Chapter 9: Conclusion
9.2. Research Question 3 and 4
Noor Ally Promotion of Mathematical Proficiency
teacher variables: highest secondary school qualification1 (Hssq), how many years of pre-service professional teacher training they had received (tt), how many years as a maths teacher (mty) and teacher score on the test from the larger study as a percentage (Mark%). A Shapiro-Wilks test of normality was first conducted on the data. It showed some variables not normally distributed at a significant level of 5%.
A non-parametric approach to correlation was conducted using Spearman’s correlation co-efficient based on ranks. The correlation result appears in table 9 below.
Table 9: Correlation table for OTDMP vs Teacher variables
OTDCU OTDPF OTDSC OTDAR OTDPD No. of strands
Total OTDMP Q4 Hssq Correlation .517* .286 .207 .443 .171 .626** .510*
Coeff.
Sig(2 tail) .028 .250 .409 .066 .499 .005 .031
N 18 18 18 18 18 18 18
Q7_tt Correlation .009 .125 .113 .154 .105 -.005 .137 Coeff.
Sig(2 tail) .973 .631 .667 .555 .687 .984 .600
N 17 17 17 17 17 17 17
Q16_mty Correlation .182 .170 -.153 .252 .151 .009 .212 Coeff.
Sig(2 tail) .469 .500 .544 .314 .550 .972 .397
N 18 18 18 18 18 18 18
Mark_% Correlation .004 .146 .075 .466 -.185 .257 .072 Coeff.
Sig(2 tail) .988 .563 .768 .051 .462 .303 .775
N 18 18 18 18 18 18 18
The sample size in this correlation was reduced by factors mentioned to just 18.
Nonetheless, there was a significant correlation (at the 5% level of significance) between Hssq and OTDCU, number of strands and total OTDMP. If we consider a 10% level of significance then the teachers’ test score is correlated with OTDAR. The correlation result suggests that the number of years of pre-service professional training and the number of years of mathematics teaching has limited material
1 It would perhaps be expected that all teachers would have a high school qualification providing access to further education. This will be discussed after the presentation of the correlations.
Noor Ally Promotion of Mathematical Proficiency
effect on the promotion of mathematical proficiency. The highest secondary school qualification of a teacher seems to have an impact during teaching. The quality of this qualification is reflected in the teachers’ opportunity to develop conceptual understanding. The higher the secondary school qualification the greater the potential for the teacher to provide opportunities to develop the concept discussed.
However, this variable is also strongly correlated to OTDMP overall. In chapter 8, a suggestion that the increase in the number of strands potentially increases OTDMP seems to also correlate with Hssq. The highest secondary school qualification of the teacher could impact on number and degree of opportunities that develop mathematical proficiency. Teachers possessing high secondary school qualification seem to be in a better position to provide opportunities to develop the strands of mathematical proficiency and therefore have a higher potential to develop the mathematical attributes of a mathematically proficient learner
The highest secondary school qualification can be traced to the history of education in the country. In the era during which education departments were divided along racial lines the highest certificate in a secondary school that could be achieved by a learner was the standard 10 matriculation certificate. Learners at the time attended racially segregated schools and colleges of education. Subjects were offered at higher grade and standard grade levels. Learners had to achieve a result of 40% or more for higher grade subjects and 33.33% or more for standard grade subjects to pass. Hssq in the teachers’ questionnaire was a reference to the quality of the pass in subjects at the standard 10 level (currently grade 12). Teachers in this study went through the system of education just described and which continue to impact in their current teaching practice. A case in point is the highest score of mathematical proficiency in a lesson which was discussed in chapter 8.5. In this lesson the scores of OTDPF, OTDAR and OTDCU were significantly higher than other lessons. The teacher who taught this lesson had the highest level for Hssq in the teacher questionnaire. The strong correlation with number of strands and OTDMP suggest that teachers with higher secondary school qualifications are capable of developing more strands of proficiency at a higher degree. Teachers with lower Hssq showed the lowest scores of mathematical proficiency.
Correlation of the teachers’ test score with OTDAR is an interesting result. The teacher test questionnaire included conceptually related mathematical problems that included for instance identifying learners’ incorrect answers. The correlation suggests that teachers who scored high in these test which ultimately involved much reasoning and justification tend to use their adaptive reasoning ability during lessons.
Research Question 4: How does the teachers’ promotion of mathematical proficiency correlate with the learning that took place during grade 6, according to the difference between the results on the two learner tests?
Learner test gain was calculated on the difference between the two tests that they wrote.
In order to link these gains to teachers, an average learner gain was calculated for each teacher. This average was then correlated with opportunities as in research question 3. A Spearman’s Rho test was conducted and the correlation results indicated in the table below.
Table 10: Correlation between OTDMP and average learner gain.
At the 10 % level of significance, OTDAR at a value of 0.051 is significantly correlated with the average learner gain. One possibility is that the generally low learning gains and the generally low OTDAR scores lead to a ‘false’ correlation. On the other hand, it is not impossible that these do link: reasoning skills, justification and explanation impacts mathematical learning. This strand holds the others together, an important
OTDCU OTDPF OTDSC OTDAR OTDPD
No. Of strands
Total OTDMP
N 18 18 18 18 18 18 18
avg_l_gain Correlation Coefficient
-.266 .168 -.104 .496 .153 .160 .172
Sig. (2-tailed) .320 .533 .703 .051 .571 .555 .524
N 16 16 16 16 16 16 16
Noor Ally Promotion of Mathematical Proficiency
aspect of mathematical proficiency that has been emphasised throughout the study.
Teachers creating opportunities that develop adaptive reasoning positively impacts mathematics understanding and learner achievement. Learners exposed to opportunities that develop their adaptive reasoning which holds the other strands together, may enhance their understanding at a content level and at a deeper, more meaningful level.