Primary Maths A1

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Swinburne University of Technology *

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Mathematics

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Feb 20, 2024

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EDU30009: Mathematics in the Primary Classroom ASSIGNMENT 1: REPORT Chelsea Smith 103694503

1 1. Executive Summary The purpose of assessing mathematics in the primary school context is to provide feedback on students’ understanding of the content being taught (New South Wales Education Standards Authority, n.d.). This report discusses three assessment types that take place in mathematics in the primary school context. The three types of assessment discussed are formative assessment, summative assessment, and self-assessment. A description as well as the benefits and limitations of the assessments are discussed with examples. Contents List 1 – Executive Summary & Contents List 2 – Introduction 3 – Findings 3.1 – Formative Assessment 3.2. – Summative Assessment 3.3. – Self Assessment 4 – Conclusion and Recommendations 2. Introduction Mathematics is a Learning Area within the Australian Curriculum and is followed throughout the entirety of the Primary School years (ACARA, 2023). The mathematics learning area is important for students to build the numeracy skills to use mathematics confidently in the real world (Department of Education & Training, 2019). Assessment is used constantly within mathematics to gain well-rounded information on student learning and understanding. This information is important for teachers to continually monitor students, to then inform teaching and learning practices. Monitoring students understanding of mathematics topics is vital to ensure students can successfully use maths in the real world and later in life. There are many ways of assessing including Formative Assessment, where the assessment is designed for learning; Summative Assessment, where assessing is done

2 of the learning and self-assessment, where students assess their own learning (New South Wales Education Standards Authority, (n.d.). The use of different assessment strategies is crucial for students’ learning styles and to determine students' true understanding of the topics (Brooker et al., 2020). 3. Findings 3.1 Formative Assessment Portfolios as a means of formative assessment are often used in the primary mathematics classroom to gather information on a student's understanding during a unit of work. "A purposeful collection of student work that tells the story of the student's efforts, progress, or achievement in given areas" is how Arter and Spandel (1992) defined portfolios (Wood, 2006). This type of assessment allows teachers to understand students' cognitive ability and strengths and weaknesses in a specific area of learning. Gaining portfolio data allows teachers to generate a successful program that reflects their student's current understanding to enhance learning ability (Leighton & Gierl, 2007). For example, in a year four class focussing on Number and Algebra, the portfolio may reveal that a student may be very confident in odd and even numbers: Content Descriptor (CD) ‘ACMNA071’, but also may be struggling in identifying other number sequences and identifying those patterns in CD ‘ACMNA074’ (ACARA, 2023). This is important for the teacher to be aware of to ensure the student receives additional support in CD, ‘ACMNA074’, or perhaps for the teacher to identify a pattern across multiple portfolios, revealing a need for revisiting teaching strategies in that learning area. A portfolio is a much less formalised type of formative assessment than more formal testing, such as recurring performance tasks completed over a unit of work to determine ongoing learning abilities. Portfolios provide a snapshot during progressive work to determine how teaching may need to be adapted and allow for a less formal assessment. The mathematics portfolio focuses on a student's learning process and includes multiple pieces of evidence of a student's work. A portfolio as a formative assessment can include anything from homework, class exercise books to quizzes taken over the unit of work (Sole,

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3 2012). Portfolios also use observations as a tool to assess during and prior to a unit of work (George, 2010). The portfolio is a place for students, peers and their teachers to revisit and evaluate to determine which areas a student may need extra assistance in and to guide students' learning. The significant benefit of the portfolio is that it provides a well-rounded understanding of the learning that has occurred (George, 2010). 3.2 Summative Assessment A summative assessment is often completed following a unit of work or year to evaluate what and how much a student has learnt. A teacher-devised, written test as a diagnostic assessment is a more formal type of assessment. A written test as a summative assessment strategy is purposeful for teachers to evaluate teaching and learning by determining a criterion devised grade (Twinkl). Written tests are simple for teachers to prepare and give a quick insight into students' level of understanding to separate those higher achieving students from those that need additional support (Morsanyi, 2022). For example, an end of year summative test will determine where students may be placed for classing in the following year. Summative assessments are beneficial in giving students extra motivation to study and therefore gaining a stronger understanding of those focus areas (Emile, 2023). Primary mathematics teachers must follow standardised criteria to ensure consistent results and validity when comparing students in the same cohort, cohorts across years or teaching success or issues. Unfortunately, even though such formal summative testing and written tests allow insight into students' cognitive ability in a specific mathematics area, this testing also has implications. Although summative testing is known to improve students' motivation to perform well, it also has the tendency to lead to 'test anxiety'. Test anxiety was found in a meta-analysis to have lowered students' ability to process information and self-regulate, leading to decreased performance levels (Robson et al., 2023). A test that only assesses right or wrong can be highly discouraging for students and does not provide an evident appreciation of students' understanding of a topic (George, 2010). Written tests often need to account for originality and the thinking process rather than the ability to get an answer

4 right or wrong. Students must be aware that the 'working out' and thinking that goes towards an answer or outcome is also considered essential rather than just the final answer. 3.3. Self-Assessment Journals can be used for many types of assessment strategies, reflective journals are highly beneficial for students to use as a way of self assessing. Students are encouraged to reflect on their learning following a lesson where they are given the opportunity to think about and record what they found (George, 2010). Students may be given prompts as to what they found they enjoyed or found difficult and how they may be feeling about the learning that just took place. By students reflecting on their own learning experience in a lesson, they are encouraged to measure their own learning and evaluate where they may need additional support (George, 2010). Reflective journals give students the chance to take responsibility for their own learning and understand what questions they may need to ask to enhance their learning. Students and teachers can then work together to create a common goal for the students' learning (New South Wales Education Standards Authority, n.d.). Through reflective journals, students are able to understand that there are multiple ways of thinking and coming to an answer which in hand leads to a stronger understanding to be connected to real-life mathematical thinking (Booker et al., 2020). The limitation of self- assessment is that it requires students to put in the effort to use reflective thinking. In order to be successful, reflective journal note-taking following a lesson takes time and honesty in order to be a successful self-assessment (Hotard, 2010). Self-assessment allows students to feel a sense of ownership and therefore empowerment over their own learning. For example, through reflective journaling, a student may identify a lack of confidence in understanding chance in terms of identifying possible outcomes, to which they can then reach out for assistance (ACMSP116). Or the contrary, a student may identify a strength of theirs and act as a ‘more knowledgeable other’ to help a peer and therefore cement their own learning (McLeod, 2014).

5 4. Conclusion Overall, assessment is vital for teaching and allowing the learning cycle to continue (NSW Education Standards Authority, n.d.). Assessing through a range of strategies can reveal students' understandings and different ways of thinking in order to plan to teach accordingly (Brooker et al., 2020). Assessing can be done through multiple ways such as formal exam testing to informal observation taking. The formative assessment discussed in this report is portfolio keeping by gathering information on students’ understanding during a unit of work. A teacher-devised written test is a summative assessment used as a diagnostic tool to determine what and how much a student has learnt. Self-assessment is discussed in relation to students keeping reflective journals to prompt students to take ownership of their learning (George, 2010). Assessing is vital to ensure students are continually building their knowledge to become confident and numerate mathematics users.

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6 References ACARA. (2023). Australian Curriculum: Mathematics . https://v9.australiancurriculum.edu.au/f-10-curriculum/learning-areas/mathematics/ foundation-year_year-1_year-2_year-3_year-4_year-5_year-6?view=quick&detailed- content-descriptions=0&hide-ccp=0&hide-gc=0&side-by-side=1&strands-start- index=0&subjects-start-index=0 Booker et al., (2020). https://ebookcentral.proquest.com/lib/swin/reader.action? docID=6236349&ppg=100 Department of Education and Training [DET]. (2019). Belonging, being & becoming - The early years learning framework for Australia. https://docs.education.gov.au/documents/belonging-being-becoming-early-years-learning- framework-australia Emile, (2023). https://emile-education.com/formative-and-summative-assessments-nqt/ #:~:text=Also%20known%20as%20the%20end,%2C%20conversation%2C%20or%20task %20tests . George, B. (2010). Teaching primary mathematics. Assessment in mathematics. Pearson Australia. Retrieved from https://commons.swinburne.edu.au/file/9af7e60e-c87d-4cce-905b- 956dee80f1a0/1/99213610000.pdf Hotard, D.J. (2010). The effects of self-asessment on student learning of mathematics. Louisiana State University. LSU Digital Commons.

7 https://digitalcommons.lsu.edu/cgi/viewcontent.cgi? article=3945&context=gradschool_theses Leighton, J.P, & Gierl, M.J. (2007). Cognitive Diagnostic Assessment for Education. Theory and Applications. Cambridge University Press McLeod, S. (2014). Lev Vygotsky. https://sleaudience.akunerio.com/public/pdf/1lVgHWtwIY7Ga0JTgwcjK1eDQWkzLTus d.pdf Morsanyi, K. (2022). More maths testing could be good for primary school children - if done in the right way. The Conversation. https://theconversation.com/more-maths-testing- could-be-good-for-primary-schoolchildren-if-done-in-the-right-way-181765 New South Wales Education Standards Authority, (n.d.). https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/understanding-the-curriculum/ assessment/approaches Robson, D. A. et al., (2023). Test anxiety in primary school children: a 20-year systematic review and meta-analysis. Journal of School Psychology, Volume 98. https://www.sciencedirect.com/science/article/abs/pii/S0022440523000158 Sole, M. (2012). The Mathematics Portfolio: An alternative tool to evaluate students’ progress. CUNY Academic works. Guttman Community College. https://academicworks.cuny.edu/cgi/viewcontent.cgi? article=1075&context=nc_pubs#:~:text=Mathematics%20portfolios%20consist%20of %20a,mathematical%20proof%2C%20a%20booK%20review%2C

8 Twinkl. https://www.twinkl.com.au/teaching-wiki/summative-assessmentn Wood, T. R. (2006). Portfolio Assessment in Primary School Mathematics: A Study of Pedagogical Implications. Science and Mathematics Education Centre. https://core.ac.uk/download/pdf/195633142.pdf

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