Seemingly, people have since thought that concrete, pictorial and abstract were catchier terms than enactive, iconic and symbolic representation…Īnother popular education term is “scaffolding” which Bruner coined while developing the three-stage process we’ve come to know as the CPA approach. “symbolic representation” (which is symbolic or language-based).“iconic representation” (which requires sketching, interpreting and building on images) and,.“enactive representation” (that requires objects and actions).Example CPA progression for one-digit addition without exchangeīruner’s theory that underpins what was developed in Singapore and elsewhere in the 1980s onwards states that there are three means of representing tasks: That said, for the most part, it should go: concrete, pictorial, then abstract. Of course, any one-size-fits-all approach in education isn’t going to work 100% of the time! There might be occasions when leading with a pictorial representation for an earlier, similar concept might work better than kicking things off with free-form play-based learning with concrete equipment relevant to the learning at hand. APC, PAC or CPA? Does it really matter in which order you teach the C-P-A approach? Using a CPA approach allows children to get to grips with new concepts by making use of their existing knowledge and experiences by providing them with a more familiar and real-world entry point to new learning. Usually, those children who find maths hard to understand are feeling that way because of how abstract the subject is and how removed many of its symbols are from day-to-day life. The concrete, pictorial, abstract approach (or CPA method) is a process of using “concrete” equipment to represent numbers (including fractions) and operations, such as addition, subtraction, division and multiplication, followed by a pictorial representation to represent the equipment or derived structures (like bar and part-whole models), before moving on to the “abstract” digits and various other symbols used in mathematics. Why is the CPA approach used in mathematics? It has become popular in other English speaking territories in recent years due to a push by the British and North American governments for their school-aged children to perform better in mathematics according to the global PISA education performance rankings, which has led to the development and promotion of Singapore-style mathematics teaching in primary and secondary schools. Singapore or mastery-style maths and its CPA approach was inspired by the research and work of Jerome Bruner The approach is inspired by the work of Jerome Bruner, an American psychologist, who developed the process in the late 1960s. The concrete, pictorial, abstract approach to mathematics has been a key feature of teaching and learning in Singapore since the 1980s. What is the CPA approach and where did it come from?
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