Education mathematics PDF

EDUCATION MATHEMATICS
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Contents
Introduction......................................................................................................................................2
Discussion Topic 1: Potential for enriching understandings of Measurement and Geometry........2
• How can you build children's understanding of measurement and geometry through these play
experiences?.....................................................................................................................................4
Share and explain the mathematical concepts these situations offer...........................................4
Discussion Topic 2: Time................................................................................................................5
• Consider the following statement: Time should not be introduced to children before they
are six years old........................................................................................................................5
Portfolio Task 7: Concrete Materials...............................................................................................7
Portfolio Task 8: Transformations: Translation, Reflection, and Rotation.....................................8

Transformation.........................................................................................................................8
Rotation....................................................................................................................................9
Reflection.................................................................................................................................9
Translation..............................................................................................................................10
REFERENCES..............................................................................................................................11
Introduction
At the level of thinking about the parts, the preschoolers can effectively match the shapes that
have different orientations. Children can learn to check if the pairs of the 2-D shapes are really
congruent by using the motions of the geometry intuitively. The child can learn to effectively
predict the effects of the motion of geometry hence assisting in the laying of the foundation of

the thinking that relates to other parts. Children can also be able to cover a piece of rectangular
space using squares and consequently present these tilling using very simple drawings.
Discussion Topic 1: Potential for enriching understandings of Measurement and Geometry
Geometry basically refers to the grasping of the space. Considering that it is about the education
of the kids, geometry will refer to the concept of grasping the space that the child moves,
breathes and lives. It is that space which the child must practice to know, conquer and explore so
as to breath, live and properly move in it. Most of the young children are capable of matching the
shapes implicitly as they play (Lehrer & Chazan 2012). Working at the level of the visual
concept or what is considered holistic stage, they can provide a proper description of all sorts of
pictures of the objects. This is done while explicitly using shapes in the recognition process. In
this process, the student learns to name the shapes especially those in the 3-D. Although most of
the culture indicates familiarity that begins with the symmetric circle all the way to the
prototypes of the triangles,3-D figures are very much familiar.
Figure 1: Student arranging various cubes to achieve specific height and volume (Lehrer &
Chazan 2012).

The children will learn the 3-D shapes by using one of the faces to generate the name, for
example, referring to a cube as a square. The ability to match 2-D to the corresponding 2-D
clearly shows their perfect skill in the differentiation of the shapes. According to the photos
indicated below, children can effectively learn how to recognize and name shapes like rectangles
and triangles. This can be possible especially in their prototypical form and possibly start
describing them using their own words. Assuming that the children already have prior
knowledge of the numbers, the description of the shapes can be done depending on the number
of sides each shape has (Clements & Battista 2012). The idea of learning about terminology and
concepts of such shapes fosters geometric thinking.
Figure 2: Different shapes modeling fostering geometry learning (Lehrer & Chazan 2012)
• How can you build children's understanding of measurement and geometry through these
play experiences?
At the level of thinking about the parts, the preschoolers can effectively match the shapes that
have different orientations. Children can learn to check if the pairs of the 2-D shapes are really
congruent by using the motions of the geometry intuitively. This starts by moving from the
strategies that are less accurate like matching of the sides or the use of the lengths to achieve the

concept of the superimposition. Superimposition basically refers to the placing of the objects on
top of the other. The child may begin to explore the concept of geometric motion through slides.
The child can learn to effectively predict the effects of the motion of geometry hence assisting in
the laying of the foundation of the thinking that relates to other parts. Children can also be able
to cover a piece of rectangular space using squares and consequently present these tilling using
very simple drawings. The children can also learn a lot about the 3-D parts of the shapes while
using the motions in the matching of the faces found in 3-D shapes to the shapes of 2-D thus
establishing a relationship with the objects(Laureate 2014a). Children may be instructed to make
models of the classrooms while making good use of the rectangular block, making small cubes
for the chairs etc.
Share and explain the mathematical concepts these situations offer
Length basically refers to the property of the object that is obtained by quantifying how far it is
between the selected two endpoints of an object. The measurement of the length normally
constitutes two aspects. One of such aspects includes the identification of the unit measure and
then performing the operation of the subdivision. The exercise of subdivision can either be
physical or mental by the unit. Secondly placing of an end to end of the object what is simply
referred to as the iteration(Reys et al 2012). The concept of the subdivision and iteration of the
units can be achieved using the ideas explored within these pictures.
The preschoolers normally lack understanding of the ideas of measurements and also procedures
including lining up of the objects by their ends when comparing the length of two objects. When
such children are given a ruler that is demarcated, very little regard will be paid to the size of the
available spaces. In fact, very few will use zero as their starting points for measurements. This
clearly shows the deficiency in the understanding of the original concept. When such figures like

the cubes given in the photos are presented to the children, they can learn how to represent length
while using the third object. Transitivity will be used to aid in the comparison of the two objects
whose comparison cannot be done directly (Doabler et al 2012). The children can also use the
given units in making inferences about the relative size of the objects especially in the cases
where the number of the units is the same. The translation of the 2-D objects into the 3-D can be
effectively used in the introduction of the concept of volume in geometry (Wilder 2013).
Discussion Topic 2: Time
• Consider the following statement: Time should not be introduced to children before they
are six years old.
Any child's first years of school are filled with many wondrous moments. It's a time of
tremendous social, emotional, physical, and intellectual growth and it can come and go before
you know it. The skills learned at this stage -- knowing what sounds the letter a makes or adding
2 + 2 -- may seem simple but they will set your child up for a lifetime of learning. Pre-K may
look like all fun and games (music, story time, dancing, art) but there's an intense amount of
brainwork going on(Clements 2014). Young children learn through play and creative activity, so
your preschooler's building blocks and train tracks aren't just entertaining; they're teaching
problem solving and physics. Preschool is also a time for developing good learning habits and
positive self-esteem. Introducing the concept of time at this time may not be proper (Twomey
2013).
• If time is introduced to young learners, explain ways you might stimulate their concept of
Haywood and Cockburn's two meanings of time and why.

The concept of recorded time can be introduced to children by utilizing the general concept of
time. Some of the general concepts of time include the following; nighttime, morning, evening
and afternoon. The kids can be familiarizing with very such concepts by associating them with
other activities. This may be followed by asking questions when such events take place
(Cakmak, Isiksal & Koc 2014). For instance, "We take breakfast in the morning alongside
brushing teeth, take lunch at noon and go to bed at night. "The children can then be asked. “What
happens at noon?”
Doing a countdown
The process of doing countdown can help children understand the concept of a time interval. The
activity can be tied with a special holiday like New Year. Generate the face of the clock by the
use of the paper plate and then inserting paper arms. The second arm of the clock is moved while
the countdown is made. The children are then asked to count along together while much
excitement is built around the activity.

Figure 3: pictorial illustration of teaching time (Weiland & Yoshikawa 2013)
Portfolio Task 7: Concrete Materials
Concrete materials are basically defined as the objects that can actually be touched and become
moved by the children. Commonly known as concrete manipulatives. These materials are used to
reinforce the concepts of mathematics (Weiland & Yoshikawa 2013). These materials represent
the concepts that are considered abstract in a way that is visual hence fostering the understanding
of mathematics to the weak students other than providing the strategies to work from (Haylock
& Cockburn 2013). An ongoing meta-examination discovered little to medium impacts for
cement manipulative utilize, however so far, regardless of whether they are a compelling system
for kids with math’s troubles has not been assessed. This survey means to set up whether there is
a proof base to help the utilization of manipulative in enhancing the science aptitudes of
youngsters with arithmetic troubles (Kelly & Lesh 2012). Discoveries demonstrated promising
proof for manipulative for youngsters with math’s challenges, giving they include certain key
segments. Confinements and future research bearings are talked about. Concrete materials like
cubes and grains make addition and multiplication concept easier
.
Figure 4:Use of concrete material for fostering learning (Wilder 2013)

Portfolio Task 8: Transformations: Translation, Reflection, and Rotation
Transformation
The transformed figures are just too cool. It very simple and much easier to change them from
something different by generating motion on pieces around. It is a lot of fun. Has anyone realized
that one can do the transformation in mathematics too? Although it does not work like the
transformation toys, the mathematical transformation allows for the changing of the figures and
shapes as well. The transformation may not only be done on the basic shapes like triangles,
rectangles, and squares, but also other shapes(Kefaloukos & Bobis 2011). Actually, any image
can be transformed. Simple Square, a picture of a car or even a house. As long as a figure or the
image is a 2-D.
Rotation
Can anyone think about what happens when the driver of a car turns at the point of the stop
light? What actually happens to the vehicle? The vehicle remains of the same size though facing
different directions. This effect is known as rotation. Rotation is a special type of turn (Yaglom
2012). In any discussion about the rotation, the image or the figure turns about a fixed point.
When one considers the second hand on the clock, the hand actually rotates around the clock but
one of its ends remains at the center without moving. The end at the center is described as the
fixed point.

Figure 5: Rotation of second hand of the clock (Wilder 2013)
The steps that may be considered very crucial for the application of this concept in class include:
Acknowledging what is being done by the children. The children should be made think that their
actions have been noticed by giving them attention that is positive. This can be illustrated by
taking a close observation of the activities of the children. The positive statements will include
those statements like “Thanks for the attempt”. Encouragements of the persistence of the efforts
that have been put into place other evaluation and praising the activities. The use of other
relevant methods like stories including “Let’s keep going”.

Figure 6:Strategies of teaching rotation
Giving very positive feedback as opposed to the general statements. The application of this
concept should be alongside model creation. The children will be shown how the activities of the
rotation can be done practically not just using general statements. The children can then be
subjected to more challenges that are considered relevant. This will actually help the children to
go beyond what has been handled in class previously. Some of the relevant challenges that the
children may be subjected to include asking them to locate the new position of the minute hand
after one minute, new position of the hour hand after two hours etc. until the concept of rotation
is completely explored and understood.
Reflection
If the rotation is regarded as the turning effect, then the reflection is regarded as the flipping.
Consider looking at the mirror. One will look exactly the same. The only difference is that
everything appears on the opposite side. When shapes are reflected, they are flipped across the

mirror line that is sometimes imaginary. The image looks the same as the object only that it is
facing the opposite direction.
Figure 7: Reflection pictorials (Wilder 2013)
In my class I tend to practice alternative ways of teaching. This starts with the identification of
the differences between different levels of the children and later matches the common way of
teaching. This effect may spread to the point of choosing objects like the two halves of the
oranges. In this particular case my role as a teacher is not just entire instructing the children on
what to do but rather passing that responsibility of being an instructor to the children. The
children thus get the opportunity to learn and progress at individual pace.

Figure 8: Halve oranges illustrating reflection.
In the other way out, I may choose to explore the vocal power in addressing the whole class
while teaching as per the provisions of the curriculum. This kind of the method of teaching may
not be recommended to those children that bare already advanced. The two halves of the oranges
perfect illustration of the reflection. The children are therefore capable of highlighting pother
relevant examples of the reflection in real life. .
Translation
Imagine that one has a playing card in front of oneself. If this card is slid across the table to
another friend, then translation has just occurred. In the process of translation, the angle or the
size of the shape never changes. The object is simply moved across, down or in the diagonal
direction.

Figure 7: Translation of object (Wilder 2013)
Asking the children to regularly change their position of sitting or just changing the sitting
arrangement may be considered perfect example of the translation illustrations.
REFERENCES
Cakmak, S., Isiksal, M., & Koc, Y. (2014). Investigating the effect of origami-based instruction
on elementary students' spatial skills and perceptions. The Journal of Educational
Research, 107(1), 59-68.
Clements, D. (2014). The geometric world of young children. Early Childhood Today; October
1999, Issue 2, p34-43, 10p.
Clements, D. H., & Battista, M. T. (2012). Development of geometric and measurement ideas.
In Designing learning environments for developing an understanding of geometry and
space (pp. 215-240). Routledge.

Doabler, C. T., Cary, M. S., Jungjohann, K., Clarke, B., Fien, H., Baker, S., ... & Chard, D.
(2012). Enhancing core mathematics instruction for students at risk for mathematics
disabilities. Teaching Exceptional Children, 44(4), 48-57.
Haylock, D., & Cockburn, A. D. (2013). Understanding mathematics for young children (4th
ed.). London, England: Sage.
Kefaloukos, M., & Bobis, J. (2011). Understanding conservation: a playful process. Australian
Primary Mathematics Classroom, 16(4), 9–23.
Kelly, A. E., & Lesh, R. A. (2012). Handbook of research design in mathematics and science
education. Routledge.
Laureate Education (Producer). (2014a). Fostering numeracy [Video file]. Baltimore, MD:
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Lehrer, R., & Chazan, D. (Eds.). (2012). Designing learning environments for developing an
understanding of geometry and space. Routledge.
Reys, R. E., Lindquist, M., Lambdin, D. V., Smith, N. L., Rogers, A., Falle, J., Frid, S., Bennett,
S. (2012). Helping children learn mathematics (1st Australian ed.). Brisbane, Australia:
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Twomey, S. (2013). Introduction to the mathematics of inversion in remote sensing and indirect
measurements (Vol. 3). Elsevier.
Weiland, C., & Yoshikawa, H. (2013). Impacts of a prekindergarten program on children's
mathematics, language, literacy, executive function, and emotional skills. Child
Development, 84(6), 2112-2130.

Wilder, R. L. (2013). Evolution of mathematical concepts: An elementary study. Courier
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Yaglom, I. M. (2012). A simple non-Euclidean geometry and its physical basis: An elementary
account of Galilean geometry and the Galilean principle of relativity. Springer Science
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