In light of Mathematical Literacy being an altogether new programme, the document would benefit from an introduction that sketches the rationale of the programme for teachers as well as sketching an image of the learner on completion of the programme.

Language and clarity
One of the greatest weaknesses of the document in its current form is that the language needs a lot of tightening up and improvement. Firstly it needs to be grammatically improved and secondly there is a need for an increased level of accuracy in use of language. Examples include:

Identify, describe, compare, classify, calculate shape and motion . . . (Unit Standard 2005)
Describe, apply, analyse and calculate shape and motion . . . (Unit Standard 3004).
Construct, analyse and calculate shape and motion in . . .
(Unit Standard 4004)

While one can "analyse shape and motion" (and even this it can mean a host of different things to different people), and "describe shapes and motions" and "compare (different) shapes and motions." One certainly cannot "calculate shape and motion" or "apply shape and motion" or "construct shape and motion."

Mathematical justifications are provided the control of costs and maximising of profits in relation to data (Unit standard 2002, assessment criteria 3.3)

This statement simply makes no sense

There are many such examples throughout the document and it is not within the scope of this submission to identify each one.

Level of specificity
There are too many instances where the descriptions are too general rather than being specific. Examples include:

Number systems (used in the titles of unit standards 2001 and 2002)
What does the "number systems" refer to here? There seems to be no mention of number systems in the specific outcomes and other design criteria. Furthermore does the use of "number systems" imply the inclusion of binary systems and complex number systems? —it certainly could and that would be beyond the scope of Mathematical Literacy!

The unit standards that deal with "geometry" speak of 2-D and 3-D shapes (technically this should read 2-D shapes and 3-D objects) do not list the shapes and objects to be considered i.e. are non-rectilinear shapes included and what about cardioids and ellipsoids not to mention volumes and surface areas of non-regular 3-D objects. Unless these aspects are specified, there exists the danger that different teachers will interpret the document very differently.

Our experience, as a nation, with Curriculum 2005 was that teachers could not implement the early version due to a lack of specificity and care should be taken to include an appropriate level of specificity throughout the document.

Coherence between and within unit standards
It is important that greater care should be taken to ensure greater coherence between the unit standards in the next iteration of the document. At this stage the document gives the feeling that it was written by a number of different authors who did not co-ordinate their efforts. Examples include:

Unit Standard 2002 Specific Outcome2 includes compound interest which is a specific case of the function A(1+r)n, yet Unit Standard 2003 only lists linear and quadratic functions in the range statement, and no mention is made of exponential functions. In a coherent and integrated set of standards one would expect all functions included in "applied" units to be also included in more purely mathematical units. Also note that the hyperbola, i.e. functions of the form appear quite naturally in simple budgetary and other financial contexts and it would make sense for this function to also be included.

Specific Unit by unit comments

NOTE these comments are by no means comprehensive and AMESA cannot claim that they are consistent either. The time frame for comment has simply not enabled us to do a better job of this. It is, however hoped that they will provide the author team with points to consider. In addition to the comments below, an addendum is provided—in this addendum one AMESA member (Moses Mogambery) gives a detailed critique of Math 2001 and in so doing highlights some of the difficulties that teachers may have with the document.

Math 2001

More specifically:

Math 2002

Math 2003

Math 2004

Math 2005

Math 2006

Math 3001

Math 3002

Math 3003

Math 3004

Math 3005

Math 4001

Math 4002

Math 4003






By Moses Mogambery

Detailed comments are provided for Math 2001 to indicate the difficulty the educator/trainer will experience in interpreting the unit requirements. Time does not permit the writing of detailed comments for all the other units.

1.1 Title: Demonstrate understanding of rational and irrational numbers, and number systems.

There is nothing in the specification to suggest what sort of an understanding of "number systems" is required. Maybe some of the number systems required should be listed, possibly in the range statement.

1.2 Specific Outcome 1: Demonstrate understanding of rational and irrational numbers

This is no more specific than the title.


How does this relate to rational numbers () and irrational numbers ()? For what activities in and should be technology be used? Should one add, subtract, multiple, divide, exponentiate in and ? Should one solve practical problems (numerical and geometric) with numeric data in and ? When using the technology to perform calculations in should answers be returned in the form a/b where a and b are integers, or will decimal answers be good enough always? Should there be activities in and in which the use of technology should be disallowed?

Without this sort of information, the educator/trainer, learner and assessor will be kept guessing as to what the minimum standards are.

It is difficult to determine what computations are required with rational numbers and what computations are required with irrational numbers. This statement does not appear to point to the outcome at all.

This statement is clear enough and it the most elementary activity for this outcome, I think. Unless of course, the use of calculators is not allowed for examples like , where rationalizing the denominator may be required.

Assessment Criteria

1.1 Rational numbers are used to develop set of odd, even and prime numbers.

This is somewhat vague. The question we need to ask is how do we set assessment tasks to determine whether this criterion is satisfied. Are learners expected to use the set of rational numbers as a basis to generate the sets of odd, even and prime numbers?

1.4 Algorithms are executed appropriately in calculation.

What algorithms are learners to use, and for what purposes? There is no mention of any algorithm in the range statements.

1.5 The viability of selected algorithms is verified and justified.

An account of the lack of clarity in the range it difficult to determine whether this criterion refers to an "operation" or "algorithm".


      1. Specific Outcome 2: Know and understand relationships among numbers and number systems, and represent numbers in different ways.

The first question that comes to mind is: does this outcome have anything to do with the title? The title refers to rational and irrational numbers.


This says very little about what should be done with rational and irrational numbers.

This is clear and requires the use of an algorithm or a calculator.

This fits in more with the third range statement of specific outcome 1, where approximation to irrational numbers can be expressed in scientific notation. As an extension, learners could apply the same rules to very small and very large numbers.

Assessment Criteria

It is not clear what the "problem types" are.

What numbers need to be represented as rational and irrational numbers? This needs to be made more specific. Is this possible?


1.4 Specific Outcome 3: Apply base 10 number systems on technology to demonstrate understanding of scientific notation and rounding off numbers.

This outcome is covered in the third range statement of specific outcome 2. Base 10 is not an issue when other bases are not considered.



This is a repetition of the range for Specific Outcome 1. The range is supposed to give the scope (depth and breadth) of an outcome. This implies that one of the outcomes is redundant.



1.5 Concluding Remarks on Maths 2001

The specifications in this unit gave the impression that the intended title is: "Use rational and irrational numbers in computations and practical problems".

Reference is made to "number systems" in the title. It is not clear what is meant by a number system – no clarity is given in either the range or the assessment criteria. It is also not clear as to how many number systems should be studied and compared in order for learners to "demonstrate understanding of … numbers systems".

In my opinion, there is no need for the 3 specific outcomes (none of which is particularly specific). A clearer title, followed by minimum standards that need to be assessed will suffice. What needs to be stated clearly is that educators could go beyond the minimum and explore ideas that are appropriate to their local circumstances, provided the minimum standards are met.