Students' difficulty with proportional reasoning in a university quantitative literacy course

Frith, Vera; Lloyd, Pam

doi:10.20853/28-3-372

Cited by 2 publications

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“…Although students are generally comfortable with straightforward, algorithmic-type calculations (almost always accomplished using a calculator, regardless of the type or simplicity of numbers involved), even a slight variation in the presentation of a problem results in confusion or blind insertion of numbers into a formula (Frith and Lloyd 2014). Even after repeated exposure to the concept of percentage change in different contexts, using what Madison (2014, 12) describes as "spaced practice" rather than "massed practice", we remained unconvinced that students had truly mastered the concept.…”

Section: Preceding Workmentioning

confidence: 99%

“…In addition, it was clear that, on the whole, students still did not have access to the appropriate language in the exposition of their reasoning and lacked clarity of expression. (For a more detailed description of this process, see Frith and Lloyd 2014).…”

Section: Preceding Workmentioning

confidence: 99%

“…In question [8] students had to quantify the relationship between the population sizes (d) given values for murder rates (r) and number of murders (n) thus: 1 ≈ 2 and 1 ≈ 4 2 → 1 ≈ 4 2 . Student responses were coded using a refinement and synthesis of the frameworks used previously Frith 2013, Frith andLloyd 2014), which is shown in Table 2. Unlike those used earlier in our study, this more generic framework can be used for analysing responses to questions where the fractions describe percentage change or rates, such as birth rates or mortality rates.…”

Section: Questions [1] [2] and [3]mentioning

confidence: 99%

“…Unlike those used earlier in our study, this more generic framework can be used for analysing responses to questions where the fractions describe percentage change or rates, such as birth rates or mortality rates. This coding enabled us to place responses systematically in terms of whether they were pre-liminal, in the liminal space, or at the threshold, as we did before in Frith and Lloyd (2014).…”

Section: Questions [1] [2] and [3]mentioning

confidence: 99%

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Investigating Proportional Reasoning in a University Quantitative Literacy Course

Frith

Lloyd

2016

Numeracy

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The ability to reason with proportions is known to take a long time to develop and to be difficult to learn. We regard proportional reasoning (the ability to reason about quantities in relative terms) as a threshold concept for academic quantitative literacy. Our study of the teaching and learning of proportional reasoning in a university quantitative literacy course for law students consisted of iterative action research, in which we introduced various teaching interventions and analysed students' written responses to assessment questions requiring students to explain their reasoning in situations that call for proportional reasoning. For this analysis we used a modified phenomenographic method to develop and refine a framework to code the responses. This enabled us to broadly describe the responses in terms of the concept of the liminal space that a student must traverse in coming to a full understanding of a threshold concept, and to further define the liminal space to facilitate finer description of students' responses. Our latest analysis confirmed that many university students cannot reason with proportions, that this kind of thinking is difficult to learn, and that it takes more time than is available in a one-semester course. The context and structure of the questions have a marked effect on students' ability to apply proportional reasoning successfully. The fraction of students who were classified as 'at or over the threshold' (i.e., fairly competent at proportional reasoning) after instruction ranged between 8% for the most difficult question and 48% for the easiest. Vera Frith is the coordinator of the Numeracy Centre, a unit within the Centre for Higher Education Development at the University of Cape Town. Her primary interests are the quantitative literacy development of university students and the appropriate curriculum for this purpose.Pam Lloyd is a quantitative literacy lecturer in the Numeracy Centre at the University of Cape Town and is responsible for the course for law students. She is interested in researching her own practice in order to improve teaching and learning.

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Section: Preceding Workmentioning

confidence: 99%

Section: Preceding Workmentioning

confidence: 99%

Section: Questions [1] [2] and [3]mentioning

confidence: 99%

Section: Questions [1] [2] and [3]mentioning

confidence: 99%

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Investigating Proportional Reasoning in a University Quantitative Literacy Course

Frith

Lloyd

2016

Numeracy

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“…From our experience of teaching quantitative literacy to university students, we have observed that proportional reasoning is a troublesome concept; it is difficult to learn and takes a long time to learn. Consequently, we regard proportional reasoning as a 'threshold concept' (Meyer & Land, 2003) for all academic quantitative literacy (Frith & Lloyd, 2014;Lloyd & Frith, 2013). This threshold concept, once mastered, opens a gateway to thinking differently about quantities.…”

Section: Introductionmentioning

confidence: 99%

Proportional reasoning ability of school leavers aspiring to higher education in South Africa

Frith¹,

Lloyd²

2016

Pythagoras

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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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Students' difficulty with proportional reasoning in a university quantitative literacy course

Cited by 2 publications

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Investigating Proportional Reasoning in a University Quantitative Literacy Course

Investigating Proportional Reasoning in a University Quantitative Literacy Course

Proportional reasoning ability of school leavers aspiring to higher education in South Africa

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