictor and outcome dependent variables before and after intervention when selected categories of Klopfer’s taxonomy and the nature-semiotic hypothetico-deductive thinking and reasoning program inform didactic transposition and teaching in the experimental sciences.
The study employed a cocktail of diagnostic Likert scale questionnaire response type items with proposals of different levels of responses to respondents to evaluate and therefore demonstrate the effectiveness of the nature-semiotic hypothetico-deductive thinking and reasoning candidate theory [
Sampling was by the De Landsheere [
The study was conducted with four (4) lessons of 60 minutes duration each on the human skeleton. These were: 1) bone structure and function; 2) skull or cranium; 3) vertebral column, ribcage and lumbar vertebrae; and 4) appendicular skeleton. The preparation and teaching of each of these lessons was guided by Klopfer’s taxonomy and the hypothetico-deductive thinking and reasoning model.
The questionnaire was designed to obtain data on respondent’s ability to appropriate the hypothetico-deductive thinking tool in problem-solving as well as personal data on their demographic, educational and socio-economic backgrounds which constituted the distal variables. Though the distal variables are not the principal variables under investigation, they are nevertheless important because they could have possible influence on the learner’s ability to appropriate the thinking and reasoning process. The first step in the development of the questionnaire was to generate an initial pool of ideas around the target constructs under investigation by jotting down as many potential test items, ideas and statements as possible that spontaneously came to mind. This strategy served as a precaution to avoid missing out on some important aspects of the constructs. Nevo [
Of the 89 items on Klopfer’s taxonomy and the hypothetico-deductive thinking and reasoning framework:
1) 19 were on the identification of problem-solving characteristics and properties of the human skeleton (CS);
2) 18 on deciphering and stating the problem necessitating the possession of the characteristics and properties identified (DSP);
3) 18 on considering the characteristics of the skeleton as its know-how in solving problems (SKH);
4) 18 on application of the skeleton’s know-how in other areas of the same discipline and in other disciplines (ASKHOASDD); and
5) 16 on application of the skeleton’s know-how in technology including society (ASKHT).
The items were developed in English and translated into French. Two alternative methods were used. Two parallel independent translations into French from the original English were done and then compared to a third equally independent translation by a third person. Back-translation into English of the French version was done by a fourth person to verify whether the translation was a faithful replica of the original English version. At the end there were two questionnaire of reference in English and in French.
The completed questionnaire was piloted to readjust the structure, content, length and to improve coherence and understanding. A two-plan (qualitative and quantitative statistical analysis) approach to piloting was adopted to test the feasibility of the questionnaire. Piloting was conducted on 50 high school students of Government Bilingual High School Etoug-Ebe in Yaoundé, split into 30 Upper Sixth students of the English-speaking subsystem and 20 Terminale D students of the French-speaking subsystem. This was done during the period ranging from the last week of September to the first week of December, 2015. On the statistical plan the differential item functioning (DIF) was assessed to ascertain whether the questionnaire is invariant with respect to gender or cultural background of the respondents and to establish the reliability and validity of measurements, as well as gain professional advice on the research questions and hypotheses [
It was not easy to obtain approval from both the school administration and parents to conduct the experiment. Assurance had to be given to the school administration that existing class structures will not be offset and there was no additional pressure on the school timetable for a new slot to conduct the experiment. On the part of the parents, assurances that the experiment was not going to interfere with the regular content of the curriculum, but rather that it was going to improve on their children’s ability to thinking critically and make school knowledge relevant by placing it within its context-of-use they readily adhered. After obtaining the approval from these major stakeholders in the education of the child, the teachers who willingly accepted to participate in the research were trained in the methodology and the questionnaire was first administered as a pre-test. After pre-testing the lessons were taught by the class teachers followed by a post-test assessment consisting of the same questionnaire as in the pre-test. To minimise the effect of familiarity due to pre-exposure, the items of the questionnaire were shuffled and the stem slightly altered ensuring that the meaning of each item remained the same. The purpose of the experimentation was not disclosed to the students to minimise the Hawthorne as well as the Henry effects, [
Data treatment consisted of careful coding and scoring of the pre- and post-intervention questionnaire by the researcher to eliminate possible discrepancies in judgments if the different class teachers were allowed to code and score them. The coded data were keyed in and sorted to identify and correct data entry errors, identify and manage outliers and missing values, verify assumptions for statistical analysis and transform the data for subsequent parametric analyses. The identification of outliers was necessary to minimise the possibilities of both Type I (“falsepositive”) and type II (“falsenegative”) errors [
Content validity was assured by preparing and submitting to experts (course teachers) for appreciation and approval of the researcher-made questionnaire. Criterion validity was assured by developing questions that required inductive and deductive reasoning as criteria for problem solving in different contexts requiring the mobilisation of knowledge and other resources from the hypothetico-deductuve thinking and reasoning framework process. Construct validity was assured through a trial test run administered to 50 randomly selected students of the study sample. An internal consistency plan to check reliability was adopted. In the first stage a PCA test run was realised to verify whether items for each type of construct “hung together”. In the second stage, Cronbach’s alpha coefficient for each item, subscale and total scale were computed. This was to ensure that whether individually or combined, the scale was actually measuring what it was intended to measure. Since this study involved working with students in a class, the effect of peer influence on one another was mitigated by setting a more stringent alpha level of ρ < 0.01 [
Statistical data analyses were both descriptive and inferential. Descriptive statistics was by the generation of univariate statistics of frequency distribution tables, and combined histograms and lined graphs for the individual and summated variables to explore the structure of the data. Inferential statistics consisted of exploring differences between interventions using paired samples t-test, and two-way factorial ANOVA. The calculated t-values from the t-test technique were used to determine the probability (ρ-values) within the lower and upper bound limits of a confidence interval (CI) of 99%. With a degree of significance below the CI, the null hypothesis stated in the problem section above was rejected and vice versa. The factorial ANOVA technique was employed to assess the influence of two or more independent variables on a dependent variable within the same analysis. This plan enabled the investigation of the main as well as the combined or interaction effect of certain independent distal variables on the dependent or outcome variable. For the independent variables with multiple levels a post-hoc multiple comparisons was further realised to locate the exact level contributing the most or least effect. Cohen’s effect size was estimated alongside the t-test to establish the magnitude of the difference between the two samples at pre- and post-intervention and to minimize the shortcomings of the ρ-value estimation [
After the piloting process questionnaire items were readjusted and reorganised around each construct, with redundant items removed to cover the following themes of the theoretical postulate:
1) identifying and describing the problem-solving characteristics of the skeleton―Klopfer’s taxonomy (reduced from 19 to 14 items);
2) deciphering the problem solved by the possession of the identified characteristics―hypothetico-deductive thinking and reasoning model (reduced from 18 to 16 items);
3) considering the identified characteristic as the skeleton’s know-how in problem-solving (from 18 to 13 items);
4) application of know-how in other areas of the same discipline and other disciplines (interpolation)―Klopfer’s taxonomy (reduced from 16 to 14 items);
5) application of know-how in technology including society (extrapolation)―reduced from 16 to 11 items; and
6) acquisition of life skills and competences for problem-solving (reduced from 16 to 11 items).
Prior to descriptive and inferential analyses, 8 missing values all representing less than 5% of the total data set with no regular pattern of distribution in their occurrence were identified and corrected. In the correction of data entry errors, no variable was tested for possibility of a systematic relationship between missingness because there was no case with up to 5% missing values. In a normality test, the mean and 5% trimmed mean values were not very far apart indicating that the presence if any of outliers in the data set may not significantly affect the results of the analysis. The Kolmogorov-Smirnov ρ-value of 0.001 for some variables under investigation led to the rejection of the null hypothesis of normality in the data set in favour of non-normality. Hence generally, the entire data set was found to consist of a mix of normal and non-normal distribution. The non-normally distributed variables violated the assumptions for t-test and regression analysis which was further confirmed by the shapes of the normal Q-Q plots, detrended Q-Q plots and boxplots for each variable. For this data to fit t-test and regression analyses, it was transformed using the summation function of SPSS v.20.0. This yielded the following new variables:
1) Total Characteristics of the human Skeleton (TCS);
2) Total Deciphering and Stating the Problem necessitating the possession of the characteristics and properties identified (TDSP);
3) Total Skeleton’s Know-how in solving problems (TSKH);
4) Total Application of the Skeleton’s Know-How in Other Areas of the Same Discipline and in other Disciplines (TASKHOASDD);
5) Total Application of the Skeleton’s Know-How in Technology including society (TASKHT); and
6) Total Acquisition and transfer of Problem-Solving Skills and Competences (TAPSSC).
Verification of the assumptions for parametric analyses on the summated data yielded a Durbin-Watson (DW) statistic of 2.251 and an ANOVA test of global significance of 0.926 respectively indicating that the regression null hypothesis of “coefficients of all independent variables equal zero” is rejected in favour of the alternative hypothesis. Based on this therefore, the data was found fit for regression analysis. Conversely, examination of the correlation matrix generated alongside the Durbin-Watson statistic revealed high correlations between some of the independent variables that predicted the dependent variables. This is an indication of possible multicollinearity and therefore an impending problem with the determination of the degree of the effect of each predictor variable on the dependent variable. The tolerance value for the independent variables ranged from 0.294 to 0.459 further suggesting possibility of multicolinearity. To resolve this problem, items on the summated scale with similar correlation coefficients equal to or close to unity were combined into one or one of them simply removed. After this, the Variance Inflation Factor (VIF) values which were all below 10 with a conditional index < 30 for all the independent variables suggested that the assumption of the absence of multicollinearity in the data set is respected. On the overall, the results revealed that the distribution of the summated data set reasonably respected the conditions for regression analysis more so than the non-summated data as seen in
In a linearity and homoscedasticity test, the histogram showed a normal distribution with a mesokurtic aspect; the P-P Plot displayed a roughly cigar-shaped distribution; and the scatter plot did not display patterns around the predicted values represented by the horizontal straight line. All of these pointed to the fact that the dependent variable’s variability is equal across all values of the independent variable in the data set. This confirmed that the summated data set is homoscedastic. These results are visualised in
A test of Cronbach’s alpha yielded a value based on standardised items of 0.901. The item total statistics also yielded values ranging from 0.894 to 0.898 for all the initial variables in the study. These results confirm a very high internal consistency of the measurement scale and therefore a good reliability according to [
Paired samples descriptive statistics of the pre- and post-intervention data of the summated scales (TCS 1 and 2, TDSP 1 and 2, TSKH 1 and 2, TASKHOASDD 1 and 2, TSKHT 1 and 2 and TAPSSC 1 and 2) yielded results visualised in histograms and line graphs in Figures 3-5.
Model | Unstandardized Coefficients | Standardized Coefficients | T | Sig. | Correlations | Collinearity Statistics | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
B | Std. Error | Beta | Zero-order | Partial | Part | Tolerance | VIF | ||||
(Constant) | 28.592 | 3.307 | 8.646 | 0.000 | |||||||
TASKHT | −0.014 | 0.105 | −0.012 | −0.135 | 0.893 | 0.025 | −0.008 | −0.008 | 0.459 | 2.177 | |
TASKHOASDD | 0.078 | 0.100 | 0.073 | 0.782 | 0.435 | 0.061 | 0.045 | 0.045 | 0.392 | 2.553 | |
TSKH | 0.012 | 0.140 | 0.008 | 0.083 | 0.934 | 0.042 | 0.005 | 0.005 | 0.332 | 3.013 | |
TDSP | 0.021 | 0.113 | 0.020 | 0.183 | 0.855 | 0.046 | 0.011 | 0.011 | 0.294 | 3.401 | |
TCS | −0.043 | 0.099 | −0.039 | −0.434 | 0.665 | 0.019 | −0.025 | −0.025 | 0.423 | 2.362 |
a. Dependent Variable: Total acquisition of problem-solving skills and competence. Source: Data collected and analysed by Nditafon (2016).
Model | Dimension | Eigenvalue | Condition Index | Variance Proportions | |||||
---|---|---|---|---|---|---|---|---|---|
(Constant) | TASKHT | TASKHOASDD | TSKH | TDSP | TCS | ||||
1 | 5.938 | 1.000 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | |
2 | 0.021 | 16.842 | 0.74 | 0.01 | 0.06 | 0.00 | 0.06 | 0.04 | |
3 | 0.014 | 20.501 | 0.03 | 0.17 | 0.14 | 0.04 | 0.07 | 0.50 | |
4 | 0.011 | 23.657 | 0.18 | 0.68 | 0.00 | 0.03 | 0.04 | 0.38 | |
5 | 0.010 | 24.309 | 0.01 | 0.00 | 0.78 | 0.18 | 0.20 | 0.00 | |
6 | 0.006 | 28.592 | 0.04 | 0.15 | 0.01 | 0.74 | 0.63 | 0.08 |
Source: Data collected and analysed by Nditafon (2016).
In all the constructs investigated, all pre-intervention data sets displayed an approximately mesokurtic aspect. Differences were seen in the post-intervention data as follows:
1) In identification of problem-solving characteristics, post-intervention data also showed an approximately mesokurtic aspect, suggesting that the identification of adaptive characteristics of organisms, objects and phenomena is not much of a problem to learners since this constitutes part of the regular curriculum in Cameroon schools at this level;
2) For deciphering and stating the problem-solved by the identified characteristics, post-intervention data were more platykurtic suggesting that the use of the
model resulted in gains in reasoning ability of students;
3) With respect to identification of the skeleton’s know-how, post-intervention scores were more leptokurtic meaning that a greater number of respondents conglomerated towards the centre of the distribution;
4) Concerning the interpolation and extrapolation of skeleton’s know-how to other areas of the same discipline, other disciplines, and technology including society, post-intervention scores were all leptokurtic in aspect.
5) In the appropriation of life skills category, a rather interesting distribution was observed. Post-intervention distribution was more platykurtic. This suggested that even though there is a difference between pre- and post-interventions, in real life situations, behaviours are determined by a combination of factors interacting together rather than by a single factor acting alone.
Inferential statistics was conducted to verify the level of significance of the research hypothesis stated earlier in the problem section of this report.
From the descriptive results presented above, it can easily be assumed that the changes observed are significant. Descriptive statistics in itself is not sufficient to enable the taking of such a decision. As a result, a within group pair-wise t-test analysis yielded the following results presented in
From these results it was observed that while performance of respondents on the TCS and TSKH constructs showed a moderately significant positive correlation between pre- and post-interventions treatments, (r = 0.36, ρ < 0.001 and r = 0.30, ρ < 0.001 respectively) according to Cohen [
Constructs | N | Correlation | Sig. | |
---|---|---|---|---|
Pair 1 | TCS and TCS 2 | 303 | 0.356 | 0.000 |
Pair 2 | TDSP and TDSP 2 | 306 | 0.399 | 0.000 |
Pair 3 | TSKH and TSKH 2 | 304 | 0.302 | 0.000 |
Pair 4 | TASKHOASDD and TASKHOASDD 2 | 307 | 0.433 | 0.000 |
Pair 5 | TASKHT and TASKHT 2 | 305 | 0.469 | 0.000 |
Pair 6 | TAPSSC and TAPSSC 2 | 302 | 0.447 | 0.000 |
Source: Data collected and analysed by Nditafon (2016).
Paired Differences | t | df | Sig. (2-tailed) | ||||||
---|---|---|---|---|---|---|---|---|---|
Mean | Std. Deviation | Std. Error Mean | 95% Confidence Interval of the Difference | ||||||
Lower | Upper | ||||||||
Pair 1 | TCS - TCS 2 | 5.68 | 8.31 | 0.48 | 4.74 | 6.62 | 11.89 | 302 | 0.000 |
Pair 2 | TDSP - TDSP 2 | 6.41 | 8.93 | 0.51 | 5.40 | 7.41 | 12.56 | 305 | 0.000 |
Pair 3 | TSKH - TSKH 2 | 3.33 | 7.34 | 0.42 | 2.51 | 4.16 | 7.95 | 303 | 0.000 |
Pair 4 | TASKHOASDD - TASKHOASDD 2 | 2.34 | 8.03 | 0.46 | 1.44 | 3.24 | 5.11 | 306 | 0.000 |
Pair 5 | TASKHT - TASKHT 2 | 2.20 | 6.51 | 0.37 | 1.47 | 2.94 | 5.91 | 304 | 0.000 |
Pair 6 | TAPSSC - TAPSSC 2 | −3.46 | 8.19 | 0.47 | −4.39 | −2.54 | −7.35 | 301 | 0.000 |
Source: Data collected and analysed by Nditafon (2016).
scored the items moderately high during pre-intervention also scored similar items moderately high during post-intervention for the TCS and TSKH constructs and similarly those who scored the items high at pre-intervention also scored same items high at post intervention in the TDSP, TASKHOASDD, TASKHT and TAPSSC constructs respectively.
Comparison of the mean scores revealed a significant difference between pre- and post-interventions in all the different constructs as displayed in
In conclusion, the null hypothesis of no significant difference between pre- and post-intervention treatments in this study was rejected in favour of the alternative hypothesis of a significant difference between treatments.
Though the t-statistic all pointed to the fact that differences observed between pre- and post-intervention treatments were influenced by Klopfer’s taxonomy and the candidate hypothetico-deductive thinking and reasoning model, it is not absolutely certain to draw such a conclusion because of the possible influence of distal factors discussed earlier in the methodology section of this report. To be fair about this assertion, statistical analyses of main and interaction effects of selected distal factors using factorial ANOVA and post-hoc multiple comparisons tests were conducted. Prior to this a Kolmogorov-Smirnov statistic with Liliefors significance correction (ρ = 0.0005) and the Sharpiro-Wilks lambda (ρ = 0.0005) tests confirmed the assumption of normality and absence of outliers for this parametric test in the distal data. There was good internal consistency assessed by Cronbach’s reliability alpha (α ≥ 0.80), [
1) Main interaction effect for: P5 (Zone of origin): F (3, 279) = 1.73; ρ = 0.16; and
2) Combined interaction effect: P5 × P4 × P3 (Region, age and sex of respondent respectively): F (4, 279) = 0.16; ρ = 0.96.
These results revealed that there were no significant differences in overall TAPSSC scores between respondents from different zones, in different age groups split into males and females. It equally suggested that the demographic factors under investigation had no effect on the student’s ability to score the items on the dependent variable into the different levels of strongly agree, agree, can’t say with certainty, disagree and strongly disagree. These variables had an
Source | Type III Sum of Squares | df | Mean Square | F | Sig. | Partial Eta Squared | Eta Squared (η2) |
---|---|---|---|---|---|---|---|
Corrected Model | 1080.735a | 25 | 43.229 | 0.881 | 0.632 | 0.073 | 0.003 |
Intercept | 98536.780 | 1 | 98536.780 | 2009.001 | 0.000 | 0.878 | 0.264 |
P5 | 255.074 | 3 | 85.025 | 1.734 | 0.160 | 0.018 | 0.0007 |
P4 | 62.752 | 4 | 15.688 | 0.320 | 0.865 | 0.005 | 0.0002 |
P3 | 111.128 | 1 | 111.128 | 2.266 | 0.133 | 0.008 | 0.0003 |
P5 × P4 | 278.091 | 7 | 39.727 | 0.810 | 0.580 | 0.020 | 0.0007 |
P5 × P3 | 205.810 | 3 | 68.603 | 1.399 | 0.243 | 0.015 | 0.0006 |
P4 × P3 | 278.615 | 3 | 92.872 | 1.893 | 0.131 | 0.020 | 0.0007 |
P5 × P4 × P3 | 31.925 | 4 | 7.981 | 0.163 | 0.957 | 0.002 | 0.00009 |
Error | 13684.294 | 279 | 49.048 | ||||
Total | 373766.000 | 305 | |||||
Corrected Total | 14765.030 | 304 |
a. R Squared = 0.073 (Adjusted R Squared = −0.010). Source: Data collected and analysed by Nditafon (2016).
extremely insignificant impact on student’s performance in appropriation of the thinking process for real life contextual problem-solving as demonstrated by the extremely small eta squared statistic (η2 = 0.0007, 0.0002, and 0.0003) for zone, age group and gender respectively.
In conclusion therefore, demographic factors combined or not had no effect on the ability of the students to appropriate the thinking and problem-solving process differently during pre- and post-intervention treatments. The differences observed earlier in the pair-wise t-test of significance could then only have been brought about by the effect of Klopfer’s taxonomy and the nature-semiotic hypothetico-deductive thinking and reasoning framework. These results are summarised in
In a similar test to determine the main and interaction effects of the educational background of respondents the results presented in
These results revealed a significant main effect on respondent’s performance by educational subsystem (English- and French-Speaking subsystems), at F (1, 299) = 4.30, p = 0.04. Students of the English-Speaking subsystem had significantly different scores on the dependent outcome variable (M = 35.12) than their counterparts of the French-Speaking subsystem (M = 33.36) though the effect size was extremely small as seen from the eta squared value η2 = 0.0006. Analysis for possible effects of school type attended by the respondents (lay private, denominational and public) also yielded a significant main effect for the different
Source | Type III Sum of Squares | df | Mean Square | F | Sig. | Partial Eta Squared | Eta Squared (η2) |
---|---|---|---|---|---|---|---|
Corrected Model | 591.049a | 5 | 118.210 | 2.494 | 0.031 | 0.040 | 0.002 |
Intercept | 282249.641 | 1 | 282249.641 | 5954.054 | 0.000 | 0.952 | 0.76 |
Educational Subsystem | 203.780 | 1 | 203.780 | 4.299 | 0.039* | 0.014 | 0.0006 |
Type of school (Lay Private, Denominational and Public) | 327.377 | 2 | 163.689 | 3.453 | 0.033* | 0.023 | 0.0009 |
P1 × P2 | 0.985 | 2 | 0.492 | 0.010 | 0.990 | 0.000 | 0.000003 |
Error | 14173.980 | 299 | 47.405 | ||||
Total | 373766.000 | 305 | |||||
Corrected Total | 14765.030 | 304 |
a. R Squared = 0.040 (Adjusted R Squared = 0.024). *Significant at p < 0.05. Source: data collected and analysed by Nditafon (2016).
levels of the school type attended by the students, F (2, 299) = 3.45, p = 0.03 indicating that students in the Lay Private schools had significantly different scores on the dependent outcome variable than those from denominational and public schools with equally a very small magnitude (etasquared η2 = 0.0009). Although the effect size is very small this constituted the most interesting and informative result because it indicated that differences observed in the population marginal means generated alongside the between-subject effect statistics depended on whether the respondent was English-Speaking or French-Speaking with students of the English-speaking subsystem demonstrating greater difficulty in appropriating the cognitive remediation thinking program for problem-solving in different contexts. Conversely, there was no interaction effect when the two independent variables were taken together, F (2, 299) = 0.01, p = 0.99. However, having observed a significant main effect in the overall analysis of variance test, a post-hoc multiple comparisons was conducted to find the exact level of the influence. These results are presented in
Comparisons of the two subsystems revealed that Upper Sixth English-speaking and Terminale D French-speaking students in Lay Private schools performed poorer on the outcome dependent variable than their counterparts in the denominational and public schools.
Finally, verification of the possible main and combined effects of selected social factors of interest in this study yielded a non-significant main and interaction effects for all three background factors investigated. However, in combination, all three factors have a significant effect. For example
(I) School | (J) School | Mean Difference (I - J) | Std. Error | Sig. | 95% Confidence Interval | |
---|---|---|---|---|---|---|
Lower Bound | Upper Bound | |||||
Lay Private | 2.00 | 2.0844* | 1.01313 | 0.041 | 0.0906 | 4.0782 |
3.00 | 2.5687* | 0.94278 | 0.007 | 0.7134 | 4.4241 | |
Denominational | 1.00 | −2.0844* | 1.01313 | 0.041 | −4.0782 | −0.0906 |
3.00 | 0.4844 | 0.96316 | 0.615 | −1.4111 | 2.3798 | |
Public (Government) | 1.00 | −2.5687* | 0.94278 | 0.007 | −4.4241 | −0.7134 |
2.00 | −0.4844 | 0.96316 | 0.615 | −2.3798 | 1.4111 |
Based on observed means. The error term is Mean Square (Error) = 4.405. *The mean difference is significant at the 0.05 level. Source: Data collected and analysed by Nditafon (2016).
Relationship with sponsor: P6 = F (4, 273) = 0.84, ρ = 0.50; non-significant;
Educational level of respondent’s sponsor: P7 = F (4, 273) = 0.89, ρ = 0.47; non-significant;
Marital status of respondent’s sponsor: P8 = F (2, 273) = 1.22, ρ = 0.30; non-significant; and
In combination: P6 × P7 × P8 = F (1, 273) = 5.32, ρ = 0.02 (significant).
These results further confirm that of the educational background and go on to show that acting in combination, the social background of the students of both the English- and French-speaking subsystems affect their ability to appropriate the cognitive remediation thinking and problem-solving tool. In the real world experiences Bouchard and McGue [
On the overall, it was concluded that the distal variables individually do not have an appreciable effect on the ability of respondents to appropriate and use the thinking program for problem-solving in present and different contexts except in the cases of the two subsystems of education taken separately, the lay private and denominational/public school types and the social background when taken in combination. Therefore within limits of these results, it can be concluded that in the greater part, the differences observed between the pre- and post-intervention treatments are brought about by Klopfer’s taxonomy and the hypothetico-deductive thinking and reasoning program.
The significance of the results especially indeciphering and stating the problem necessitating the possession of the characteristics and properties (TDSP) construct is that students acquired skills that enabled them to start identifying possible problems linked to solutions observed in nature after mediation informed by the hypothetico-deductive thinking and reasoning program. As a result, the problem-based approach to the teaching of biology and the experimental sciences Orange and co-workers [
With a Cohen’s effect size (d = 0.72), the results on considering the characteristics of the skeleton as its know-how in solving problems (TSKH) have important significance as biology is essentially an observational science. Effective observation and measurement of phenomena and events in the learner’s surrounding makes learning more meaningful as learners explore what is real and concrete to their lives before moving onto the abstract things which can only be perceived through logical and rational reasoning. As an observational science therefore, Vygotsky’s [
The results from the foregone three constructs (TCS, TDSP, TSKH) agree with Bachelard’s [
Concerning the constructs “application of the skeleton’s know-how in other areas of the same discipline and in other disciplines (TASKHOASDD)” and “application of the skeleton’s know-how in technology and society (TASKHT)”, respondents during post-intervention showed mastery of the thinking process compared to their performances at pre-intervention. This implied that the hypothetico-deductive thinking and reasoning model acting as guide supported student’s appropriation and use of analogical thinking to transfer learning from one context of use to another. However, compared to the TCS, TDSP and TSKH constructs discussed above, respondents exhibited increasing difficulties in proceeding to find analogues of the identified know-how in other areas of the same discipline, other disciplines and in science and technology including society in that order. This is justified by the small effect size (Cohen’s d = 0.29 and 0.34 respectively), of the model on their ability to bridge the knowledge learned in one context to find analogues in novel contexts. During the experimentation however, a rubric that emphasised the interpolation and extrapolation of the knowledge acquired to other areas for problem-solving was associated with the mediation process. This possibly accounted in part for the improved performances of respondents in the post- than in the pre-intervention. Effective teaching of the sciences therefore should bring out the linkages between the knowledge acquired in one field with similar situations in the same discipline, other disciplines and in technology including society. Such skills once acquired can be extrapolated to other areas of life including problem-solving. Identifying problems in nature and the way nature sets about solving them can also be extrapolated to similar problems in different areas including technology and the human society. With the introduction of the hypothetico-deductive thinking framework, respondents were systematically helped to sought for and find the links in their school knowledge in other areas of the same discipline, other disciplines, and in technology including society. By systematically studying the way nature solves its problems and linking such to the human society, school knowledge is being put into its context-of-use [
With respect to the educational background of the respondents in this study, there was evidence for a significant main effect on the appropriation of the model between English-speaking and French-speaking students, with French-speaking students appropriating the process better than their English-speaking counterparts. This could be explained in part by the fact that logical thinking and reasoning are introduced to French-speaking students earlier in their school life through the teaching of Philosophy in both the first and second cycles. Conversely, the English-speaking child in Cameroon does not have a similar exposure. Worse still, an English-speaking science student is completely alienated from Philosophy, which introduces the basic concepts of logic, thinking, reasoning and the origin of knowledge. Evidence for a significant main effect of the prior school type attended by the respondents (lay-private, denominational and public) was also found showing that denominational and public institutions mastered the concept better than the lay-private institutions. It is difficult to justify these statistical findings though some factors appear to militate in favour of this state of affairs, namely:
1) while public and denominational institutions select the best candidates through the variously organized entrance examinations, the weak and often rejected candidates are absorbed by the lay-private school;
2) academically weak students who have been dismissed for poor academic performances compounded by disruptive behavior are readily absorbed by the lay-private institutions;
3) lay-private school teachers are hardly full time and in the most part are very poorly paid.
This study also provided evidence for a combined significant effect in the social background of the students.
The distal variables investigated in this study, are similar to Tzuriel’s [
Some practical and academic significance of this study
The study finds relevance and is therefore significant in the fields of 1) didactics of the experimental sciences; 2) epistemology of experimental sciences; and in 3) pedagogic practices. From the didactical point of view, the hypothetico-deductuve thinking and reasoning framework is a didactisation tool which informs internal didactic transposition, teaching and learning of the experimental sciences. Due to the tool’s inbuilt characteristic of bridging, the transfer of knowledge learned in one context for application in other contexts, it poses as a suitable mediator of the didactic situation. Once mastered and appropriated therefore, the student will quickly attain Brousseau’s [
1) learning is driven by challenging, open-ended problems with no one “right” answer;
2) problems/cases are context specific, establishing the contextual relevance of school knowledge;
3) students work as self-directed, active investigators and problem-solvers in collaborative groups; and
4) teachers appropriate their role of facilitation, guiding the learning process and promoting an environment of inquiry, contextual problem-solving and exchange.
Rather than have a teacher provide facts and then test student’s ability to recall these facts via memorization, PBL attempts to get students to apply knowledge to new situations. Overall, the study provides direct relevance to the educational system of Cameroon especially, with the on-going reforms in secondary education that prescribes the competency-based approach with entry point into lessons being real life contextual situations, (see for example [
1) provides a set of strategies that students can use again and again to make informed decisions and judgments when faced with problems in novel contexts;
2) increases students’ interest and motivation in learning both critical thinking skills and science lesson content since thinking skills are infused into the lesson; and
3) provides opportunity for the same content material to be used to teach a wide variety of critical thinking skills such as compare and contrast; problem-solving; making informed decisions and acting on them with confidence; making inferences; making judgments; causal reasoning; argument; prediction; and creativity, amongst others.
Limitations in this study include among others the fact that the study:
1) used a researcher-made questionnaire which may have inherent errors that may need refinement in future researches;
2) used only students in the investigation whereas in a typical didactic situation there are four components (learner, teacher, knowledge and the situation). Future studies should widen the horizon of the research to include the other components that have not been investigated;
3) was limited to the use of Likert scale type questionnaire that was summated into a continuous scale for quantitative analyses. A multiple choice test with scores in pre- and post-interventions as well as qualitative observation could be more elucidating in future studies;
4) could not adopt a true experimental design because it had to be conducted in schools with already pre-existing structures and defined programs of study. Parents and school authorities usually resist the idea of reorganizing already existing class structures for the purpose of experimentation.
5) parents particularly do not appreciate the use of their children in experimentation and so the informed concern was not easy to obtain.
This study demonstrates how the nature-semiotic hypothetico-deductive thinking and reasoning program triggers structured thinking as well as “thinking out of the box” through the seeking of analogies using interpolation and extrapolation as bridging techniques. This way of thinking broadens student’s thinking horizons, developing creative, innovative, critical and inferential thinking skills and competences. All of these confer on the student the feeling of autonomy of action and thought and therefore flexibility and open-mindedness in searching for relevant problem-solving cues when faced with a problem situation. The advantage of this framework is that once appropriated, students can apply it to existing real life situations now and in the future.
In conclusion therefore, one of the best ways for ensuring that school knowledge is used to solve societal problems and therefore establish a clear link between school and society is to turn to nature and copy from its perfect and precise skills in problem-solving. Interpolating and extrapolating as well as reinvesting such knowledge, skills and scientific methodologies to seek solutions to societal challenges establish the bridge between school knowledge and the society. The ability to appropriate this way of thinking, transferring knowledge and solving societal problems constitutes higher order intellectual attainment as it enables learners to handle abstractions and logical operations as a result of interaction with their physical and the socio-cultural environments. This widens learner’s scope of thinking, transferability and applicability of knowledge, skills and methods learned in the classroom for problem-solving in novel contexts in society. Work in progress seeks to demonstrate how the hypothetico-deductive thinking and reasoning candidate theory of didactic transposition, teaching and learning of the experimental sciences (Nditafon et al., 2016) can be used as a tool to foster the development of meta-cognition skills and chunking in students.
The authors declare no conflicts of interest regarding the publication of this paper.
Nditafon, G.N. and Noumi, E. (2018) Didactic Transposition for Inferential and Analogical Thinking, Reasoning and Transfer of School Knowledge for Societal Context-of-Use. Open Access Library Journal, 5: e4785. https://doi.org/10.4236/oalib.1104785