Accessing and assessing young learner’s mathematical dispositions

Mellony Graven

doi:10.4102/sajce.v2i1.21

Abstract

It is argued in this paper that there is an absence of literature relating to research on learner mathematical dispositions, particularly with young learners. Drawing on Kilpatrick, Swafford and Findell’s (2001) five interrelated strands of mathematical proficiency, which include: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition, it is argued that there has been little engagement with productive disposition in the field of mathematics education and how we might access and assess this strand. Despite competence in all strands being essential for mathematical proficiency, literature and assessments that seek to establish learner levels of mathematical proficiency have tended to focus on the first four and have neglected the last; productive disposition. Finding ways in which to access student mathematical learning dispositions can be challenging, especially with young learners who struggle to articulate their views. An instrument is shared that the author has designed with doctoral fellow, Debbie Stott, in order to access and assess the productive disposition of learners participating in maths clubs run within the South African Numeracy Chair. The findings that emerge in one Grade 3 club with six learners is shared. These findings are related to the data collected through instruments that assess the other four strands of mathematical proficiency. This enables a holistic picture of learner’s mathematical proficiency as intended in the conceptualisation of the interrelated five strands of proficiency.

Highlights

It is argued in this paper that there is an absence of literature relating to research on learner mathematical dispositions, with young learners
Subsequent to the piloting we extended this instrument to include a few additional items as shown in our revised instrument: Figure 1: Revised mathematics learning disposition instrument
In our clubs we consider learner mathematical histories rather than work with notions of learner abilities and reject the notion that a learner may be mathematically stupid and instead focus on the ways in which learners learn and their disposition towards learning. This concurs with Askew et al.’s (1997) finding that ‘effective’ numeracy teachers believe that almost all children are able to become numerate, and ensure that all students are challenged and stretched, not just those perceived to be more able. In this club we would hope that with time learners would begin to provide responses indicating a rich connected understanding of mathematics and Graven – Accessing and assessing young learner’s mathematical dispositions mathematics competence, in terms of the processes and ways in which learners approach and tackle problems, and with regards to their willingness to participate in meaningful engagement in mathematics learning

Summary

Contextual background and empirical field for the study

South Africa is facing a crisis in numeracy education as evidenced by sustained poor performance across international, regional and national assessments (cf. Fleisch, 2008; SACMEQ, 2010; Carnoy, Chisholm, Addy, Arends, Baloyi, Irving & Raab, 2011; DoE, 2008). The focus of these Chairs is twofold: To nurture research in the field of numeracy education that is focused on searching for sustainable ways forward to address the ‘crisis’ and to improve learner numeracy performance in the schools where we do this work. Our Chair has partnered with numeracy teachers (ranging from Grade 0 to Grade 6) in 15 schools in the broader Grahamstown area to work towards the improvement of numeracy teaching and learning in these schools This partnership enables access to numeracy classrooms as the empirical field for research. Negotiated sociomathematical norms (Yackel & Cobb, 1996) which may differ from inschool time rules

Reviewing the literature

Looking at one learner across the instrument and strands

Conclusion