Mathematical Investigations and discussions Essay Example
 Category:Education
 Document type:Research Paper
 Level:Undergraduate
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 Words:1222
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AusVELS mathematics provides students with essential mathematical skills and knowledge. It enables students have a clear understanding of the numbers and algebra, measurement and geometry and also the topics of probability and statistics. Therefore AusVELS ^{1}enriches and creates equal opportunities for all Australians in various fields of study.
In geometry, an angle ^{1} is the figure formed by two rays or line segments. Various activities can be used to promote students understanding of angles. These activities are discussed as follows;

Folding a strip of card around various objects, doorways in classroom and even an overhead projector and also branches of various plants outside the classroom. This helps a student understand various types of angles that exist. Students attain knowledge of determining types of angles based on their properties.

Looking at angles at various crossings. A good example is the scissors. Students should be allowed to practice with scissors.

Roller blading. The students should discuss the angles of feet while carrying out blading or skating and the effects experienced at each specific angle.

Swimming. Young people especially students like swimming. Therefore they figure out best angles for arms and hands to attain maximum efficiency while swimming on different strokes.

Football. A ball follows a different curve when kicked at a different angle. Students ought to know the best angles for kicking a ball.

Folding papers and discussing which angles the papers will make when unfolded.
Students at times encounter various misconceptions of angles. This critical issue affects their judgment of angles. Some students have only images of right angles while in “L “position. Others may only consider right angles as corner of a room they are in. These are few instances of misconception.
Counting counters and memorizing of facts ^{2} are two approaches that can be used with students to make the links between addition basic facts thinking strategies and the subtraction basic facts thinking strategies.
The first step towards calculation involves learning basic number facts behind each operation. Using addition is the most effective way or strategy to help students learn basic subtraction facts. Subtraction is the inverse of addition. Both operations involve the quantities vary. With addition, the parts are known but not the total whilst in subtraction, total and one part are known.
Counting counters and memorizing facts are often the two approaches used to link the addition and subtraction basic facts thinking strategies. The main instruction of counting counters is to guide students improve their counting strategies. The process of optimizing addition strategies goes from counting all, to counting from first and to counting from larger. To calculate 2+5=? By counting all: you show two fingers and show five fingers and then count all. A more advanced strategy is counting on from first. A child calculating 2+5=? Begins the counting sequence at 2 and goes on for 5 counts.
For a child calculating 52=? The child begins by showing 5 fingers and later dropping 2 fingers and ends up with only showing three fingers. This shows that the answer to that calculation is 52=3.
Memorizing facts is another approach with a goal of enhancing students’ capability. The students learn the hundred addition facts and the hundred subtraction facts. The hundred addition is of this order (0 + 0 = 0, 0 + 1 = 1, , , , , 9 + 9 = 18) while the hundred subtraction facts is of this kind of order (0 − 0 = 0, 1 − 0 = 1, . . . , 0 = 9 – 9). The two hundred facts cover all possible situations called the number facts. So if the student can memorize all these facts, then he or she is able to carry out what is called the mental calculations with the 1place numbers.
(a) what does her response indicate about her understanding of numeration?
Jennifer wrote the next two numbers would be 2910, 2911
297, 298, 299, ____, _____
Jennifer was asked to complete the following counting pattern:
Jennifer understanding of numeration is not beyond a two digit number. She does not that a three digit number exists. What she clearly knows at the moment is the numeration of the one and two digit numbers. She accurately counts from 9, 10, and 11 and so on and may be up to 99. She has a clear understanding of one and two digit numbers.
(b) Describe fully an activity to help her overcome this difficulty.
Jennifer can overcome this difficulty by learning that a three digit number exist and practicing on counting of the three digit number. She must know how to count from 100 to 999. All the numbers in between values of 100999 are three digit numbers.
Jennifer can engage herself in Roll 3 Digit ^{3 }exercise. This is an activity involving numbers in between 100 and 999.
Roll 3 Digit activity entails the following.
3 dice marked 16 and two dry erase markers of different colors.

Work with a partner. Take turns to roll the dice to form a three digit number.

Read sentence frame that describes your number and write down the answer in the correct frame. For example;
…………….is in between 100199
…………….is in between 200299
…………….is in between 700799

Keep playing in turns till you fill all the rectangular frames.
By Jennifer engaging herself with the 3 Roll Digit activities, she will learn all the numbers from 100 to 999.
‘By year 6, children no longer need models in order to study geometry.’ I disagree with this statement and therefore put forward two reasons to support my argument.
A model is a replica or prototype of the real object while geometry is the branch of Mathematics that concerns itself with the questions of shape, size, and properties of space and relative position of figures.
Children start learning geometry by looking and touching models ^{4 }of various objects they come across during their childhood. I disagree with the statement stating that children at six years no longer need models in order to study the geometry.
Children at this age are conversant with common shapes such as circles, rectangles, squares but they cannot name complex shapes such as the rhombus, certain triangles, and semicircles and so on.

Circle (b) Triangle (c) Rhombus
Therefore they need the models so that they can study them and have the capacity to remember and name those complex shapes when tasked to do so especially in their examinations.
Secondly, use of models helps to match children activities to level of thinking about the shapes. Children at the prerecognition stage work best with the shapes of the world. It helps them determine between the relevant and irrelevant in terms of shape, orientation and color attributes of the shapes they encounter while learning.
Children at this visual stage can measure, color, fold and cut shapes of the models they are learning with. This clearly depicts the importance of using models while teaching children of this age.
References
^{1 }Janice, Pratt VanCleave. Mathematical recreations. New York: Wiley & Sons, 1994
^{2} Thornton, Payne. Strategies for basics facts. Reston, VA: National council of Teachers
Of Mathematics, 1990
^{3} Marilyn, Burn’s. About Teaching Mathematics .Math Solutions Publications, 1992.
^{4 }Clements, Douglas H. “longitudinal study of the Effects of LOGO Programming on Cognitive Abilities and AchievementJournal of Education Computing Research 3 “(1987): 7394