‘At the heart of mathematics is the investigation of patterns. There are all sorts of patterns’
Pattern can help students organize their world and understand mathematics. Pattern has repeating arrangements. From this the patterns can be grown. These patterns children can be thinking about patterns by describing and extending patterns with pictorial models.
Through the observation of these patterns, there can be cultivation of the students’ ability of mathematical observation and logical thinking, from which to find out the rules and apply algebraic model to express, this is a kind of mathematical ability that can be developed using this model.
‘Data analysis, statistics and probability provide a meaningful context for promoting problem solving and critical thinking, enhancing communication, developing number sense and applying computation.’ (Robert Reys 2012 pp. 430)
Usually numbers have a mean value, this can be understood from a simple explanation of finding the secret number of a person’s birthday. In most cases the estimated value is similar; on the other hand, for the estimation of the secret number, usually results to deduce the number is unknown, such as formula 2*n+3-5=8 means (8+5-3)/2=5;
Through the measurement of interactive activities, students can not only understand the various objects with different proportion but also understand about the different measurement as to how to how they should apply in real life. For instance the example of balance measurement could be used to understand with a liter of water and a kilo of shot put. For this the basic understanding of image to a liter of water is in the size of the number of shot put. This can lead to more intuitive conversion between different units of measurement.
“Students need concepts from 2-dimension shapes in order to more completely describe 3-dimensional objects” (Robert Reys 2012, pp 376)
Students should be able to describe properties of 3-dimensional objects to explain how the objects alike and dissimilar. Students should need to know the learning skills of 2D and 3D objects. They should also need the guidance of teachers play to the imagination, with aids to assist learning of 2d and 3D concept.
For instance, students can use Tangram to understand the impact of 3D. In order to truly understand understand what is a 3D, cube they should understand the impact of basic mathematical knowledge.