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Pedagogical Content Knowledge in Mathematics
Pedagogical content knowledge has become increasingly important for science teacher education. The delivery of rich educational content to learners in the modern classroom environment demands a profound understanding of the subject matter in question. The history of educations shows that teacher-training courses have been focusing on the teachers content knowledge. However, recent developments in teacher education concentrate on pedagogy. For this reason, teachers are required to conduct deep research on pedagogical content knowledge with a view of helping students relate the classroom theories to real-life situations. This approach enables them to connect ideas while addressing mistaken beliefs that occur in everyday life. This study focuses on pedagogical content knowledge with a view of discussing courses that are designed to deepen the preservice understanding of elementary mathematics and pedagogy.
Pedagogical content is seen as the most useful form of representing the most powerful and useful ideas, analogies, illustrations, examples, explanations, and demonstrations to learners. This phenomenon also entails the realization of various teaching methods that improve the understanding of content amongst the students. This undertaking corrects the misconstructions that are developed in the learners minds, thereby enabling them to relate theoretical knowledge to real-life situations.
Content knowledge refers to the level of familiarity with a certain subject and its organization in the mind of a teacher. On the other hand, pedagogical knowledge entails the strategies and principles of classroom management and organization in education. Learners need a teacher who has expertise in their subject besides having sufficient pedagogical skills to articulate the content matter. Training programs align the knowledge of the subject to instruction and learning to prepare preservice teachers effectively. It is emphasized that preservice teachers should have knowledge that goes beyond the common understanding of mathematical concepts. Therefore, teacher-training programs should consider improving their mathematics courses that focus on teaching the subject to improve self-efficacy.
Teachers with strong pedagogical content knowledge are confident in the delivery of instruction. Additionally, teachers who are less confident in their ability to teach can affect the development of their knowledge. Various studies have revealed that mixing mathematical and pedagogical tasks enhances mathematics knowledge among preservice teachers. The mastery experiences can develop the acquired subject matter to pedagogical knowledge. This knowledge prepares the teacher to apply the appropriate instructional techniques to deliver the desired content to the students. Besides, numerous researchers have also identified that a relationship exists between teaching efficacy and pedagogical content knowledge. It is also known that content-specific knowledge acquired through pedagogical emphasis significantly increased the self-efficacy levels amongst the instructors. Notably, it enables the preservice teachers to formulate and represent the subject to students in a comprehensible manner.
Furthermore, it enables them to comprehend what makes certain concepts either difficult or easily understood by the children. The best approach to the delivery of instruction to the learners entails teaching known to unknown knowledge. This practice enables the learners to connect known knowledge with the newly taught concepts. Teachers should involve themselves in deliberation, debate, and decision-making on how to teach since it is the best way to develop sufficient pedagogical content knowledge. In this regard, deliberation, debate, and participation in the formulation of decisions improve the teachers self-efficacy in content delivery.
Pedagogical content knowledge focuses on improving the skills of teachers to make them science instructors rather than technical experts. Preservice instructors need to articulate the knowledge about the specialization subjects. This position enables them to develop students who have in-depth knowledge about the concepts they learn in class. However, the amount of mathematical knowledge needed to deliver the scientific content to the learners demands the teachers to undergo a variety of courses to improve their resourcefulness. As a result, teachers should frequently review the content knowledge about their subjects of specialization with a view of improving the literacy levels of the students.
The accomplishment of this objective requires the teachers to focus on both mathematical and pedagogical skills. This situation enables the learners to understand concepts both within and outside the subject. Teachers also need mathematical knowledge to acquaint the learners with the necessary skills for not only educational purposes but also application in everyday real-life scenarios. For instance, pedagogical content knowledge helps the teacher encourage the students to be respectful to other people in society besides providing the opportunity to inquire about new information. Most importantly, it enables them to connect the ideologies learned in class to practice.
Today, teacher education has shifted its focus from content to pedagogical knowledge. Teachers are expected to have a professional understanding of the need for improving both literacy and numeracy skills, especially in science subjects. Furthermore, there is a need to link such subjects to actual phenomena in which they are applied. The current world is driven by technological pressure due to increased industrialization, globalization, and information-based factors. Therefore, the professional development of both the curriculum and learners is inevitable if schools have to ensure competence in the labor market.
Preservice teachers can fail to get adequate time to conduct adequate practical lessons with the learners. However, the application of the case-based approach to learning can provide a powerful framework for the delivery of scientific knowledge. This approach entails practices such as collaborative learning and role-play. Therefore, reviewing the classroom cases can allow the preservice teachers to improve the reasoning abilities of the children significantly. However, the accomplishment of this objective also demands the instructors provide the learners with the reflective knowledge that connects theory to practice.
The effective delivery of mathematical knowledge requires the teacher to challenge the learners with some real-life problems together with the specific methods for deriving the desired solution. In this manner, preservice teachers stand a position to know the strengths and weaknesses of the learners. This situation helps them identify learners with special difficulties or needs. Therefore, preservice instructors should use curriculum resources to link their learners to the most appropriate knowledge that provide opportunities for discovering, attaining, and synthesizing new information.
In conclusion, teachers should be encouraged to switch from traditional to the pedagogical content-based knowledge that combines a variety of instructional methods. For instance, they should use methods that utilize the students knowledge about the mathematics content as a vehicle to develop a pedagogical framework for realizing, inquiring, and analyzing new information. This practice is seen in some courses such as Teaching Mathematics in Elementary School (330) that offers an opportunity for the students to use a variety of materials for learning. The adoption of pedagogical methods practices helps the teachers integrate subject-specific knowledge into a variety of methods of delivering mathematical instruction. This practice encourages the students to use a range of conceptual models to perform activities that develop new perspectives while demonstrating scientific proficiency, especially in elementary mathematics.
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