Mathematics is a skill subject where most students encounter difficulties (Ali, 2011; Postelnicu, 2011). However, Akweittey, Appiahene, Emmanuel, Michael and Richard (2014) argued that this subject must be learned because, at present, in our evolving world, every citizen needs substantial mathematical knowledge and a fixed set of skills to excel at school, and most especially in daily life. This implies that schools, specifically the teachers, are tasked to discover means such that the difficulties encountered by the students be aided. With this, the learners’ mathematical competency can be attained.
Moreover, mathematical competence rests on the development of the knowledge of both concepts and procedures (Rittle-Johnson & Scheider, 2014). Having this proficiency in math, the learners will be able to verbalize the connections among mathematical concepts and representations that could help them solve mathematical problems easily.
In addition, in achieving mathematical proficiency, many things are to be considered. In connection, Ntshalintshali (2014) stated that, for the mastery and transfer of learning, it is necessary for a student to learn subject-related facts, compare concepts that belong to a particular field, and apply techniques to solve problems. Therefore, in order for a learner to excel in math, he must know the facts and terminologies in the subject, understand the relationship among different mathematical concepts and when to use them, and master the processes in solving mathematics-related problems.
Knowledge about facts is declarative knowledge (Octavio, 2015), knowledge and understanding of the principles, theories and concepts refers to conceptual knowledge (Ntshalintshali, 2014), and procedural knowledge is the knowledge of how to do something (Budding & Koziol, 2012). Declarative knowledge helps the students to identify and understand the different concepts in mathematics. On the other hand, conceptual knowledge allows them to ascertain the connections among the different mathematical concepts. And, the procedural knowledge is used by them to compute for problems in mathematics.
These three are fundamentals in solving different problems in Math. Hence, the development of a program to increase students’ declarative, conceptual and procedural competence is deemed necessary by the researcher.
Evidence-based teaching strategies (Chard, n.d.) refer to instructional approaches that work to a large-scale research. Meaning, these pedagogical methodologies have been tested using specific methods and have been proven effective. Several studies (Miller & Hudson, 2007; Haber & Wood as cited by Haber, Jacobs, Krainovich-Miller, & Yost, 2009; Barnett & Cleary, 2015; Slavin, 2002 as cited by Jin & Yun, 2010; ) have shown that the evidence-based teaching strategy is a great help in increasing academic performance. Therefore, the researcher believes that this strategy can be a means to improve the mathematical proficiency of the learners.
The aforementioned statements indicate that the need for developing the different type of knowledge arises. The enhancement of the learners’ declarative, conceptual and procedural knowledge, altogether, would ensure the success in achieving their mathematical proficiency. Competence in mathematics could also be aimed by using well-established and already-proven effective methodologies – the evidence-based teaching strategies.
Thus, the researcher finds it theoretically possible to create an evidence-based instructional guide that will improve students’ declarative, conceptual and procedural competence.
Background of the Study
As the mandated by RA 10533, also known as Enhance Basic Education Act, every learner should choose one track of their interest. One of these tracks is the Academic Track which includes ABM (Accountancy, Business, and Management), HUMSS (Humanities and Social Sciences), STEM (Science, Technology, Engineering and Mathematics) and GAS (General Academic Strand).
Moreover, in the STEM strand, learner encounters two math-related special subjects – Pre-calculus and Basic Calculus. However, the researcher observed that the topics covered in pre-calculus are congested since they involve Analytic Geometry, Advanced Algebra and Trigonometry. Thus, the creation and application of new pedagogical strategies were deemed necessary and beneficial for the improvement of the learning outcomes by the researcher.
Added to that, for the accomplishment of this change in curriculum, the need for mathematical competence in the Philippines increases. The teachers in STEM strand are responsible in assuring that the K to 12 graduates under STEM possess the mathematical skills needed in college.
Furthermore, since the School Year 2018-2019 is only the second year of the implementation of Senior High School in the K to 12 curriculum for non-pilot schools like Santa Maria Academy, the researcher observed that it has been hard for both the teachers and learners to adapt and meet the requirements brought about by this new program. Therefore, this research inquiry would be an avenue for the researcher to assess and further develop his pedagogical methods to be able to attain the objectives mandated by the DepEd.
In the same vein, the researcher, being one of the mathematics teachers of Santa Maria Academy, wants to discover means to prepare his students in college. He believes that the implementation of these strategies, which have been found by many researchers effective, will be of great assistance to attain his goal.
Cognizant to the above situations, the researcher decided to conduct a study on the relationship among students’ different types of knowledge – declarative, conceptual and procedural knowledge, and create an evidence-based teaching strategy for the improvement of these types of knowledge.
Objectives of the Study
This study attempted to determine the relationship among students’ declarative, conceptual, and procedural knowledge which was used as basis for creating an evidence-based instructional guides.
Specifically, this sought to achieve the following objectives:
1. Ascertain the level of declarative, conceptual and procedural knowledge in Pre-calculus of the respondents, specifically on:
1.3 Ellipse; and
2. Reveal if there is a significant relationship among Grade 11 student-respondents’ declarative, conceptual and procedural knowledge in Pre-calculus
3. Create instructional guides and learning materials that utilize evidence-based teaching approach
4. Determine the learner’s attitude towards the use of evidence-based teaching strategy in terms of:
4.2 Usefulness; and
There is no significant relationship among Grade 11 STEM students’ declarative, conceptual and procedural knowledge in Pre-calculus.
Significance of the Study
As this study attempted to determine the relationship among students’ declarative, conceptual and procedural knowledge which will be used to create an evidence-based instructional guide, this research undertaking could be beneficial to the following:
Students. As ultimate recipient of the educational system, students would be benefited in this research for they would become aware of the importance of the declarative, conceptual and procedural knowledge in their mathematical proficiency. Specifically, the students who take STEM strand would benefit in this research since the developed evidence-based instructional guides are for the enhancement of the skills in the topics: circles, parabola, ellipse, and hyperbola which are topics on Pre-calculus.
Teachers. The result of this study would add to their current awareness on the development of learners’ cognition. Moreover, this would be of great help especially for the Pre-calculus teachers for they can adopt and improve the teaching strategy developed in this research.
The result of this study could provide information that would help them to improve their curriculum and how they plan of the activities in relation to the development of students’ declarative, conceptual and procedural knowledge.
Future Researchers. This study might be of great help for the future researchers who would conduct same nature as this study. This would serve as their guide in conducting and assessing pilot tests on different teaching strategies.
Scope and Limitations
This study was restricted in determining the relationship of Science, Technology, Engineering and Mathematics (STEM) students’ declarative, conceptual, and procedural knowledge in Pre-calculus, specifically on conic sections.
This study was conducted in the selected schools in Unit 5 of the Division of Laguna that offer STEM strand comprising Santa Maria Academy, Sta. Maria Integrated High School and Siniloan Integrated High School. Further, the pilot test of the developed evidence-based teaching strategy was conducted at Santa Maria Academy.
A total of 84 respondents were chosen to be assessed on their declarative, conceptual and procedural knowledge. In addition, 39 students were selected as the chosen class where the pilot test of the use of evidence-based instructional guide was conducted.
Test for the level of declarative, conceptual and procedural knowledge was limited to the self-made questionnaire which is comprised of a restricted-response type items. It covers the topics on conics and their applications, circles, parabola, ellipse and hyperbola. Moreover, the level of learners’ attitude towards the evidence-based instruction was limited to the self-made likert-scale questionnaire which covers the parameters: appeal, usefulness and effectiveness.
The time frame of this research was from January 2018 to March 2019.
Definition of Terms
For clarity of the words in this research, the following terms are defined conceptually and operationally.
Appeal refers to the impression of students on the content, and activities on a certain material (Cabuyao, 2012). In this study, this refers to the degree on how the developed instructional guide increases student’s interest in the subject.
Attitude toward the instructional guides is the learners’ perception on the application of the evidence-based teaching plan. Furthermore, in this student, this pertains to the learners’ view on the appeal, usefulness and effectiveness of the instructional guides. (Curia, 2012)
Conceptual knowledge involves understanding the principles in a subject matter (Alibali & Nathan, 2012). In this study, it refers to the knowledge of the learners in finding the relationship between the concepts in conic sections.
Conic Sections, also called Conics, are geometrical figures formed by intersecting a double-napped right circular cone with a plane. With the different positions of the plane, the figures formed are circle, ellipse, parabola, and hyperbola (Orines, 2016). In this study, the topics of the subject Pre-calculus are focused here. Specifically, conic sections are the subject matter of the questionnaire on declarative, conceptual and procedural knowledge.
Declarative Knowledge refers to the knowledge about facts (Octavio, 2015). In this study, this involves the different formula, definitions and properties of the conic sections.
Efficiency means realizing transfer of learning among students even the time and effort has been maximized or the human interaction has been lessened (Curia, 2012). In this study, it refers to the degree of success by the learners in learning the concept of conic sections using the developed instructional guide.
Evidence-based instruction also known as research-based instruction, is “an instructional approach, practice, or methodology that is derived from empirical research, resulting in reliable, trustworthy, and valid substantiation suggesting that a program or practice is effective and that all proofs or facts that support such a program or practice are scientifically based” (International Reading Association, 2002 as cited by American Institutes for Research, 2015). In this study, this refers to the developed instructional guides which are patterned to already established researches, and aim to improve specific knowledge-types. Specifically, these made use of concrete-representation-abstract, problem-solving and constant time delay strategies.
Instructional Guide is defined as a systematic process that is employed to develop education and training programs in consistent and reliable fashion (Reiser, 2007 as cited by Aguado, 2017). In this study, this refers to the instructional manual being developed integrating the evidence-based strategies.
Pre-calculus, or Precalculus, refers of a subject that involves algebra, analytic geometry and trigonometry at a level which is intended to prepare students for the study of calculus (Cangelosi, 2012). It is the main subject of this study. The focus of Precalculus in this research is the conic sections.
Procedural knowledge refers to the “child’s ability to execute action sequences to solve problems.” (Alibali, 2005 as cited by DeCaro, 2016; Budding & Koziol, 2012). In this study, this indicates to the ability of the learner to compute such as transforming conics in standard form to general form and problem solving involving conic sections.
Usefulness is the quality of having a worth to the user (Curia, 2012). In this study, this refers to the extent on how the developed instructional guide helps the learners in learning the concepts of conic section.