The ability to reason about numbers in relative terms is essential for quantitative literacy, which is necessary for studying academic disciplines and for critical citizenship. However, the ability to reason with proportions is known to be difficult to learn and to take a long time to develop. To determine how well higher education applicants can reason with proportions, questions requiring proportional reasoning were included in one version of the National Benchmark Test as unscored items. This version of the National Benchmark Test was taken in June 2014 by 5 444 learners countrywide who were intending to apply to higher education institutions. The multiple choice questions varied in terms of the structure of the problem, the context in which they were situated and complexity of the numbers, but all involved only positive whole numbers. The percentage of candidates who answered any particular question correctly varied from 25% to 82%. Problem context and structure affected the performance, as expected. In addition, problems in which the answer was presented as a mathematical expression, or as a sentence in which the reasoning about the relative sizes of fractions was explained, were generally found to be the most difficult. The performance on those questions in which the answer was a number or a category (chosen as a result of reasoning about the relative sizes of fractions) was better. These results indicate that in learning about ratio and proportion there should be a focus on reasoning in various contexts and not only on calculating answers algorithmically.

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渴望在南非接受高等教育的离校生的比例推理能力

对相对数字进行推理的能力对于定量扫盲至关重要，而扫盲对于研究学术学科和公民身份至关重要。但是，众所周知，按比例推理的能力很难学习并且需要很长的时间才能发展。为了确定高等教育申请人可以按比例推理的程度，要求按比例推理的问题已作为一种未评分项目纳入了国家基准测试的一个版本中。该版本的国家基准测试于2014年6月由全国范围内的5444名打算申请高等教育机构的学习者参加。选择题在问题的结构，所处的环境和数字的复杂性方面各不相同，但都只涉及正整数。正确回答任何特定问题的候选人比例从25％到82％不等。正如预期的那样，问题的上下文和结构影响了性能。另外，通常发现最困难的问题是，答案以数学表达式的形式给出，或者以句子的形式解释分数的相对大小的原因。在答案是数字或类别（由于分数的相对大小的推理而选择）的那些问题上的表现较好。这些结果表明，在学习比率和比例时，应着重于在各种情况下进行推理，而不仅仅是在算法上计算答案。正如预期的那样，问题的上下文和结构影响了性能。另外，通常发现最困难的问题是，答案以数学表达式的形式给出，或者以句子的形式解释分数的相对大小的原因。在答案是数字或类别（由于分数的相对大小的推理而选择）的那些问题上的表现较好。这些结果表明，在学习比率和比例时，应着重于在各种情况下进行推理，而不仅要通过算法来计算答案。正如预期的那样，问题的上下文和结构影响了性能。另外，通常发现最困难的问题是，答案以数学表达式的形式给出，或者以句子的形式解释分数的相对大小的原因。在答案是数字或类别（由于分数的相对大小的推理而选择）的那些问题上的表现较好。这些结果表明，在学习比率和比例时，应着重于在各种情况下进行推理，而不仅仅是在算法上计算答案。通常被认为是最困难的。在答案是数字或类别（由于分数的相对大小的推理而选择）的那些问题上的表现较好。这些结果表明，在学习比率和比例时，应着重于在各种情况下进行推理，而不仅仅是在算法上计算答案。通常被认为是最困难的。在答案是数字或类别（由于分数的相对大小的推理而选择）的那些问题上的表现较好。这些结果表明，在学习比率和比例时，应着重于在各种情况下进行推理，而不仅仅是在算法上计算答案。