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Mosaic floor

Open- ended questions

-        Point out all the different 2D patterns can you see in this picture?

-        Can you point out lines of symmetry within the shapes?

-        What size of angles do you see within the shapes?

Using real life photographs creates the opportunity for children to engage in open-ended problems where they use multiple approaches and solutions to the problem as well as strengthen children’s participations in the lesson as they will start to see mathematics in different perspectives (Bragg& Nicol, 2011). the photograph of the Mosaic patterns can provide learning for early stage students as they are required to sort, describe and name familiar two- dimensional shapes in the environment (ACMMG009). It is also suitable for stage 2 year 1 students as they have to identify the line of symmetry within the shapes and other shapes in the environment. (ACMMG066). In addition, they will also identify angles, in particular right angle and measure of turn and compare angle sizes in everyday situations (ACMMG064). As a future teacher, it is integral for me to ask my students open questions as I will gain an insight into their observations skills and their cognitions at the same time as open questioning will give students authority in constructing their own individual knowledge (The Arithmetic Teacher, 1993).

References

Bragg, L.A., & Nicol, C. (2011). Seeing Mathematics through a new lens. 67 (3) 3-9. Retrieved from https://acu-edu-primo.hosted.exlibrisgroup.com/primo-explore/fulldisplay?docid=TN_ericEJ943723&context=PC&vid=61ACU&lang=en_US&search_scope=61ACU_All&adaptor=primo_central_multiple_fe&tab=61acu_all&query=any,contains,Using%20photographs%20in%20mathematics&sortby=rank&offset=0

NSW Education Standards Authority (2018). Two-Dimensional Space. Retrieved from https://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/content/695/

NSW Education Standards Authority (2018). Two-Dimensional Space. Retrieved from https://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/content/1131/

NSW Education Standards Authority (2018). Angles. Retrieved from https://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/content/1133/

The Arithmetic Teacher. (1993). Questioning in the mathematics classroom. 41 (2) 88. Retrieved from https://search.proquest.com/docview/208770684?accountid=8194&rfr_id=info%3Axri%2Fsid%3Aprimo

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Circle fun shapes development $ 149.95 – allow Children to discover different shapes that can be rearranged to fill in a colourful circle. Beside recognising and classifying shapes and colours. Children will also

Develop the conceptual knowledge about proportions, mirror images and mathematical concepts such as half, quarter and an eighth. This manipulative will enhance students critical thinking, hand-eye coordination and problem-solving skills.

Hands on maths trays $129.95 – allow early stage students to sort, count, create patterns. Children can put the counters into right trays, which gives them opportunity to explore the concept sorting and classifying a group of familiar objects in different way(ACMNA005).

Magnetic designer pattern cards $ 19.95 – is an open-ended manipulative and suitable for age 3+. It allows early stage children to Copy, continue and create patterns with objects and drawings(ACMNA005).

It is integral for teachers to provide useful and appropriate manipulatives that stimulates and enhance children’s conceptual knowledge. According to Burns & Hamm (2011) children who manipulate concrete object for mathematical purposes have clearer mental images, represent abstract reasoning and increases the opportunities for constructing mathematical knowledge. In addition, children will also have opportunities to explore, discover concepts and use these manipulatives to strengthen their problem-solving skills, enhance reasoning and presenting them with real life experience which helps them to make connections between mathematical concepts and the real world (Carbonneau,2013).

References:

Burns, B.A., & Hamm, E.M. (2011) A Comparison of Concrete and Virtual Manipulative Use in Third-and Fourth- Grade Mathematics. 111 (6) 256-261. DOI: 10.111/j.1949-8594.2011. 00086.x

Carbonneau, K.J., Marley, S.C, & selig, J.P. (2013) A Meta-Analysis of the Efficacy of Teaching Mathematics with Concrete Manipulatives. 105 (2) 380-400 DOI: 10.1037/a0031084

NSW Education Standards Authority (2018) Patterns and Algebra. Retrieved from https://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/content/684/

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The online mathematical platform, Matific is a great tool provided for K-6 students to engage in a trial-and-error method to solve mathematical problems so that they can enhance and scaffold their conceptual knowledge. Matific is covering all the sub-strands such as number, place value, patterns and algebra with multiple visual games in which supports student’s ability to learn, to draw links to their real world and most importantly is supporting every individual student with diverse learning style to come with solutions and master the content on their own phase (Willacy,2017). Students will strengthen their one-to-one correspondence, strengthen their subitising ability, solve addition and subtraction task with help of strategies such as partitioning, rearranging parts and more in an independent and engaging way. Matific is also a helping tool for teacher as they can have an overview of students learning progress and work on areas of improvements. Having mentioned these advantages and in order to prepare students for the 21st centuries technological inventions (Eyyam & Yaratan, 2014), it is integral for teachers to provide student with technological resources such as IPad and mathematical learning apps as they support the children to develop a positive attitude towards mathematics, makes the lesson enjoyable (Hilton,2018), stimulates children creative thinking, encouraging inquiry, broaden students learning perspectives and self -expression (Eyyam & Yaratan, 2014)

References

Eyyam, R. & Yaratan, H.S. (2014). Impact of use of technology in mathematics lessons on students achievement and attitudes. 42 P. 31-42. Retrieved from https://search-proquest-com.ezproxy2.acu.edu.au/docview/1551001755?accountid=8194&rfr_id=info%3Axri%2Fsid%3Aprimo

Hilton, A. (2018). Engaging Primary School Students in Mathematics: Can ipads Make a Difference? 16 (1) 145-165. DOI:10.1007/s10763-016-9771-5

Willacy,H. & Caider,N. (2017). Making Mathematics Learning More Engaging for Students in Health Schools through the Use of Apps. 7 (2) 1-20. DOI:10.3390/educsci7020048

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‘’ what number could I be’’ is a mental warm up suitable for stage 3 year 5 as it requires the students to identify and describe factors and multiples of whole numbers and use to solve problems (ACMNA098) (NESA, 2018).  I am 2-digit number and 2 and 4 are 2 of my many factors is one of many mental warm up that invite children to use their higher level of thinking skills (Reys, 2018) to find the number. This open- ended question allows the children to record multiple answers for this question, for instance 36, 52 and 64 can be one of a few answers provided by the children and that 72,104 and 128 are the multiples.

According to Reys (1984) mental computation support children to develop a better understanding of number structure and their properties, support children to become creative and independent thinking who develop inventive ways to handle numbers. Moreover, he also emphasises that children from an early age should be introduced to mental computation so that they can solve basic addition problems such as 3+2= 5 as it will naturally lead them to some greater addition problems such as 20.000+ 30.000.

This means that my role as a future teacher avoid written algorithm which discourage creative and independent thinking decreases the chances misconceptions (Reys, 1984).

References

NSW Education Standards Authority (2018) Working Mathematically and Content strands. Retrieved from:

https://syllabus.nesa.nsw.edu.au/mathematics/mathematics-k10/working-mathematically-and-content-strands/

Reys, R.E. (2018). Testing Mental- Computation Skills. 33 (3) 14-16 Retrieved from http://www.jstor.org/stable/41194069?seq=1#page_scan_tab_contents

Reys, R.E. (1984). Mental Computation and Estimation: past, present and future. 84 (5) 556-557 Retrieved from https://www.journals.uchicago.edu/doi/pdfplus/10.1086/461383

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These manipulatives are stage 2 appropriate. I have used a place value grid for the first manipulative as I believe children will easier visualise the difference between ones, tens and hundred places. Here, I have used beans for tens place, bathroom cups for tens place and solo cups for hundred places. The rule for this activity is that once there are more than 9 beans in one’s place, they then need to be transferred into a bathroom cup in the tens place, and ten-bathroom cups has to be moved inside a solo cup in the hundred places. The second resource is bathroom cups with place value, this can also be more advanced when adding to thousand places. Not only children should learn place value using MBA blocs but also many familiar resources in children’s lives. In their research of representation of place value, Boulton- Lewis and Halford (1992) explains primary school children achieved a better results and interest in mathematics when using manipulatives.

Using range of manipulatives to visualise the place value decreases children misconceptions about the digit places (Monteleone, 2017). It is integral to consistently teach children place value as it is believed that they develop a deep understanding later but not as expected in 1st and 2nd grade (Cooper et al. 2011).

References

Boulton-Lewis, G., Halford, G. (1992). The processing loads of young children’s and teacher’s representation of place value and implications for teaching. 4 (1) 1-23. Retrieved from https://link.springer.com/content/pdf/10.1007%2FBF03217229.pdf

Cooper, L.L., & Tomayko, M.C. (2011). Understanding place value. 17 (9) 558-567. Retrieved from http://www.jstor.org.ezproxy2.acu.edu.au/stable/pdf/41199777.pdf?refreqid=excelsior:0eace1abb94f9bb453675200201451d8