Major Reflection
Numeracy is the ability to apply learnt mathematical knowledge across different contexts involving real life situations (Goos, Dole & Geiger, 2012).
Numeracy education is critical to a student's ability to function successfully in society as adults. The Melbourne Declaration on Educational Goals for Young Australians integrates the importance of mathematics and numeracy throughout the second goal of “all young Australians becoming successful learners, confident and creative individuals, and active and informed citizens” (Ministerial Council on Education, Employment, Training and Youth Affairs [MCEETYA], 2008, p. 8, Education Services Australia [ESA], n.d.). In order to develop successful learners, they require “essential skills in literacy and numeracy” (MCEETYA, 2008, p. 8); and for confident and creative individuals they need to be “prepared for their potential life roles” (MCEETYA, 2008, p. 9). The importance of this is recognised by the Department of Education and Training in the Early Years Learning Framework which fosters the need for positive attitudes to numeracy in order for children to be successful learners (Charles Sturt University Early Years Learning Framework Consortium, 2009; Doig, McCrae and Row, 2003). Additionally, the framework encourages children to find mathematics in everyday life (Department of Education and Children’s Services South Australia, n.d.). Following the early years, children are exposed to the national curriculum which is designed to deliver on goal 2 of the Melbourne Declaration. The Australian Curriculum, Assessment and Reporting Authority developed the curriculum to address the document and to develop numeracy skills that all people require in their personal, work and civic life (ESA, n.d.). Numeracy is a focus across all areas of the curriculum from Foundation to Year 12.
Research by Hunter, Turner, Russell, Trew and Curry (1993) showed that 42% of primary school children interviewed were not able to connect mathematics in the classroom to real life everyday activities. This could be improved by incorporating a child’s existing, and outside the classroom, mathematics knowledge to lessons (Hunter et al., 1993). I feel that linking mathematics to other disciplines can only further develop students’ understanding of how widely mathematics is used in real life. I endeavour to provide students other real life experiences that are numeracy related such as cooking, or having props for shops or restaurants as mentioned by Pound and Lee (2010). These connect children’s existing experiences to mathematics and “can be used to extend mathematical thinking and learning” (Pound & Lee, 2010, p. 56). Additionally, I think geography is useful for integrating discussions about distance, and history is useful for integrating learning about time. I feel that students also need regular practice at problem-solving so these skills become effortless. I personally enjoy mathematics and use it every day with cooking, shopping, budgeting for the household and planning holidays, as well as previous careers that had a strong mathematical focus that included analytic and problem-solving skills. These are important skills for any person in society today.
References
Charles Sturt University Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective communicators. Retrieved from
http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Department of Education and Children’s Services South Australia. (n.d.). Numeracy matrix. Retrieved from
http://www.earlyyears.sa.edu.au/files/links/24_Numeracy_Matrix.pdf
Doig, B., McCrae, B., & Rowe, K. (2003). A good start to numeracy: Effective numeracy strategies from research and practice in early childhood. Retrieved
from http://research.acer.edu.au/learning_processes/3/
Education Services Australia. (n.d.). Mathematics overview: Rationale. Retrieved from http://www.australiancurriculum.edu.au/mathematics/rationale
Goos, M., Dole, S., & Geiger, V. (2012). Numeracy across the curriculum. Australian Mathematics Teacher, (68)1, 3-7. Retrieved from
http://search.informit.com.au.ezproxy1.acu.edu.au/fullText;dn=052217827670486;res=IELHSS
Hunter, J., Turner, I., Russell, C., Trew, K., & Curry, C. (1993). Mathematics and the real world. British Educational Research Journal, 19(1), 17-26. Retrieved
from http://www.jstor.org/stable/1500508
Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA). (2008). Melbourne declaration on educational goals for young
Australians. Retrieved from
http://www.curriculum.edu.au/verve/_resources/National_Declaration_on_the_Educational_Goals_for_Young_Australians.pdf
Pound, L. & Lee, T. (2010). Teaching mathematics creatively. Retrieved from http://reader.eblib.com.ezproxy1.acu.edu.au/(S(4foe3akswtialezqoawug32z))/
Reader.aspx?p=667824&o=168&u=kBKb8d2Tplr6Aii55AmCPw%3d%3d&t=1429052355&h=7373F75FABB8B2FAEE1C831043E61787C843E5D5
&s=34703789&ut=459&pg=1&r=img&c=-1&pat=n&cms=-1&sd=2#
Numeracy education is critical to a student's ability to function successfully in society as adults. The Melbourne Declaration on Educational Goals for Young Australians integrates the importance of mathematics and numeracy throughout the second goal of “all young Australians becoming successful learners, confident and creative individuals, and active and informed citizens” (Ministerial Council on Education, Employment, Training and Youth Affairs [MCEETYA], 2008, p. 8, Education Services Australia [ESA], n.d.). In order to develop successful learners, they require “essential skills in literacy and numeracy” (MCEETYA, 2008, p. 8); and for confident and creative individuals they need to be “prepared for their potential life roles” (MCEETYA, 2008, p. 9). The importance of this is recognised by the Department of Education and Training in the Early Years Learning Framework which fosters the need for positive attitudes to numeracy in order for children to be successful learners (Charles Sturt University Early Years Learning Framework Consortium, 2009; Doig, McCrae and Row, 2003). Additionally, the framework encourages children to find mathematics in everyday life (Department of Education and Children’s Services South Australia, n.d.). Following the early years, children are exposed to the national curriculum which is designed to deliver on goal 2 of the Melbourne Declaration. The Australian Curriculum, Assessment and Reporting Authority developed the curriculum to address the document and to develop numeracy skills that all people require in their personal, work and civic life (ESA, n.d.). Numeracy is a focus across all areas of the curriculum from Foundation to Year 12.
Research by Hunter, Turner, Russell, Trew and Curry (1993) showed that 42% of primary school children interviewed were not able to connect mathematics in the classroom to real life everyday activities. This could be improved by incorporating a child’s existing, and outside the classroom, mathematics knowledge to lessons (Hunter et al., 1993). I feel that linking mathematics to other disciplines can only further develop students’ understanding of how widely mathematics is used in real life. I endeavour to provide students other real life experiences that are numeracy related such as cooking, or having props for shops or restaurants as mentioned by Pound and Lee (2010). These connect children’s existing experiences to mathematics and “can be used to extend mathematical thinking and learning” (Pound & Lee, 2010, p. 56). Additionally, I think geography is useful for integrating discussions about distance, and history is useful for integrating learning about time. I feel that students also need regular practice at problem-solving so these skills become effortless. I personally enjoy mathematics and use it every day with cooking, shopping, budgeting for the household and planning holidays, as well as previous careers that had a strong mathematical focus that included analytic and problem-solving skills. These are important skills for any person in society today.
References
Charles Sturt University Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective communicators. Retrieved from
http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Department of Education and Children’s Services South Australia. (n.d.). Numeracy matrix. Retrieved from
http://www.earlyyears.sa.edu.au/files/links/24_Numeracy_Matrix.pdf
Doig, B., McCrae, B., & Rowe, K. (2003). A good start to numeracy: Effective numeracy strategies from research and practice in early childhood. Retrieved
from http://research.acer.edu.au/learning_processes/3/
Education Services Australia. (n.d.). Mathematics overview: Rationale. Retrieved from http://www.australiancurriculum.edu.au/mathematics/rationale
Goos, M., Dole, S., & Geiger, V. (2012). Numeracy across the curriculum. Australian Mathematics Teacher, (68)1, 3-7. Retrieved from
http://search.informit.com.au.ezproxy1.acu.edu.au/fullText;dn=052217827670486;res=IELHSS
Hunter, J., Turner, I., Russell, C., Trew, K., & Curry, C. (1993). Mathematics and the real world. British Educational Research Journal, 19(1), 17-26. Retrieved
from http://www.jstor.org/stable/1500508
Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA). (2008). Melbourne declaration on educational goals for young
Australians. Retrieved from
http://www.curriculum.edu.au/verve/_resources/National_Declaration_on_the_Educational_Goals_for_Young_Australians.pdf
Pound, L. & Lee, T. (2010). Teaching mathematics creatively. Retrieved from http://reader.eblib.com.ezproxy1.acu.edu.au/(S(4foe3akswtialezqoawug32z))/
Reader.aspx?p=667824&o=168&u=kBKb8d2Tplr6Aii55AmCPw%3d%3d&t=1429052355&h=7373F75FABB8B2FAEE1C831043E61787C843E5D5
&s=34703789&ut=459&pg=1&r=img&c=-1&pat=n&cms=-1&sd=2#
Week 5
Multiplicative thinking includes numerous models of multiplication and division that need to be supported through teaching in order for students to develop the skills necessary to solve any problem, as well as understand the big concepts. The concepts for multiplication and division are that multiplication is closely connected to addition, particularly repeated addition, while division is closely related to multiplication (Van de Walle, Karp & Bay-Williams, 2014). Research has also shown that the “higher-order multiplicative thinking” (p. 41) skills are developed through addition (Clark and Kamii, 1996). The close relationship between multiplication and division necessitates the teaching of division soon after multiplication (Van de Walle et al., 2014). It is hard to remember whether I was taught the different models in primary school but as a teacher I will provide my students many opportunities to solve problems with different structures so opportunities to “increase their ability to handle these calculations” (Haylock, 2014, p. 134) are maximised.
References
Clark, F. & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1-5. Journal for Research in Mathematics Education, 27(1), 41-51.
Retrieved from http://www.jstor.org.ezproxy1.acu.edu.au/stable/749196?origin=crossref&seq=1#page_scan_tab_contents
Haylock, D. (2014). Mathematics explained for primary teachers. London, England: SAGE Publications.
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson
Education.
References
Clark, F. & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1-5. Journal for Research in Mathematics Education, 27(1), 41-51.
Retrieved from http://www.jstor.org.ezproxy1.acu.edu.au/stable/749196?origin=crossref&seq=1#page_scan_tab_contents
Haylock, D. (2014). Mathematics explained for primary teachers. London, England: SAGE Publications.
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson
Education.
Week 6
It is important to start multiplication instruction with student-invented strategies in order to develop relational understanding (Van de Walle, Karp & Bay-Williams, 2014). If standard algorithms are introduced to early students become reliant on the one strategy and may not have a real understanding of the distributive properties of multiplication over addition (Van de Walle et al., 2014). I also need to consider my students computational and understanding levels in order to move their reliance on existing and less efficient strategies to more efficient strategies (Bobis, 2006). I remember in primary school always having issues completing standard algorithms. My place value never lined up properly which always caused errors and then there was the fact that when multiplying the tens you just had to put a zero on the second line. For many, many years I never understood why, just that I had to do it. This is a perfect example of Skemp’s (1978) instrumental understanding. I found Bobis’ (2006) strategies for teaching multi-digit numbers very useful and I will use the array model to initially teach the concept of multi-digit multiplications. The array model makes the concept of multiplying tens and ones explicit before moving on to more abstract methods.
References
Bobis, J. (2006). From here to there: The path to computational fluency with multi-digit multiplication. Australian Primary Mathematics
Classroom, 12(4), 22-27. Retrieved from https://web-b-ebscohost-com.ezproxy2.acu.edu.au/ehost/pdfviewer/pdfviewer?
sid=b74664d6-d1d4-4902-90f7-02ba8269a7fc%40sessionmgr114&vid=1&hid=128
Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9-15. Retrieved from
http://www.jstor.org.ezproxy1.acu.edu.au/stable/41187667?seq=1#page_scan_tab_contents
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.
References
Bobis, J. (2006). From here to there: The path to computational fluency with multi-digit multiplication. Australian Primary Mathematics
Classroom, 12(4), 22-27. Retrieved from https://web-b-ebscohost-com.ezproxy2.acu.edu.au/ehost/pdfviewer/pdfviewer?
sid=b74664d6-d1d4-4902-90f7-02ba8269a7fc%40sessionmgr114&vid=1&hid=128
Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9-15. Retrieved from
http://www.jstor.org.ezproxy1.acu.edu.au/stable/41187667?seq=1#page_scan_tab_contents
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex,
England: Pearson Education.
Week 7
There was a lot of information to take in this week with lesson planning and problem solving. Lesson planning is particularly involved with catering for diverse learners. In my schooling years we used a lot of drill and practice. We would sit as a class and recite our timetables up to 10 x 10. I found Van de Walle, Karp and Bay-Williams’ (2014) definitions of drill being “repetitive non-problem-based” (p. 45) tasks and practice as “different problem-based tasks or experiences” (p. 45) thought-provoking and feel that my teaching philosophy is much more aligned to the problem-based or practice approach. Research has also shown students’ perspective of drill practice with ICT is that they are not challenging and prefer the freedom to choose their own activities even though ICT is thought to motivate students (Kuiper & Pater-Sneep, 2014). I feel the problem-based approach is more memorable for students but also provide opportunities for higher level thinking tasks (Van de Walle et al., 2014). My year 4 teacher was more hands on and I remember one unit of work where we used metre trundle wheels to measure distances around the playground which was memorable and fun. As a teacher I would like mathematics lessons to be a time for exploration and creativity of mathematical concepts through word problems. I would plan lessons that provide students opportunities to use hands-on manipulatives to work through problems and use graphic organisers so students can demonstrate their understanding.
References
Kiuper, E. & Pater-Sneep, M. (2014). Student perceptions of drill-and-practice mathematics software in primary education. Mathematics Education Research
Journal, 26(2), 215-236. doi: 10.1007/s13394-013-0088-1
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson
Education.
References
Kiuper, E. & Pater-Sneep, M. (2014). Student perceptions of drill-and-practice mathematics software in primary education. Mathematics Education Research
Journal, 26(2), 215-236. doi: 10.1007/s13394-013-0088-1
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson
Education.
Week 9
Measurement is an interesting and fun area of mathematics due to the use of real world hands-on activities. If hands-on experiences are lacking it can pose difficulties for students as learning is no longer meaningful (Preston & Thompson, 2004). Hands-on experiences can also incorporate historical and cultural activities. Forms of measurement have changed over the years so using non-standard units can be linked back to the history and culture of their origins. Van de Walle, Karp and Bay-Williams (2014) state that measurement is one of the most useful content strands as it is a necessity for “mathematically literate citizens” (p. 397). I think the importance of measurement is solidified by its inclusion in the cross-curriculum priorities of the Australian curriculum and it has a strong focus on use in authentic contexts. These include investigating “measurement concepts in Aboriginal and Torres Strait Islander contexts” (Education Services Australia, n.d., para 2); developing understanding of measurement knowledge and examples from the Asia region (Education Services Australia, n.d., para 3); and applying measurement “to gauge local ecosystem health” (Education Services Australia, n.d., para 4). From childhood, measurement is the most memorable area of mathematics for me. That is due to the hands-on activities we used at school. In addition to using the trundle wheel in year 4, we also had coloured water and beakers for different volume activities. In my classroom, I will focus on providing multiple opportunities for students to explore and experiment with different measures, along with activities that support estimating, comparing and the use of measurement instruments.
References
Education Services Australia. (n.d.). Mathematics: Cross-curriculum priorities. Retrieved from http://www.australiancurriculum.edu.au/mathematics/cross-
curriculum-priorities
Preston, R. & Thompson, T. (2004). Integrating measurement across the curriculum. Mathematics Teaching in the Middle School, 9(8), 436-441. Retrieved
from http://www.jstor.org.ezproxy2.acu.edu.au/stable/41181964?seq=6#page_scan_tab_contents
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson
Education.
References
Education Services Australia. (n.d.). Mathematics: Cross-curriculum priorities. Retrieved from http://www.australiancurriculum.edu.au/mathematics/cross-
curriculum-priorities
Preston, R. & Thompson, T. (2004). Integrating measurement across the curriculum. Mathematics Teaching in the Middle School, 9(8), 436-441. Retrieved
from http://www.jstor.org.ezproxy2.acu.edu.au/stable/41181964?seq=6#page_scan_tab_contents
Van de Walle, J., Karp, K., & Bay-Williams, J. (2014). Elementary and middle school mathematics teaching developmentally (8th ed.). Essex, England: Pearson
Education.
Week 11
The Early Years Framework and Australian Curriculum has a strong focus on geometry throughout Primary School (Charles Sturt University Early Years Learning Framework Consortium, 2009; Education Services Australia, n.d.). This is evident in the Australian TIMMS results of 2011 which showed that year 4 students were “strongest in geometry shapes and measures” (Thomson, Hillman, Wernert, Schmid, Buckley, & Munene, 2012, p. 9). Additionally, there is an extensive range of hands-on manipulatives including geometry software that allows students to explore, visualise, reason and make sense of geometry (Teaching Geometry, 2011). Nason, Chalmers and Yeh’s (2012) research of literature showed that teachers require sound pedagogical-content knowledge to engage students in co-constructed mathematical knowledge. Although I really enjoy geometry and feel somewhat confident about the subject-matter, it is such a broad strand of mathematics that I feel I will need to continue expanding my knowledge to successfully assist my students. Geometry can be recognised in all areas of society including architecture so I feel it would be beneficial to include these in lessons. Experiences that develop an understanding of the close connection between geometry and measurement should be included in classroom activities (Steele, 2013). I will look at the geometry and measurement sub-strands collectively so that a strong understanding of the connection between shapes and measurements are established.
References
Charles Sturt University Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective communicators. Retrieved
from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=3#page=3
Nason, R., Chalmers, C., & Yeh, A. (2012). Facilitating growth in prospective teachers’ knowledge: Teaching geometry in primary schools. Journal of
Mathematics Teacher Education, 15(3), 227-249. doi: 10.1007/s10857-012-9209-0
Steele, M. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks.
Journal of Mathematics Teacher Education, 16(4),245-268. doi: 10.1007/s10857-012-9230-3
Teaching Geometry. (2011). The Mathematics Teacher, 105(4), 244. doi: 10.5951/mathteacher.105.4.0244
Thomson, S., Hillman, K., Wernert, N., Schmid, M., Buckley, S., & Munene, A. (2012). Monitoring Australian year 4 student achievement internationally: TIMSS
and PIRLS 2011. Retrieved from http://www.acer.edu.au/files/TIMSS-PIRLS_Monitoring-Australian-Year-4-Student-Achievement.pdf
References
Charles Sturt University Early Years Learning Framework Consortium. (2009). Document 16 outcome 5: Children are effective communicators. Retrieved
from http://www.earlyyears.sa.edu.au/files/links/16_Outcome_5.pdf
Education Services Australia. (n.d.) Curriculum. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=3#page=3
Nason, R., Chalmers, C., & Yeh, A. (2012). Facilitating growth in prospective teachers’ knowledge: Teaching geometry in primary schools. Journal of
Mathematics Teacher Education, 15(3), 227-249. doi: 10.1007/s10857-012-9209-0
Steele, M. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks.
Journal of Mathematics Teacher Education, 16(4),245-268. doi: 10.1007/s10857-012-9230-3
Teaching Geometry. (2011). The Mathematics Teacher, 105(4), 244. doi: 10.5951/mathteacher.105.4.0244
Thomson, S., Hillman, K., Wernert, N., Schmid, M., Buckley, S., & Munene, A. (2012). Monitoring Australian year 4 student achievement internationally: TIMSS
and PIRLS 2011. Retrieved from http://www.acer.edu.au/files/TIMSS-PIRLS_Monitoring-Australian-Year-4-Student-Achievement.pdf