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