We have written and produced three maths books to help to meet specific needs in Tanzanian primary schools. These are books to guide teachers step-by-step to teach pupils of pre-primary, standard
I and standard II. The books are in Swahili with illustrations, charts and diagrams, and several appendices detailing how to make and use the materials for activities and games. The books cover
the Tanzanian syllabus and complement it with explanations, activities and the inclusion of essential basic demonstrations so that key, core concepts are grasped. They are called WWW.Hisabati,
Wasaidie Wanafunzi Wafahamu (Let’s Help the Pupils to Understand Maths).

The problem with mathematics teaching and the current primary syllabus in Tanzania is that pupils are not learning by doing. This non-active approach is not successful with young children who are
still developing.

If a syllabus takes account of the development stage of the pupils, and follows steps in mathematics that build logically and systematically then there is little difficulty in pupils learning
mathematics. This applies throughout the world.

Teachers in pre-primary, standard I and standard II are laying the foundations for ALL future mathematics. These foundations need to be solid and well understood. The element that will
enable all children to understand is the use of the ‘concrete’ (real objects).

The books start at the very beginning with learning to count. There are sub-skills in learning to count that need to be taught to establish this concept of number:

- Knowing the number words in the correct order
- 1:1 correspondence (assigning one number word to one object)
- Objects can be counted in any order
- The size of the set is the last number counted
- If a pupil gets two different answers, he has made a mistake

Once pupils in pre-primary can reliably and accurately count up to 10, then addition and subtraction can be taught in a similar way using real objects. Writing in exercise books is not important
in pre-primary, and, indeed, it is a completely separate skill from understanding the concept of number.

A firm foundation in ‘number bonds’ (all the addition and subtraction of numbers from 0 to 10) is essential for all future mathematics. Knowing that 3 + 2 = 5, is the basis for many extended
number facts: 13 + 2 = 15, 23 + 2 = 25, 30 + 20 = 50, 300 + 200 = 500 etc.). Mathematics is full of patterns, and teaching pupils to see and understand these patterns will enable them to continue
to make links for themselves. (If I know that 3 + 2 = 5, then I know that 2 + 3 = 5, 5 - 2 = 3 and 5 - 3 = 2).

Similarly, in standard I teaching the algorithms (sets of rules) for getting the answer to addition and subtraction sums to 99 by-passes understanding, and, therefore, is not transferable to other situations or real life. The element that is missing is the concrete. Abstract sums are outside a child’s zone of proximal development. Pupils need concrete experience of numbers 11 to 20 before larger numbers are introduced. This means that pupils must have an understanding of ‘place value’ (units, tens, hundreds etc). This is of crucial importance. This can be done with bundles of sticks and single sticks. Overlapping place value cards makes the link between the concrete and the abstract clear (a bundle of ten and two sticks is the same as 10 and 2 and the same words apply to both: “kumi na mbili”)

Many important skills are missing from the primary mathematics syllabus: thinking and problem solving skills; application skills (applying knowledge gained); skills in measuring; skills in
sorting and classifying; skills of estimating; visual/spacial-awareness skills; skills in logical progression; skills of logical deduction.

The books introduce mathematical language in pre-primary such as, “Sofia has more oranges than David. How many more oranges does she have?” “David has fewer oranges than Sofia. How many fewer?”
Children need to articulate their learning and by doing so, they reinforce it. In the 3 + 2 = 5 example, a child should able to articulate that, “I can see that when I put Sofia’s three oranges
with David’s two oranges, there are five oranges altogether.” Questions such as, “How do we know that is the right answer?” “How did you work it out?” “Can you explain what you did?” are all
questions that help children to analyse the processes they went through and so reinforce their learning. This analysis is the beginning of the development of thinking skills which is essential
for the real world.

The teaching and learning of mathematics is deficient in schools in Tanzania, as is evidenced by the results not only in the Primary School Leaving Examinations of St VII, but also in the
secondary school Form IV national examination results. Tanzania is now producing students who have passed through its education system who are not mathematically literate. This is a serious
failing which needs addressing and redressing as soon as possible.

In the primary school syllabus some of the learning, and most of the introductions of topics are beyond the actual mental development of the children in that standard. This results in the pupils
very early on feeling that mathematics is hard and they cannot do it. This in turn creates a negative mind-set for the rest of their education.

Topics are taught at separate, discreet times, and there is no integration of mathematical ideas, processes or concepts. The syllabus more often than not goes immediately into ‘abstract’
concepts before the pupils have an opportunity to develop a sound understanding of the basic mathematical idea or process.

Below are some example pages from all three books:

Children need to be prepared for each stage of their learning. This is done by building up from one topic to another. Each must start with ‘concrete’ activities so that the mathematics can be
SEEN and can be done by each pupil. From there the abstract use of numbers can be introduced. By the end of the teaching of that topic the pupils will be using sums alone and answering
problem-solving questions. In this way pupils will understand, and enjoy their learning. Success breeds success, and only if pupils can understand the very basic stages in mathematics will they
succeed in their future studies.

If the teaching and learning of mathematics is to improve then the primary school syllabus needs to be re-written to take account of the issues mentioned above. It is hoped that our maths books
will help to bring about change. Already on our pilot projects the books are being used with great success and pupils are demonstrating understanding and enjoyment for the first time.

In addition, we have prepared and produced six guides for teachers of mathematics in standard III to standard VII. These guides cover topics which cause great difficulty and in which the teachers lack knowledge and confidence. The guides are for teachers to gain a thorough understanding of the topics before they attempt to teach them. The topics include fractions, graphs, geometry, plane shapes, 3D shapes, prime numbers and algebra. The teachers’ guides have been translated into Swahili and combined to form one book. The book has the rather long title of,

*Jifunze njia nzuri ya Kufundisha Sehemu Grafu Jeometri Aljebra Pembe tatu Vigawo Vigawe Namba Tasa*

The book is a self-study guide but it is best if teachers are taken through the topics in group sessions, and then there can be discussion about how to teach the topic in question, as putting the
information across to pupils is another skill.