Master of Education (Secondary) Diagnostic Test on Numbers Report

This report examines a diagnostic test designed to assess students' prerequisite knowledge of numbers within the context of a Master of Education (Secondary) program. The introduction highlights the role of diagnostic tests in education, emphasizing their use in identifying student learning gaps and informing instructional strategies. The report details the purpose of such tests, focusing on how they help students apply mathematical concepts in daily life and make informed decisions. It discusses suggested teaching strategies, including the importance of aligning with the Australian Curriculum, differentiating instruction, and utilizing various teaching aids like diagrams and real-world examples to enhance understanding of topics such as prime numbers, composite numbers, and lowest common multiples. Furthermore, the report emphasizes the importance of assessment, including regular check-ups, progress tracking, and the use of portfolios to monitor student performance. It concludes by referencing relevant literature on mathematics education and assessment.

Running head: MATHEMATICS 1
Master of Education (Secondary)
Name
Institution

MATHEMATICS 2
Diagnostic Test to assess Student Prerequisite Knowledge on Numbers
Introduction
In education, a diagnostic test provides an avenue to assist students in learning the
problems and their solution so that teachers can be able to provide them with solutions. As a
result, these solutions are used to remedy the problems as experienced by the students (Brahier &
Speer, 2011). Students’ performance in these tests will provide teachers with opportunity to
understand the best cognitive skills that the students still need to learn in class. It occurs before
the lessons since teachers have to understand establish prior student knowledge about the topic
(Ellis, 2007).
Purpose of the Diagnostic Test
Diagnostic tests in numbers help to the learners to use mathematical ideas effectively in
participating in daily life making decisions thus removes the misconception about the
mathematics difficulties. This includes the use of spatial, numerical, statistical, and algebraic
concepts in the pre-test analysis. Numbers diagnostic test involves students’ recognizing and
understanding the role of mathematics in daily life. Use of numerical involves interpretation and
evaluation of mathematical strategies that helps Australian students to communicate and reason
mathematically in real world situations (Joseph, 2011).
Numerical assessments play a major role in exemplifying new types of numeral learning
that students must achieve (Goos et al., 2007). It helps to indicate to students what they should
learn and master through giving concrete meaning to the valued learning materials. For instance,
if the students need to learn how to perform the BIDMAS theory, they will need to be assessed
on the numerical mixed numbers and its applications.

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Suggested teaching strategies
The availability of common teaching programs which require teachers to follow the set
programs agreed by the HOLA helps to provide an effective program based content which is
specified in the Australian Curriculum. As a result, educators will also have the opportunity to
differentiate different needs per students (Clements et al., 2013). Teaching numbers is linked to
the progression of the strategies that form the numeracy continuum i.e. counting on and back,
split, and jump strategies which are very essential to students in gaining understanding of the
place values that result in to numerates.
Students need to have a flexible view of the numbers and develop a written strategy that
helps in solving mathematical problems (Leonard et al., 2010). In Australian Curriculum, grade
7-10 mathematical syllabuses provides a strong emphasis on the mathematical progressive that
provides students with an opportunity to develop skills that allows for reasoning and reflecting,
communication characters, and problem solving techniques.
Use of real world identity such as numerical description has been found to be significant
in providing the learners with a clear diagnostic test once they come to understand the topics on
study. For instance, given the following rectangular shape;

MATHEMATICS 4
Figure 1.0: Rectangular shape
Learners will always find it easy to actualize the shape once they understand the
definition and type. Numeral analysis in terms of numbers can easily be learned from the above
rectangular shape in figure 1.0. From the description of the shape, it can easily be noted that the
rectangle has length and width with both distances given as shown above. However, if a student
is asked to find the distance around the rectangular shape above, it will be easy to sum it up since
the distances for both length and width is given (Magiera et al., 2013). This is different if given
the below diagnostic test on umbers without diagrams;
Diagnostic Test on Numbers
1. Which of the following numbers is prime?
A. 28 B. 58 C. 18 D. 13
2. Which of the following numbers is composite?
A. 109 B. 145 C. 157 D. 13
3. What is the lowest common multiple of 3, 4 and 6?
A. 60 B. 12 C. 30 D. 15
From the above example of the diagnostic test, it is worth noting that student will not be
able to understand the meaning of the prime numbers, composite numbers, and the lowest
common multiple numbers if not introduced to their definition and application in the early stages
of learning. As a result, it will always be prudent to develop teaching aid to assist learners to
understand the introductory part of the numbers as a topic in grade 7, 8, 9, and 10.
Teaching aid to learners on numbers

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Provision of a concrete, symbolic, and pictorial understanding to learners when working
on numbers including divisible and multiplication numbers will enable students to conceptualize
how and why various methods in mathematics works. Here, the application of pre-test
understanding on fraction and operational numbers will be much more important. However, it is
also essential to give students time to develop their conceptual understanding of the numbers
which allows them to apply the learning ad provided by the teachers in class.
It is worth noting that learner will be required to develop mental mathematical
understanding on the numeral understanding including the ability to master non-calculator and
calculator operations since the topic will be taught using different learning aids including
mathematical calculator, pen, mathematics square books, and text books.
Effectiveness and Assessment
There should be regular check-up on the completion of the tasks including homework
which provides an avenue for students understanding of the topic in discussion. Monitoring
through common test-comparison between students can be organized once the lesson comes to
an end in order to understand the best way to which students grasp on the importance of the
number as a topic in mathematics (Victorian Curriculum & Assessment Authority, 2002).
Teachers can also organize for the progress map-tracking that provides the opportunity to track
the student’s performance throughout the year in each learning stage. In addition, there should be
provision of the students’ portfolio folder that help to collate and track their weaknesses in each
topic in the mathematics.
To assess the numerical topic, as per discussed above, there should be a pre-assessment
criteria which is fair and reliable in terms of marking criteria across all topics in mathematics

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(Wilcox & Monroe, 2011). Learners can also be obliged to undertake tests, exams, oral
presentations, or practical investigations in order to assess their understanding on the topic.
Midterm, and end term examinations will also be incorporated to establish student’s learning
abilities.

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References
Brahier, D.J., & Speer, W.R. (Eds.) (2011). Motivation and disposition: Pathways to learning
mathematics. Reston, VA: NCTM
Clements, M.A., Bishop, A. J., Keitel, C., Kilpatrick, J., Leung, F.K.S. (Eds.) (2013). Third
international handbook of mathematics education. New York, NY: Springer.
Ellis, A. (2007). The influence of reasoning with emergent quantities on students’
generalizations. Cognition and instruction, 25(4), 439-478
Goos, M., Stillman, G., &Vale, C. (2007). Teaching secondary school mathematics: Research
and practice for the 21st century. Sydney: Allen & Unwin. [text]
Joseph, G. G. (2011). The crest of the peacock: Non-European roots of mathematics (3rd ed.).
Princeton: Princeton University Press. (Earlier editions are also available)
Leonard, J., Brooks, W., Barnes-Johnson, J., Berry III, R. Q. (2010). The nuances and
complexities of teaching mathematics for cultural relevance and social justice. Journal of
Teacher Education, 61(3), 261-270.
Magiera, M. T., van den Kieboom, L.A., & Moyer, J. C. (2013). An explanatory study of pre-
service middle school teachers’ knowledge of algebraic thinking. Education Studies in
Mathematics, 84(1), 93-113.
Victorian Curriculum & Assessment Authority. (2002). Curriculum and standard framework II
mathematics: Reasoning & strategies levels 1-6. Melbourne: VCAA.
Wilcox, B., & Monroe, E. E. (2011). Integrating writing and mathematics. The Reading Teacher,
64(7), 521-529.