Summary
Children observe and interact with two-dimensional and three-dimensional objects through daily activities in the environment such as building blocks, books, balls or puzzles. Learning geometry is one of outcomes in Victorian Essential Learning Standards. Geometry offers an opportunity for students to engage in mathematical thinking that allows them to make conjectures. This report will reflect the lesson plan on four points:
• Key mathematical ideas and skills.
• Link to relevant curriculum documents and understanding of the learning sequence.
• Teaching approaches, developing children’s understanding, appropriate models and materials for learning.
• How children learn the mathematics concepts.
1. Key Mathematical Ideas and Skills
Geometry is a branch of mathematics which involves the study of properties of points, lines, planes and of curves, shapes and solids (Booker et al. 2010, pp. 395). It is applied in wide areas of knowledge such as graphics, design, art and geography. The rationale in area for primary children is learning about common two-dimensional figures and three-dimensional solids by exploring a variety of objects in the environment. Children are encouraged to participate and practice in team work through activities. It helps them to improve some skills such as visualizing, explaining, reflecting, recording and sketching as well as mathematical language.
According to Victorian Essential Learning Standards, there are two forms of geometry which children study at primary school
• Visual geometry: it engages children in the use of space, shape and form by symbolic representation, intuitive and personal level (Booker et al. 2010, pp. 396). Mathematical language used in this area is natural and informal...
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...d variety to the range met by children.
• Describe activities and relationships: By having to use language, children begin to clarify and connect what they have learned from the activity with what they already know. Reflecting through the use of written and oral language is an important feature of developing understanding of geometrical concepts. Teacher needs to provide children open-ended tasks and questions for reasoning and explanation rather than for memory checking.
4. How Children Learn The Mathematics Concepts
According to Piaget’s stages of cognitive development, children in the age group two to seven start to have symbolic representation of the present and real. They prepare for understanding concrete operations. Language and imagination are used to extend their thinking abilities and understand the world around them. In the stage 7 – 12 years of age
While the studies at Governor’s School are noticeably more advanced and require more effort than at regular public schools, I see this rigor as the key to my academic success. For me, the classes I take that constantly introduce new thoughts that test my capability to “think outside the box”, are the ones that capture all my attention and interest. For example, while working with the Sierpinski Triangle at the Johns Hopkins Center for Talented Youth geometry camp, I was struck with a strong determination to figure out the secret to the pattern. According to the Oxford Dictionary, the Sierpinski Triangle is “a fractal based on a triangle with four equal triangles inscribed in it. The central triangle is removed and each of the other three treated as the original was, and so on, creating an infinite regression in a finite space.” By constructing a table with the number black and white triangles in each figure, I realized that it was easier to see the relations between the numbers. At Governor’s School, I expect to be provided with stimulating concepts in order to challenge my exceptional thinking.
For me geometry is the most basic concern for artists. Roland Shearer quotes poet Apollinaire where he explains, “geometry is to the plastic arts what is to the art of the writer”. This is not to say that artists are geometers, because most of us are far from it (Shearer 1992:143).
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
Concrete operations (ages 7-11) – As a child accumulates experience with the physical world, he/she begins to conceptualize to explain those experiences. Abstract thought is also emerging.
I assume the point of teaching this skill was to help apply it to real life situations, but sadly, triangles simply aren't the same thing as world
Students will be able to identify the shapes in the book. (circle, triangle, square, and rectangle)
Thatcher, Debra. “The Tangram Conundrum.” Mathematics Teaching in the Middle School. 6 no 7, 397-9. March 2001.
This question will be referred to in relation to Piaget’s cognitive development theory. This theory depicts that there are four stages in which “children actively construct knowledge as they manipulate and explore their world”. (Berk, 2012, Pg.19) These stages are; sensory motor stage, pre-operational stage, formal operational stage and concrete operational stage. (Berk, 2012, Pg.19) Berk explains that children’s drawing development progresses in three phases: scribbles, first representational stage and more realistic drawings. (Berk, 2012 Pg.310) This essay will explain the connection between children’s mental development in relation to drawing at the more realistic drawings phase, focusing on the concrete operational stage of Piaget’s cognitive development theory.
On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry. M.C. Escher used his knowledge of geometry, and mathematics in general, to create his tessellations, some of his most well admired works.
Skemp, R (2002). Mathematics in the Primary School. 2nd ed. London: Taylor and Francis .
Sherley, B., Clark, M. & Higgins, J. (2008) School readiness: what do teachers expect of children in mathematics on school entry?, in Goos, M., Brown, R. & Makar, K. (eds.) Mathematics education research: navigating: proceedings of the 31st annual conference of the Mathematics Education Research Group of Australia, Brisbane, Qld: MERGA INC., pp.461-465.
The theory of cognitive development also happens in stages. Piaget believes that children create schemata to categorize and interpret information. As new information is learned, schemata are adjusted through assimilation and accommodation. Assimilation is when information is compared to what is already known and understand it in that context. Accommodation is when schemata is changed based on new information. This process is carried out when children interact with their environment. Piaget’s four stages include sensorimotor, preoperational, concrete operational, and formal operational.Sensorimotor happens between the ages of 0-2, the preoperational stage happens between the ages of 2-6. The concrete operational stage happens between the ages of 7-11, the formal operational stage happens between ages 12 and up. During the first stage, children develop object permanence and stranger anxiety, the second stage includes pretend play and egocentrism language development. The third stage includes conservation and mathematical transformations, the last stage includes abstract logic and moral
? Calculators and computers are reshaping the mathematical landscape, and school mathematics should reflect those changes? (NCTM 24). My view of mathematics and geometry is that they go hand in hand. You have to know some algebraic procedures in order to be able to perform geometry problems.
Getting children to work together on projects which require problem solving is a great way for them to interact with each other and learn mathematical concepts on the way. It will also help them to boost their communication skills. Teachers can also facilitate learning by scaffolding the children’s learning and offering guidance when needed. Getting children to talk about what they are doing and what their plans are actually helps them to learn. Through their projects, children will learn to describe the mathematical concepts that they present using different materials. For example, drawing a house for art class, they learn the names of the different kinds of shapes that make up a
Many parents don’t realise how they can help their children at home. Things as simple as baking a cake with their children can help them with their education. Measuring out ingredients for a cake is a simple form of maths. Another example of helping young children with their maths is simply planning a birthday party. They have to decide how many people to invite, how many invitations they will need, how much the stamps will cost, how many prizes, lolly bags, cups, plates, and balloons need to be bought, and so on. Children often find that real life experiences help them to do their maths more easily.