Essay Sample on Math Education: Developing Procedural & Conceptual Understanding

Introduction

Research is to enable an individual, to understand the reasons for one to have both the procedural and conceptual understanding in Mathematics. It allows both the teacher and the student to associate the objectives of mathematics in education which are to providing both the teachers and students with mathematics skills, explanations, and the various mathematical concept. The purpose of students' procedural and conceptual understanding of Mathematics is that through the theoretical knowledge, it helps a teacher to know the student's capability to reason and understand concepts, operations and relations of mathematics. And in return, it helps answer and explain the non-routine problems relating to mathematics when he or she is asked to( The National Council of Teachers of Mathematics, NCTM, 2000).

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The problem of making a student understand mathematical concepts through procedures id well-formulated, and this is where the idea learned examined so that the teacher can know whether what he taught has been recognized or not. And which areas he or she should put more emphasis on incase the whole procedure was not understood. For the teachers to do that, Isleyen, (2003) talks about how Turkish National Education System emphases on the need and importance of the mathematics teachers to teach focusing on both procedural and conceptual understanding in high school mathematics education, hence making teachers to have different focuses when teaching to have better results and prepare students to have a clear understanding of the subject taught. The theoretical concept of students' procedural understanding and conceptual understanding of Mathematics took place in Malaysia, where quantitative research based on numerical data analyzed statistically carried out using the survey method. At the end of the study, those investigating the report become realistic and suggested that conceptual understanding is high while the procedural knowledge is shallow, urging the teachers to shift their teaching process by focusing on balancing between procedural and conceptual understanding. It is also advisable that every student should study mathematics with understanding (Hope, 2006).

The analytical research was conducted for both pre-service teachers in teacher training colleges to understand the level of and students from secondary school to help the researchers to know the level of both parties when it comes to procedural and conceptual understanding of mathematics. First, the study was on 25 students from secondary schools from Malaysia. They used the algebra test comprising of 14 conceptual and procedural items. The procedure identified the individuals who were not in a position to give correct answers to the algebraic questions given from different schools that offered their students to take part in the research and the result showed that the students' level of procedural understanding is excellent whereas the level of conceptual understanding is low. Zakaria and Zaini (2009) studied the conceptual and procedural knowledge of 105 teachers in three teacher training colleges in Malaysia. The result of the whole procedure was that theoretical and procedural knowledge is high-average with a mean score of 44.72 points out of 68 points the overall score.

The method used for recruiting the students was through handing out questionnaires to headteachers in school and requesting them to give the quizzes to the best students in mathematics and then mark the questions answered. The best score recruited to be part of the survey; this was done from each school to sit for the algebra test. The method used for recruiting the teachers was the concept of Faulkenberry (2003), which contains 17 subjective objects connecting fractions.

Observation and immersion were the qualitative approaches used during the survey where the results analyzed for all the participants and the conclusion made. Another qualitative method used was focus groups and content analysis of visual and textual materials where the results were displayed so that those responsible for coming up with conclusions could note down the trends of the effects of each participant. The method was well designed and well-executed since the researchers used Faulkenberry`s concept when they analyzed the results of the 105 teachers in three teacher training colleges. On examining the student from secondary school`s achievement, they used the idea from The National Council of Teachers of Mathematics (NCTM) to come up with the conclusion statement. The audit trail is present since the results rank from the first person to the last. The average calculated to know whether both the procedural and conceptual understanding for each participant is low or high.

The results for the secondary school students, according to Yaakob (2007) was that eleven students achieved an A and fourteen students failed. As for the teachers in the training college, their mean score of 44.72 points from the overall score of 68 points (Zakaria and Zaini 2009). The result scored by both the parties shows the need for both the teachers and the students to have mathematical skills that will enable them to reason and understand the different procedures and concepts used in mathematics. The data and the assumptions made by the researchers sound because both participants expected to recognize both the methods and the thoughts in case they are to understand the complexity in mathematics Wilkins (2000). And according to Hope (2006), he talks about the need for both the teachers and students to know the procedural mathematics since it focuses on skills and step-by-step procedures without explicit reference to mathematical ideas. The findings are useful since they enable both the teacher and the students to concentrate on concepts and methods in solving a mathematical problem without looking at the ideas from a different source.

The practical application that the research offer is the need for a teacher to have excellent mathematical skills so that he or she can be in a position to explain a mathematical concept using the correct procedure that students understand with ease. As a practitioner, I find the findings from the research useful since the results makes an individual eager to acquire mathematical skills and apply the skills learned in reasoning in a mathematical concept to make a student understand what the teacher is teaching and use the same idea when given a test and give appropriate answers hence adding knowledge in mathematics as a subject.The limitations of the study include when a teacher is explaining a concept to a student, the typical arithmetic problems in most cases delay learning of Mathematical equivalence hence making the student find it difficult to understand the same procedure when given a different concept on the same topic since he or she will cram the method and apply at random in the question asked. This limitation is because most students have a higher procedural understanding compared to conceptual understanding. The author did not identify the weakness in his research.

Conclusion

The research on students' procedural and conceptual understanding of Mathematics is good quality research since it offers evidence that is correct after conducting a survey and the results on the study given out so that the researchers can come up with conclusions. The evidence provided is decent, stands up to study by encouraging teachers to have adequate mathematical skills that will enable them to explain concepts well using the correct procedures, and the same pieces of evidence used to make policy such as for an individual to be considered a qualified mathematical teacher he or she must first sit for an exam that measures his ability and reasoning when it comes to procedural and conceptual understanding of mathematics. The study also obeys principles of expertise, transparency, answerability in the teaching as a profession.

Reference

Faulkenberry, E. E. D. (2003). Secondary mathematics preservice teachers' conceptions of rational numbers (Doctoral dissertation, Oklahoma State University). https://shareok.org/bitstream/handle/11244/44660/Thesis-2003D-F263s.pdf?sequence=1

Marchionda, H. (2006). Preservice teachers' procedural and conceptual understanding of fractions and the effects of inquiry-based learning on this understanding.https://tigerprints.clemson.edu/cgi/viewcontent.cgi?referer=https://scholar.google.com/&httpsredir=1&article=1037&context=all_dissertations

Isleyen, T., and Isik Ahmet., 2003. Conceptual and procedural knowledge in mathematics. Journal of the Korean Society of Mathematical Education Series D: Research in Mathematical Education, 7(2): 91-99. https://doi.org/10.1111/j.1949-8594.2000.tb17329.x

Wilkins, J. L. (2000). Special Issue Article: Preparing for the 21st Century: The Status of Quantitative Literacy in the United States: This article continues our October 2000 Special Issue theme of "A Vision for Science and Mathematics Education in the 21st Century.". School Science and Mathematics, 100(8), 405-418. https://doi.org/10.1111/j.1949-8594.2000.tb17329.x

Adnan, M., & Zakaria, E. (2012). Students' procedural and conceptual understanding of mathematics. Australian Journal of Basic and Applied Sciences, 5(7), 684-691. file:///C:/Users/Admin/Downloads/Correlation_Article_Math%20(1)%20(1).pdf

Zakaria, E., & Zaini, N. (2009). Conceptual and procedural knowledge of rational numbers in trainee teachers. European Journal of Social Sciences, 9(2), 202-217. https://www.researchgate.net/profile/Effandi_Zakaria/publication/238772674_Conceptual_and_Procedural_Knowledge_of_Rational_Numbers_in_Trainee_Teachers/links/5840e5a408ae2d21755f41c1/Conceptual-and-Procedural-Knowledge-of-Rational-Numbers-in-Trainee-Teachers.pdf