public%2Farticles%2Fojs-arje-305%2Fg298

Sep 2, 2026

This document focuses on enhancing pupils' problem-solving skills through Cognitively Guided Instruction and the Concrete-Pictorial-Abstract (CPA) approach. It outlines the performance indicators for word problems, emphasizing comprehension, modeling techniques, solution strategies, and accuracy. The document details how to develop pupils' abilities to understand problems, model them using CPA, manipulate concrete and visual models, recognize relationships, use counting strategies, articulate solutions, and make sense of answers. The CPA approach is further explained as a progression from manipulating concrete materials to pictorial representations and finally to abstract notation. The document also addresses problem-solving skills, including conceptual understanding and procedural knowledge of fundamental operations, and presents various visualization models such as those with numerals, symbols, tallying, and number sentences, illustrating different levels of complexity in problem representation.

LanguageEnglish

CategoryExam

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Cognitively Guided Instruction

To develop pupils' ability to:

Understand the problem

Model the problem in various ways including CPA Approach

Manipulate the concrete model and/or visual model

Recognize the relationships of the elements of the model

Use counting strategies or algorithmic procedures

Articulate the solution verbally, in symbols or in a number sentence

Make sense of the solution and answers

Concrete-Pictorial-Abstract Approach

Physical manipulation of concrete materials

Pictorial representation from concrete manipulation

Problem solving using abstract notation (Witzel, 2005)

Problem Solving Skills of Pupils

Conceptual Understanding

Procedural Knowledge on the four fundamental operations

Models/Pictures

FAQs

What is Cognitively Guided Instruction?

Cognitively Guided Instruction is an approach aimed at developing pupils' abilities to understand, model, and solve word problems effectively, progressing from concrete representations to abstract concepts.

What does the Concrete-Pictorial-Abstract (CPA) approach entail?

The CPA approach involves three stages: first, the physical manipulation of concrete materials, second, creating pictorial representations from these manipulations, and third, problem-solving using abstract notation.

What are the key elements of performance in word problems as manifested by Cognitively Guided Instruction?

Performance is manifested through comprehension of the word problem, the modeling techniques used, the solution strategy employed, and the accuracy of the solution and answer.

Sep 2, 2026

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