week 8

Understanding Measurement for Kids using challenging tasks

DIY Ramp for understanding distance

PAW Patrol Toy Cars - Top left is Chase; Top Right is Skye; Bottom Right is Marshall; and Bottom Left is Rubble

From the Maths K-10 Syllabus of the Australian Curriculum

Strand: Measurement

Sub-strand: Length

Stage: Early Stage 1

Content: Use direct and indirect comparisons to decide which is longer, and explain their reasoning using everyday language (ACMMG006)

• use everyday language to describe distance, eg near, far, nearer, further, closer

The Challenging Task:

Ryder, the leader of PAW Patrol wants to test the cars of his 3 dogs namely:

• a.      the police dog, Chase
• b.      the firefighter dog, Marshall, and
• c.      the aviator dog, Skye

All of the cars are pushed down the ramp at the same time.

Ryder needs to know which car is:

• a.      near the ramp,
• b.      far from the ramp,
• c.      nearer from the ramp,
• d.      further from the ramp,
• e.      the nearest from the ramp,
• f.       the farthest from the ramp

Enabling prompt:  Look at the three cars. Notice how far they are from the ramp. Where is the ramp from Chase’s car? Is it near or far? How about Marshall’s and Skye’s? Is Marshall’s car nearer than Chase’s car from the ramp? Which car went the farthest?

Extending prompt: If Ryder will remove the ramp, will the cars’ distance be the same? Make a chart that shows the first task cars’ distances and your 1^st guess, and then the last tasks result and show your explanation to your group mates.

Reflection

The above task that I created can be a fun task to do to Kindergarten students. This can be an engaging activity due to the following reasons:

First, I used the characters from PAW Patrol which is popular to Kindergarten students. I just chose three dogs from the famous children TV show, which are mostly seen, and one of the dogs is a female dog for some children who have gender preference.

Second, this can be performed in the class as long as there are materials and if possible, using the PAW Patrol character cars.

Lastly, teachers can use play-based approach side-by-side with the intentional teaching (DEEWR, 2009) which is introducing distance vocabulary words.

The given statement is my example that imply an open-ended task.

The enabling prompts which is to reduce its complexity is by giving questions to draw the students’ attention to important aspects (Ferguson, 2018). I used questions that will lead students to compare three objects for them to use comparative languages – near, far, nearer and further, as well as superlative adjectives - the nearest and the farthest.  The names of the PAW Patrol dogs could possibly help them identify which are these objects that they are comparing with.

The extending prompt is to make students think more without doing additional work (Ferguson, 2018). The prompt given is just by removing the ramp and observe if the distance from each other are still the same from the first task's result. By making a chart of the results and their guesses, it will require them to reason out to their peers their thinking while using the intended mathematical language for this task.

References

DEEWR (2009). Being, Belonging and Becoming: The Early Years Learning Framework for Australia. Barwon, ACT Commonwealth of Australia.

Ferguson, S. (2018). Developing prompts with challenging tasks [online]. Prime Number, 33(4), 21. Retrieved on 15/05/2020 from https://search-informit-com-au.ezproxy1.acu.edu.au/documentSummary;dn=905946453114743;res=IELHSS

New South Wales. Board of Studies (2012). Mathematics K-10 syllabus: NSW syllabus for the Australian curriculum. Board of Studies NSW, Sydney

week 7

How to set up and manage mathematical learning experiences.

There are 10 things that can make Maths teachers create an engaging Maths class. These are the following:

1. Know the students and how they learn (Pemberton, 2020a;  AITSL, 2010) – there are students who have diverse needs. Knowing what each student needs can help teachers create their strategies to teach a content to foster and develop student’s learning.
2. Know the content (Monteleone, 2014; AITSL, 2010) – this is one of the main components of the role of a teacher – being able to demonstrate their knowledge and understanding of the mathematical concepts, substance and structure of the content, using effective learning and teaching sequence and strategies that are aligned with the curriculum, assessment and reporting requirements.
3. Setup the learning environment (Pemberton, 2020; Fraser, 2012) – is considered as the third teacher as it is responsive to the interests of students, provides opportunities for them to make their thinking visible and fosters more learning and engagement.
4. Use Open-ended tasks (Sullivan, 2011; Pemberton, 2020a) –  These are tasks or problems that have endless possible solutions that contributes to learning. Sullivan (2011) elaborated only two types of open-ended tasks that I believe are greatly essential. These are investigations and content specific tasks. Investigations refers to tasks that let students investigate using different mathematical approaches while content specific tasks are manageable for students and teachers and aligned with a sequential and topic specific curriculum.
5. Use Enabling prompt – a strategy that gives support to students experiencing difficulty throughout a given task (Sullivan, 2011).
6. Incorporate Extending prompt – a strategy that makes students who are ready to go further their learning (Sullivan et al., as cited by Sullivan, 2011)
7. Make use of 'Which One Does Not Belong' task (Pemberton, 2020) – this task makes student explore numerous ways of identifying the odd one out of the set recalling mathematical concepts learned and lets students improve their reasoning skills, as well as communication when asked to share their thoughts of their answer.
8. Follow a mathematics lesson structure (Bobis, Mulligan, & Lowrie; Sullivan et al., as cited by Monteleone, 2014; Sullivan, 2011; Pemberton, 2020b; Russo & Hopkins, 2017) – the format Launch, [Introduce], Explore and Summarise/Review is recommended usually to Australian teachers. This format allows students to foster communication and individual and group responsibilities, utilise students’ reports to the class as learning opportunities, with teacher’s summarisation of key mathematical ideas.
9. Utilise models or representations (Sullivan, 2011) – Having interesting models or representations that illustrate main mathematical principles can provide student engagement. This may be a good aid for visual learners.
10. Differentiate (Sullivan, 2011; Pemberton, 2020) –  Differentiation means having the same curriculum and overall experience to all students but the tasks in which they work with are differentiated. These can happen by doing the general principles of differentiation which are giving challenging tasks, having flexible grouping and doing continuous assessment and adjustment.

References

Australian Institute for Teaching and School Leadership [AITSL]. (2010). Australian professional standards for teachers. [online document]. Retrieved on 14/05/2020 from https://www.aitsl.edu.au/docs/default-source/national-policy-framework/australian-professional-standards-for-teachers.pdf?sfvrsn=5800f33c_64

Fraser, S. (2012). Authentic childhood: exploring Reggio Emilia in the classroom. Toronto, ON: Nelson Education.

Monteleone, C. (2014). What to do in a good mathematics lesson. Retrieved on 14/05/2020 from Australian Catholic University LEO website https://leo.acu.edu.au/pluginfile.php/3878388/mod_resource/content/1/What%20to%20do%20in%20a%20good%20Mathematics%20lesson%20colour.pdf

Pemberton, M. (2020a). Week 9 Lecture. [PowerPoint slides]. Retrieved on 14/05/2020 from Australian Catholic University LEO website https://leo.acu.edu.au/pluginfile.php/4015810/mod_resource/content/1/Week%209%20Lecture%20EDMA241%20262.mp4

Pemberton, M. (2020b). Week 4 Tutorial. [PowerPoint slides]. Retrieved on 15/05/2020 from Australian Catholic University LEO website

Russo, J., & Hopkins, S. (2017). How does leson structure shape teacher perceptions of teaching with challenging tasks? [online]. Mathematics Teacher Education and Development, 19(1), 30-46. Retrieved on 15/05/2020 from https://search-informit-com-au.ezproxy1.acu.edu.au/fullText;dn=218717;res=AEIPT

Sullivan, P. (2011). Teaching mathematics: using research-informed strategies. Australian Council for Educational Research.

Week 6

Using Manipulatives to learn Place Value

learning place value using paper clips 

using cut out squares and strips to learn place value

When I was in primary school two decades ago, place value was not valuable to me especially after I finished my written Maths exams. Now that I am studying here in Australia on how to teach Maths, I learned that place value is the basic yet one of the most important arithmetic concepts in the very young students’ mathematics learning, the ability of children to do mental mathematics and be flexible with numbers, and the social conventional knowledge of the value of each digit (Tanase, 2011).  

To set the mathematics learning foundation of very young children, there should be a wide range of objects and materials in early childhood centres (Ginsburg and Ertle, 2016). The above pictures are two sets of resources to help children understand place value. The first image shows the number of paperclips attached together and grouped according to hundreds, tens and ones depending on the numeral shown or to be identified. The second one illustrates that a big square paper composed of 10 by 10 small squares means the hundreds digit, a strip of paper having 10 squares refers to the tens digit, and an individual small square means the ones digit.

I believe that these manipulatives can be helpful for children to do hands-on learning (Hynes, as cited by Swan & Marshall, 2010). The materials – coloured paper clips and paper are very cheap, accessible and flexible to variations of use.  These objects ‘can be handled [by students] in a sensory manner during which conscious and unconscious mathematical thinking will be fostered’ (Swan & Marshall, 2010, par. 3).  Likewise, these manipulatives can heighten students’ interest and motivation to learn, provide assistance in concrete visualisation and build a better understanding (Swan & Marshall, 2010).

References

Ginsburg, H. P., & Ertle, B. B. (2016). Giving away early mathematics: big math for little kids encounters the complex world of early education. In Durkin, K., & Schaffer, H. R. (Eds.). The wiley handbook of developmental psychology in practice : Implementation and impact (pp. 221-260) Retrieved from https://ebookcentral-proquest-com.ezproxy2.acu.edu.au

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+. Retrieved from https://link-gale-com.ezproxy2.acu.edu.au/apps/doc/A229718050/AONE?u=acuni&sid=AONE&xid=1b95090c

Tanase, M. (2011). Teaching Place Value Concepts to First Grade Romanian Students: Teacher Knowledge and its Influence on Student Learning. International Journal for Mathematics Teaching and Learning, International Journal for Mathematics Teaching and Learning, 15 June 2011. Retrieved from http://www.cimt.org.uk/journal/tanase.pdf

Week 5

The Benefits of using 'Matific' app 

A screenshot of a Matific game

The integration of technology in learning has been my concern if this can absolutely provide positive effects in students learning especially in Mathematics that has been perceived as a difficult subject for young students. There are many apps that market themselves being a high-quality educational app. However, two research being conducted by Catherine Attard (2016) and Edith Manny-Ikan and colleagues (2016) proved the benefits of using this app called Matific. Their findings are that Matific provides assistance in learning Mathematics, makes students be focused on the concepts and skills of mathematics because of the number of questions and its structure of each game, uses scaffolding approach that is built for each game when problems are answered incorrectly, has an immediate reward for students’ continuous engagement, is interactive, user-friendly and shows that learning Mathematics is fun. Also, it is noteworthy to highlight that the app is greatly beneficial to teachers for its relevance to their instruction and alignment to Australian Curriculum.

After trying to play some Matific games, the above-mentioned benefits are undeniably true. Overwhelmed, I even suggested my brother back in my home country to introduce it to his Kindergarten son. 

The Australian Curriculum and Reporting Authority (ACARA) pointed out that the use of Information and Communication Technology (ICT) is part of the general capabilities of students stated in the Australian Curriculum and teachers need to incorporate this to their class (ACARA, 2012; Attard, 2017). If this is the case, there should be Internet-accessed computers and portable technologies such as iPads in every classroom and school across Australia, so that teachers are able to provide the benefits of using technology like this educational app, Matific. Even though Matific is a commendable app, teachers must not limit themselves in using subscription based learning resource package like Matific as it may be like the traditional way – following the prescribed book.

References

Attard, C. (6 September 2017). Technology in the classroom can improve primary mathematics.

 https://engagingmaths.com/2017/09/06/technology-in-the-classroom-can-improve-primary-mathematics/

Attard, C. (September 2016). Research evaluation of Matific mathematics learning resources: project report. https://doi.org/10.4225/35/57f2f391015a4

Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2012). Australian curriculum: information and communication technology. [online document] Retrieved on 13/05/ 2020 from https://www.australiancurriculum.edu.au/f-10-curriculum/general-capabilities/information-and-communication-technology-ict-capability/

Manny-Ikan, E., Berger-Tikochinski, T., & Marmor, A. (2016). Research evaluation of ‘Matific’. Henrietta Szold Institute: The National Institue for Research in Behavioural Sciences. Retrieved on 12/05/2020 from https://www.matific.com/home/resources/media/documents/HS-matific-study.pdf

Week 4

Discuss and reflect on how the working mathematically proficiencies integrate with use of an inquiry-based approach in mathematics education.

I remember that how I learned Mathematics was just by doing worksheets by myself. I just realised that there are more to be learned when it studied with others. I believe that the Working Mathematically proficiencies: communicating, problem solving, reasoning, understanding and fluency (NESA, 2012) are perfect to be the core in the graph as these are the main skills that students will use in daily activities. This will allow them to make meaningful connections with what the already know, build their capacity in determining what mathematics needs to be known and done, transfer their mathematical skills strategies across key learning areas, and explain mathematical ideas and workings (Pemberton, 2020).

It is essential that teachers must be knowledgeable to demonstrate inquiry-based approach.  Inquiry-based approach engages young learners to discover rules and procedures through investigating mathematics (Linder, Powers-Costello & Stegelin, 2011). “Pedagogical practices in early childhood mathematics education include the need for teachers to act as facilitators, asking open-ended questions and scaffolding for students as they work collaboratively to make sense of mathematics through meaningful tasks” (Hiebert et al. 1997; Baroody and Wilkins 1999, as cited by Linder et al., 2011).

Teachers may receive various response from students’ different perspectives if teachers steer away from the lower order knowledge-based questions which focus on recalling of facts (Daines, as cited by Way, 2011). Badham’s (1994, as cited by Way, 2011) Open-ended mathematical tasks – starter questions; questions to stimulate mathematical thinking; assessment questions; and final discussions may be used by educators in guiding children through investigations while their mathematical thinking are being stimulated and information about their knowledge and strategies are being gathered (Way, 2011).

I believe this approach will be beneficial if teachers are knowledgeable in choosing the straightforward language while also introducing mathematical terminologies. Chapman (997, as cited by Ellerton, Clements & Clarkson, 2000) claimed that as mathematics has interrelated dimensions of social context, culture and language, thus, she suggested that “language, in any or all of its forms, must contribute to both the interactional and thematic development of any mathematics lesson” (p.31).

References

Ellerton, N., Clements, M.A., & Clarkson, P.C. (2000). Language factors in mathematics teaching and learning. In K. Owens & J. Mousley (Eds.). In Research in mathematics education in Australasia 1996-1999, 29-96. Retrieved from https://www.researchgate.net/publication/310607835_EllertonN_ClementsMA_ClarksonPC_2000_Language_factors_in_mathematics_teaching_and_learning_In_KOwens_JMousley_Eds_Research_in_mathematics_education_in_Australasia_1996_-_1999_pp_29-96_Sydney_Mathemati

Linder, S. M., Powers-Costello, B., & Stegelin, D. (2011). Mathematics in early childhood: research-based rationale and practical strategies. Early Childhood Educational Journal 39, 29-37. https://link.springer.com/article/10.1007/s10643-010-0437-6

NSW Board of Studies or Education Standards Authority [NESA]. (2012). Guide to the new NSW syllabuses: kindergarten to year 6. Retrieved from Australian Catholic University LEO website: https://leo.acu.edu.au/mod/resource/view.php?id=2927145

Pemberton, M. (2020). EDFD262 lecture 4 [PowerPoint slide]. Retrieved from Australian Catholic University website LEO: https://leo.acu.edu.au/pluginfile.php/3973803/mod_resource/content/1/Lecture%20Week%204.pdf

Way, J. (2011). Using questioning to stimulate mathematical thinking. Retrieved from https://nrich.maths.org/2473

Week 3

Discuss and reflect on the ‘ingredients’ required in developing a child’s number sense in the pre-primary and early primary years.

I still remember how I was taught by my parents and teachers about numbers. It was by memorisation and the usual algorithm of answering mathematical operational problems. I realised that at the early age, children should have various interactive and engaging numeracy activities. They are possibly to appreciate and continue to engage in mathematical learning from primary until post-secondary levels if they interact with meaningful and engaging mathematical learning experiences at the pre-primary level (Seefeldt and Galper; Van de Walle and Lovin; NRC as cited by Powers-Costello et al., 2011).

 Developing number sense to children can be developed into numerous ways. Mildenhall (2014) stated the use of representations such as signs, language, gesture, objects which are “communicative (semiotic) resources” (par. 4) and tools such as drawings, gestures, and concrete materials can be useful to their understanding of mathematics. The Early Years Learning Framework (2009) stated that “children develop understandings of themselves and their world through active, hands-on investigation” (p. 36). Likewise, their minds are “undergoing significant developmental change and are stimulated by more complex and engaging learning activities rather than rote counting or drilling” (Linder, Powers-Costello and Stegelin, 2011).  

 Another way is to incorporate Big Ideas – “a statement of an idea that is central to the learning of mathematics, one that links numerous mathematical understandings into a coherent whole” (Randall and Carmel, 2005, par. 3). I believe it will be easier to not focus only to one concept, but it will also connect it to another, especially when the one teaching it knows how to implement this. Thus, there will be an “active involvement in learning”….which “…builds children’s understandings of concepts and the creative thinking and inquiry processes that are necessary for lifelong learning” (DEEWR, 2009, p. 36).

References

Department of Education, Employment and Workplace Relations [DEEWR]. (2009). Belonging, being and becoming: the early years leaning framework for Australia. Retrieved from https://www.acecqa.gov.au/sites/default/files/2018-02/belonging_being_and_becoming_the_early_years_learning_framework_for_australia.pdf

Linder, S. M., Powers-Costello, B., & Stegelin, D. (2011). Mathematics in early childhood: research-based rationale and practical strategies. Early Childhood Educational Journal 39, 29-37. https://link.springer.com/article/10.1007/s10643-010-0437-6

Mildenhall, P. (2014). Number sense development in the pre-primary classroom how is it communicated?. Australian Primary Mathematics Classroom, 19(3). Retrieved from https://go-gale-com.ezproxy1.acu.edu.au/ps/i.do?p=AONE&u=acuni&id=GALE|A387827401&v=2.1&it=r

Randall I., C., & Carmel, C. A. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. Journal of Mathematics Education 7(3), 9-24. Retrieved from https://www.mathedleadership.org/docs/coaching/MK-A-CHARLES.pdf

Week 2

Highlight, discuss and reflect on the current challenges in mathematics education in Australia.

I came from a time when Mathematics standardised scores were indicator of intelligence. Thus, I was forced to be an academic servant than be a wise man knowing how to connect and perform the knowledge being taught and gained in daily activities. Learning that there have been dramatic changes on the curriculum these days, I felt enlightened to re-learn Mathematics using the new curriculum and eventually teach with confidence to young learners.

The flexibility of teachers “to make decisions about the sequence of learning, the emphasis to be given to particular areas of content, and any adjustments required based on the needs, interests and abilities of their students” (NSW Board of Studies, 2012, p. 1) is a much better approach than following some previous traditions of school mathematics in Australia which were methods of rote teaching and learning connected with rigidly defined courses of study, prescribed text books, and written examinations and preparation of students for tertiary courses as the core reason of studying mathematics (Ellerton and Clements, 1988). This also adheres to the Australian Professional Standards for Teachers (2018) “know your students and how they learn” and Australian Association of Mathematics Teachers standards for excellence teaching in mathematics Domain 1.1: Knowledge of students and 1.3: Knowledge of students’ learning of mathematics (AAMT, 2006).

Having the National Numeracy Learning Progression indicators can be beneficial “to identify the numeracy performance of individual student” (ACARA, 2020, p. 6) as they have different abilities and pacing if teachers have skills in discerning students’ numeracy capabilities and if the class size is small. However, for teachers, tensions like the existence of schools depends on the rating of the students results in testing such as NAPLAN and PISA (Attard, 2020). Thus, the possibility of neglecting individual needs in understanding mathematics might still happen.

References

Attard, C. (21 January, 2020). Mathematics education in Australia: new decade, new opportunities?. Retrieved from https://engagingmaths.com/2020/01/21/mathematics-education-in-australia-new-decade-new-opportunities/

Australian Association of Mathematics Teachers Inc. [AAMT]. (2006). Standards for excellence in teaching mathematics in Australian schools. Retrieved from http://www.aamt.edu.au

Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2020). National numeracy learning progression. [online document]. Retrieved from https://www.australiancurriculum.edu.au/media/3635/national-numeracy-learning-progression.pdf

Australian Institute for Teaching and School Leadership [AITSL]. (2018). Australian professional standards for teachers. [online document]. Retrieved from https://www.aitsl.edu.au/docs/default-source/national-policy-framework/australian-professional-standards-for-teachers.pdf?sfvrsn=5800f33c_64

Ellerton, N. F., & Clements, M.A. (1988). Reshaping school mathematics in Australia 1788-1988. Australian Journal of Education, 32(3), 387-405. https://doi.org/10.1177/000494418803200310

NSW Board of Studies. (2012). Guide to the new NSW syllabuses: kindergarten to year 6. Retrieved from Australian Catholic University LEO website: https://leo.acu.edu.au/mod/resource/view.php?id=2927145