6.4 ANSWERS TO RESEARCH QUESTION 4: WHAT WERE SOME FACTORS THAT
6.4.3 Learner Constraints
classified as a Level 4 question in the SAML taxonomy (DoE, 2008, p.28), it is more demanding than the usual comparison task which asks for the better option based on comparison of prices or costs.
b. Misconceptions
Three areas of misconceptions were identified in the study. To calculate the discount on an amount is relatively easy and would be classified as a level 1 question. To calculate the amount after the discount would require an additional step of subtracting the discount to the normal price. The idea is one of given the input, find the output. When the output is given and the input needs to be found in a multilevel task, the task becomes a higher order task.
Question 5.1.3 is an example of such a task which required learners to calculate the price before the discount was added. This required a reversal or an inverse technique, normally the setting up of an equation which is mathematically more challenging. This explained why 97% of learners failed to score any marks for this question. The common misconception is to calculate the discount on the final amount and subtract it from the final amount. There was a misconception in the understanding that 8:1 meant eight times more as opposed to 2:1, which meant twice (double) more. Learners also misinterpreted the concept of ¼ when comparing discounts.
In their paper, Luneta and Makonye (2010) focus on analysing Grade 12 learners’ errors and the misconceptions in calculus at a secondary school in Limpopo Province, South Africa. The analysis showed that most of the errors and misconceptions were due to knowledge gaps in basic algebra because learners failed to build procedures (know-how) from conceptual (know- why) knowledge. In my study, learners know the procedure to calculate a percentage of a number and hence are able to calculate the VAT of an amount. However, to calculate the original price of the item before VAT was included required conceptual knowledge (know- why), which some learners did not possess.
c. Language related misinterpretation of questions
“Contextual questions in examinations serve as barriers to some learners because of poor literacy levels and often prevent them from identifying the mathematical skills involved”
(Sasman, 2011). Words like “deduction” in Question 1.3.2, “last week” in Question 1.3.1,
“last” in Question 2.2.3, “margin” in Question 2.2.3(b), and “including VAT” and “excluding VAT” in Question 5.1.3 caused particular problems for learners and affected their performance in the examination task.
The word “deducted” in the scenario and “deduction” in Question 1.3.2 and the question setter’s further hint that deduct meant ‘subtract’, contributed to learners’ misinterpretation and thus affected their performance in the examination task. The phrase “last week” in the scenario implied Monday to Friday of the previous week (i.e. a total of five days); however, in the learners’ interpretation, “week” meant seven days they hence made their calculation on seven days instead of five.
The word “last” in Question 2.2.3 was found to be ambiguous and affected learners’ response to the examination task. The term as used in the context meant the final match and hence there was one remaining match to be played. Some learners (P3) interpreted ‘last’ as the previous match and thus there would be more matches to be played. This resulted in the learner suggested scores based on more than one match instead of only one match.
Shorrocks-Taylow & Hargreaves (1999) explain how some familiar words could be used in unfamiliar ways or in different ways in different disciplines. For example, the word
“solution” in mathematics would mean to find the solution to a problem, but in science the same word would mean to mix contents in a liquid form. Even the meaning of the word
‘margin’ in ‘win (by a margin of 1 goal)’ in Question 2.2.2 was not known to some learners.
Question 5 posed problems to learners who did not know that ‘including VAT’ meant that VAT was already included in the price or whether the VAT had to be added to the price.
Some of these language related misinterpretations were experienced by the second language speakers, which shows that they were disadvantaged because they did not understand the language. Dempster & Reddy (2007) found that more than 50% of learners from African schools chose option D from a multiple choice set of questions from the TIMMS study.
Option D was the only one that contained a term that was found in the question (Atmosphere), suggesting that most English second language learners did not understand the question and merely selected an answer by matching words found both in the question and the answer. These language-related issues affected the way learners engaged with and responded to the tasks.
Evidence that complex terms and phrases affect student learning is documented in a study by Abedi & Lord (2001). These researchers tested about 1 200 Grade 8 learners on items from the National Assessment of Educational Progress (NAEP). Some of the items were rewritten in simpler language by rephrasing them, personalising them, and reworking or replacing conditional and relative clauses. The interview facet of the study showed that learners
preferred the modified items as they felt them easier to comprehend and would choose them over the items worded in the NAEP if under duress. The performance facet of the study found that English language learner (ELL) and students of low socio-economic status (SES) performed significantly lower on the standard items than their English speaking or higher SES counterparts. The researchers also found that by modifying the items, the gap between the performance of English speakers and ELL as well as between learners of low SES and more affluent groups, decreased. These studies show that assessment designers must take steps to ensure that learners know what is being asked. Understanding the questions that are asked, is crucial for success in examination task.
Another language related issue experienced by all the learners was the use of the context- specific terminology such as “infant mortality rates”, This phrase was misinterpreted by all the learners, some of whom missed it because of its placement. The values represented deaths per every 1000 live births. Learners misinterpreted these values as percentages and actual number of infants who died. The misinterpretation is based on the fact that it is not a phrase that learners have encountered but is specific to the context. The task designer should have taken greater care that the meaning was easily available so the learners could be given the opportunity to reason and reflect on the results in the table. Context specific concepts such as
‘base occupancy’, ‘additional person supplements’, and ‘tariffs for an additional child’ used in a holiday context posed similar problems for learners in Khan’s study of the Grade 9 Learners experiences of the Common Tasks for Assessment (Khan, 2008).
d. Non-recognition of Crucial Information
Inability to recognise crucial information affected the learners’ responses to the examination tasks. Question 2.2.2 required learners to look at the log table and use the information provided on the number of goals scored by teams in each of the four matches to calculate the points gained according to the fanatics scoring system. Many learners failed to identify this crucial information and were unable to complete the calculation.
Question 4.2.1 required learners to calculate the number of babies who survived their first birthday. The figures in the table were based on the number of deaths per 1000 live births.
This information was presented at the beginning of Question 4. Learners failed to identify
this crucial information, with 73 learners failing to answer this question correctly. Many learners complained that the crucial information was too far away from where it was required.
Missing crucial information due to layout of the examination task is not peculiar to this study only. Ahmed & Pollitt (2000) in their study found that learners missed crucial information as a result of the layout of the task and that this in turn affected their performance in the task. In the subsequent interview, one learner responded: “I didn’t realise it was the same question from before and I was thinking where’s this boat from? I’d done the whole particle bit and then it asks you a question that relates to the bit before – I was thinking about particles and stuff rather than the other bit of the question – it tests how well you’ve actually read the thing – it’s reading comprehension…and the number 2 makes you think it’s a different question”.
In this case, the boat context was used in the first few parts of the question, followed by a general question in the second part about molecules. The student had lost track of the ‘story’
that was running through the question, and did not link this with previous parts (Ahmed &
Pollitt, 2000).
The information presented in the scenario in Question 2.1 was not considered ‘crucial’
information by learners to complete the table of values showing the relationship between the number of workers and the time taken to complete the stadium. Values could be found through sequential number patterns. Since the preceding four sub-questions did not require any crucial information from the scenario, learners’ did not consider the scenario to have any crucial information to answer sub-question 2.1.5, which actually required the crucial information about the time required to complete the stadium. The result was that learners based their response on the relationship between the number of workers and cost rather than the number of workers and time. Missing crucial information affected the way learners responded to the examination task. Khan (2008), in analysing learners’ experiences with the Common Task for Assessment (CTA), found that learners missed ‘crucial information’
because of the overload of ‘context information’ (Bansilal &Wallace, 2008).