Methods or Approaches Used to Teach Mathematics in Primary Schools - Coursework Example

Running head: Mathematics Education Name Course name Professors’ name Date Introduction Writers have made comments in relation to evolution of school mathematics and incessant societal and technological changes. They defined mathematics as the study of blueprints and relationships, a way people think, see and organise nature, a language, an instrument, a structure of art, and as power and social filter. Research points out that mathematical concepts are learnt best when the concepts are presented progressively. Teachers are under obligation to provide the conceptual base and experiences that will enable students to understand new and more difficult mathematical ideas. At the same time, student’s prior knowledge is critical in any teaching-learning situation. This proofs the significance of articulating students’ mathematics experiences through lower learning levels and aligning them with their experiences both inside and outside school. It recognises the fact that development of a child entails several diverse setting including: home, neighbourhood, school and other places. The purpose of this report is to present an overview of methods or approaches used to teach mathematics in primary schools. It will necessitate use of real life examples to demonstrate how children learn mathematics in both geometry and measurement strands. At the strand of space and geometry, the objective is to develop knowledge, skills and understanding in visualizing space and employing geometrical reasoning. With the measurement strand, the objective is to develop skills and understanding in identifying and quantifying aspects of shapes and objects while applying measurement strategies. Guiding principles and ideas when teaching mathematics To effectively teach complex mathematical ideas, an educator requires a set of ideas and guiding principles (Zevenbergen, 2004). By taking into consideration these principles, a teacher would be able to facilitate and encourage growth among learners. Such kinds of principles ensure that students improve in their learning while teachers become efficient educators. Consideration and adoption of these teaching principles and ideas into teaching mathematics increases effectiveness of the lesson and ability of a student to access information being taught. Some of these principles which will be discussed in subsequent paragraphs include: Understanding students, differentiating instructions, diverse assessment and continuing education. Understanding learners It is vital for a Math teacher to understand learner’s educational needs in addition to their personal outlook and daily experiences. Students at a primary school level go through different daily experiences which tend to shape their lives. Teachers therefore should develop an understanding of their students and consequently create lessons that build interest and increase motivation. An example is a Math teacher who understands students well would rather provide toys instead of an imaginary story problem which requires higher intelligence (Reys, 2009). Moreover, an educator must have knowledge of student’s educational needs. Learners at a primary school level learn best by utilizing visual aids. Other students are able to understand math content if a teacher makes use of auditory simulations. Through a vivid understanding of students, a teacher can adjust instructions to ensure that individualized needs are met. Differentiated instructions Even though all students must learn similar concepts, it is not mandatory that they learn them in the same manner. A wise teacher therefore offers multiplicity of educational openings in a class. Mathematics teacher who is effective allocates enough time to students with learning complications before progressing to advance category of learners. This allows each group a more individualized form of learning. Research specifies that most teachers do not differentiate their learning simply because of extra effort required. Nonetheless, learning is enhanced by differentiating students according to their mental, psychological and physical abilities. Diverse Assessments In recognition of the fact that some students excel at test while other succeed in projects, a teacher must employ diverse assessment methods. A common phenomenon is where written tests are used exclusively for assessment. Even though this standardized criterion is effective, some students may not do well in it thus miss a chance to demonstrate potentials. Successful mathematics teachers incorporate practical activities and presentation into daily learning process with an intention of promoting comprehension and consequently allow learners to demonstrate varied abilities. Continuing education Comparative studies of education in different countries show that continuing education is required to avoid revocation of a teaching license. Whereas principles in mathematics do not change, educational practices keep progressing with time. For this reason, it is necessary for math teachers to take on continuing education so as to gain new and innovative principles and teaching techniques which are relevant in the present age. At the moment, more scientific teaching method is utilized when disseminating knowledge in a classroom environment. Failure to understand these methods renders a teacher obsolete and ineffective. Teaching method Booker (2010) states that a teacher must recognize that students learn in varied manners. Direct instruction, collaborative learning, inquiry learning and other ways are integrated in a teaching-learning process for maximum result. It is obvious that a teacher cannot reach all students at the same time but if a sample of teaching methods is implemented, all students will have an opportunity of learning in a method that matches needs. Before utilizing any of the method, it is important to note that the best way to learn is by allowing students construct individual knowledge instead of imposing on them. The idea is explained by constructivist theory which states that learning is the creation of meaning from various experiences. In this situation, a teacher guides students while learning. All factors considered, a teaching method must obey the law of progression where concepts are learnt from simplicity to complexity and known to unknown. Application of the method in a measurement lesson Shapes Space and geometry involves representation of shapes, size, and other shapes. Sub-strands for space and geometry are: three dimension shapes, two dimension shapes and position. The skills that will be acquired by students are those of recognizing, visualizing, and drawing shapes. Furthermore, it involves description of both two and three dimensional objects in static and dynamic situations. Capacity of an individual student to manipulate real object leads to development of imagery, language and depiction. When teaching space and geometry, a teacher must note inclusiveness of classification system. Research indicates that trapeziums are inclusive of the parallelograms which then are part of rectangles and rhombuses (Bobis, 2004). This background information is essential to a teacher since it allows for the manipulation and adjustment of the shapes. Teacher is under obligation to plan learning experiences that capture key Understanding and projected outcomes. Key understanding Stage of schooling KU1. When creating or coping objects and figures, a leaner must be aware of how parts relate to each other and to the whole object Middle KU2. Net of an object has to relate correctly with parts and component of an object Middle KU3. An understanding of a drawing is enhanced by combining what is seen with what is thought to exist. Extraordinary drawing technique emphasizes various aspects of an object. Middle In Free hand drawing activity, a teacher invites students to draw a house using simple shapes. The teacher goes ahead and asks students the kind of shapes in the picture drawn. There should be correlation between positions of shapes in the drawing with that shown on the picture (Frid, 2001). In the figure below, students are asked to identify different observable shapes like circle, curves and squires. Measurement Measurement simply entails identifying and quantifying features of objects so that they can be compared and arranged. Any measurement procedure involves approximation thus enables a student to comprehend how objects are estimated. Estimation is particularly essential where a student is not in a position to use measuring device. To perfect the art of estimation, constant practice and utilizing a variety of units in different context is essential. When learning attribute of length, the process will progress from identifying attributes and drawing comparisons, utilizing informal then formal units, then finally applying and generalizing (Willis, 2005). In respect of progressivism, deducing the attribute and drawing comparison is the first step. This simply involves recognizing the fact that objects have features that can be measured. At this stage students touch and compare two or more objects in relation to specific feature, say length. By questioning and drawing conversations, students build a language that is used to describe the features. The second step when learning measurement revolves round repeated use of informal units. A learner appreciates: constancy of units during comparison, relevance of chosen units, interrelationship between size of unit and its corresponding number, and structure of units which are repeated. This step is an eye opener to students who will realize the need for a standard unit of measurement. Interaction with formal unit allows students to understand size of a unit, deduce level of accuracy, and choose well both attribute and unit of measurement, record appreciations and covert unit e. g kilometres to meters. The last step in this progression is application and generalization. This is where students apply skills gained in a variety of contexts to evaluate areas, volumes, and perimeters in general format. Before demonstrating an example of learning measurement, one must note the importance of planning experiences that develops key understanding and will give required outcome. The learning activities must correlate with students own knowledge and understanding rather than grade (Willis, 2005). This planning is illustrated in the table below. Key understanding Stage of primary school KU1. Ability to make direct comparison of objects and events with an intention of deducing length, mass, capacity, area, volume, angle, or time. Middle KU2. Ability to compare indirectly two objects by introducing other objects as go-betweens or rather manipulating the object in a way that does not affect quantity. Middle KU3. In a bid to exercise consistency, an instrument that matches units with object to be measured is used. middle KU4. Scales which are calibrated may be utilized as substitute for repeating units Middle KU5. Different representation of the same unit may be used in measurement provided quantity is held constant. Middle KU6. Time is judged and measured using natural changes like day and night or tools such as watches. Middle Learning activities and key pointers for these learning activities are illustrated as follows (Willis, 2005). Learning activity Pointer of progress made Sports Day A teacher cuts strings into different lengths and mixes them together. At this stage, the students goes ahead to arrange these parts while ensuring that the strings placed in different boxes have the same length. One of the questions to ask students is how to ensure that strings placed in one box are of the same length. Learners are able to choose objects of the same kind when classifying things. Students recognize that the same things can be ordered differently. Changing Shapes of balloon A teacher organizes learners into different groups and assigns them with balloons. One representative of the group is asked to blow up a balloon. The question now is: What aspect is changing on blowing up a balloon? Is it length, volume, or area? After completing this activity, all students are invited to blow up the remaining balloons and consequently order them by an external measuring tool. Understand changes in volume, length and area. Judging the biggest Students are invited to identify attributes that can be compared between apple and orange. In this context, the biggest pumpkin is explained by circumference, weight, the one that gives the most content when eaten or largest skin. After discussing with the students, the teacher should draw conclusion on appropriate attribute for the largest pumpkin (orange or apple). Subsequent to obtaining the attribute, students should use it to order them starting from the smallest to the largest. Compare correctly attributes order correctly attributes Mass or Volume Students are given a collection of items sourced from supermarket and asked to classify them according to mass or volume as a criterion for measurement. Questions that arise are: why milk and other soft drinks are measured in litres? Why maize meal is sold in terms of kilograms and not litres? Students make a correct choice of attributes when measuring things. Understand that choice of units depends on fitness of comparison e. g solids and volumes. Body measurement The first step is to have students choose objects that will use in measuring and recording information about themselves. Aspects to be measured include: weight, mass, distance around waist, length of arm and area of footprint. Students are then asked to make a comparison between their own measurements with that of their partners. The following issues are pertinent to the learning activity: What the student have chosen as basic unit of measurement size of the unit chosen Respond correctly to use of comparative language such as shorter, taller, same length, far and higher. Understand that several attributes can be used in description to give explicit explanation. Conclusion Even though mathematical principles remain constant, pedagogies face continuous changes brought about by unstable social, political and economic environment. Mathematics, which is classified as both an art and a science ought to be taught progressively while taking note of student’s entry knowledge and skills. In this case student’s experiences must be articulated with mathematical concepts in order to enhance understanding. While focusing on major content of the strands, shapes and measurement, teachers should integrate other materials that will broaden and deepen student’s knowledge and eventually stimulate him or her to learn other areas of mathematics. The concepts discussed is not only applicable to teaching mathematics but can be applied to other subjects. Read More