EDMA342 - Assessment Three

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Australian Catholic University *

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342

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Mathematics

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Apr 3, 2024

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EDMA342 – Assessment Three Jessica Chahine S00224457 PART ONE: RATIONAL NUMBER OVERVIEW Rational Number Interview Record Sheet: Image 1 Image 2

Student Analysis: Jenny, Year 5 – Stage 3 Jenny’s content knowledge and mathematical understanding for Fractions and Decimals is at a Satisfactory level for Stage 3 (NESA, 2012). Jenny was able to answer the questions with confidence and in a timely manner. Her overall engagement within the interview remained consistent and she was able to demonstrate a strong sense of wellbeing and resilience (Churchill, et al., 2018). Jenny was successful in using different strategies to support her thinking and answers which include investigating strategies, visualising, pausing and pondering, using her fingers to point and express her answers therefore, going along with the Working Mathematically Proficiencies of problem solving, reasoning as well as communicating (Bragg, et al., 2016). For Q1, Jenny confidently used mental strategies to express her understanding for the fraction pie diagram . She was able to give reasoning and provide a good explanation. Jenny was able to excel in Simple operations and was quick to answer questions A to C. However, she showed a bit of hesitation answering question D (1/3 of ½) and estimated her answer. She was also vocal about her thinking strategy explained that she was ‘picturing a circle and halfling it’ when asked to justify her answer for question D, which NESA (2012) explains that this is a technique used associated with problem solving. Although Jenny was able to demonstrate a satisfactory understanding for Fractions through the Rational Number Interview (RMI), it is evident that Jenny needs to further her engagement with understanding mathematical language. This is response to her confusion in Q3. Dots array, where Jenny estimated her answer of “2/3” and could not give reasoning to her answer. It was clear through her body language that the wording had confused her. During Q8, Jenny was seen fiddling around with the numbers before estimating her answer. When asked to give reasoning she justified her answer by saying “1/6 isn’t that much and 7/5 is more than that”. This misconception reflects her lack of appropriate mathematical terminology, thus affecting her ability to give clear reasoning for her answers. The Working Mathematically Proficiencies of reasoning plays an important role when furthering a child’s understanding and promotes the idea of using correct mathematical language to enhance their understanding as well as their reasoning (Vale, Bragg, Widjaja, Herbet & Loong, 2017). Throughout the RNI, it was observed that Jenny was using a visualisation thinking strategy was seen using her fingers to support her understanding of the questions. This means that Jenny could benefit from incorporating concrete materials in her learning to activate her thinking in a sensory manner (Swan & Marshall, 2010). She was also able to apply self-corrections several times, therefore prompting questions would be helpful to enhance Jenny’s learning to activate her thinking process (Clarke, Mitchell & Roche, 2005).

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PART TWO: ASSESSMENT RUBRIC WITH OPEN TASK Open Task Work Sample: Image 3

Rubric: Links to the Syllabus: A OUTSTANDING B EXCEPTIONAL C SATISFACTORY D BASIC E WORKING TOWARDS Content Knowledge ( Understanding) Demonstrates an understanding between equivalent fractions and decimals through modelling, comparing and converting fractions to decimals. Student demonstrates outstanding knowledge regarding modelling, representing and comparing for ALL equivalent fractions. Student demonstrates outstanding level of skill in which they apply correct metal strategies to convert fractions into decimals and generate equivalent fractions. Student demonstrates outstanding ability to correctly place the fractions appropriately on the number line. Student demonstrates exceptional knowledge on how to model, compare and represent equivalent fractions limited to the following denominators 2,3,4,5,6,8,10,12 and 100. Student demonstrates a high level of skill in which they apply the correct mental strategies to convert fractions into decimals and generate equivalent fractions. Student demonstrates exceptional knowledge on fractions and can appropriately place them on a number line. Student demonstrates a satisfactory understanding how to model, compare and represent equivalent fractions limited to the following denominators 2, 4, 6, 8, 10, 12 and 100. Student demonstrates adequate level of skill in which they apply mental strategies to convert fractions into decimals and generate equivalent fractions. Student demonstrates the correct way to appropriately place them on a number line. Student demonstrates a basic understanding how to model, compare and represent equivalent fractions limited to the following denominators 2, 4, 8, 10, and 100. Student demonstrates a basic level of skill when applying mental strategies however may also demonstrate misconceptions when calculating fractions. Student is working towards understanding basic ways to model, compare and represent equivalent fractions limited to the following denominators 2, 10 and 100. Student is working towards using mathematical operations to calculate factions Student demonstrated misconceptions and errors. Application (Problem Solving and Student can correctly explain, justify and Student can explain, justify and give Student can explain how they achieved Student can describe how they achieved Student is working towards describing

Reasoning) Demonstrates an understanding on how to apply content knowledge about equivalent fractions and successfully place the correct answer on the number line. give reasoning for the strategies they have used to achieve their answer. Student uses a range of complex strategies to achieve their answer. Student can successfully apply to clear and correct answers to the number line with no errors. reasoning for the selected strategies they have used to achieve their answer. Student can use 1 or more complex strategies to achieve their answer. Student can apply the correct answers to the number line with no errors. their answer in an appropriate manner. Student can use 1 strategy to achieve their answer. Student can apply the correct answers to the number line. their answer. Student can use 1 strategy to achieve their answer however may also demonstrate misconceptions. Student can apply the correct answers to the number line however many also demonstrate misconceptions. how they achieved their answer. Student is working towards using strategies to achieve their answer. Student is working towards understanding fractions and applying them correctly on a number line Student will demonstrate misconceptions. Expression/ Representation (Fluency) Demonstrates understanding on how to use diagrams, number lines, fraction walls or any other creative methods to represent their answers. Student demonstrates outstanding understanding of content knowledge through critical and innovative ways. Student expresses complex ideas in creative ways, E.g. - Number lines - Diagrams - Fraction walls - ICT programs Student has in-depth understanding of content knowledge through critical and innovative ways. Student expresses their ideas in creative ways, E.g. - Number lines - Diagrams - Fraction walls - ICT programs - Pie charts Student understands content knowledge through critical and innovative ways. Student expresses their ideas in creative ways, E.g. - Number lines - Diagrams - Fraction walls Student understands some content knowledge through critical and innovative ways. Student expresses their ideas in creative ways, E.g. - Number lines - Diagrams Student is working towards understanding content knowledge through critical and innovative ways. Student uses numeral representation only to express their ideas.

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- Pie charts Mathematical Language (Communicating) Demonstrates ability to use a wide range of appropriate mathematical language regarding fractions both verbally and vocally. Student demonstrates exceptional amount of mathematical terminology. Student displays a wide range of sophisticated language when expressing ideas and answers. Student uses the following language but is not limited to - Whole - Equal parts - Half - Quarter fraction - Whole number - Is equal to - Equivalent - Numerator - Denominator - Proper fraction - Improper fraction - Simplest form - Simplify. Student demonstrates outstanding ability to carefully select the appropriate words Student demonstrates sophisticated amount of mathematical terminology. Student displays a range of mathematical language appropriate to fractions and uses words such as: - Whole - Equal parts - Half - Quarter fraction - Whole number - Is equal to - Equivalent - Numerator - Denominator Student demonstrates a satisfactory amount of mathematical terminology. Student uses language such as: - Whole - Equal parts - Half - Quarter fraction - Is equal to - Equivalent - Numerator - Denominator. Student demonstrates limited amount of mathematical terminology. Student uses language such as: - Whole -Equal parts - Fraction - Is equal to. Student is working towards demonstrating mathematical terminology. Student may use language such as: - Whole - Equal parts - Fraction

when explaining their answer. Student can successfully use and define the words related to fractions.

PART THREE: EVALUATION OF ASSESSMENT STRATEGIES The Rational Number Assessment The Rational Number Assessment is an excellent formative assessment tool that links directly with the Mathematics K-10 syllabus. The RNI successfully highlights and assess students understanding within the Number and Algebra Strand , more specifically Fractions and Decimals (NESA, 2012). The RNI gives open opportunity to students to express their answers in a non-traditional way in comparison to written assessments (Clarke, Clarke & Roche, 2011) therefore, evoking the students to think effectively and strategically. Additionally, during the RNI students are being assessed on their content knowledge and on their current cognitive processing. This goes in line with Vygotsky (1978), where educators can reflect on the data collected from the RNI and work within the student’s zone of Proximal Development. Through the one-on-one aspect of the interview educators are given the opportunity to gain further insight into how students may think with mathematics. This means they will be able to construct and program effectively foe their students in their future learning (Clarke, Clarke & Roche, 2011). Using this assessment tool, educators can use the data collected to focus and come up with class learning goals, thus prompting a positive, effective and safe learning environment for their students in turn furthering an affective learning trajectory being able to target their needs and monitoring their progression (Churchill, et al., 2018). Research demonstrates that educators who use the RNI to conduct formative assessment, can enhance on their PCK (pedagogical content knowledge). In doing this, they are curing their ideas of rational number and are introduced to several different unfamiliar strategies and can observe new ways of thinking, therefore allowing them to easily identify the misconceptions (Clarke, Clarke & Roche, 2011). The RNI effectively promotes the use of Working Mathematically Proficiencies . This is because the RNI gives opportunity to students to demonstrate problem solving, reasoning, demonstrating understanding, as well as being able to communicate their ideas verbally throughout the interview (NESA, 2012). Moreover, the RNI effectively links with the development of several mathematical strategies in which students can engage with (Charles & Carmel, 2005, p. 12.).

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Assessment Rubric Utilising Assessment Rubrics within the classroom, educators are allowing room for students to experience authentic learning and the complex skills can fairly be assessed according to the specific learning outcomes from the syllabus (Smit, Bachmann, Blum, Birri, & Hess, 2017). This means that teachers will be implementing “developmental sequence in which students are challenged to acquire new knowledge, skills and understanding” (NESA, 2012, p. 468). According to Vygotsky’s theory assessment rubrics can be utilised to further identify the how students learn. This is because it allows room for educators to solidify what the students already know and can do on their own (the level of actual development) and what students can do with guidance from either their educators or peers (the zone of proximal development), therefore allowing guidance for both levels of achievement (Quinlan, 2012, p. 14). Gardeners’ theory of multiple intelligence (1983) extensively supports the idea of rubrics as it is highly effective when considering all the different types of learners. This means the rubric is successful in providing a balanced success-criteria that can cater to all the diverse learners within a classroom (Quinlan, 2012). By implementing rubrics students are given the opportunity to have a clarification on where they are sitting on the academic scale. They are also told what areas they will need to focus on and improve in. Moreover, rubrics are an effective way for teachers to provide their students with powerful feedback supporting their metacognitive development (Quinlan, 2012). A study by Bangert-Drowns (1991), showed that when students receive effective feedback on their learning, their anxiety rates drop and they can regulate their self-learning (Smit, Bachmann, Blum, Birri, & Hess, 2017, p. 606). Teachers can use the rubrics for data collection, allowing them to effectively program the next phase of learning according to their students needs. This can also be individualised or for a whole class (Briggs, Woodfield, Swatton, & Martin, 2008). In turn, the teacher will be able to identify any misconceptions students may have, any objectives they did not meet or any areas of difficulty. Moreover, the rubric can also be used to highlight academic achievements, students who have exceeded the learning expectations, thus providing data to further develop their current knowledge and ideas through more challenging tasks (Briggs, Woodfield, Swatton, & Martin, 2008).

REFERENCE LIST Australian Curriculum Assessment and Reporting Authority. (2016). Mathematics Proficiencies. Retrieved from: https://www.australiancurriculum.edu.au/resources/mathematics- proficiencies/ Bragg, L., Herbert, A., Loong, S., Vale, E., & Widjaja, Y. (2016). Primary teachers notice the impact of language on children’s mathematical reasoning. Mathematics Education Research Journal, 28 (4), 523- 544, doi: 10.1007/s13394-016-0178-y Briggs, M., Woodfield, A., Swatton, P., & Martin, C. (Eds.). (2008). Assessment for Learning and Teaching in Primary Schools (2 nd ed.). England: SAGE Publications. Charles, R. I., & Carmel, C. A. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education Leadership, 7 (3), 9-24. Churchill, R., et al (2018). Teaching: Making a Difference . (4 th ed.) Milton, Queensland: Wiley. Clarke, D., Mitchell, A., & Roche, A. (2005). Student one-to-one assessment interviews in 226 doi: 10.1016/S0883-0355(02)00061-7 Ginsburg, H. P. (2009). The challenge of formative assessment in mathematics education: Children's minds, teachers' minds. Human Development, 52 (2), 109-128, doi:http://dx.doi.org/10.1159/000202729 NSW Education Standards Authority. (2012). NSW Syllabus for the Australian Curriculum [Ebook]. Sydney. Retrieved from https://www.educationstandards.nsw.edu.au Quinlan, A. M. (2012). A complete guide to rubrics assessment made easy for teachers of K-college (2 nd ed.). Lanham, Md.: Rowman & Littlefield Education. Swan, P., & Marshall, L. (2010). Revisiting mathematics manipulative materials: Paul Swan and Linda Marshall revisit the use of manipulatives. They look at the different types and the ways in which they are used by teachers. Australian Primary Mathematics Classroom , 15 (2), 13-19. Vale, C., Bragg, L. A., Widjaja, W., Herbert, S., & Loong, E. Y.-K. (2017). Children's mathematical Mathematics Classroom , 22 (1), 3-8.

EDMA342 - Assessment Three

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