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Topic Needs in Advanced Mathematics Courses of Bachelor in Secondary Education – Mathematics Students

Oscar L. Barboza

Mathematics Coordinator, Secondary Education Department, College of Teacher Education, Quirino State University, Philippines

Abstract: This study presents the topic needs in the Advanced Mathematics courses of the Bachelor in Secondary Education (BSE) program major in Mathematics. The study sought topics needed by prospective Mathematics teachers in the Secondary based on the Commission on Higher Education framework and the National Competency-Based Teacher Standards (NCBTS) for the BSE Program relative to the Philippine Licensure Examination for Teachers (LET). It was found out that most of the topics in each of the courses offered in the program conform to the aforementioned standards. However, there are topics which were found to be less needed. Hence, a revisit to the existing course content is highly wanting through proper and correct benchmarking procedures. Moreover, the introduction of softwares in Mathematics, especially in Statistics, was also recommended.

Keywords: advanced mathematics courses, bachelor of secondary education program, learning competencies

Citation: Oscar L. Barboza, Topic Needs in Advanced Mathematics Courses of Bachelor in Secondary Education – Mathematics Students. American Journal of Educational Research, 4 (3). 268-272. January 2016. doi:10.12691/education-4-3-7

1. Introduction

Mathematics, the core of this study, considering all its branches or areas, is a subject that demands a careful study. This is one of the subjects that is often feared by learners as from among all other areas, this is one defined by too much abstraction and logical analysis. These are two characteristics of mathematics which posit cogent mental activity and a broad sense of understanding [1]. From among the several studies conducted, Mathematics, aside from English and Science, has been found out to be of low learners’ achievement level [2]. In fact, in an International Assessment Test in Mathematics, participated in by 25 countries, the Philippines ranked 23rd [3]. Mathematics is a very important field of study. This is evidenced by the fact that Mathematics is a part of almost every human endeavor, from the home to the market place, where it occupies a significant place, thus contributing to our workplace much needed solution towards well – balanced life [4,5].

Further, Mathematics is a process – oriented activity. This is so because of its logical nature, where contents are sequenced in order, that is, a new lesson is premised on the previous lesson. To explain this more understandably, it is best to anchor the illustration on the four fundamental operations [6]. These are learned in order where addition is the initial stage, followed by subtraction, then multiplication to wind up in division. These operations serve as springboards to higher study in mathematics by providing the basics to get into more complex lessons [6,7,8].

Today, with the inflow of modernization, man must be able to cope with the demands of the changes that are prevailing. Most of these changes are time – bound and it is on this aspect where mathematics yields its force [9,10]. Man must be master of these changes; otherwise, he will simply be an automation dictated upon by these changes [11,12].

The researcher is teaching Mathematics at the Quirino State University. In his observation, students usually encounter difficulty in understanding the mathematical principles, concepts and processes, most especially in the application of these concepts in solving problems. This is a great challenge to mathematics instructors and professors in making the lessons interesting. His observations on the pitfalls of students in learning the subject gave him the drive to conduct a study on the topic needs of students to afford them an easier and more gainful way in learning the subject. Do the instructors and professors address the topic needs of the students? Are their needs properly addressed? Do the instructors discuss the pre – requisite topics so that students can understand the requisite ones? It is at this juncture that this research study was conducted.

2. Materials and Methods

The descriptive research was used in this research study. A survey questionnaire was used to determine the level of needs of the student and faculty respondents. The topics on the different Advanced Mathematics courses were enumerated by concepts and sub-concepts, and the respondents indicated their assessments on the level of needs of the students. The arithmetic mean was used to determine the level of needs of the students as indicated by the student-respondents themselves and their instructors/professors. The level of needs was identified by using a 5-point Likert Scale.

The content analysis on the topic needs of BSE (Mathematics) students in Advanced Mathematics courses is conceptualized.

Figure 1. Conceptual Paradigm of the Study

Figure 1 presents the conceptual paradigm of the study. The INPUT – PROCESS – OUTPUT model of evaluation was used in this research study. The researcher perceived the input to include the topic needs of BSE (Mathematics) students in all Advanced Mathematics courses, the BSE (Mathematics) students from third year to fourth year, and their Instructors/Professors as the main respondents of the study, and the Survey Questionnaire. There were 20 male student-respondents and 72 female-respondents. For the faculty respondents, there were seven male faculty members and eight females. With regards to the curriculum year of the student-respondents, there were 49 third year and 43 fourth year students.

The perceived output of the research is a database on the identified topic needs of BSE (Mathematics) students in Advanced Mathematics courses offered in the curriculum of the BSE (Mathematics) Program in State Universities in Cagayan Valley Region.

3. Results and Discussion

Table 1. Topic Needs of BSE (Mathematics) Students in Math 102 – Solid Geometry

It is shown in the Table 1 that the indicated topics in almost all of the chapters are “very much needed” by the BSE (Mathematics) students. The topics which are “much needed” are Transformation of Linear, Second, and Third Degree Equations, Linear Equations, Perimeters of Plane Figures, and Interior and Exterior Angles of Any Polygon.

This is so because these topics are already covered in high school and are very basic. Among the topics which are very much needed by the students are Cubes, Rectangular Parallelipiped, Right Circular Cylinder, Right Circular Cone, Cones, Pyramid, Frustum of a Cone and Pyramid, and Prismatoid.

This means that these topics should be emphasized by the instructors in teaching this subject especially on the applications which were rated very high by the respondents. Furthermore, application of the principles and concepts to real life situations is very important because if these are not applied in solving problems, Mathematics is meaningless.

Table 2. Topic Needs of BSE (Mathematics) Students in Math 103 – Analytic Geometry

There are many topics in Analytic Geometry which are being given in the Licensure Examinations for Teachers (LET) according to the takers in the past years, therefore the topics in this course should also be emphasized by the instructors so that the chance of passing the said board examination is high.

Table 3. Topic Needs of BSE (Mathematics) Students in Math 104 – Advanced Algebra and Trigonometry

These are the only topics which are very much needed by the students because there are many topics in Advanced Algebra and Trigonometry which are taught in High School Mathematics subjects particularly in Grade 8 Mathematics (Intermediate Algebra) and Grade 10 Mathematics (Advanced Algebra and Trigonometry.

Table 4. Topic Needs of BSE (Mathematics) Students in Math 106 – Differential Calculus

There are many Secondary Schools in the country that offer Science Curriculum and one of the subjects is Calculus. It is therefore advantageous for a BSE student to master the topics so that they will not encounter difficulty in teaching the subject once they are assigned to teach the subject.

Table 5. Topic Needs of BSE (Mathematics) Students in Math 107 – Integral Calculus

As it can be gleaned from the mean responses of the respondents, all the sub – topics were rated as “very much needed” by the BSE (Mathematics) students. Again, the topics in this course should be discussed thoroughly by the instructors because this is one of the most important courses in the BSE major in Mathematics program.

The respondents indicated mean responses ranging from 4.37 to 4.47 which are classified under the “very much needed” category.

Table 6. Topic Needs of BSE (Mathematics) Students in Math 108 – Advanced Statistics

The introduction of technology as an academic infrastructure in academic learning has brought shift in the pedagogical structures of most institutions of learning – from the dogmatic classroom structures to contemporary learning structures. In statistics, for example, academic learning from the manual computation to the analytical mode using academic softwares. For this to happen, students should be exposed to these academic softwares and use it for academic endeavors. In fact, there was an instructor – respondent who recommended the addition of Computer – Aided Statistical Packages like the Microsoft Excel and the SPSS Programs in making statistical computations. This is very important in order to facilitate the computations.

Table 7. Topic Needs of BSE (Mathematics) Students in Math 110 – Linear Algebra

Among the five major topics of Linear Algebra, three were indicated to be very much needed by the respondents. Linear equations and matrices include Linear Systems, Matrices, Properties of Matrix Operations, Solutions of Equations, and the Inverse of a Matrix. On the other hand, vectors and vector spaces include the following sub-topics: Vectors in a Plane, N-vectors, Cross Product in Rh, Vector Spaces and Subspaces, Linear Independence, Bases and Dimensions, and Rank of a Matrix and Orthogonal Bases in Rh. Moreover, sub-topics on linear transformation and Matrix of a Linear Transformation were included on Linear Transformation and Matrices.

Table 8. Topic Needs of BSE (Mathematics) Students in Math 111 – Probability and Statistics

As it can be gleaned on the foregoing results, three of the seven topics in the course were evaluated to be very much needed. This includes the topics on Probability, Discrete Probability Distribution, and Continuous Probability Distribution. However, a topic in Counting Techniques was suggested by one of the respondents to be discussed first before the Probability, Combination, and Permutation topics.

Table 9. Topic Needs of BSE (Mathematics) Students in Math 112 – Abstract Algebra

As presented in the foregoing results, seven of the nine topics in Abstract Algebra were assessed with a lesser need. This could be attributed to the fact that they are already discussed in High School Mathematics.

Table 10. Topic Needs of BSE (Mathematics) Students in Math 113 – Number Theory

As it can be gleaned on the table, nine of the 15 topics in number theory were categorized as very much needed by the respondents. The topic on Summation and Multiplication Symbol includes Properties of Summation, Properties of Multiplication, and Factorial. Mathematical induction includes Steps in Proving Mathematical Induction, Properties of Divisibility, and Divisibility Criteria. On the other hand, Properties of Modulo, Properties of Pertaining a Division, and Multiplicative Inverse were included in Congruence Modulo.

Table 11. Topic Needs of BSE (Mathematics) Students in Math 115 – Differential Equation

As it is shown in Table 11, all the topics in the course were implicated with a lesser need when compared with the other courses offered in the program. It is noted that this is not required in major requirement of the Commission on Higher Education (CHED) and the National Competency-Based Teacher Standards (NCBTS) for Teacher Education; however, it would be an advantage to the students who will be teaching in the Senior High School or in Tertiary level, particularly in Engineering programs.

Table 12. Topic Needs of BSE (Mathematics) Students in Math 117 – Advanced Calculus

As it is shown in table, two of five topics in Advanced Calculus are rated as very much needed; however, it can be said that Advanced Calculus, in general, is rated with a lesser need. This could be due to the fact that this topic is rarely discussed in High School particularly in the Junior High School. Volumes include topics on Solids of Revolution, Hollow Solids of revolution, and Alternate method on the Cylindrical Shell.

On the other hand, the researcher suggested that the topics Infinite Series should be emphasized because these topics are found in Grade 8 Mathematics. This topic includes Sequences and Series, Convergent and Divergent Series, Integral Test for Convergence, Comparison Test for Convergence, Ratio Test for Convergence, Alternating Series Test for Convergence, Absolute and Conditional Convergence Test, and Power Series.

Table 13. Topic Needs of BSE (Mathematics) Students in Math 118 – Modern Algebra

Presented in the table are the topic needs in Modern Algebra. It shows that Modern Algebra is drawn with a lesser need as much of these topics were extensively discussed in the lower Mathematics courses in the program. Equations include Inequalities, Open Sentences and Open Equations, Formulae, and Word Problem.

Number Pattern, on the other hand, includes topics on Cumulative Properties, Associative Properties, identities and Inverses, Distributive Properties, Algebraic Expressions, Division Process, and Number Theory.

On the other hand, Real Numbers include topics on Integers, Rational Numbers, Decimal Representation of Rational Numbers, Real Numbers, Solving Inequalities, Squares and Square Roots, and Approximations of Real Numbers by Rational Numbers.

Moreover, Polynomials in Two Variables include Operations with Polynomials in Two Variables, Powers of Monomials and Binomials, and Special Factoring.

Table 14. Topic Needs of BSE (Mathematics) Students in Math 120 – Advanced Algebra

As it can be gleaned in the foregoing table, all the topics included in the course are perceived as very much needed. This is due to the fact that all of the sub – topics are very important to the students and therefore it needs complete and thorough discussion by the instructor. This is because most, if not all of these topics, are contained in Grade 10 Mathematics and as future high school teachers, it is very necessary that these topics should be emphasized.

Moreover, of all the Mathematics courses included in the NCBTS–Based Table of Specifications for Licensure Examination for Teachers, Basic, as well as Advanced Algebra, is given the heaviest weight of 25% which means that one-fourths of the total number of items in every examination in the LET is Basic or Advanced Algebra.

Table 15. Distribution of Respondents as to Recommendation, Comments, and Suggestions

Table 15 shows the frequency of the recommended topics by the instructor/professor – respondents. It shows that there were five respondents who recommended the inclusion of computer – aided statistical packages including interpretation of results and the application of data computation using Microsoft Excel and Statistical Package for Social Sciences (SPSS). These recommendations ranked first. This was followed by the use of Graph Calculators or Computers to show the graphs of the different functions and computer – aided graphs with frequencies of three and a rank of 2. Counting Techniques and most of the topics are already contained in other subjects and so duplication should be avoided. There were two frequencies in these recommendations with a rank of 3.

4. Implication to Education and Practice

1. Based on the informal interview, majority of the instructors/professors do not use graph calculators and only several of them use computers in graphing functions. Since the respondents recommended the use of graph calculators and computers in graphing functions, this should be done by the Mathematics instructors.

2. According to the majority of the respondents, there are no supplies of graph calculators and computer units are not enough for instructional purposes. With this situation, the administration of the three SUCs should provide graph calculators to their Mathematics Faculty members and acquire additional computer units for instructional purposes.

3. In Statistics, it is also recommended by the respondents that computer programs like the Microsoft Excel and SPSS Program Package should also be used in instruction.

4. There are several faculty members who are not knowledgeable in the use of graph calculators and SPSS program, the administration should send their Mathematics faculty members to attend to seminars/trainings or workshops along these topics.

5. Majority of the Mathematics Faculty members are not PhD/EdD holders. There are only three out of the fifteen faculty members who are PhD/EdD holders. These faculty members should improve their educational qualifications by finishing a doctorate degree. The administration of the three SUCs should encourage or motivate the faculty members to enroll advanced studies.

6. School administrators should send their Mathematics Faculty members to seminars/trainings/workshops being conducted by the three centers of excellence in Mathematics, the University of the Philippines, Ateneo de Manila University and De La Salle University in Manila in order to improve or upgrade their teaching competencies.

References

[1]   | M. Battista, The Mathematical Miseducation of America’s Youth. (Phi Delta Kappan), 1999.
[2]   | T. Romberg. Changing the Teaching and Learning of Mathematics. AMT, 56(4) 2000.
[3]   | Pascual, Myla C.Development Needs in Mathematics IV and The Learning Competencies: An Analysis. Luzon Science Consortium Journal, Vol.3. 2006, pp. 1-16.
[4]   | Danganan, Rodel R., A Flashback to Education 2000, The Modern Teacher. Vol. LVII, No. 9, February 2008.
[5]   | Heidi Janzen and Jennipher Willoughby. “Standards – Based Instruction in Mathematics.” (Glencoe/ McGraw – Hill, 2000 – 2005, New York 10020).
[6]   | U. S. Department of Education. Mathematics Equals Opportunity. White Paper Prepared for U. S. Secretary of Education. Washington D.C., 1997.
[7]   | D. Ball et al., (2005). Reaching for Common Ground in K – 12 Mathematics Education. (Washington D.C.) American Mathematical Society.
[8]   | S. Cavanagh., Big Cities Credit Conceptual Math for Higher Scores. Education Week., January 11, 2006.
[9]   | National Council of Teachers of Mathematics. The Use of Technology in Learning And Teaching of Mathematics. Retrieved March 24, 2006 from htpp://nctm.org.
[10]   | Teaching Today. Standards – Based Instruction in Mathematics. Retrieved November 11, 2005 from http://www.glencoe.com.
[11]   | Teaching Today.Using the Japanese Lesson Study in Mathematics Retrieved February 11, 2006 from http://www.glencoe.com. http: // www. Doe. K12. ga.us.
[12]   | National Council of Teachers of Mathematics.The Use of Technology in Learning and Teaching Mathematics. (http://nctm.org.) Retrieved March 24, 2006.