Problem Centered Mathematics Projects(PCMP) is aimed at helping children construct and use increasingly abstract units of number. Initially for young children, a number like 27 means only 27 single objects. It is a number in a counting sequence, like 5 or 9 and there is no understanding of the number in terms of place value concepts. The goal is to help the children see that the number cab take on a number of meanings. In addition to 27 ones, it also means 20 and one 7 or 25 and one 2 and so on. The basic approach in PCMP classes is to help children construct these increasingly sophisticated concepts of different units, including ten and to build these concepts on children’s counting based meanings by encouraging increasingly abstract counting strategies and child generated computational algorithms.
Children do not use structured tools like base-10 blocks, which embody base 10 groupings. Instead they use loose counters, collect them into groups of tens and count.(e.g. 10, 20, 30, 31, 32, 33, 34). Children have two sets of numeral cards: multiples of ten and one. To represent the numeral 34, for example they take the 30 card and the 4 card and place 4 over zero of 30. At this stage, the representation of two digit numerals is handled as the juxtaposition of two numbers: a tens number and a ones number
Computational procedures build directly on children’s number concepts and their knowledge of properties of number operations rather than on connections to operations with manipulative materials. Any computational procedure involves transforming the given task to one or more easier tasks that children already know how to do. The process of changing the task to equivalent but easier subtasks involves three distinguishable sets of subtasks
- Transformation of the number
- Transformation of the given computational task
- Carrying out of the computation
For example, the addition of 24 + 38 involves the transformation of numbers 24 = 20+4 and 38= 30 + 8. The computational task (20 + 4) + (30 + 8) is transformed to the equivalent task [(20+ 30)+4]+8. The resulting computations involve tasks that are familiar and may be based on recall of known number combination together with knowledge of number concepts: 20 + 30 = 50; 50+ 4 = 54; 54 + 8 = 62.
