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

Week 1

Highlight, discuss and reflect on the mathematics curriculum, the organisation of learning, and the implications for you as future teacher.

In my home country, the Philippines, when people know you are good at Maths, you are considered genius. I still remember that there would always be a class of genius in Maths from the 10 classrooms (having 40 students each) of each year level. I was always wondering why these batchmates of mine could excel in Maths while the majority could not. When, I graduated from college and started to have a job, I realised that I still experience difficulty in dealing with numeracy especially on practical matters like managing cash collections with my peer group or scaling a big picture to a small one. Also, as I had the chance to engaged with different nationalities, I realised that they managed to be quick on dealing with numeracy problems while I automatically jokingly responded, “It’s Maths, I can’t”. That made me think that their system of teaching Maths can be used not just academically but practically.

We were more into memorisation than into application. It is because “..Mathematics curricula in Asia are known to emphasise mastery of mathematics content as expressed in official documents and curriculum framework of these countries” (Vistro-Yu and Toh, 2019, p. 4). We were into Mathematics “as a body of knowledge” (Pemberton, 2020, slide 14) than into numeracy which is “the disposition to use, in context, a combination of: underpinning mathematical concepts and skills from across the discipline (numerical, spatial, graphical, statistical and algebraic): mathematical thinking and strategies; general thinking skills; and grounded appreciation of context” (The Australian Association of Mathematics Teachers [AAMT], 1997, p. 2).

I agree to the rationale of the NSW Mathematics curriculum (2019) that studying mathematics should make students “develop a positive self-concept as learners of mathematics, obtain enjoyment from mathematics, and become self-motivated learners through inquiry and active participation in challenging and engaging experiences” (NSW Education Standards Authority [NESA], 2019, par. 6). As a pre-service teacher, to be able to implement these to students, I must have the three domains of excellent teaching: professional knowledge, attributes and practice (AAMT, 2006).

  

References

Australian Association of Mathematics Teachers Inc. [AAMT]. (1997). Policy on numeracy education in schools. Retrieved from http://www.aamt.edu.au

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

NSW Education Standards Authority [NESA]. (2019). Rationale. [online document]. Retrieved from https://educationstandards.nsw.edu.au/wps/portal/nesa/k-10/learning-areas/mathematics/mathematics-k-10/rationale

Pemberton, M. (2020). EDFD262 lecture 1 [PowerPoint slide]. Retrieved from Australian Catholic University website LEO: https://leo.acu.edu.au/mod/resource/view.php?id=2988969

Vistro-Yu C.P., Toh T. L. (2019) School mathematics curricular reform: an Asian experience. Singapore: Springer.