Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge: Why the conjunction is important for teachers - Article 4

Oct 15, 2026

Uploaded by Franzy

The paper examines how teachers and teacher educators understand conceptual knowledge and procedural knowledge in mathematics instruction. It synthesizes existing and seminal literature to explain their roles in the classroom and to address key pressing issues and understandings surrounding these two forms of knowledge. The analysis aims to guide teachers on how deeper insight into conceptual and procedural knowledge can improve the quality of mathematics teaching.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages16

Reading Time40 min

AccessFree to download

Introduction

What do we mean by Concepts and Conceptual Knowledge?

Conceptual knowledge (Relational Knowledge)

Connections and relationships in conceptual knowledge

Australian Journal of Teacher Education | Volume 46 Issue 2 | Article 4 | | --- | --- | | 2021
Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge:Why the conjunction is important for teachers
Derek P. Hurrell
University of Notre Dame Australia
Follow this and additional works at: [https://ro.ecu.edu.au/ajte](https://ro.ecu.edu.au/ajte)
Part of the Teacher Education and Professional Development Commons | | Recommended Citation Hurrell, D. P. (2021) . Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge:Why the conjunction is important for teachers. Australian Journal of Teacher Education, 46(2) . [http://dx.doi.org/10.14221/ajte.2021v46n2.4](http://dx.doi.org/10.14221/ajte.2021v46n2.4) [This Journal Article is posted at Research Online.](This Journal Article is posted at Research Online.)[ ](This Journal Article is posted at Research Online.)[https://ro.ecu.edu.au/ajte/vol46/iss2/4](https://ro.ecu.edu.au/ajte/vol46/iss2/4) Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction is Important to Teachers Derek Hurrell University of Notre Dame Abstract: The terms conceptual knowledge and procedural knowledge are often used by teachers and never more so than when discussing how teachers teach, and children learn mathematics. This paper will look at literature regarding conceptual and procedural knowledge and their place in the classroom, to offer teachers and teacher educators ’ advice on some of the more pressing issues and understandings around them. A thorough synthesis ofextant and seminal literature will provide advice to teachers and teacher educators on how a deeper insight into conceptual and procedural knowledge could improve the quality ofmathematics teaching. Keywords Conceptual knowledge, Procedural knowledge, Teacher understanding Introduction Recently, when working with a group of highly motivated, mathematically perceptive, experienced primary and lower secondary teachers, questions were raised around conceptual and procedural knowledge. The teachers were asked if it was always better to teach to develop conceptual knowledge or procedural knowledge, and then offered the opportunity to justify and qualify their responses. This question was raised in the knowledge that it was a‘loaded’ question, one that might provoke responses which were either strong, or guarded, due to expected conventions about teaching and learning. What emerged after some discussion, was that the collective understanding regarding conceptual and procedural knowledge, seemed worthy of further scrutiny. In essence, the teachers indicated that they carried the belief that conceptual and procedural knowledge were mutually exclusive, and that conceptual knowledge was, without exception, more appropriate or necessary than procedural knowledge. What do we mean by Concepts and Conceptual Knowledge? According to Westwood (2008) a concept can be defined as “a mental representation that embodies all the essential features of an object, a situation, or an idea. Concepts enable us to classify phenomena as belonging, or not belonging, together in certain categories”(p. 24). Chinn (2012) defined concepts as characteristics that determine either the inclusion orthe exclusion of something from a set or class. The focus is on classifying, categorising, ordering and on labelling. Concepts, according to Rittle-Johnson and Koedinger (2009), are ideas that are generalised from specific instances and that govern a domain; for example, place-value. If a student can recite the place value of a number as an isolated piece of information due to remembering the ‘verbal labels’ of each position, this is not conceptual knowledge. It becomes conceptual once that knowledge is linked to other knowledge, such asthe grouping of objects by ten and the multiplicative nature of each

FAQs

Why does the paper focus on conceptual knowledge and procedural knowledge for teachers?

It addresses how these terms are commonly used in discussions of how teachers teach and how children learn mathematics, and it seeks to clarify their importance for classroom instruction.

What does the paper aim to provide to teachers and teacher educators?

It provides advice based on a synthesis of literature about the pressing issues and understandings related to conceptual and procedural knowledge.

How does the paper describe conceptual knowledge?

It characterizes conceptual knowledge as relational and as a connecting web of relationships among mathematical ideas, not just isolated verbal labels.

Oct 15, 2026

Uploaded by Franzy