Piggott (2011) argues that creativity in the mathematics classroom is not only related to what pupils do but also to what teachers do, where the mathematical experiences that teachers offer their students can open up opportunities for them to be creative. Torrance (1972) describes several ways to teach students to think creatively. We adopted in the present research one of these ways, namely complex programmes involving packages of materials. As mentioned above, here we used the CoRT programme developed by De Bono (1992a) to teach Grade 6 students to think creatively. We examined how the participation in such programme affects students’ creativity in problem solving, where this creativity is represented by its three components: fluency, flexibility and originality, as well as overall creativity. Our reported experiment follows different previous attempts (e.g. Craft, Cremin, Burnard & Chappell, 2007), but ours is concerned with mathematical creativity. In our case, we engage upper primary students with a programme that aims to cultivate their thinking. In the mathematics classroom, studies suggest open-ended tasks (e.g. Mihajlović & Dejić, 2015) or multiple solution tasks (e.g. Levav-Waynberg & Leikin, 2012) for cultivating students’ mathematical creativity. Here, we followed a different way of cultivating students’ creativity, namely the CoRT programme. The different studies, including the present, point to different possible ways to develop students’ mathematical creativity. This development would provide the student with powerful tools as a learner of mathematics in particular and of school disciplines in general.

Haylock (1997) points out that mathematical attainment can limit students in overcoming fixation and in working with divergent problems, although it does not determine their mathematical work. This statement agrees with research on the relation between creativity and achievement, which has been long researched (Baird, 1985; Torrance, 1962). We argue that this agreement means that mathematical attainment could influence one’s creativity, but this influence could be mediated or moderated by other individual or social variables, such as motivation and teacher support. This conception of the relation between attainment and creativity can explain the literature that does not agree regarding the effect of achievement in a discipline on students’ creativity in that discipline. While some studies have reported high correlations between academic achievement and creativity (e.g. Torrance, 1962), some have found low correlations between these two variables (e.g. Baird, 1985). Other studies have not found significant relations between achievement and creativity (e.g. Nori, 2002).

One of the studies that found significant differences in mathematical creativity and which is related to achievement is that of Mann (2005) who explored the relationship between mathematical creativity and mathematical achievement, attitude towards mathematics, self-perception of creative ability, gender and teacher perception of mathematical talent and creative ability. The research results indicated that 35% of the variance in mathematical creativity scores could be predicted by the studied variables. Mathematical achievement was the strongest predictor accounting for 23% of the variance. Students’ attitudes towards mathematics, self-perception of their own creative ability and gender contributed the remaining 12% of variance.

Baer and Kaufman (2008) argue that no simple conclusions can be drawn from the empirical evidence on gender differences in creativity test scores (general creativity tests, not specific in a specific discipline). They enumerate studies that report women scoring higher than men in creativity (e.g. Misra, 2003), studies that report the opposite (e.g. Cox, 2003) and studies that report no difference (e.g. Kaufman, Baer & Gentile, 2004).

In addition, some studies found significant and insignificant differences at the same time regarding the effect of gender on mathematical creativity. For example, Evans (1964) reported significant differences in Grade 7 and 8 students’ scores of some creativity measures that could be attributed to gender, where girls outperformed boys. At the same time, Evans (1964) reported no significant differences between students’ creativity scores in Grades 6 and 7.

In the present research, our main interest is with the interaction of the two variables, achievement and gender, with implementing the CoRT programme and how these interactions affected Grade 6 students’ creativity. To evaluate students’ creativity, we used multiple solution tasks.

A multiple solution task is a task that requires the student to solve a mathematical problem in different ways (Leikin, 2009). A multiple solution task has three solution spaces (Levav-Waynberg & Leikin, 2012): expert solution space, individual solution space and collective solution space. An expert solution space includes the set of solutions to a problem known to an expert at a particular time. An individual solution space includes all the solutions produced by an individual. A collective solution space includes all the solutions produced by a group of students. These spaces are used for exploring students’ mathematical creativity.

In the present study, we used multiple solution tasks to evaluate Grade 6 students’ creativity in mathematics and to compare this creativity before and after participating in a CoRT programme.

A number of studies have shown that the CoRT programme affects significantly higher-order thinking, including creative and critical thinking (e.g. Birdi, 2005). Al-Edwan (2011) explored the effectiveness of a training programme based on CoRT programme to develop Grade 7 students’ critical thinking in a history course. The results showed statistical differences in the participating students’ critical thinking in history as a result of the CoRT training programme. Moreover, Melhem and Isa (2013) explored the effect of using the CoRT programme on critical thinking skills among Grade 6 student with learning difficulties in mathematics. They found that the training programme positively and significantly affected the participants’ critical thinking. In the present study, we intend to study the effect of the CoRT training programme on Grade 6 students’ mathematical creativity.

Researchers have reported that the CoRT programme was effective for encouraging communication skills (e.g. Alshurman, 2017). Alshurman (2017) found that educating university students using the first section of the CoRT programme (Breadth) resulted in statistically significant differences between the pre and post communication skills scores in the experimental group in favour of the post measurement. Moreover, no statistically significant differences were found based on gender in the post scores.

Concerning educating for creative thinking skills, researchers found that the CoRT programme helped in encouraging these skills (e.g. Al-Jallad, 2006). Al-Jallad (2006) reported that using the CoRT programme, as an educating programme, was effective for developing creative thinking skills among the female university students of the Arabic Language and the Islamic Studies. Little research has been done on the influence of the CoRT programme on mathematical creativity, which is the aim of the present research.

The present research intended to explore how a CoRT programme could affect Grade 6 students’ mathematical creativity. The research was conducted in an Arab public elementary school in a small town (with population of approximately 30 000) in the Haifa district in Israel. The school students come from middle socioeconomic backgrounds. The research sample included two groups, with overall 53 Grade 6 students. The first group, the experimental group, included 27 students who participated in learning an Arithmetic unit based on the fourth section of the CoRT programme, that is, the creativity section, which included 10 lessons that encourage students’ creativity. The second group, the control group, included 26 students who did not participate in the CoRT programme.

The present study is a quasi-experimental study. A quasi-experimental is an empirical study used to find the causal impact of an intervention on its target population without a random assignment. According to the definition of quasi-experimental research (see, for example, Kosslyn, 2017), this research shares similarities with the randomised controlled trial, but it specifically lacks the element of random assignment to experimental or control. Instead, the quasi-experimental design allows the researcher to control the assignment of subjects to the treatment condition, using some criterion other than random assignment (in our case scores in creativity and its components).

In addition to the above, the research design could be characterised as two-group design, with non-random selection and pre-test and post-test. This design is represented in Table 1.

The experimental group learnt the CoRT creativity section in groups of 3–5 students, in which student discussion was encouraged. The students were encouraged not to be afraid of having different answers, even if they were strange or controversial, and to discuss these answers with the rest of the group members. Moreover, the students had homework assignments to practise the new concepts and skills they learnt.

The data were collected through pre- and post-tests on creativity. The two tests were similar but not identical. An example of a question in the pre-test is:

An example of a question in the post-test is:

To evaluate the components of creativity and overall creativity, we depended on the work of Leikin and Kloss (2011). We now describe our computations. Fluency (Fl) was evaluated by the number of solutions in the individual solution space. Flexibility (Flx) was evaluated after building groups of solutions for the multiple solution tasks. Two solutions belonged to different groups if they employed solution strategies based on different representations, properties (theorems, definitions, or auxiliary constructions) or branches of mathematics. With respect to the corresponding solution spaces, we evaluated flexibility as follows: Flx₁ = 10 for the first appropriate solution. For each following solution, Flx_i = 10 if it belonged to a group of solutions different from the solutions performed previously; Flx_i = 1 if the solution belonged to one of the previously used groups but had a clear minor distinction; Flx_i = 0.1 if the solution was almost identical to a previous solution. A student’s total flexibility score on a problem was the sum of the student’s flexibility on the solutions in the student’s individual solution space. Originality (Or) was evaluated as follows: if P is the percentage of students in the group that produces a particular solution, then Or_i = 10, when P < 15% and for an insight-based or unconventional solution; Or_i = 1, when 15% ≤ P < 40% or for a model-based or partly unconventional solution; Or_i = 0.1 when P ≥ 40%. A student’s total originality score on a problem was the sum of the student’s originality of the solutions in the student’s individual solution space. The creativity (Cr) of a particular solution is the product of the solution’s originality and flexibility: Cr_i = Flx_i × Or_i. The total creativity score for a multiple solution task is the sum of the creativity scores for each solution in the individual solution space of a problem: Cr=∑i=1nFlxi×Ori

The scores of the components of creativity and overall creativity were coded in SPSS 21 to test the research hypotheses. The following computations were performed: means and standard deviations of the different creativity components and the overall creativity, one-way analysis of co-variance (ANCOVA) to verify the effect of the CoRT programme on students’ creativity, analysis of variance (ANOVA) to verify the effect of the reported ability and the overall achievement on students’ creativity and Eta squared (η²) as estimate of effect sized of the variables.

As for the verification of the first hypothesis, we ran ANCOVA and post-hoc tests to test whether there are significant differences between the creativity scores in the two research groups after the experiment, and ran paired t-test to test whether there were significant differences between the creativity scores in the CoRT group before and after implementing the CoRT programme.

As to the distribution of the participants regarding the independent variables, Table 2 describes the number and percentage of participants in terms of gender, reported ability and overall achievement.

The students in the two groups did not have significant differences in the components of creativity in the pre-test of creativity that the two groups took, as can be seen in Table 3.

Before collecting the data, the second researcher received the permission of the Ministry of Education and the school headmaster. She also sought the permission of the participating students’ parents.

To verify Hypothesis 1, we examined the effect of participation in CoRT programme on Grade 6 students’ mathematical creativity using two methods: running ANCOVA and post-hoc tests to test whether there are significant differences between the creativity scores in the two research groups. In addition, to verify Hypothesis 2, we ran paired t-test to test whether there are significant differences between the creativity scores in the CoRT group before and after the implementing the CoRT programme.

Table 4 shows the means and standard deviations of the scores of creativity and its components in the two research groups after the experiment.

We see from Table 4 that the scores of the experimental group are higher than those of the control group in creativity and its components. To examine the significance of the differences in the means of creativity and its components of the two research groups, we ran ANCOVA. According to Montgomery (2013), running ANCOVA should be done after ensuring normality and equality of variance of the residuals of scores of the groups participating in the research. Testing for normality of the residuals of creativity scores in the two research groups, using the Shapiro-Wilk test (Shapiro & Wilk, 1965), we found that the residuals of the creativity scores, including the components’ scores, were distributed normally. We also ran Levene’s test (e.g. Carroll & Schneider, 1985) to examine the equality of variances of the residuals of creativity scores in the two research groups, which gave equality of variances of the residuals. We ran ANCOVA to examine whether there was significant difference between the creativity scores of the two research groups that could be related to the intervention, that is, participating in the CoRT programme. Though ANCOVA takes into consideration the creativity scores before the experiment, we ran independent t-tests to examine the difference in creativity scores of the two groups before the experiment. The results showed, as described above, that the means of the creativity scores of the two research groups before the experiment were not statistically significant at the 0.05 level.

The results of the ANCOVA test showed significant differences in creativity scores after the experiment between the CoRT programme group and the control group, with F(1, 50) = 16.46, p = 0.000 for fluency; F(1, 50) = 18.177, p = 0.000 for flexibility; F(1, 50) = 17.13, p = 0.000 for originality; F(1, 50) = 13.95, p = 0.000 for creativity. A look at R-squared (r²) showed that r² = 0.520 for fluency, r² = 0.561 for flexibility, r² = 0.441 for originality and r² = 0.402 for creativity.

The previous results show that the group of students who participated in the CoRT programme scored significantly higher in mathematical creativity and its components than the group of students who did not participate in the programme. These results indicate the acceptance of Hypothesis 1. At the same time, they imply that the CoRT programme accounted for 40% of the total variance in creativity as a consequence of the CoRT programme. This percentage is the r² value above for creativity and it indicates the contribution of the CoRT programme to the variance in creativity scores between the experimental and control group. This accounting for the variance is more in the components of creativity, where the r² values ranged between 0.441 and 0.561.

To verify Hypothesis 2, a paired-samples t-test was conducted to compare the creativity scores of the CoRT group before and after the experiment. The results showed that the creativity scores in the post-exam were significantly higher than those in the pre-exam: t(52) = 4.677, p = 0.000, d = 0.783 for fluency; t(52) = 4.955, p = 0.000, d = 0.793 for flexibility; t(52) = 3.396, p = 0.001, d = 0.585 for originality; t(52) = 3.304, p = 0.002, d = 0.612 for creativity. The effect sizes indicated that the difference between the creativity scores after and before the CoRT programme were medium to large (Dunst, Hamby & Trivette, 2004). These results indicate the acceptance of Hypothesis 2.

The results of the independent sample t-test showed no significant differences before the CoRT programme in creativity scores of Grade 6 students that could be attributed to gender. Moreover, to verify Hypothesis 3, we ran ANOVA test to examine the effect of gender on the creativity of students who participated in the CoRT programme (the effect of the interaction between the programme and gender). The results gave: F(1, 49) = 3.162, p = 0.061 for fluency; F(1, 49) = 2.332, p = 0.133 for flexibility; F(1, 49) = 1.197, p = 0.279 for originality; F(1, 49) = 0.962, p = 0.332 for creativity. All the significance values of Fs indicate that the interaction of gender with the intervention did not yield significant differences in the creativity of Grade 6 students who participated in the CoRT programme. These results indicate the acceptance of Hypothesis 3.

The results of ANOVA test on creativity and its components’ scores before the CoRT programme showed significant differences in fluency scores of Grade 6 students before the CoRT programme that could be attributed to achievement, F(3, 49) = 7.869, p = 0.000. ANOVA also showed significant differences in flexibility scores before the experiment and that could be attributed to achievement, F(3, 49) = 8.011, p = 0.000. Moreover, ANOVA showed no significant differences in originality or overall creativity scores that could be attributed to achievement. A look at r² showed that r² = 0.325 for fluency and r² = 0.329 for flexibility. At the same time, the post-hoc analysis, using Bonferroni’s post-hoc test (e.g. Garcia & Herrera, 2008), showed that fluency scores before the experiment in the 86–100 achievement group (M = 0.97, SD = 0.23) was significantly higher than in the 0–55 achievement group (M = 0.64, SD = 0.33) and significantly higher than in the 56–70 achievement group (M = 0.62, SD = 0.26). Furthermore, the post-hoc analysis, using Bonferroni’s post-hoc test, showed that flexibility scores before the experiment in the 86–100 achievement group (M = 9.60, SD = 2.07) was significantly higher than in the 0–55 achievement group (M = 6.43, SD = 3.25) and significantly higher than in the 56–70 achievement group (M = 6.15, SD = 2.58).

In addition, to verify Hypothesis 4, we ran the ANCOVA test to examine the effect of the interaction between the CoRT programme and mathematical achievement (the effect of mathematical achievement on the creativity of students who participated in the CoRT programme). The results gave: F(3, 45) = 2.598, p = 0.064 for fluency; F(3, 45) = 2.986, p = 0.041 for flexibility; F(3, 45) = 1.418, p = 0.250 for originality; F(3, 45) = 1.831, p = 0.155 for creativity. The significance values of Fs indicate that the interaction of achievement with the programme yielded significant differences only in flexibility scores of Grade 6 students who participated in the CoRT programme. These results indicate partial acceptance of Hypothesis 4.

Post-hoc analysis was conducted using Bonferroni’s post-hoc test. The post-hoc analysis showed significant differences in students’ fluency scores, as a result of the interaction between the programme and achievement. The fluency of students in the 56–70 achievement group (M = 0.70, SD = 0.30) was significantly lower than in the 86–100 achievement group (M = 1.74, SD = 0.73). At the same time, the post-hoc analysis showed significant differences in students’ flexibility scores, as a result of the interaction between the programme and achievement. The flexibility of students in the 86–100 achievement group (M = 16.84, SD = 6.48) was significantly higher than in the 0–55 achievement group (M = 8.67, SD = 3.21) and significantly higher than in the 56–70 achievement group (M = 7.00, SD = 2.98).

The post-hoc analysis also showed significant differences in students’ originality and overall creativity scores, as a result of the interaction between the programme and achievement. The originality of students in the 86–100 achievement group (M = 7.75, SD = 6.16) was significantly higher than in the 56–70 achievement group (M = 0.07, SD = 0.03). Moreover, the creativity of students in the 86–100 achievement group (M = 215.98, SD = 198.91) was significantly higher than in the 56–70 achievement group (M = 0.70, SD = 0.30).