Numeracy Centre Research: A journey over a decade
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What does it mean for a university student to be quantitatively literate (numerate)? What kind of teaching and learning experiences encourage the development of academic numeracy practices? We have been approaching these questions from several vantage points, including considering the effectiveness of using technology, the question of assessment for quantitative literacy and more theoretical considerations of the role of numeracy practices in higher education. The presentation will briefly outline the story of this research trajectory as well as our current thinking about the nature of academic numeracy and what kinds of teaching and learning practices and curriculum structures promote it. Presented by Vera Frith, Robert Prince and Jacob Jaftha
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Numeracy Centre Research: A journey over a decade
- 1. Vera Frith, Robert Prince, Jacob Jaftha, Pam Lloyd, Sheena Rughubar-Reddy, Kate Le Roux, Duncan Mhakure Numeracy Centre, ADP Centre for Higher Education Development, University of Cape Town Numeracy Centre Research: A journey over a decade.
- 3. Overview of Numeracy Centre research What is academic QL and how can it be promoted? Some considerations about the use of technology Questions for further investigation Outline of presentation
- 4. Some reflections Defining the domain of Academic Numeracy (Quantitative Literacy) practice A brief overview of the Numeracy Centre’s research An overview of the Numeracy Centre research
- 5. Academic numeracy (quantitative literacy) is a social practice in which people : - manage situations or solve problems in real disciplinary contexts, - by responding to quantitative (mathematical and statistical) information (which may be presented verbally, graphically, in tabular or symbolic form). - It requires the activation of a range of enabling knowledge, behaviours and processes - and can be observed when it is expressed in the form of a communication, in written, oral or visual mode. Refs: International Lifeskills Survey; Lave, 1988; Street, 2005; Street and Baker, 2006; Johnson, 2007; Yasukawa, 2007 Definition of academic numeracy (quantitative literacy) practices
- 6. Educational Our Practices Disciplinary Academic Numeracy (QL) Practices Nature of QL Framework School Academic development Graduateness Postgraduate Affect Technology Feedback Testing
- 7. Framework for a Quantitative Literacy Test
- 8. Framework for a Quantitative Literacy Test cnt.
- 9. Some initial results across the Higher Education sector
- 10. Some initial results across the Higher Education sector cnt.
- 11. Educational Our Practices Disciplinary Academic Numeracy (QL) Practices Nature of QL Framework School Academic development Graduateness Postgraduate Affect Technology Feedback Testing
- 12. Marco Polo: “ To distinguish the other cities’ qualities, I must speak of a first city that remains implicit. For me it is Venice.” Kublai Khan: “ You should then begin each tale of your travels from the departure, describing Venice as it is, all of it, not omitting anything you remember of it.” Invisible Cities, Italo Calvino
- 14. Health and Rehabilitation Studied in first year Speech and Hearing Science
- 15. Psychology – first year Psychology
- 16. Extract from judgement in: Government of South Africa v Grootboom 2001 (1) SA 46(CC) (studied in first year Constitutional Law course) “ The housing shortage in the Cape Metro is acute. About 206 000 housing units are required . . . the number of shacks in this area increased by 111% during the period 1993 to 1996 and by 21% from then until 1998. . . . The scope of the problem is perhaps most sharply illustrated by this: about 22 000 houses are built in the Western Cape each year while demand grows at a rate of 20 000 family units per year. The backlog is therefore likely to be reduced … only by 2 000 houses a year. Law
- 17. Elaboration of the competencies involved in QL practice 1. Know Know the meanings of quantitative terms and phrases ( verbal representations). Know the conventions for the symbolic representation of numbers, measurements, variables and operations Know the conventions for the representation of quantitative information in tables, charts, graphs, diagrams and objects. ( visual representations). 2. Identify Identify connections and distinction between different representations of quantitative concepts Identify the mathematics to be done and strategies to do it Identify relevant and irrelevant information in representations 3. Derive meaning Understand a verbal description of a quantitative concept/situation/process Derive meaning from representations of data in context Derive meaning from graphical representations of relationships Derive meaning from diagrammatic representations of spatial entities Translate between different representations 4. Apply Use mathematical techniques - calculating, estimating, measuring, ordering, modelling, applying algebraic or graphical techniques etc. 5. Think Synthesise information or ideas from more than one source Reason logically Conjecture Interpret, reflect and evaluate. 6. Express quantitative concepts Represent quantitative information using appropriate representational conventions and language Describe quantitative ideas and relationships using appropriate language
- 18. So what difference does this knowledge make?
- 19. Disciplinary context Extract from statement of outcomes for QL in first year MBChB Content Contexts used “ Reasoning/thinking” Understand and work with percentiles (including median, quartiles) of a distribution. Read off values for the percentiles of a distribution from a cumulative curve. Distribution of body weights and heights in a normal population, Body Mass Index Make conceptual links between different representations of the same concepts Generalise ideas from specific cases Understand, calculate and work with the statistical measures for central tendency; mean and median Body weights and heights, Body Mass Index Reason about distributions - data and uncertainty
- 20. Questions relating to choice of contexts for QL courses Do they serve our purposes for teaching QL? Should contexts be familiar to students? What is the appropriate balance between context and content in QL courses? Ref: Frith, V. et al (2010) Tensions between content and context in a quantitative literacy course for university students. In preparation: Mathematics Education and Society conference
- 21. Purposes for teaching quantitative literacy Tertiary study Professional life and work Everyday life Citizenship Social justice Ref: Frith, V. et al (2010) Tensions between content and context in a quantitative literacy course for university students. In preparation: Mathematics Education and Society conference
- 23. Contexts in the curriculum “ I found like that first section of the course … quite tedious in a way. Uhm, it didn’t really seem to justify getting up so early in the morning to, to like get to university … the stuff that you could sort of just blag my way through ….” “… the first 3 units … I found them very useful in terms of that they really made you think and analyse something differently ….they kind of like made you look beyond the surface meaning and even go deeper … it was something that I thought, wow, I could actually use this in the future when I am working . . .” “… I just thinked the course was very difficult because I did maths and so the whole writing and analysing sentences and all it was like, oh my word. … I was like oh my what am I going to have to write so long and all …”
- 24. In 2009, we are administering computer-based learning materials to approximately 1800 students: Numeracy Centre courses for Law and Humanities: ~ 400 Psychology: ~850 Sociology: ~200 Health Sciences: ~350 Use of computers
- 25. Spreadsheets as a productivity tool Computer technology in QL
- 26. Project to conduct a survey that either c onfirms or disproves that Cape Town’s youth is indulging in risky behaviour (first year QL students in the psychology major stream) A mini research project in a course (MAM1016S) Student answers saved Conduct survey Save data database Analyse own data Retrieve data Submit tutorial Write report Complete tutorial Tutorial feedback
- 28. Aspects of feedback Affective issues Learning environment design Technology in QL: Quo Vadis?
- 30. Educational Our Practices Quantitative disciplinary practices Nature of QL Framework School Academic development Graduateness Motivation Technology Feedback Testing Transfer Language
- 31. See our posters! Or e-mail: [email_address] [email_address] . [email_address] For more information:
Notas do Editor
- Vera to introduce the presentation as Co-ordinator of the Numeracy Centre.
- The Numeracy Centre was established in 1999 with the main goals of: 1. To assist the university with ensuring that students and graduates are quantitatively literate in a manner that is appropriate for their course of study and intended role in the community. and 2. To promote access to and foster success in quantitatively demanding programmes of study. (overhead of goals) Notice that we were named “the Numeracy Centre”, but we often refer to what we do as quantitative literacy. From the beginning of 1999 till the end of 2007, Robert Prince was the coordinator and built the unit up from a staff of 2.5 to its present size. This year we have 5 and 2 half lecturers: myself, Jacob Jaftha, Pam Lloyd, Sheena Rughubar-Reddy, Kate Le Roux, Duncan Mhakure and Jumani Clarke. (INTRODUCE the people)
- First Robert will give an overview of the Numeracy Centre’s research, then I will talk briefly about our understanding of “What is academic QL and how can it be promoted?”, which is our primary overarching research question. Jacob will say something about the research on the use of computer technology for teaching and then I will wrap up by mentioning areas which we believe require further investigation. It is hard to do justice to the all the different areas of research we have engaging in over the last 10 years in a short presentation, so our discussion will necessarily focus on selected insights. I hope that anyone who is interested in more details will talk to us at the “poster sessions”. Hand over to RP
- RP: (12 minutes) NC research overview, including testing. [I will give a very brief overview of the research that we, in the Numeracy Centre, have been doing over the past ten years.
- One of the thrusts of our research has been to develop a definition of Academic Numeracy (QL) practice (overhead of def) and to elaborate it into framework for describing what a student needs to be able to do in order to practice QL. Quantitatively literate behaviour can be understood in terms of the disciplinary context in which the QL is practiced, the maths and stats content that is required and the kinds of thinking that the student must engage in.
- VF: some specifics about our understanding of the nature of QL in HE and what we know about and/or are learning about how to address it in the curriculum Our “problem” is to ensure that our students are appropriately quantitatively literate “ both as a means of improving learning capacity and as a contribution to informed citizenship” (Concept Paper ‘Enhancing the quality and profile of UCT graduates’ (2009)) Robert has outlined the different lenses we have used to understand our problem. I am going to describe some of our insights in terms of what it means for a student to be appropriately QL and what we know and are learning about how to address it in the curriculum. So first we consider “what does it mean to be appropriately quantitatively literate for an academic discipline.”? What do students experience? I am going to show a few examples of extracts from curricular texts. To give a flavour of the problem.
- This graphic is introduced to first year students of audiology and speech therapy and underlies the understanding of some of the most fundamental concepts in the study of the science of human hearing. It is a two –dimensional representation of a three dimensional surface (using non-linear scales) and students in first year are expected to use it to understand and explain the ways in which the human ear reacts differently under different circumstances.
- This is the kind of table that appears in many of the readings psychology students engage with. It requires students to have the competence to read tables and to understand various statistical measures.
- Students are introduced to the Grootboom case in their first year. The significance of this case is that it was the first decision by the Constitutional Court on the so-called 'socio-economic rights', which are rights such as the right to housing and education that are relatively unique to our Constitution . Even this very brief extract from the judgement contains a number of tricky quantitative concepts (such as 111% increase, compounding effect of consecutive % increases, growth rates). So what does it take to engage with quantitative information within a discipline? This is the crux of understanding what it means for a student to be quantitatively literate. When engaging with quantitative information one has to keep the understanding of the disciplinary context, and the understanding of the mathematical or statistical content in constant interplay, as well as bring to bear the necessary thinking and critical capacities.
- One of the thrusts of our research has been to develop a definition of QL (as described by Robert) and to elaborate it into framework for describing what a student needs to be able to do in order to practice QL.. Briefly we analyse QL behaviour in terms of knowledge of: conventions of representation, ability to identify and distinguish relevant information and concepts, to derive meaning from representations, to do the necessary mathematics and statistics, to think logically and critically and to express quantitative concepts in a variety of ways. (There is a poster that gives more information about the use of the framework and shows how it can be used to analyse curricular events) The framework was first required for our work in QL test specification. We have used versions of it for QL events in the disciplinary curriculum and for our engagement with curriculum design for our courses (was the subject of the sections we wrote for HESA’s 2006 publication about the NBT, and of our presentation at the Learning conference in Jbg in 2007 and our paper in SAJHE this year)
- So what difference does this knowledge make? Our task is to apply our understanding of QL to curriculum design. I will only have time to discuss briefly, as an example, one important question, which is the one of contextualisation of material in our courses. We have stressed the primacy of the disciplinary context and one of our challenges is to embed everything that we do with students in appropriate context, while at the same time identifying and teaching the necessary mathematical and statistical content.
- In interventions that are integrated into the disciplinary courses, such as in the Health Sciences, the context is determined by the courses we work in, and our task is often then to identify the quantitative content that we need to focus on while mastering the context sufficiently well ourselves in order to teach within it. (In the slide point out that the middle column is determined by the MBChB curriculum, the first column is also determined by them, but “discovered” by us)
- In designing stand-alone quantitative literacy courses for specific disciplines, the major challenge has to do with the identification and selection of suitable curriculum contexts, that will anticipate the disciplinary curriculum that these students will encounter in other courses. I am going to discuss three issues relating to the choice of contexts: do they serve our purposes for teaching QL?, Should they be familiar to students? And What is the appropriate balance between context and content in our courses?
- Choice of contexts for QL courses: 1. Contexts used need to serve our purposes for teaching QL: What are our purposes? -First, the centre exists at the institution to assist students with the quantitative demands of their chosen discipline with a view to their future careers. -Secondly, our work is driven by a social justice agenda, one aspect of which is to try to sensitize students to the social problems in our country. --Lastly, we aim to equip students to become functioning citizens of the country.
- Here is a small extract from the materials for our first semester course for Humanities students, to give an idea of the kind of curriculum I am talking about in this discussion. 2. Should contexts be familiar? If we use contexts with which we can assume all the students are very familiar (if these in fact exist) their practice of quantitative literacy is less likely to be hindered by their unfamiliarity with the context. However, such a choice of context could then compromise our goal of sensitising students to social issues in society (our social justice agenda) and also our goal of preparing them for citizenship. There is a dilemma here – some writers argue that there are issues of power involved in the selection of contexts, and that contexts chosen should have relevance to students current lives. If we teach them for example about home loans it could be argued that it is not a context they need to engage with now, and that we would be indoctrinating them into a capitalist way of thinking, but we also want to prepare students for the role in society which they have clearly chosen for themselves, which will surely (and may already) include the management of loans. However, If we use contexts that students are not familiar with, we may be overloading them with having to learn about two different things at the same time (the mathematics and the facts about and features of the context), at the risk of letting the mathematics become submerged. Given our experience that the students entering higher education have significant difficulties with the required mathematical and statistical knowledge and techniques, how much of our limited time with them should we be spending on teaching them about the features of specific contexts? 3. Balance between content and context We have a choice between a ‘content-driven’ curriculum and a ‘context-driven’ one.. Our belief has always been that ideally we should strive for a higher degree of contextualisation, where students would engage with substantial real contexts, and the necessary mathematics and statistics would arise and be developed as needed. The motivation for this is that it more closely mimics the reality of the practice of QL in the disciplines; our assumption being that similarity between the features of the social practices represented by the context selected for the stand-alone QL course and of the disciplinary context will enhance transfer of what students learn in our courses to their practice in the disciplines. Our concern is that we do not have evidence that this assumption is in fact justified, although we do have some evidence that students believe they are able to transfer their knowledge from our courses, it is often those parts of the course in which the content is most explicit that they refer to. We have a poster that summarises the results of a survey we did of past students – and the striking result was that their perception of the relevance on usefulness of the course increases as they progress through their program.
- Student quotes : have audio if possible. One of the tensions that students experience with the kind of material is that they are often confused about the objectives of the course and do not clearly see the quantitative content that is attempting to develop. The coherence of the mathematics that we want them to learn is not clear and is often submerged while on the other hand we as lecturers are often frustrated by the students’ apparent lack of interest in and superficial engagement with the context. Students also stress the difficulty they have with the amount of dependence on language and the amount of writing and explaining they have to do.
- Introduce JJ’s bit I have just outlined a few issues to give a flavour of the kinds of questions that our current research is engaging with and the factors that influence our curriculum choices. However, since so many of the interventions we have either consist of or contain series of Excel-based learning materials and I have not as referred to them, I would like to give Jacob a chance to talk about them.
- The case of technology – JJ (5 min) Hoghlight 2 or 3 “research results” and demonstrate how they are used to inform Excel tutorial design (Graphic of a worker) Just like any other worker, QL professionals use productivity tools. In the case of QL a spreadsheet such as microsoft excel is such a productivity tool. We consider the proficient use of spreadsheets for example microsoft excel to be an important competence for QL in higher education. Next slide illustrates an example of our approach.
- Picture of workflow. Data collection Data capturing Data analysis Reporting Students in the social sciences generally are expected to collect data, capture it, analyse it and report on their findings. Sometimes an exercise expect them to do the complete cycle, and at other times only one or more of the activities even including the research design. Excel is a useful tool for design of template for data collection, for data capturing and for analysis – and in mam1016s it is used in exactly that way for a project done by for six students. Of course, this happens only after a series of interactive (excel-based) tutorials where the necessary skills are developed. (before this … students do a series of interactive excel-based tutorials that scaffold the necessary competencies required by the project) In developing these tutorials various design and learning issues are important.
- Nature: Integrated part of the course Focus on student learning & interaction QL within Excel (not only the tool!) Facilitators (tutors) (tutor/student ratio small) Student active participants Allow students to proceed at their own pace, and provide assistance where and when they need it Not just drill & practice not just delivering material, so website will not suffice Reported: VF,JJ,RP: Interactive Excel Tutorials in a Quantitative Literacy Course for Humanities Students in Integrating Technology in Higher Education ( Eds) M.O. Thirunarayanan & Aixa Pérez-Prado, 2005 Features: Data management is handled within the learning environment, have different components (office suite + database + network file system, for example) VBA scripting used for interaction Feedback (immediate and delayed)<formative and summative> Don’t intend to develop an ITS (intelligent tutoring system), even though aspects of design are influenced by research in the ITS field Maxim of 20% of functionality satisfies 80% of the uses (and users). Unfortunately we’re part of the other 20% that requires much more than the 20% functionality. Pushing boundaries to use the office suite, university infrastructure and other components to provide a (tutorial) learning environment. Enhance the quality of the learning Efforts to provide adaptive feedback have resulted in making the marking of electronic assessments more efficient and easier to maintain consistency in marking. (eg. Psy2006f and pph1002s – large classes, issues of consistency and efficiency) Reported: AD,JJ,DH: Customising Microsoft Office to develop a tutorial learning environment BJET 35(2), 2004 Math anxiety, computer anxiety/fear (confidence). Are these correlated, and how do you minimise possible interrelated consequences – VF,JJ,RP: Interactive Excel Tutorials for learning Mathematics and Statistics, ICMI, 2005 Learning issues: Concepts delivered first electronically or in classroom (scheduling or learning design) visualization of mathematical (function) concept Evaluating the effectiveness of interactive computer tutorials for an undergraduate mathematical literacy course, BJET 35(2), 2004
- The concept of learning environment: Tutor (human) touch with technology Feedback (timing, granularity etc) Learning design Embedded within university infrastructure Affective issues?? Office suite as a changing environment
- Other things we need to know more about: I would just like to conclude by mentioning some of the lines of enquiry that we still need to pursue. Student motivation/expectations –Many students come with a fear or hatred of mathematics, which translates to a reluctance to doing our courses (statement like “I came to do Law especially because I never wanted to have to do any maths again” are common) Alternatively they see our courses as being “not proper mathematics” and consequently a waste of time or as having stigma attached to them. We need to understand these phenomena better in order to develop strategies for dealing with them. CLICK And I don’t think dressing up will be the answer!
- So we could add a lens for student motivation so our research agenda - CLICK 1 The second question that we could explore further is to do with transfer. – we need to find a way of establishing if students are actually able to transfer most of what they learn in our courses to situations in their disciplinary curriculum that call for it. This is related to the question of what is the optimal position for our interventions within programmes (is it necessarily at the beginning? Does it need follow-up throughout the program? CLICK 2 Lastly there is the big question of Language – we need to know a great deal more about the role of language in QL and how language may act as a barrier, especially to disadvantaged students. There is also the question of how best to teach the fluent use of the specific quantitative language that is used in quantitative disciplines. CLICK 3 Concluding remark: We have been on our research journey now for a decade, and the arena we are in is changing and continues to be very complex and many-facetted. So we have learned a great deal but we also look forward to achieving a greater integration of all the various insights we have gained. We no doubt have many interesting years ahead.
- Questions for any of the speakers.