A response to the paper "Using Learning Study to improve the teaching and learning of accounting in a school in Brunei Darussalam

Citation

Mun Ling, L. (2012), "A response to the paper "Using Learning Study to improve the teaching and learning of accounting in a school in Brunei Darussalam", International Journal for Lesson and Learning Studies, Vol. 1 No. 2. https://doi.org/10.1108/ijlls.2012.57901baa.002

A response to the paper "Using Learning Study to improve the teaching and learning of accounting in a school in Brunei Darussalam"

A response to the paper "Using Learning Study to improve the teaching and learning of accounting in a school in Brunei Darussalam"

Article Type: Discussion From: International Journal for Lesson and Learning Studies, Volume 1, Issue 2.

I read with great interest Andrew’s (2012) paper in the last issue, which reports a learning study carried out by teachers in Brunei on cash budgets. The lesson was constructed around the following exercise (p. 26) (Figure 1).

A PowerPoint presentation incorporating “systematic variation” (p. 23) was designed and improved upon over the three research lessons, resulting in progressive improvement in student learning outcomes. However, unless we can unpack what “systematic variation” means and why it worked in terms of variation theory, we would not be able to draw insights and make generalization that we can apply to other cases. This paper makes an attempt to do this.

According to Marton and Booth (1997), at least two conditions are necessary for students to appropriate an object of learning. They must experience patterns of variation that allow them to:

1. 1.

   discern the critical features and aspects; and

2. 2.

   discern the structure – how the critical aspects are related to each other and to the whole, i.e. the part-whole relationships as referred to in Andrew’s paper.

In order to understand cash budget, two part-whole relationships are important, one relates to sales distribution, the other relates to cash contribution.

(1) Sales distribution – how sales in each month are distributed and become a part of the cash received in the current month (in terms of cash sales), and the following two months (in terms of credit sales being paid up). This relationship was dealt with using the patterns of variation shown in Table IV (p. 36) in the paper. As the author explained, the patterns of variation were intended to highlight the following two critical part-whole relationships:

1. 1.

   The 20+80 per cent=100 per cent relationship.

2. 2.

   The 70+30 per cent=100 per cent relationship.

I would like to argue that focusing on these two relationships is necessary but not sufficient because they do not help students to understand how the cash in each month is made up of contributions from different months. That is why after the first lesson, a student commented that, “[…] but [we don’t know] what is going on in each month, so what's going on with the current situation. We just know the steps but we don’t understand what is really going on” (Student S3, 020808) (p. 30).

(2) Cash contribution – the ability to calculate the cash received in a certain month, say in March, is more complicated than understanding the above two critical part-whole relationships, but a “fusion” (Lo and Marton, 2012) of these two critical aspects is needed. The cash received in any particular month is made up of its constituent parts (i.e. the current month's cash sale+credit sales paid up from the previous two months). First, ignoring discounts and bad debt, and taking only the contributions from the credit of the previous months into account, the part-whole relationship for “cash contribution” would be:

20 per cent of the sales in March+70 per cent of (80 per cent of the sales in February)+30 per cent of (80 per cent of the sales in January).

However, one must note that in this case, the 20 per cent of sales in March does not constitute 20 per cent of total cash received. Furthermore, the 70 and 30 per cent from credit sale of February and January, respectively does not constitute 70 and 30 per cent cash from credit sales in March, because the percentages refer to different “wholes” (total sales) in different months. Such relationships were not addressed by the two critical part-whole relationships mentioned above. Thus, being able to discern the cash contribution relationship, which requires fusion, is also a necessary condition for learning cash budget.

In the learning study, the cash contribution relationship was intended to be addressed by means of the “systematic variation” in the PowerPoint presentation, but it was only successfully in the third research lesson which resulted in a dramatic improvement (70 per cent gain) in the student learning outcomes.

Since the only major changes over the three research lessons were in the “systematic variation” in the PowerPoint presentation, the explanation for the improved student learning outcomes must be found in how the teacher in the third cycle dealt with cash contribution. According to variation theory, if students were able to discern the part-whole relationship in cash contribution, they must have experienced relevant patterns of variation. So, what patterns of variation were possible for the students to experience to make this “systematic variation” work?

Revealing the patterns of variation embedded in the “systematic variation” in the PowerPoint

To discern the component parts when the cash for each month is summed up, students need to contrast the calculation of “cash received” with and without the component part. To demonstrate how this had to a certain extent been achieved in the third cycle, I have made some slight modifications to the PowerPoint used in the lesson by moving the positions of some of the arrows, but the content remains essentially unchanged (Figure 2).

Part A relates to the sales in January, and is made up of three parts: cash received (20 per cent of the sales in January less 3 per cent discount), bad debt expected for the month, and credit sales (80 per cent of the sales to be paid in the next two months). Part A shows the sales in a month and what happens to it only, and in this case, A is the whole. To consider the cash received in a month, cash paid for the credit sales from the previous months must also be included. As such, the representation in the January column is incomplete. In the February column, both the cash contribution from sales in February (i.e. part A), and the cash contribution from credit sale in January (70 per cent of (80 per cent of the sales in January) less 2.5 per cent discount) are included. Thus, part A now becomes a “part” of the whole, “B”. Here, part A (representing the value of sales and what happens to it in the month) is invariant, while the whole varies (as another component part, the cash received from the credit sales of the previous month, is added). Put in this way, the contrast will help students to discern the component parts of the whole. Again, this calculation is incomplete because the contribution from the credit sales two months ago is not included. Finally, in the March column, in addition to part B, the cash from credit sales from two months ago (January) is also included. Note that part A remains invariant throughout. Thus, the patterns of variation consist of part A remains invariant while the whole varies from part A to part B to part C and part B remains invariant while the whole varies from part B to part C. Such patterns of variation help students both to discern the component parts (the critical aspects), and to see the relationships among the components (part-whole relationship). Because these patterns of variation remained implicit throughout the three lessons, students might or might not have discerned them. In the first and second lessons, the notion of “bad debt” and how it fits into the structure was not clearly explained. Thus, the necessary condition for learning the cash contribution part-whole relationship had not been fulfilled and this may explain why there was little improvement shown in the student learning outcomes. In the third lesson, the teacher included the distribution of “bad debt” across the contributions from three months. The structure of the PowerPoint presentation was also greatly improved to make it possible for students to discern the part-whole relationships via the implicit pattern of variation, with a consequent improvement of 70 per cent. Nevertheless, some students still might not have experienced this variation, which may account for the failure of the 30 per cent of students to learn in the third cycle.

Conclusion

Learning study is informed by variation theory, but it can also test and further develop variation theory in the process. Thus, it is possible both to apply variation theory to inform practice (testing its predictive power), and to explain practice by making use of the theory (testing its explanatory power). The teachers in this learning study may or may not have been aware of the patterns of variation embedded in what is referred to as “systematic variation”, but I tend to believe that good teachers use appropriate patterns of variation intuitively. However, if the teachers had a clear idea of the patterns of variation they were using and how they worked, they could have used them more explicitly – for instance, by using the modified PowerPoint presentation I suggested, and by making use of boxes to highlight the variations in the part-whole relationship. They could also have made generalizations about such patterns of variation – that is, one way to highlight part-whole relationships may be to keep a component part constant and vary the whole by progressively including other component parts to make up the whole. For example, in this case, the three A wholes should appear first, then the two B wholes (with corresponding arrows) and finally C (with corresponding arrow), in three cumulative steps. Students can thus contrast the whole with and without the component parts; in this way, the component parts and its relationship to the whole can be discerned. Such a pattern of variation may be applied to other objects of learning in other topics and other subject areas. In fact, such a pattern of variation has been reported by Chik and Lo (2004). They illustrated with two cases how the patterns of variation brought about by arranging the lesson content in what they referred to as a hierarchical structure (p. 96) had been effective in helping students to discern part-whole relationships.

Finally, I thank Andrew for describing in detail the research lesson, thus enabling the readers to re-interpret the findings such that professional dialogue can take place.

Lo Mun Ling