An analysis of undergraduate core material in the light of hand-held computer algebra systems

Pointon, A. J.; Sangwin, Chris

doi:10.1080/0020739031000148930

Cited by 34 publications

(19 citation statements)

References 6 publications

(4 reference statements)

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“…Indeed, several studies have shown that students are mainly given tasks that promote the use of predetermined algorithms, procedures, and/or examples of how to solve the task rather than opportunities to engage in a problem-solving struggle without instruction (Stacey and Vincent, 2009;Denisse et al, 2012;Boesen et al, 2014;Jäder et al, 2019). For example, Jäder et al (2019) examined mathematics textbooks from 12 countries and found that 79% of the textbook tasks could be solved by merely following provided procedures, 13% could be solved by minor adjustments of the procedure, and only 9% required students to create (parts of) their own methods (for similar findings, also see Pointon and Sangwin, 2003;Bergqvist, 2007;Mac an Bhaird et al, 2017). In response to these findings, Lithner (2008Lithner ( , 2017 developed a framework arguing that the use of instructions in terms of predefined algorithms has negative long-term consequences for the development of students' conceptual understanding.…”

Section: Introductionmentioning

confidence: 89%

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

2020

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In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension.

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Section: Introductionmentioning

confidence: 89%

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

2020

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“…The MATH taxonomy classifies tasks according to the skills needed to solve them, with various categories arranged in three broad groups; these are summarised in Table 1. A similar classification scheme was later developed independently by Pointon & Sangwin (2003) and by Tallman et al (2016). The similarity of these taxonomies supports the validity of the approach.…”

Section: Taxonomiesmentioning

confidence: 57%

Reliable application of the MATH taxonomy sheds light on assessment practices

Kinnear

Bennett

Binnie

et al. 2020

Teaching Mathematics and Its Applications: An International Journal of the IMA

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The MATH taxonomy classifies questions according to the mathematical skills required to answer them. It was created to aid the development of more balanced assessments in undergraduate mathematics and has since been used to compare different assessment regimes across school and university. To date, there has been no systematic investigation of the reliability of the taxonomy when applied by multiple coders, and it has only been applied in a limited range of contexts. In this paper, we outline a calibration process which enabled four novice coders to attain a high level of inter-rater reliability. In addition, we report on the results of applying the taxonomy to different secondary school exams and to all assessment questions in a first-year university mathematics module. The results confirm previous findings that there is a difference between the mix of skills assessed in school and university mathematics exams, although we find a notably different assessment profile in the university module than in previous work. The calibration process we describe has the potential to be used more widely, enabling reliable use of the MATH taxonomy to give insight into assessment practices.

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“…The impact of technology on the style of examination questions has been discussed in detail by authors such as Brown (2001), Drijvers (1998), Kokol-Voljc (1999 and Pointon and Sangwin (2003). However, the focus of these authors was on the impact that the graphics calculator had on the style of the questions, whereas the analysis detailed in this paper is focussed on the impact that the graphics calculator has had on the type of mathematics skills assessed.…”

Section: Literature Reviewmentioning

confidence: 95%

Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested?

Brown

2009

Educ Stud Math

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The paper reports on the introduction of the graphics calculator into three centralised examination systems, which were located in Denmark, Victoria (Australia) and the International Baccalaureate. The introduction of the graphics calculator required those responsible for writing examination questions to consider how to assess mathematical skills within this new environment. This paper illustrates the types of mathematics skills that have been assessed within the graphics-calculator-assumed environment. The analysis of the examination questions indicated that only two out of the six mathematics examinations considered demonstrated any significant change in the types of skills assessed in conjunction with the introduction of the graphics calculator. The results suggest that it is possible to reduce the use of questions assessing routine procedures (mechanical skills) with a graphics calculator, but it is also evident that there have not been major changes in the way that examination questions are written nor the mathematics skills which the questions are intended to assess.

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An analysis of undergraduate core material in the light of hand-held computer algebra systems

Cited by 34 publications

References 6 publications

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

Gaining Mathematical Understanding: The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

Reliable application of the MATH taxonomy sheds light on assessment practices

Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested?

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