Assignment 1 Assistance In an essay of approximately 1000 words (approximately 3 pages), discuss your understanding of physical and virtual manipulatives (not games or apps). Based on the...

Contents
PHYSICAL AND VIRTUAL MANIPULATIVES    2
Introduction    2
Definition, Similarities and Differences of Physical and Virtual Manipulatives    2
Importance of Manipulatives with Insightful links to Relevant Theories of Learning    4
Effectiveness of each type of Manipulative in the Teaching and Learning of Mathematics    5
Links between theory and practice    7
Activity    8
Conclusion    10
References    11
PHYSICAL AND VIRTUAL MANIPULATIVES
Introduction
It cannot be underestimated the function played by mathematics in almost every field of life creation. All technical advancements in the world are focused on mathematics. Without adequate and proper knowledge of mathematics, no significant advancement in this new technological environment can be accomplished. The analysis of mathematics improve one's worldview through symbol language and abstract phenomenon representation. In nearly every school subject, mathematical knowledge is applied. Mathematical manipulations are objects that are used in the education of Mathematics: students are provided with mathematical concepts or processes to discover, learn or research them and ca
y out problem-solving activities that rely on perceived evidence (visual, touch, or sensory evidence in general).
In this essay, we will talk about both physical and virtual manipulatives and understand their development, implementation and evaluation. I have presented a theoretical framework for the use of mathematics in learning and teaching manipulatives from early childhood through primary years, and analyse empiric evidence to support this theory. We revisit the role of both the manipulative methods in helping students learn mathematics from this reformulation.
Definition, Similarities and Differences of Physical and Virtual Manipulatives
There are various types of manipulations practiced in schools and training, however, two classifications which arise from literature, which relate to the consistency either of the interaction manipulative or the origin of the manipulative, can be suggested: physical and virtual manipulative.
Physical manipulatives are objects that students can manage concretely and that gives them a comprehensive and deep sense experience. Virtual manipulators are digital devices that imitate physical objects and can be handled in the same way as real, usually with the mouse. Virtual Manipulatives consist of any digital interface or instrument such as smartphones, laptops, tablets, calculators or online tools. Both aspects might look similar in the way that digital objects seem like physical objects and can be operated using a mouse the same way as with real objects. These two manipulations are, however, very distinct. When considering the differences between the two manipulatives, aspects such as efficiency of the manipulatives in
teaching the concepts, style of learning, cost factors, time taken to teach a concept and material or examples used to learn are taken into consideration. Physical manipulations state that true objects are used when the context is interpreted, therefore information can be visually and aesthetically perceived. Furthermore, it is much easier to grasp because students can sense the objects that hold them in mind. In contrast, virtual manipulatives comprises of the mathematical models that are interpreted using interactive methods in order to learn and teach mathematical concepts. Virtual manipulative methods help teachers to incorporate pictorial, ve
al and symbolic representations effectively, while enabling learners to apply objects as in the physical manipulations (Johnson et al. 2012). Virtual manipulations gives versatility to teachers and an opportunity to the learners to ask for explanations, as the responses and suggestions are faster in the case of virtual manipulatives as compared to the physical manipulatives (Johnson, et. al.). Therefore, manipulatives are materials that students can use from our own environment to learn or shape mathematical concepts. In other terms, any object or entity to allow mathematicians to understand.
Now, we would consider some of the aspects like centre of learning, century of learning, cost of manipulatives, material used and examples of materials used for learning and compare the two manipulatives of these grounds.
Physical manipulations are seen as teacher oriented because the instructor has to explain the doubts or queries and relate the definitions, diagrams and illustrations. This helps us to understand the material more thoroughly. Whereas, virtual manipulative is more focused on students because different depictions or illustrations of the same mathematical concept are presented using a computer or tablet and students have to figure out which concept is best for them. That is, the student discovers his own way of learning and technique. For physical manipulations, the teacher provides the content used to learn a specific concept and thus helps the student to grasp the idea they are being taught by materials selected by the teacher. This helps students to interact step by step with this material and to grasp what it means. However, students need to explore different methods to solve a problem on their own in virtual manipulations. In order to solve a problem, they need to explore different methods that could take longer, and a child may feel eager to perform the tasks that may lead to e
ors (Hunt, Nipper and Nash 2011:6).
It is often stated that physical manipulatives uses old teaching methods or techniques. The concepts and principles are divided and presented in a way that they can never forget whereas virtual manipulations, relies more on the new teaching method and attracts the focus of the new technological generation. When we consider the cost aspect of the two manipulations then it is found that physical manipulatives are expensive, since it requires the procurement of resources. Virtual handling is cheaper comparatively since everything is done online with various apps and online applications. However, there are countries like South Africa where the children studying in schools are poor and underprivileged and cannot afford to buy these online resources.
Finally, the aspect, material used and examples of materials used for learning are discussed and it is found that students use their senses, such as touch and sight, hearing, etc. to grasp the principles of physical manipulation practises. Pencils, sticks and strings are examples of physical objects. The material helps students and educators pick things better and improve themselves kinaesthetically because while using digital stuff students do not communicate with objects but can display them on a computer and learners must communicate with the items on the screens they can see.
Importance of Manipulatives with Insightful links to Relevant Theories of Learning
The task of a mathematics teacher is to make the students learn the subject and implement it in real life situations. However, many studies have shown that high school students are little interested in learning mathematics (Eshun, 2000; Awanta, 2000). The available records also indicate that students in the West African School Certificate Examination (WASCE) have unsatisfactory mathematical results. The Chief Examiners’ Report of the West African Examination Council in recent years illustrated the difficulty of students in solving problems in mathematics (WAEC Chief Examiners’ Report, 2005, 2006, 2007).
The knowledge of mathematics is not intrinsic, according to Yackel, Co
and Wood (as cited in al – Absi & Nofal, 2010), and therefore develops with the interaction between the learners and the environment and individuals. Learning...