Bazzi Jesline 16831791 EDP343 Ass2[1558] Maths PDF

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Summary

Inquiry task and lesson plan on grade 5 Geometry. Links made to FSiM standards and teh topic of Data handling and probability....

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Jesline Bazzi Student # 16831791

EDP343 2019 Assessment 2 - Portfolio

Inquiry task and lesson plan on geometry

A geometry inquiry task that can be used over an extended period of time is “Cities Taking Shape” where students build a model city of shapes (adapted from Bezear, n.d.). The purpose of this task is to develop the students’ understanding of two-dimensional shapes and three-dimensional objects by investigating; their properties; their contexts, such as places where they occur; and their relationship to three-dimensional shapes through exploring different resources, such as using the Google SketchUp (www.sketchup.com) software and Scootle’s Shape Maker Series (Education Services Australia, 2013). Next, three-dimensional objects are visualised and sketched from different viewpoints, Google Earth is used to assist in observing buildings from above. Then, nets of different three-dimensional objects are predicted, explored and created. Finally, students use three-dimensional nets to design a city of shapes. Transforming shapes Date/Time: 22nd July, 12.00pm-1.00pm Learning area(s): Geometry – Two-dimensional shapes Year: 5 Learning

 Describe the properties of different two-dimensional shapes

objectives

 Identify two-dimensional shapes in real-life contexts

Curriculum links

 Investigate two-dimensional rotation and reflection  ACMMG088 – Compare and describe two-dimensional shapes.  ACMMG114 – Describe translations, reflections and rotations of two-dimensional shapes.

First Steps in Mathematics (FSiM) links

(ACARA, 2019a)  Represent Location (RL), KU3 – Placement and relative size of things from top-view.  Represent Transformation (RT), KU1 – imagine how things

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Jesline Bazzi

EDP343 2019

Student # 16831791

Assessment 2 - Portfolio

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look after changing our view of it.  RT, KU2 – Things can be moved around by reflecting and rotating. (DoEWA, 2013a) Prior knowledge

 Identify features of 2D and 3D shapes  Understand the spatial relationships within objects (DoEWA, 2013a)

Resources

 Geometric City Project Activity (appendix A)

Introduction

 http://www.scootle.edu.au/ec/viewing/L1058/index.html Guided discussion:

(10 minutes)

 Previous background knowledge of two-dimensional shapes is assessed.  The word “Sides” and then the numbers “one”, “three”, “five”, “six”, “seven” and “eight” is written on the board.  Students are asked to name shapes based on their number of sides. For example; triangle is written under “three”  Students are questioned further about their properties, for instance, “what if the triangle has only two equal sides, what would that be called?”  Students are chosen to draw these shapes on the board.  Ask questions such as; -

What about irregular shapes?

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Which shapes would have parallel lines?

Body of the

- What can you tell me about their angles? Whole class:

lesson

Different shapes are drawn on the board and students are

(45 minutes)

prompted with;

Jesline Bazzi

EDP343 2019

Student # 16831791

Assessment 2 - Portfolio

-

Think about your everyday surroundings.

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Where would you find this shape?

-

What does it remind you of?

Small group work:  In groups of three, students use their knowledge of twodimensional shapes to complete the Geometric City Project activity (Turner, 2019) (appendix A).

Individual work:  Students use the Scootle Shape Maker interactive activity to investigate the extrusion and rotation of two-dimensional shapes.  Prompts include; -

What shape do you think this will make if it is extruded/rotated?

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How is this linked to three-dimensional objects?

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Consider the axis of symmetry when rotating twodimensional shapes.

Differentiation  Less able student may require peer or teacher support.  More able students may work with more difficult shapes and asked to transform shapes without assistance from the

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Jesline Bazzi

EDP343 2019

Student # 16831791

Assessment 2 - Portfolio

Concluding the

software.  Students reflect on different shapes based on their properties.

lesson

 Students identify two-dimensional shapes in their

(5 minutes)

surroundings.  Students reflect on the Shape Maker activity and the link between two-dimensional shapes and three-dimensional objects.

Effective teaching of data handling and probability The use of inquiry and problem solving “Solving problems lies at the heart of mathematics”, and should be, “integrated into mathematics teaching and learning” (Fox & Surtees, 2010, p. 47). Problem solving contests with the conventional linear methodology and supports the constructivist methodology for mathematical pedagogy (Fox & Surtees, 2010); furthermore, it is an important aspect of effectively teaching data handling and probability as it provides students with the opportunity to apply their skills and knowledge, and manifests the purpose and relevance of learning such skills in their lives (Jones, 2003). These concepts can be better understood and implemented through methodically working through the problem. George Polya devised a strategic problem solving process that can be effective in the teaching of data handling and probability and consists of four principles (Polya, 1957). The initial step, understand the problem, involves understanding exactly what is required, redefining the problem, identifying the unknowns, and determining the important and

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Jesline Bazzi Student # 16831791

EDP343 2019 Assessment 2 - Portfolio

irrelevant parts of the problem (Airth, 2014). The second step, devise a plan, entails predicting and checking, methodically arranging records , ruling out possibilities, determining similarities and looking for patterns and symmetry (Shirali, 2014). The next step, carry out the plan, involves using the ideas from the previous step to work carefully through the steps and solve the problem (Seward, 2011). The final step, look back, requires checking the answer and ensuring it makes sense, determining the substantial and unsubstantial processes to predict what strategies to use for problems in the future (Irvine, 2018). Studies have shown that students implementing Polya’s problem solving steps results in increased success when solving data handling and probability problems (Logoglu & Uredi, 2017). The process of systematically working through an inquiry task aligns with the constructivist approach of students interpreting information based on prior knowledge and experiences (Reys et al., 2017). Another problem solving process supporting the constructivist approach is identifying the mathematics key aspects in the students’ thinking to assist in constructing on their previous knowledge (Chamberlin, 2010). The Australian Curriculum (AC) emphasises the importance of teaching through the proficiencies of reasoning and problem solving as it provides students with the mathematical strategies required to make informed decisions and communicate solutions in familiar, unfamiliar and meaningful situations (ACARA, 2019b). Furthermore, inquiry for data handling and probability, while teaching through these proficiencies, challenges students to think beyond their current understanding and provides them with the active mathematical processes of exploring, formulating, estimating, modelling, testing, reasoning, conjecturing, proving and explaining (Sakshaug, Olson & Olson, 2002; Hurst, 2019).

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Jesline Bazzi Student # 16831791

EDP343 2019 Assessment 2 - Portfolio

Key content in teaching data handling and probability The key content in effectively teaching data handling and probability to primary children is directly impacted by classroom practices and the pedagogical content knowledge; interwoven with the concepts of statistical investigation (Wessels & Nieuwoudt, 2011). The components of the PCAI cycle for statistical investigations may be implemented linearly, or revisited whilst making connections between them; and they include pose the question, collect the data, analyse the data and interpret the data (Lee & Mojica, 2008). The first component involves analysing the problem to formulate a specific series of questions; initially younger students may require assistance in posing purposeful questions, however as their understanding develops so will their ability to ask questions (Reys et al., 2017). The second PCAI element demands the gathering and organisation of data and, where necessary, alterations can be made; during early years data is collected using simple tables and tallies and eventually progresses to using digital formats (Booker, Bond, Sparrow and Swan, 2014). The next PCAI component requires scrutinising and, if necessary, re-organising and summarising the data for management purposes through the commonly used, descriptive statistics (Reys et al., 2017). The final PCAI component involves drawing conclusions based on the data, while noting any issues with data collection methods and considering the original questions posed in relation to the data (Booker et al., 2014). This student-centred, statistical investigation promotes meaningful data handling and probability proficiencies as students devise the tasks, take control of the problem and are actively engaged in the processes they have used (Giardini, 2016). An experimental probability approach can be applied to rectify misconceptions of the key content in teaching data handling and probability (Booker et al., 2014). The concept of experimental probability is based on conducting concrete experiments with chance and probability while looking for patterns to confirm ideas, whereas theoretical probability

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Jesline Bazzi Student # 16831791

EDP343 2019 Assessment 2 - Portfolio

involves abstract contextual thinking while entailing logic and calculation; they are both connected as they are required to “prove” (Ireland & Watson, 2009, p. 350) each other and in time they will both converge. FSiM describes the primary years key content of chance events and probability to incorporate; the recognition of unpredictability in familiar situations while developing the use of chance terminology; the description and ordering of events from least likely to most likely; and the quantification of the likeliness of an occurrence (DoEWA, 2013b). The AC’s sub-elements for statistics and probability are understanding chance and interpreting and representing data; which incorporates describing and comparing occurrences of chance and all possible outcomes, measuring probability of events using fractions, percentages and compound events, comparing predicted and determined chance events, representing information using one-to-one data display, interpreting data scales with the use of descriptive statistics, graphically representing data and recognising biased statistical elements (ACARA, 2019c).

Teaching the concepts of the data handling process The data handling process can be effectively taught through implication of the PCAI cycle while using a problem-based and constructivist approach. Initially, data handling skills for younger students are developed by working with collected, counted and sorted concrete objects from their surroundings; for example, concrete representation of collected fruits, which are transferred into a pictorial representation, and then symbolic representation (Reys et al., 2017). Data is collected from surveys, experiments and simulations, through counting and measuring, and then organised and recorded with tallies, tables and digital formats (Booker et al., 2014). Data can be quickly graphed and

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Jesline Bazzi Student # 16831791

EDP343 2019 Assessment 2 - Portfolio

viewed with the use of sketch graphs, spreadsheets, statistical programs and graphing calculators; and it can be represented with more intricacy through the use of plot graphs, picture graphs, bar graphs, histograms, pie graphs and line graphs (Reys et al., 2017). The use of concrete materials is an effective strategy in supporting the comprehension of data handling processes, for instance when teaching descriptive statistics and the statistical measures, such as mean, mode, range and quartiles. “Who says I’m average?” is a concrete activity for students to visually comprehend the concept of the statistical mean through recording the range of the students’ heights on paper strips and then balancing the paper strips to represent the mean height for the class (Booker et al., 2014, p.514). Data handling is effectively taught through using exemplars and posing purposeful questions that interest and motivate the students while identifying and anticipating sources of mathematical misconceptions (Aisling, 2015). The use of real-life situations helps promote an inquiry-based approach and assists in effectively developing data proficiencies through; collecting, organising and describing data; constructing and interpreting tables, charts and graphs; and developing data-based implications, arguments and decisions (Hurst, 2019). ‘Brainstorm’ sessions can be effective in guiding students to more accessible methods of data handling and to developing a systematic approach for solving problems (Jones, 2003). Teaching with a range of innovative technologies, combined with a game-based approach and the use of project-based inquiries, develops knowledge and skills when working with tables and charts, and encourages student engagement, motivation and learning in context; where students pose their own questions, work with real data rather than textbook problems and choose statistical topics that interest them (Papancheva, 2017a; 2017b). An objective and real-context data activity that makes the correlation of data simpler to perceive could include representing the frequency of colours in a tube of sweets; where Microsoft Excel spreadsheets are

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Jesline Bazzi Student # 16831791

EDP343 2019 Assessment 2 - Portfolio

used and the visual representation of sweets relates to the visual representation of a graph (Teachers TV, 2005). Adapting the strategies and activities facilitates differentiation for a range of students. The use of inquiry-based approaches when teaching data handling means the problem can be made appropriately more challenging for more able students (Jones, 2003). Providing less able students with additional structural support, such as; a recording system, and visual and spatial problems, can assist in simplifying the process of solving data handling problems (Jones, 2003). Educators are required to evaluate and record each student’s strengths and weaknesses for specific data handling processes and encourage their development through appropriate and reasonable adjustments to support access and attainment for all (Adu & Gasa, 2014). Differentiating mathematics instruction efficiently can be achieved through the two core strategies of open questions and parallel tasks (Small & Lin, 2010). The “Collecting cans” activity (DoEWA, 2013b, p.160) requires students to collect data using a dot plot, the use of parallel tasks could include asking; “can you count the number of dots in each column and which column has the most?” or for more able students; “what does the height of the columns show?” The FSiM Chance and Data booklet is a useful resource that incorporates data handling activities while supporting the PCAI cycle, for example the booklet’s key understandings are centred on; “Collect and organise data” (p.83); “Summarise and represent data” (p.139); and “Interpret data” (p.213) (DoEWA, 2013b). The AC resources section provides above satisfactory, satisfactory and below satisfactory work samples for statistics at each year level (ACARA, 2019d). The NSW education department provide useful resources that incorporate four stages of strategies and activities for teaching data handling processes (NSWDoE, 2017). The Australian Mathematical Science Institute’s

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EDP343 2019 Assessment 2 - Portfolio

modules coincides with the AC’s Statistics and Probability strand that consists of content knowledge, strategies and exercises at each year level (AMSI, 2019).

Word count: 2189

References

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Adu, E. O., & Gasa, L. J. (2014). The role of data handling in teaching and learning of mathematics in grade7 classes: South African experience. Mediterranean Journal of Social Sciences, 5(23), 1151-1159. Doi: 10.5901/mjss.2014.v5n23p1151 Airth, M. (November 12, 2014). Polya’s Four-Step Problem-Solving Process [Video file]. Retrieved from https://study.com/academy/lesson/polyas-four-step-problem-solvingprocess.html Aisling, L. (2015). Looking at practice: revealing the knowledge demands of teaching data handling in primary mathematics. Mathematics Education Research, 27(3), 283-309. Doi: 10.1007/s13394-014-0138-3 Australian Curriculum Assessment and Reporting Authority (ACARA) (2019a). The Australian Curriculum: Mathematics, Year 4, Measurement and Geometry, Shape (ACMMG088). Retrieved from http://www.australiancurriculum.edu.au/Download/F10

Australian Curriculum Assessment and Reporting Authority (ACARA) (2019a). The Australian Curriculum: Mathematics, Year 5, Measurement and Geometry, Location and transformation (ACMMG114). Retrieved from http://www.australiancurriculum.edu.au/Download/F10 Australian Curriculum Assessment and Reporting Authority (ACARA) (2019b). The Australian Curriculum: Mathematics proficiencies. Retrieved from https://www.australiancurriculum.edu.au/resources/mathematics-proficiencies Australian Curriculum Assessment and Reporting Authority (ACARA) (2019c). The Australian Curriculum: Understanding how the numeracy progression works.

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Retrieved from https://www.australiancurriculum.edu.au/resources/national-literacyand-numeracy-learning-progressions/national-numeracy-learningprogression/statistics-and-probability/ Australian Curriculum Assessment and Reporting Authority (ACARA) (2019d). Mathematics work samples portfolios. Retrieved from https://www.australiancurriculum.edu.au/resources/work-samples/mathematics-worksamples-portfolios/ Australian Mathematical Science Institute (AMSI) (2019). Time Modules. Retrieved from https://schools.amsi.org.au/times-modules/ Bezear, M. (n.d.). Years 4-5: Cities taking Shape. Retrieved from https://aamt.edu.au/content/download/17389/231992/file/uw_003_cities_taking_shape .doc Booker, G., Bond, D., Sparrow, L., & Swan, P. (2014). Teaching Primary Mathematics (5th ed.). Melbourne, Australia; Pearson Australia. Chamberlin, S. A. (2010). Mathematical problems that optimize learning for academically advances students in grades K6. Journal of Advanced Academics, 22(1), 52-76. Retrieved from https://files.eric.ed.gov/fulltext/EJ906121.pdf Department of Education Western Australia (DoEWA) (2013a). First steps in Mathematics: Space. Retrieved from http://det.wa.edu.au/stepsresources/redirect/? oid=com.arsdigita.cms.contenttypes.FileStorageItem-id13684838&stream_asset=true

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Department of Education Western Australia (DoEWA) (2013b). First steps in Mathematics: Data and chance. Retrieved from http://det.wa.edu.au/...