Note: This submission is a response to the SAQA call for comments on Mathematical Literacy.
AMESA (the Association for Mathematics Education of South Africa) has prepared this submission to SAQA through its Curriculum Committee and in consultation with a range of members.
AMESA's position with respect to Mathematical Literacy
- We recognise the need for and support the introduction of Mathematical Literacy as a compulsory credit for all learners at NQF levels 2, 3 and 4. That is, we see the learning of Mathematics as the right of all learners.
- We believe that all learners at NQF levels 2, 3 and 4 have the ability to learn Mathematics to the extent that it has meaning in their lives.
- Agreeing with SAQA's stated aim of the FETC, namely that: the primary purpose of the FETC "is to equip learners with the knowledge, skills and values that will enable meaningful participation in and offer benefits for society as well as providing a basis for continuing learning in higher education and training, and enable learners to be productive and responsible in the workplace," we believe that relevance should be the measure against which the inclusion and exclusion of content is determined.
- We are concerned that Mathematical Literacy should not be a "watered down" academic Mathematics but rather Mathematics with a different emphasis. If the purpose of the FETC is among other things to benefit society then the Mathematics needed by the learner is not necessarily more (in terms of knowledge) than that covered at the GET level, but rather the Mathematical thinking skills-habits of mind-to be able to apply that learning in various contexts.
AMESA's general concerns regarding Mathematical Literacy
AMESA is concerned about the following aspects regarding the introduction of Mathematical Literacy and the development of the associated unit standards:
- One of our most significant concerns regarding the Mathematical Literacy Unit Standards is the learning assumption on which they are based, namely: "The credit value is based on the assumption that people starting to learn towards this unit standard are competent in Mathematics and Communication at NQF level 1." Our concern is not with the assumption per se but with the reality that the assumption is currently invalid for the vast majority of learners in South Africa. This lack of fundamental competence compromises the successful implementation of the Unit Standards.
- Recognising that the FET (and the proposed Unit Standards) serve both labour and education, we are particularly concerned at the lack of clarity with respect to the proposed implementation in schools from the NDoE. We understand that there may be a move by the NDoE toward a whole qualification route for schools. If this is the case, how will Mathematical Literacy Unit standards be incorporated?
- While there may be some political imperative to implement Mathematical Literacy in 2003, we are concerned that this timing (especially with respect to schooling/education) is too rushed. In particular we are concerned that introduction in 2003 will not allow for:
- Proper piloting of the programme
Piloting is essential if the introduction of Mathematical Literacy it is to be successful, especially given that Mathematics Literacy will be taught to more than double the number of learners currently taking Mathematics (at all three levels)
- Sufficient teacher recruitment
It is well known that there is an existing shortage of qualified Mathematics teachers. Considering the nature of the proposed unit standards, AMESA is convinced that only well trained Mathematics teachers can make a success of this programme. In that light large-scale teacher recruitment will need to be effected to provision this programme.
- Adequate teacher training
The proposed unit standards will require teacher training, even for the currently employed (and qualified) teacher corps. To effect this on the scale required for full implementation in Grade 10 in January 2003 seems near impossible.
- Development of learning support materials
The successful implementation of Mathematical Literacy will depend in large part on the development of appropriate learning support materials. We have no experience of teaching Mathematical Literacy and as such no existing resources. As a result the development of learning support materials is both critical and difficult, and by implication: time consuming.
- In developing Mathematical Literacy Unit Standards we recognise a tension between on the one hand a need to ensure progression beyond the GET band (NQF level 1), and on the other hand setting standards attainable by the participants in the programme.
- It is clear that the proposed unit standards have been developed using existing Mathematics programmes as points of departure. While practical, AMESA questions the wisdom of this. Would it not have been better (and OBE appropriate) to begin with an image of the Mathematical Literacy learner and their needs and to develop the unit standards from that? We do not see Mathematical Literacy as necessarily developing a lot of new mathematical knowledge, but rather being about using and applying GET mathematics in more sophisticated contexts and at higher levels of analysis and understanding. As such, Mathematical Literacy could in all probability be limited to the following areas:
- Financial Literacy
- Reading and Interpreting Data and Chance
- Modelling and Measuring.
- The organising framework suggested in point 5 could-stressing again that progression for Mathematical Literacy should be specified in terms of the complexity of the contexts and expected analytic skills required of students-be further developed as follows:
- Financial Literacy
We see Financial Literacy as the ability to solve and interpret problems in financial contexts using mathematical knowledge and skills. The latter includes knowledge of ratio and proportion, percentages, behaviour of relationships between variables, reading and developing graphs and using formulae. The Specific outcomes and range statements for Unit Standards 2002, 3002 and 4002 adequately capture the contents and progression of Financial Literacy for this phase.
- Reading and Interpreting Data and Chance
We see this area as involving the critical reading and interpreting of numerical information in a range of contexts using mathematical knowledge and skills. The latter includes knowledge of collecting, organising, representing and summarising data, making predictions on the basis of data trends, critically evaluating and interpreting data, posing questions for the collection of data. Probability must be included only in so far as it supports the reading and interpretation of data and not for the sake of studying probability models (which we feel should be included as an elective in this band). Unit Standards 2006 and 3005 deal with reading and interpreting data. Specific outcomes 1 and 3 and their range statements adequately capture the contents and progression of reading and interpreting data for this phase. However, Specific outcome 2 feels inappropriate since it deals with probability for the sake of probability. Unit Standard 4005 also deals with reading and interpreting data. The range statements of Specific Outcomes 1 & 3 (except for the last 4 bullets of Specific Outcome3) adequately capture the contents and progression for this phase. Again, Specific outcome 2 feels inappropriate since it deals with probability for the sake of probability.
- Mathematical Modelling
We see this area as being about solving contextual problems using a range of mathematical knowledge and skills. The latter includes identifying variables and relationships between variables, representing relationships in various forms such as words, tables, graphs and equations and translating between these forms. The Unit standards that currently refer to mathematical modelling do not capture our understanding of what is required for this phase. They include contents we think should be part of the core mathematics.
We see measuring as including work with geometrical properties such as surface area and volume, issues of appropriate precision and accuracy and the ability to describe shapes and objects as related to the contexts in which learners study and work.
AMESA is concerned that the unit standards developed for Mathematical Literacy (NQF levels 2, 3 and 4) are simply not ready for registration.
We specifically feel that:
AMESA furthermore pledges its support to the process and avails itself for further consultation and involvement.
Compiled by Aarnout Brombacher
- Further debate regarding the selection and organisation of Mathematical knowledge, skills and values as appropriate for Mathematical Literacy needs to take place,
- The document in its current form needs significant revision and modification and in this light we would like to have it made available for another round of public comment. This is seen as critical given enormous shift in Mathematics education implied by the introduction of Mathematical Literacy,
- Further to the previous point, we do not feel that "tinkering" with the current document is the most appropriate way to address the various concerns raised, and finally
- A longer development period is needed to ensure the success of this venture.
For the AMESA Curriculum Committee
11 September 2001
94 Myburgh Road
Tel: (021) 689-9154
Fax: (021) 685-5675
Click here for Addendum A and Addendum B