Mathematics can be defined as a science, or a group of closely related sciences, which deal with the logic of shape, quantity, arrangement, changeand structure. Through logical reasoning and abstraction, mathematics has evolved from measurement, calculationand counting into the study of motions,shapes, patterns, and conjectures. Over the years, mathematics has been an essential tool in such fields as social sciences, medicine, engineering, and natural sciences. This utility has prompted mathematicians to develop a branch referred to as applied mathematics (Mason & Stacey, 1982). Applied mathematics facilitatesthe application of mathematical skills in a manner that inspires the discovery and development of, in addition to the aforementioned disciplines, game theory and statistics. On the contrary, there are mathematicians who are engaged in the subject without the intension of applying the concepts in real life. These mathematicians are referred to as pure ones. All the same, the difference between pure and applied math is indistinct. For instance, recent studies have uncovered practical applicability of aspects, which have been perceived to belong to the pure math category(Kahn & Kyle, 2002).
There are several experiences,which present opportunities for students to have a culturally relevant learning and application of mathematical concepts. For instance, during the recent economic downturn, everyone endeavored to save as much as possible to reduce the impact of uncertainty. During those difficult periods, the ability to apply mathematics in dairy life became a source of empowerment, as making informed decisions was the only way that losses would have been minimized. In schools, teachers apply mathematics to pose everyday challenges aimed at enabling students to mathematize real life experiences. As students evaluate such everyday scenarios as the comparison of prices of products, they are empowered to make realistic economic decisions based on mathematical calculations. In this chapter, mathematizing is presumedto be the capacity to identify quantities and relationships associated with specific contexts (Nunes& Bryant, 1996).
Mathematics empowers students to make logical decisions, a capacity which advances equity and social justice in various aspects of life. Bright students consider elementary math lessons as foundations, which willfacilitate the evaluation of challenging equations in the future. Elementary math lessons should avail necessary rigor enabling students to succeed during the future learning of mathematics. Various studies have indicated that the promotion of mathematical equity and literacy is enhanced by having equations whose contexts are culturally relevant (Mason & Stacey, 1982). In this regard, teachers ought to utilize those teaching methods that facilitate the development of cultural competence, as this would enhance the student’s capacity to mathematize various life events. Effective teaching of mathematics promotes literacy in a manner that enables learners to have the capacity to solve problems intuitively. Equity is said to increase when students find mathematics useful for their daily life. They begin appreciating math after they perceive it as a facilitator of access to higher education and prime job opportunities. Consequently, mathematics becomes an empowerment and not a hindrance to academic advancement(Kahn & Kyle, 2002).
Even with the identification of math as a central subject in the education system, teachers continue facing challenges as they attempt to determine the most appropriate examples and teaching methods applicable in a classroom setting. This is especially so when students with different learning capacities attend the same lessons. An increasing number of teachers have been expressing concerns over the failure of traditional methods to break down obstacles that hinder effective learning. Teachers report that many of their students find mathematics an uninteresting, disconnecting, and irrelevant subject that has a reduced level of utility in their daily lives. This scenario calls on all stakeholders to provide an effective infrastructure to help draw on the social and cultural capital that the diversity of students avail to their classrooms (Mason & Stacey, 1982).
The Description of Methods of Teaching Math
There are several methods of facilitating teaching and learning of math concepts. Every teacher attempts to evaluate which one would be the most effective when students have varying capacities to learn. Different educators propose varying modes of teaching, and the knowledge of a couple of them will enable an educator to devise the best teaching strategy as par the prevailing classroom circumstances. The studies have indicated that it would be inappropriate for a teacher to be committed to a single method, as none will fit the nature of students, their interests and a level of maturity, as well as availableresources with precision. In fact, all methods have their merits and demerits, and it is upon teachers and other stakeholders to decide the best strategy with regard to students in question (Nunes& Bryant, 1996).
Examples of teaching methods include lecturing, an inductive-deductive approach, heuristics, an analytical-synthetic approach, brainstorming, the think-pair-share, learning by doing, andaproblem-solving method. These methods are categorized into two three broad classes:traditional face-to-face teaching/learning, online teaching/learning, and hybrid teaching/learning. The appropriateness and suitability of these methods vary with such factors as the level of students in question andtheir cultural diversity. Teachers ought to evaluate these and other factors, as well as the merits and demerits of each method before devising their own methods byimbibing beneficial qualities in these methods (Mason & Stacey, 1982). The ultimate method ought to be the one which:
- Ensures optimum participation of students;
- Aid in devising abstract ideas from a concrete phenomenon;
- Avail knowledge in a manner that caters for the level of students.
Traditional Face-to-Face Teaching/Learning
The traditional face-to-face method of teaching/learning refers to the situation, when students and their teachers interact within a certain space and time, mostly in a classroom situation. The following section explicates some of the face-to-face learning methods that are common in a math classroom(Li, 2010).
The Lecture Method
Over the years, the lecture method has been the most widely applied mode of presentation. Every teacher is expected to have the knowledge of developing and presenting his/her lectures, and this necessitates his or herunderstanding of the scope and limitations of lecturing. In most instances, the lecture method proves appropriate during the introduction of new topics, summation of ideas, indication of relationships between theories and practice, andunderscoring the main points. This method has been considered adequate in a variety of settings whether with small or large groups. In this regard, most teachers have opted to utilize lectures during the introduction of units and complete courses (Rasmussen et al, 2005). These teachers base their decisions on the fact that the lecture method can effectively be combined with a host of other teaching methods in an endeavor to advance the direction and meaning of the concept in question.
The effectiveness of lecturingis enhanced when teachers allow for active students’ participation. In fact, the utility of a lecture is determined by the teacher’s capacity to getengaged in effective communication with his/her students. However, this method lacks obvious feedbacks, and as such, teachers are required to design keen perceptions for subtle reactions as per students’ facial expressions, their capacity to take notes, and their apparent likes or dislikes of a lesson. The interpretation of the meanings behind these reactions enables teachers to adjust their lessons accordingly, a situation which enhances the effectiveness of the method. Nevertheless, chances of misinterpretation have rendered pure lecturing as an ineffective method of teaching math. The following subsections explain some important aspects of the lecture method (Selden & Selden, 2005).
Preparing for Lectures
The lecture method commences with preparation, and preparation is what kicks-off planning and other systematic procedures. These procedures commence with teachers establishing their objectives and desired outcomes. This enables them to lay the basis for conducting a thorough research intothe subject before they organize their material in a manner that is deemed productive for a host of classroom activities (Mezirow, 1997). As they prepare for lectures, teachers endeavor to support the points to be addressed with logical examples, testimonies, statistics, and comparisons. This means that an optimum level of experience is crucial to the effectiveness of teaching math. Upon the completion of the preliminary planning, teachers design lesson plans, which enable them to rehearse their lectures until they have built enough confidence to deliver optimally. Rehearsing involves the procedure of polishing visual aids, notes, and other instructional devices (Sarangapani, 2000).
Delivering a Lecture
The studies have indicated that the use of simple terminologies is the best way to facilitate effectiveness of lecturers. Therefore, a teacher ought to be well-acquitted with the language being utilized as amedium of communication. This would eliminate instances, whenthe teacher applies substandard sentence constructions,since this will end up in confusing students. In fact, effective teaching necessitates a proper definition of terminologies, which may appear technical to students. Nevertheless, teachers ought to utilize specific words as much as possible generalizing results into confusion(Kwan et al, 2011).
According to Driscoll, it has been established that varying the tone and the pace of speaking results in adding vibrancy to a lecture. He adds that the use of sentences with a varying length reduces monotony duringa lecture. In this regard, variety and clarity are ensured by constructing sentences that are short or medium in length. These merits are guaranteed by ensuring that the teacher prepares consistent notes. Using such notes modestly enables a teacher to keep the lesson on track, especially when they are prepared in a typed and legible format. The notes should also be situated in a fashion that facilitates their accessibility (Silverthorn, 1999).
The Merits of Lecturing
Lecturing presents an opportunity for the teacher to expose his/her students to a variety ofmaterials. It also enables the teacher to determine the organization, the content, the direction, and the pace of a lecture with precision. This arouses interest, which enables the student to concentrate onthe entire lecture. Moreover, lecturing is the best way to clarify and complement text materials. Such complements prove useful, especially when a section of students have got some learning preferences. Finally, lecturing is one of the best methods for engaging a large class in communication. It saves teacher’s and students’ time and as such, it avails time for covering more contents than most other methods of teachingdo (Tall &Harel, 1991).