PICKTORIAL 3 VS BRIDGE HOW TO

and let the student count those objects.)Įxample 2: Solving a linear equation in 1 variable CPA Stage (By showing concrete objects like marbles, pens, balls etc. Here are some such examples where the CPA approach is used in Mindspark.Įxample 1: Addition of single-digit numbers: CPA Stage The concrete objects will be replaced with virtual objects and animations. The CPA approach can be used in digital learning tools. They also outperformed general education students on a subtest on word problems that had fractions and equivalency embedded in the problem.Ĭan the CPA approach be used in digital learning tools like Mindspark? In a study by Butler, Miller, Crehan, Babbitt, & Pierce (2003), students with learning disabilities receiving CRA instruction performed at least as well as general education 8th grade students on assessment on fractions.

PICKTORIAL 3 VS BRIDGE HOW TO

In another study, Witzel, Mercer, and Miller (2003) showed that students who learned how to perform algebra transformation equations through a concrete to representational to abstract (CRA) sequence outperformed peers receiving traditional instruction during both post instruction and follow-up tests. Mercer and Miller (1992) reported that students taught using the CSA sequence acquired the target skills, demonstrated an understanding of the respective operation, and were able to maintain the skills over time. It is very important for the teacher to select appropriate manipulatives at the concrete stage and make meaningful connections to the pictorial and the abstract stages. Shown below are some examples of the CPA approach used for teaching addition in grade 1 from NCERT Mathematics textbook and teaching equivalent fractions from Elementary and Middle School Mathematics by Van De walle. At this stage, the teacher helps to develop the mathematical concept at a symbolic level, using numbers, notation, and mathematical symbols to represent the number algorithm. The Abstract stage uses abstract symbols to model problems. In the Pictorial stage, the teacher transforms the concrete model into a representational (pictorial) level, which may involve drawing pictures using circles, dots, bars, a number line etc. chips, cubes, base ten blocks, fraction bars etc). In the Concrete stage, the teacher begins instruction by modelling each mathematical concept with concrete materials (e.g. It is a three-stage learning process where students learn through physical manipulation of concrete objects, followed by learning through pictorial representations of the concrete manipulations, and then solving problems using abstract notation. The idea was developed by Jerome Bruner in 1960.

The Concrete-Pictorial-Abstract (CPA) is also referred to as Concrete-Representational-Abstract (CRA) or Concrete-Semi Concrete-Abstract (CSA). The CPA approach is a key instructional strategy advocated by the Singapore Ministry of Education.

Singapore is one country out-performing others in the international benchmarking studies like PISA and TIMSS. (2020) found “Motivation to learn in students who are subjected to the CPA approach is better than learning motivation in students who are subjected to conventional approaches. In this approach, students learn to enjoy mathematics than seeing it as a subject with formulas and procedures. The Concrete-Pictorial-Abstract instructional approach provides meaningful connections between different stages of learning and develops both conceptual and procedural knowledge. To master any mathematical concept students should develop both the conceptual understanding and the procedural fluency. “Any curriculum for primary mathematics must incorporate the progression from the concrete to the abstract and subsequently a need to appreciate the importance of abstraction in mathematics” (NCERT,2006).

Picktorial 3 vs bridge