PRESENTATION AND ANALYSIS OF FINDINGS
5.1 LEARNERS SUCCESS WITH PROBLEM TASKS
DISCUSSION OF FINDINGS
In the previous chapter, the individual Problem tasks used in the study were described and learners' responses to individual tasks were analysed. In this chapter, analysis and discussion is presented on the problems as groups, e.g. individual problems and group problems, and
comparisons are made with other tests e.g. TIMSS. The learners' success at different problem types is also discussed. In addition, findings in relation to differences between the different groups of learners in grade six such as gender groups and classes are presented. Attempts are made to link the findings in this study to other studies.
In some, they did well e.g. Planet problem, but in others, they did poorly e.g. Food Web.
The same applies for the reasons they gave for the answers. For example in the Snow problem, forty percent could choose the correct answer but only three percent could provide good reasons.
However, with the Weight problem it was the opposite with only fifteen percent unable to supply reasons but thirty-one percent getting it correct with a reason.
When looking at the characteristics of the problems there was no strong pattern but rather some preferences. For example, learners seemed to perform better in inside type problems compared to outside type problems. Learners had more success with the Party, Planet and Machine problem (inside) than the Weight and Snow problem (outside). This could be because the outside type problems required the learner to rely on previously learnt knowledge, which appeared to be a challenge for some learners. The exception was the Heavy Bear problem which was categorised as an inside type problem and yet learners did not perform well in this task. The reason for this could be that the Heavy Bear problem was an open problem with multiple answers, just like the Food Web problem. Learners performed poorly in both these open Problem tasks.
Careful consideration was given to the presentation of each task as suggested by McGhee (1997) and there was no indication that the presentation of problems affected learners' success.
In general learners achieved higher marks for the four problems with tables (average 46 %) than the three with diagrams (average 29 %) but this is not significant given the large differences within each group. For example, sixty-three percent had the correct answer for the Planet problem but only twenty-seven percent had the correct answer for Snow problem yet both are presented as tables. Obviously, it is not the presentation alone that is causing this large difference but it is more likely to be a combination of factors.
In an attempt to investigate these variables all, the responses were submitted to a factor analysis. Factor analysis is a data reduction technique, which attempts to show if there is an underlying factor to a group of variables. It can be seen that the factors loaded strongly into three
components (Table 5.2) with the first component group being the Party and Planet problem, the second component was the Weights, Food Web and the Heavy Bear problems and third component was the Snow and the Machine problem.
Table 5.2 Rotated Component Matrix for the Factor Analysis of Problem tasks
Task Weight Task Snow Task Party Task Food Web Task Planet Task Machine Task Heavy Bear
1
0,793 0,781
Component 2 0,606
0,632
0,687
3 0,792
0,697
Extraction Method: Principal Component Analysis.
Rotation Method: Varimax with Kaiser Normalization, a Rotation converged in 5 iterations.
The problems were then analysed in an attempt to find the most likely underlying factors.
These appear to be:
1. Component One - simple reasoning: These two problems were easier as they only required the application of one condition at a time in order to produce the answer. In addition, both problems were inside type problems as all information needed to solve the problem was given, the information was presented in a table format and the problem had only one answer i.e. closed.
2. Component Two - conditional reasoning: These three problems all required the learner to apply linked or conditional reasoning i.e. there were at least two reasoning steps to the answer. In addition all three problems were presented via diagrams and required some prior knowledge i.e. they were outside problems
3. Component Three - number manipulation: Both these problems required the learner to manipulate numbers in some way to obtain a solution. In addition, they required reasoning with two linked variables. The Snow problem involved temperature as well as precipitation.
The Machine problem was concerned with the relationship between the area of field
cleared, amount of gasoline used as well as the time. In addition, these problems were closed with only one feasible answer but there was more than one possible path to the solution.
Taken together with the preliminary analysis it appears that there might be factors, which are related to learners' success. Firstly, learners are more successful with problems, which only require one step simple reasoning compared to multiple step linked reasoning. Secondly, learners find information in tables easier than information presented in sketches or diagrams.
Thirdly, learners have difficulty reasoning while manipulating numbers.