American Journal of Educational Research, 2017, Vol. 5, No. 3, 310-315
Available online at http://pubs.sciepub.com/education/5/3/12
©Science and Education Publishing
DOI:10.12691/education-5-3-12
Prospective Teachers’ Conceptual and Procedural
Knowledge in Mathematics: The Case of Algebra
Habila Elisha Zuya
*
Department of Science and Technology Education, Faculty of Education, University of Jos, Nigeria
*Corresponding author: elishazuya2@gmail.com
Abstract The study investigated prospective mathematics teachers’ conceptual and procedural knowledge in
algebra. Thirty six prospective teachers participated in the study. The independent variables of conceptual
knowledge and procedural knowledge were investigated using quantitative methods. A 20-item instrument was used
for collecting data. Descriptive and inferential statistics were used in analyzing the data collected. Specifically, the
research questions were answered using the means and standard deviations, while the hypothesis was tested by
conducting a paired t-test of difference. One of the findings of the study was the low performance of the respondents
on conceptual knowledge test as against their performance on procedural knowledge test. The respondents differed
significantly in their performances on conceptual and procedural knowledge, and the difference was in favor of
procedural knowledge. It was recommended that teachers should give equal attention to both teaching of concepts
and procedures in mathematics.
Keywords: conceptual knowledge, procedural knowledge, algebra, prospective teachers
Cite This Article: Habila Elisha Zuya, “Prospective Teachers’ Conceptual and Procedural Knowledge in
Mathematics: The Case of Algebra.” American Journal of Educational Research, vol. 5, no. 3 (2017): 310-315.
doi: 10.12691/education-5-3-12.
1. Introduction
The knowledge of concepts and procedures is
imperative for competence in mathematics. For a
mathematics teacher to be competent and effective in
teaching, he must possess the subject matter knowledge.
Subject matter knowledge is a combination of the
knowledge of both concepts and procedures. Ideally,
teachers are expected to demonstrate knowledge of both
concepts and procedures, as some researchers have argued
that the relation between the two types of knowledge is bi-
directional e.g. [30]. [30] Asserted that there is a bi-
directional relation between conceptual knowledge and
procedural knowledge. In other words, the knowledge of
one supports the other and vice versa. Similarly, [34]
pointed out that conceptual knowledge and procedural
knowledge are similar in many respects, which makes
them difficult to differentiate. He said although
researchers often discuss them as separate entities,
conceptual knowledge and procedural knowledge rely on
each other to develop in mathematics.
Prospective mathematics teachers must possess a good
knowledge of mathematical concepts and procedures, if
they are to succeed in their teaching profession. A good
understanding of mathematical concepts and procedures
gives the mathematics teacher confidence in the
mathematics classroom. This knowledge, combined with
the knowledge of pedagogy enhance the competence of
the teacher, and help him to address the student’s learning
difficulties and misconceptions. Hence, the possession of
conceptual and procedural knowledge is necessary for
effective teaching.
1.1. Literature Review
A concept, according to [40] is, “an idea of something
formed by mentally combining all its characteristics or
particulars”. Conceptual knowledge, which is knowledge
of concepts, has to do with abstraction and generalization
of particular instances. Knowing definitions and rules in
mathematics is not having conceptual knowledge.
Students may recall certain definitions, rules and
procedures, but it cannot be said they possess conceptual
understanding. To demonstrate conceptual understanding,
the student must be able to justify why a statement in
mathematics is true or where a mathematical rule comes
from. For instance, [35] pointed out that “there is a
difference between a student who can summon a
mnemonic device to expand a product such as (a+b)(x+y),
and a student who can explain where a mnemonic comes
from”. Therefore, the ability to recall into memory either a
mathematical rule, definition, or procedure and to apply
such is not enough justification of having conceptual
knowledge. Being able to explain the rule, definition or
procedure involved is required for conceptual knowledge
evidence. This is because the knowledge of concepts
involves understanding of meaning, and not just ability to
recall definitions, rules or procedures.
An individual can commit into memory that two
negative numbers can result into a positive number when
multiplied or divided, but it is not the same as
understanding the reason for the product or quotient to be