Case study assignment help UTAS
ASSESSMENT:
CASE STUDY
Table of Contents
Critical reflection on the learning sequence
Appendix 1: Completed consent form
Appendix 2: Lesson
plan 1: what are odd and even numbers?
Appendix 3:
Lesson plan 2: Applying place value to odd and even numbers to at least 10 000
Introduction
Australian
Curriculum: Mathematics had been introduced for guiding the Australian
mathematics curriculum from K–12. This National mathematics curriculum will
provide the basis for the planning, teaching as well as assessment of the
school mathematics and can be used by the experienced as well as the less
experienced teachers from K-12 (Australiancurriculum.edu.au. 2021). The obvious
imperative for this curriculum is to provide opportunity for improving teaching
and learning situation and adapt and communicate the mathematical concepts in a
better way (Woodward
et al. 2017). Successful mathematics learning is the foundation for any
discipline and numeracy skills is very important for helping the students to
interpret practical situations. There are three kinds of contents strands that
are introduced in this curriculum. The content strand are accumulated concepts
that lead the foundation of this curriculum for maximizing interconnections and
clarity, the concepts are grouped into sequences that are called strands. Based
on pedagogical reasons three content stands are included in the curriculum that
are Number and algebra, Measurement and geometry, and Statistics and probability
(Scarino,
2019). Out of the three content strands, the stand that has been chosen
for this report is Number and algebra.
Learning
sequence
|
Lesson |
Concept |
Lesson aim |
|
Lesson 1 (appendix 2) |
Odd and even number |
To introduce the basic algebra concept of odd and even
number to help child distinguish between even and odd number |
|
Lesson 1 (appendix 3) |
Place value of Odd and even number |
To revisit the concept of even and odd number To identify the place value of complex odd numbers To identify the place value of complex even numbers |
|
Lesson 3 |
Multiplication of double digit Odd and even number |
To revisit the concept of place value To revisit the concept of even and odd number To introduce multiplication of complex odd and even numbers
|
Theory
informing pedagogy
Leading behaviourist
B.F. Skinner had introduce the theory of mental bonds that stated
that in mathematics teaching it is very important to associate concepts and
that drill and practice is very important for reinforcing desirable behaviour
(Budiman, 2017). According to Yangirova & Nosirov (2020) this theoretical
framework’s focus is on "process-product" of is very important for
student achievement. The pedagogical approach towards developing the lesson
plan for later years in early childhood teaching is also influenced by the theory
of instruction by Brownell. According to Kennedy et al. (2017), the
theory maintained that it is very important to make sense of what was being
learnt in the process of providing arithmetic instruction. As per Stein et
al. (2017), it needs to be ensured that the student is able to make sense of what
instructions are being provided and necessary changes need to be made in the
instructions accordingly. Moreover, as noted by Hanfstingl et al. (2019)
Piaget's theory of developmental constructivism further states that
every student has the capability of good mathematical reasoning provided that
attention is given to his or her interest. Moreover, Liu (2020) argues that the
emotional innovations that creates a sense of inferiority in the student
regarding mathematics learning need to be removed. The theories and associated
with the mathematics learning of students in the later years of early childhood
learning such as for student of 3 years.
Learning
sequence rationale
It
becomes difficult for the children to understand mathematical concepts and in
this process they require the aid of the teacher for to understand the
mathematical concepts. In this kind
of content strand, focus is on complex number calculations in early years
followed by focus on algebra in the end of compulsory years. Studies by Moss et al. (2019) have revealed that algebraic
perspective is very important to be included in the late primary years.
Moreover the integration of algebra and number in representing relationships
can enhance the mathematical perspectives in secondary years. In the first lesson, the child, the child would
make connection between the initial concepts of algebra that is odd and even
numbers. This would also help the child to understand class learning and
connect it to higher mathematical concept. ACCARA state that in the sub strand
of algebra, connection should be made between mathematics and creative
thinking. For instance, after the jelly
activities on odd and even number is done, they should be asked by the teacher
to link between odd and even
numbers. Researchers have suggested that progression should be made in the form of
engaging them in concepts that leads one to the other. The progression is
achieved by at first introducing the concept of odd and even number and then
introducing place value to the odd and even numbers to numbers at least10 000.
Case
study
Participant
The child that
has been selected for the case study is Ben Rogers who is studying at the
primary level. Ben is 3 years old. Ben is a shy boy and usually does not
willingly participate in class activities. He is also very weak in mathematics
and takes time in taking part in class activities.
Behaviour
and the observation
Lesson 1
In the process of determining the identification of the odd and even
numbers, It has been
observed from the first lesson plan (refer to appendix 2) that the jelly baby
activity introduced in the class on the screen reader was very successful in
the sense that Ben was responding to the screen reader and was paying attention
to the odd and even numbers being introduced. This means that Ben was drawing
on his earlier knowledge of sorting numbers and so was using her knowledge to
grab the concept.
As
part of the jelly activity, jellies were introduced in the class in odd and
even numbers and Ben was asked to identify which group of sorted jellies were
odd and which were in even count. Initially the jellies introduced was in
single numbers and then double digital jellies were introduced.
The
real difficulty however was a noted in applying confusion between the odd and
even numbers. This might be associated with the fact that the introduction of
odd and even numbers and the connection between them was not followed by drill
and class activities (Anderson, 2021). It is because of this reason that Ben
was found to be hesitant in answering the teacher when she asked him to identify
odd and even number 57 and 64 (refer to appendix 2). He seemed confused and
took a lot of time to identify even numbers out of which the response was
incorrect for 64. It has been observed that out of all the classes on odd and
even numbers double digit odd and even number were taught only in 2 classes that was not
enough practice sessions introduced in the class activity.
Lesson 2
Similarly
it was noted that in lesson plan 2 (refer to appendix 3). Class activity was
introduced on place value to the odd and even numbers. Ben was able to
understand the concept of place value for the single digit odd and even number
when he was called on the board to identify the place value of single digits.
This means he used his previous knowledge of place value and odd and even
number.
Ben
was initially given solved questions of two and three digit odd and even
numbers separately and place value was suggested of the underlined number. Then
unsolved questions of two and three digit odd and even numbers separately and
place value was asked to fill up in the paper
Ben
had difficulties in understanding any new technique that was introduced, partitioning
technique. When was asked to solve and place value of odd and even numbers on
the class activity board. He was able to solve the small numbers place value
but took a lot of time that shows difficulty in giving the place of the bigger
numbers. This shows that Ben was using his earlier knowledge of place value for
solving place value of the odd and even numbers.
Lesson 3
In
the third lesson, single digit multiplication of odd and even number was
introduced and it was noted that Ben was able to identify the odd and even
number and also knew what had to be done. This means that he was using his
previous knowledge of multiplication and odd and even number so he was able to
know what he needs to do and did not ask
the teacher what he needs to do.
The teacher
asked Ben to do multiplication on the board of two odd numbers and wrote the
number on the board. Then the double digit was introduced on the white board
for doing multiplication of big numbers. Ben was again called on the board to
do double digit multiplication by identifying only the odd numbers from the set
of the words provided.
It
was noted that Ben was able to solve the single digit multiplication of the
even and odd number but he took a lot of time and that showed that he still
needed practice. Moreover when the double digit was introduced on the white
board for doing multiplication of big number, Ben looked confused and could not
follow what was being shown on the board. He was asked to come to the board and
do a double digit multiplication but was not able to do anything and was
standing quietly.
Critical
reflection on the learning sequence
Based on the
observation of the outcome of the lesson plans and the response of Ben, it has
been learnt that it is very important to focus on practice sessions and drills
as part of class activities for successful reinforcements (Australiancurriculum.edu.au,
2021). As noted by Yangirova & Nosirov (2020), for developing
mathematical knowledge it is very important to ensure that the student is able
to make sense of the Arithmetic instruction being given in the class. The
confusion and the time taken by Ben to respond shows that somewhere is not able
to make sense of what is being taught in the class. It has been noted by Dole et al.
(2018) that it is very important to give more time to the child to
rediscover or reconstruct the previous knowledge to assess the knowledge that
is being imparted at present. It has also been observed that Ben was paying
attention to visual presentations in the class and was also paying attention to
the response of its fellow students. However, as noted by Budiman (2017) to
enable a child to process the mathematic instruction provided in class
activities it is important that the process of instructions is made more
interesting and revised in the learning time.
Conclusion
It can be
concluded from the study that development of mathematics knowledge is the
result of process that includes reinforcement and practice sessions. Behavioural
theories have reflected upon the factors that need to be focused upon for
developing the efficiency of the instructions being provided in the classroom
for improving the learning of new mathematical concepts for early learners such
as aged 3. Based on the lesson plans and the related observations the following
recommendations can be made for further improvements:
·
It is important to
introduce rewards and punishments as a part of reinforcing new mathematical
concepts in the classroom. This is very important for enhancing the outcome of
reinforcements for the young learners.
·
It would be suggested
that more time to be given for practice sessions and classroom activities apart
from visual presentation of mathematical instructions in the classroom
·
There is also need for
giving individual attention to Ben for addressing his inferiority related to
mathematics that inhibits his interest to be responsive in the classroom
References
Anderson, J. (2021). The Mathematics
Curriculum: a guide for teaching and learning. Teaching Secondary
Mathematics, 222.
Budiman, A. (2017). Behaviorism and
foreign language teaching methodology. ENGLISH FRANCA: Academic Journal
of English Language and Education, 1(2), 101-114.http://journal.iaincurup.ac.id/index.php/english/article/download/171/220
Dole, S., Carmichael, P., Thiele,
C., Simpson, J., & O'Toole, C. (2018). Fluency with Number
Facts--Responding to the Australian Curriculum: Mathematics. Mathematics
Education Research Group of Australasia.https://files.eric.ed.gov/fulltext/ED592431.pdf
Hanfstingl, B., Benke, G., &
Zhang, Y. (2019). Comparing variation theory with Piaget’s theory of cognitive
development: more similarities than differences?. Educational Action
Research, 27(4), 511-526.https://www.researchgate.net/profile/Barbara-Hanfstingl/publication/330321812_Comparing_variation_theory_with_Piaget's_theory_of_cognitive_development_more_similarities_than_differences/links/5c9b130292851cf0ae9a046a/Comparing-variation-theory-with-Piagets-theory-of-cognitive-development-more-similarities-than-differences.pdf
Kennedy, M. J., Rodgers, W. J.,
Romig, J. E., Lloyd, J. W., & Brownell, M. T. (2017). Effects of a
multimedia professional development package on inclusive science teachers’
vocabulary instruction. Journal of Teacher Education, 68(2),
213-230.https://files.eric.ed.gov/fulltext/ED572886.pdf
Liu, X. (2020). A Review of Piaget’s
Theory of Children’s Intellectual Development.https://pdf.hanspub.org/AIRR20190100000_98797358.pdf
Mathematics. Australiancurriculum.edu.au.
(2021). Retrieved 24 September 2021, from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?year=11754&strand=Number+and+Algebra&capability=ignore&capability=Literacy&capability=Numeracy&capability=Information+and+Communication+Technology+%28ICT%29+Capability&capability=Critical+and+Creative+Thinking&capability=Personal+and+Social+Capability&capability=Ethical+Understanding&capability=Intercultural+Understanding&priority=ignore&priority=Aboriginal+and+Torres+Strait+Islander+Histories+and+Cultures&priority=Asia+and+Australia%E2%80%99s+Engagement+with+Asia&priority=Sustainability&elaborations=true&elaborations=false&scotterms=false&isFirstPageLoad=false.
Moss, J., Godinho, S., & Chao,
E. (2019). Enacting the Australian curriculum: Primary and secondary teachers'
approaches to integrating the curriculum. Australian Journal of Teacher
Education, 44(3), 24-41.https://files.eric.ed.gov/fulltext/EJ1211652.pdf
Scarino, A. (2019). The Australian
Curriculum and its conceptual bases: A critical analysis. Curriculum
Perspectives, 39(1), 59-65.https://www.researchgate.net/profile/Angela-Scarino-2/publication/331515422_The_Australian_Curriculum_and_its_conceptual_bases_a_critical_analysis/links/5c86ed1d92851c831973a7e7/The-Australian-Curriculum-and-its-conceptual-bases-a-critical-analysis.pdf
Stein, M. K., Correnti, R., Moore,
D., Russell, J. L., & Kelly, K. (2017). Using theory and measurement to
sharpen conceptualizations of mathematics teaching in the common core
era. AERA Open, 3(1), 2332858416680566.https://journals.sagepub.com/doi/pdf/10.1177/2332858416680566
Woodward, A., Beswick, K., &
Oates, G. (2017). The four proficiency strands plus one?: Productive
disposition and the Australian Curriculum: Mathematics. In 2017
Mathematical Association of Victoria Annual Conference (MAV17) (pp.
18-24).https://www.mav.vic.edu.au/files/2017/MAV17-Conference/Conference_Proceedings_011217.pdf
Yangirova, Z. Z., & Nosirov, D.
S. (2020, July). General Psychological Basis for the Formation of Education at a
Technical University. In International Scientific Conference on
Philosophy of Education, Law and Science in the Era of Globalization (PELSEG
2020) (pp. 401-407). Atlantis Press.https://www.atlantis-press.com/article/125941911.pdf
Appendices
Appendix
1: Completed consent form
Respected
sir/madam,
This is to
bring to your notice that I give my consent to the five lesson plans that would
be introduced in the class to record the observation and responses of Ben over
a period of 2-3 weeks. I support the purpose of the lesson plans to introduce
higher mathematical concepts related to number and algebra and I give consent
to study, observe and record the response and performance of Ben during the
course of the lessons plan introduced in the classroom for academic purpose.
Thanks and
regards
Nina Roger
(Ben’s mother)
Appendix
2: Lesson plan 1: what are odd and
even numbers?
|
Aim |
To introduce the basic concept of numbers and algebra: odd
and even numbers |
|
|
Activities (week 1-2) |
White
board activity showing jelly babies on
odd and even numbers White
board activity showing jelly babies on
even and even numbers Introduce
concept and link between odd and even numbers Worksheet
activities |
|
|
|
||
|
White
board Jellies
activity video Black
board Activity
sheet |
||
|
Resources
|
|
|
|
Description |
In
the first lesson plan in consistent with teaching the Students number and
algebra, the children were introduced with basic concepts in complex numbers
calculation that odd and even numbers. Jelly baby activities for reinforcing
factors were also shown in the white board in the introductory class of odd
and even numbers. The students in the class were asked to repeat odd and even
numbers and simultaneously the teacher show the odd and even numbers on the
whiteboard. Along with the odd and even numbers the teacher also individually
asked 10 students in random in the class about doing naming odd and even
numbers in work sheet. For the first two weeks the
learning activities continued for 30 minutes. A total of 4 classes in a week
were taken followed by 2 classes in which double digit odd and even number
was introduced |
|
|
Details
of the child response: |
Initially
Ben was very happy to see the video of the jelly baby activities in the
class. Later it was noted that he was losing interest in the class when a
class activity was introduced. He was found to be talking to the children
around him and also looking at them when they were answering and being
attentive to their responses. This might also be because of the fact that Ben
is a shy child and was hesitant to respond individually in the class. He was
not very hesitant to respond in the second week when we introduced the double
digit odd and even number class activities of odd and even numbers. He was
also paying attention to what his friends were answering in the class. |
|
|
Language
used |
Simple
language and simple words were used for the class lessons so that the
children can understand the concept clearly. |
|
|
Conclusion
|
More practice needed for identifying and solving double digit odd
and even number identification |
|
Appendix
3: Lesson plan 2: Applying place value to odd and even numbers to at least 10 000
|
Aim |
To introduce the basic concept of numbers and algebra:
place value of odd and even numbers |
|
|
Activities (week 2-3) |
Asking
students to apply place value to odd
and even numbers to at least 10 000 Presenting
sample, solved and unsolved questions |
|
|
|
||
|
Screen reader White board Activity sheet |
||
|
Resources
|
|
|
|
Description |
In
the second lesson plan under the content strand of number and algebra, the
children were introduced with another basic concept in complex numbers
calculation that is partitioning and understanding place value. In the
previous classes the students were already introduced with single digit place
value of odd and even numbers so this time the complexity of place value and
regrouping was increased. In the first two classes of week 1 on Tuesday and
Wednesday new techniques for regrouping numbers was shown on the screen
reader. The partitioning technique that can be used for higher level
mathematics was also shown by the teacher on the white board on Thursday. In
the next two classes on Friday and Monday in the following week, sample,
solved questions where shown on the whiteboard to reinforce the lessons
taught on the previous two days. On Tuesday the teacher gave more
instructions regarding using the partitioning technique easily. She also
solved sums using the partitioning technique on the class board. In the next
2 days, solved and unsolved questions we practiced in class activities. On
Thursday in 2nd week five students including Ben were asked to solve
regrouping and place value on the class activity board. |
|
|
Details
of the child response: |
It
was observed that Ben was attending to the screen when the instructions they
provided. He was also seen to be talking to his friends when they solved
questions shown on the board in week 1. In the second week it was evident
that Ben was not able to understand the partitioning technique very easily.
However he tried to solve the sum when he was called to the board although he
took a lot of time for resolving the sum. |
|
|
Language
used |
The
teacher used simple language and explained the instructions using simple
words |
|
|
Conclusion
|
More practice needed for double digit odd and even number and more
activity and classes needed on place value of complex numbers |
|
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