Introduction
Mathematics is a special subject that requires a strategic teaching practice, which should be used to ensure effective delivery. To understand and apply the required teaching strategy, many factors have been raised as to the suitability of certain effective ways of teaching. Therefore, it is very important to outline the best practices in teaching and learning mathematics, especially how to approach the topics of space geometry, manipulative and technology.
Sometimes, understanding of the subject becomes difficult for the students, even though the teacher can handle several concepts. It is in this regard that there is a call for doing this research to come up with alternative ways of handling geometry. The students in most instances need to relate what is contained in the book and the practical approaches to this subject matter.
The teaching and learning strategies need to be fabricated towards the achievement of both immediate and long term goals in mathematics. This becomes the basis of discussion for this work because it will reveal how geometry helps in the understanding environment while in class or any other place.
Main body
Mathematics is a subject that involves measurements and relationships of the numbers, symbols, and figures, which help in the interpretation of any given value (Carpenter, Hebert, Murray, Wearne, Fuson & Fennena, 1997). Mathematics alone is a wide concept and it involves sub-branches like geometry, algebra and other space manipulative. It involves reasoning and understanding of the values and shapes depending on the circumstances of the presentation. Mathematics is important because it helps us in analysis, understanding of the figures and ratios. All adult persons and children appreciate mathematics. It is applicable in administration, business, teaching and understanding the values of finance.
Geometrical mathematics, for instance, our families and children need to understand the shapes involved in their daily living. For instance, they need to know why some things like paper and walls are rectangular. Researchers have previously brought out geometric situations that emphasized shape and space as very important in helping children solve problems in mathematics. These applications of geometry include visualizing spatial arrangements, communicating orally, drawing and making of models, having logical thinking and general application of geometric concepts and knowledge. Mathematics is generally supported by the curriculum and in particular, geometric mathematics is very useful in the primary syllabus because it is at that point that recognition of shapes and lines is realized.
According to the National Research Council and the committee on early childhood mathematics (2009), they had proposed development on the use of geometrical mathematics to teach younger children on the construction of shapes in a classroom setting by use of free materials which included the use of clay, boxes, and cartons. Construction with papers through folding, drawing shapes and patterns. These were very practical in enabling the children to understand the shapes and apply them most appropriately.
Geometry, for instance, enables the children to understand real objects that reflect shapes of objects. These include polygons and other patterns, which are useful in the child’s learning process. The other major use and application of geometry and shapes include location and associated representations. The location and movement describe directions, distance, and position. This observation enables the children to describe their world and understand the surrounding. Also, the students can build mathematical concepts like positive and negative numbers plus skills relating to other subjects. Geometry also enables the understanding of patterns and transformations
How Children Learn Mathematics
The knowledge of how children learn mathematics is vital because it enables better understanding, which makes the teacher know their behavior and generally allows for efficient and appropriate ways of teaching. In the mathematical learning process, there is an outline for the development of spatial concepts, which create five levels of understanding during the learning of the process.
According to Van Hiele’s theory, the five levels are grouped as “analysis, visualization, rigor, formal deduction, and informal deduction” (Booker, Bond, Sparrow & Swan, 2010). According to Van Hiele, no child can miss these levels because they are all sequential. Each level has got its unique characteristics and contains useful interconnections with one another. These levels are useful in accounting for the effective development of geometric thinking and also in the organization of teaching and learning activities.
The first level is recognition or visualization. This level emphasizes that children normally operate based on the appearance of items without reference to properties. They describe a shape as a whole but never identify its uniqueness (Reys, Lindquist, Lambdin & Smith, 2009). They relate the object to what it is familiar with. Problems are solved through trial and error or by visual means. They still do not have precise language for description generally. The second level is analysis. This is where the children start to notice and acknowledge the attributes and properties of shapes (Muschla & Gary, 2006). For example, the children begin to identify certain triangles through the properties of their shapes. However, they do not understand that some properties at this stage are a necessary consequence of others. At this time, the teacher imposed definitions may not be interpreted well nor applied.
The next level is level three. This involves ordering or informal deductions in learning mathematics. The children begin to note the relationships between properties and shapes. For instance, parallel lines must just form equal angles. There is a reflection on the concrete experiences on the provided information. The children are then able to see the relationship between various geometrical concepts and give properties of a shape that defines it. The major example here is that an equilateral triangle can be identified as having three equal angles, three equal sides and that the angles are adding up to 180 degrees. This is only applicable to some children because the learning process varies accordingly.
The fourth level is the formal deduction. The children can reason abstractly and logically to come up with proof. The children can develop their proofs instead of just remembering. The last stage is the fifth level known as rigor or meta-mathematical. There is analytic reasoning of the students that deals with the relationship between formal constructs.
From the experience of learning mathematics, there is a better understanding and application of mathematical ideas by the children. This is shown in the presentation of the annotated maps drawn by the children at various stages. Their ability to draw and locate the places indicate distances, labeling of trees and general presentation of drawing is made in such a way that it reflects their understanding of geometry. The children have various capabilities depending on the level to show the distances, roads and relevant symbols capturing the real picture of the environment. Their sample annotated maps are clearer depending on the understanding of geometrical shapes, use of scale in the estimation of distances and ability to use three-dimensional presentations. All these are possible because of the mathematical knowledge that the children have.
Strategies for Teaching Mathematics
There are various strategies for teaching mathematics, which enable the children to have a full understanding of the concepts and get knowledge accordingly. The first strategy is the constructivist strategy. This approach enables the student to understand any given mathematical concept and apply it reasonably. They can create the necessary mental image of the topic of learning given is by teaching the children from the perspective of known shapes or issues to the unknown (Deborah, 2009).
This is because by presenting three-dimensional shapes first, it was quite possible to explore their knowledge from familiar three-dimensional shapes such as a ball and blocks. When this strategy is used, then the children will have the opportunity to develop knowledge accordingly. The children away from learning from known to unknown will be able to understand the concepts effectively. This enables the gradual development of skills and learning processes (Willis, 2010).
The other strategy involves the use of intermediate activities. The intermediate activities involve making students form small groups and solve some problems in the form of riddles. When they are learning through a riddle, it is very easy to understand what is taught by the teacher. Another strategy is by involving the students in certain advanced activities. The activities will majorly focus on the topic of discussion like describing and sorting shapes. The children should be able to describe and identify three-dimensional objects.
Resources that Can Support Children’s Mathematics Learning
Mathematics requires certain resources that guide the proper learning process. The resources, for instance, depending on the topic that the students are learning at a particular time (Joanne & Martin, 2007). In this case, it is crucial to note that learning of geometry and space is guided by the use of lines, shapes and building up of pyramids. Children can learn from models in understanding mathematics. This resource model may include prisms, boxes, truncated prisms and development of edge models. Also, the models are made from straws, pipes, cleaners or sticks that could be connected with tape or clay (Wilder & Mason, 2005). These enable understanding of the mathematical concepts, and the children can draw some useful information from the figures. Plain drawing papers are also useful especially when they are introduced in drawing of shapes.
The children can draw something they know from circles, triangles, and rectangles (National Library of Virtual Manipulative, 2010). They will be able to identify the number of sides that each figure has. The learning resources should be present at all times when teaching geometry in mathematics. The children will have a better understanding of the concepts and be able to apply the knowledge relatively based on the provided circumstances in life.
Conclusion
Learning geometry and shapes provide a good opportunity for the children to understand their surrounding. Mathematics is useful in such analysis apart from being able to evaluate, calculate and make a clear presentation of the facts in any given condition. It is important to note that children learn mathematics in states or levels of developing special concepts. According to the above discussion, Van Hiele’s theory highlights the five levels, which include, but not limited to analysis, visualization, rigor, formal deduction, and informal deduction. Each level means there is a certain concept that becomes known by the children. This enables the professional teachers to understand the levels and present relevant ideas that the students can master effectively.
The strategies for teaching mathematics, especially geometry is also important and includes learning the known to unknown and having intermediate teaching methods among others. This helps in good understanding. Also, there should be good resources that guide in the teaching process, which include models of various shapes for the practical approach in handling geometry. Finally, mathematics is generally applied in various areas of operation in our daily life and it is important when incorporated in the syllabus especially geometry for the young children to give better foundation and skills in appreciating figures.
References
Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). Teaching Primary Mathematics (4th edition). Frenchs Forest, NSW: Pearson Australia.
Carpenter, P., Hebert, J., Murray H., Wearne, D., Fuson, C. & Fennena, E. (1997). Making Sense: Teaching and Learning Mathematics. Portsmouth: Heinemann Publishers.
Deborah, M. (2009). Strategies for Teaching Mathematics. Huntington Beach: Shell Education Publisher.
Joanne, P. & Martin, K. (2007). Supporting Mathematical Learning: Effective Instruction, Assessment, and Student Activities. San Francisco: Jossey- Bass.
Muschla, A. & Gary, R. (2006). Hands-Onn Math Projects with Real-Life Applications. San Francisco: Jossey- Bass.
National Library of Virtual Manipulatives (2012). Web.
National Research Council & Committee on Early Childhood Mathematics (2009). Mathematics Learning in Early Childhood. Washington DC: National Academies Press.
Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). Helping Children Learn Mathematics (9th Ed.). New York, NY: John Wiley & Sons.
Wilder, J. & Mason, J. (2005). Developing Thinking in Geometry. California: Sage Publications Ltd.
Willis, J. (2010). Learning to Love Mathematics: Teaching Strategies that Change Student Attitudes and Get Results. Alexandria: Association for Supervision& Curriculum Development.