Discussion+Forum

__Discussion Forum__

"Numeracy empowers people by giving them tools to think for themselves, to ask intelligent questions of experts, and to comfront authority confidenty". (Steen, 2001, p.2) When reading through Booker's Textbook this week I was surprised to learn that each of the maths strands play a crucial part to assisting the development in other strands. For example for students to be able to or subtract decimals they need to have a strong understanding of place value and the order of value numbers after the decimal point hold... e.g. 34.767 can be recognised as 3 tens, 4 ones, 7 tenths and 67 hundreds. Before this week I had naively assumed that fractions and decimals were one component of maths and patterns and algebra were another without any real connection. It goes to show why students who haven't established some of those core understandings in the earlier years such as place value then fail to comprehend new concepts such as 'adding decimals'.
 * Wk 1**
 * 29/02/12**

Regards Talia

Number: //The logic behind the Arabic Algorithms// Found it incredibly interesting learning that the reason 1 is one 2 is two, etc was based on the amount of angles each number shape had. See the PowerPoint below:
 * Wk 2**
 * 7/03/12**

Regards Talia

After perusing The Australian Curriculum – Mathematics in an effort to establish some early understandings of the Number and Algebra strand I discovered the Glossary section of the curriculum. This section could be very useful as it offers clear and concise definitions of all things mathematics. This glossary may be particularly useful if you do not have a mathematics dictionary.
 * 8/03/12**

Matt. Upon reading this I went searching and have also found this very useful as it contains all the necessary vocabulary and definitions needed to implement the curriculum at all levels. better to have the one cocument in front of you whilst planning lessons than having to shift back and forth opening and closing books and windows to find the information. I have printed it a bound it into a booklet which I carry with me and have used more than once in my prac classroom this year. A valuable resource indeed. Thanks for pointing it out Matt
 * 10/03/12**

Regards Brooke

Hey Guys, Was flicking through some more of Booker's "Teaching Primary Mathematics" textbook and found an interesting framework for establishing **early mathematical thinking:**
 * 8/03/12**
 * Conservation of Number- the ability to determine how many objects regardless of their spatial arrangement.
 * Classifying- grouping according to specified criteria such as colour, shape, size, texture, thickness or number.
 * Comparing- establishing a relationship between two objects on the basis of some specific attribute such as height, mass, thickness, texture, number.
 * Ordering- ordering builds on comparing.
 * Patterning- the ability to recognise patterns is basic to mathematical insight.

(Booker, et. 2004, page 87). Any thoughts on how effective this might be in the older years also?

Regards Talia


 * Wk 3**
 * 12/03/12**

**Numeracy Analysis:**

The development of the Australian National Curriculum (ACARA) began when educators noticed a significant gab in the results of students’ achievement in Literacy and Numeracy from approximately year 3 onwards. Students in years 6 and 7 were achieving a variation that were as far as five years apart; considering the lowest and highest scores. In Queensland specifically students were on average 6 months behind every other state in Australia due to starting school in year 1 rather than a foundation year of school or prep. Another implication was the approach to learning and __assessment__ in the early years. Teachers would observe students literacy and numeracy achievements rather than standardised testing. “Over time systems and schools have recognised the value of utilising a variety of assessment tasks for different purposes” and “they also recognise that assessment tasks should reflect the diversity of experiences, needs and interests of children, including social, cultural and economic differences” (Commonwealth Department of Education and Training, n.d.).

__Now__ because of ACARA there will expectantly be a change in the imbalance of literacy and numeracy results, a greater focus of teacher’s professional competencies and development and education authorities strengthening and establishing a variety of programs and initiatives to enhance numeracy outcomes in schools. (Commonwealth Department of Education and Training, n.d.).

Regards Talia

=The Difficulties of Fractions - An interesting thought for Pre-service teachers = It has become evident through a number of readings I have read associated with fractions and decimals that most students find this a difficult area of mathematics to understand. The word fraction itself refers to the different mathematical ways of dealing with parts of things (Booker et al, 2004). This is where the difficulty of understanding fractions and decimals lay, the fact that students have to acquire the knowledge of part of whole and whole number relationship. Common fractions, decimal fractions and per cent are all part and used in everyday life. Fractions taught and learnt at school however go beyond this and exceed the practical point. Why then do students need to acquire the skills of these fractions – beyond practical use? The answer lies with Booker et al (2004) who insists that these skills are the foundation and provide the basis for the development for further mathematics. The challenge of learning and teaching fractions is supported by Smith. Smith (2002, Cited in, Booker, 2004) states there is no area of mathematics that is as mathematically rich, cognitively complicated and difficult to teach as fractions. The teaching of the language and skills from the beginning (Year 1) and beyond is imperative for the later years. Booker et al (2004) outlines the importance of teachers recognising the difficulties young students have focusing on ‘the size of parts’ rather than their occurrence as ‘part of a larger whole.’ As a pre-service teacher these readings have outlined to me the importance of starting from the beginning to ensure all students understand the meaning of fractions. Students’ progression should be continually measured through practical experiences that develop their higher order thinking around the concept of mathematics. ** References ** Booker, G., Bond, D., Sparrow, L., & Swan, P. (2004). //Teaching primary mathematics (3rd ed.).// Frenchs Forest, New South Wales: Pearson Education.

Smith, J. P. (2002). The Development of Students' Knowledge of Fractions and Ratios'. In G. Booker, D. Bond, L. Sparrow, & P. Swan, //Teaching primary mathematics// (p. 133). Frenchs Forest, New South Wales: Pearson Education. ** Matt : ) **


 * 12/03/12**

When doing some research into how and why the Australian Curriculum was developed I came across an interesting appendix:



If you look at the line for __Queensland__ there is no Assessment or resources that are expected to be used and as well as this students started school a year later than most other states. This Graph is from a government document developed early 2000's- As a result of Queensland's low scores and achievements we now have Preparatory before Year 1 so students across Australian will soon be working at the same level and hopefully achieving equal scores for their age.

Regards Talia


 * Wk 4**
 * 22/03/12**

Hi Everyone,

I've put up a little analysis i've been working on over the past few weeks- What it discusses is fractions and decimals and how current year 6 students are working through a variety of sums. It can be found in the **"Fractions and Decimals (Sub- Strand)"** section on the side bar and includes some work samples. At my next prac visit i'm going to give Rob Proffit- White's "Think Tables" a go with my year 6 class and i'll let you know how they do and hopefully provide some photos. For now though i'd like to show you an example of a Year 6 girls work- This was a fractions question she answered as part of a mid term test- As you can see in the picture although she showed her working out and provided the right answer (Top right corner 1/ 10) she was unable to communicate how this on the page and therefore it wasn't evident to the teacher that she actually knew what the answer was. When the teacher discussed it with her she could explain her working but couldn't articulate that in her response. The teacher encouraged her to next time write a conclusive sentence along the lines of "9/10 of the class had black and brown hair and 1/10 of the class had neither". See Below:



Regards

Talia :)



Halves and Quarters- We already know that! As a pre-service teacher I found the following very interesting and insightful for when the time comes to teach young students the concepts of halves and quarters. It would seem that most children even before setting foot inside a classroom have some understanding of fractions. For example children can associate with half an orange or a quarter of a sandwich. However Siemon et al (2011) refers to this association of halves and quarters as merely a connection with the language and not a deep understanding of the ideas involved. As teachers it becomes our responsibility to ensure that we convert this association with the language into understanding and acquisition of the key fundamentals involved with fractions. Siemon (2011) outlines the following points as the key ideas involved in making sense of fraction: Siemon (2011, P.397) In the classroom a variety of resources (counters, string, plasticine and cardboard) should be manipulated in different ways to focus on students understanding the concepts of equal and unequal, the naming of equal parts and seeing the part in relation to the whole. Activities should be hands on, interactive and enjoyable for students to begin the difficult concept of fractions. ** References ** Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2011). //Teaching Mathematics: Foundations to Middle Years.// South Melbourne, Victoria: Oxford University Press.
 * Equal parts are necessary
 * The number of parts name the parts
 * There is an inverse relationship between the number of parts and the size of each part
 * The size of each part depends on the size of the whole

Matt : )

Hi Guys,

Just as a note on the side.

I must say that I have found this assignment to be practical and extremely valuable moving forward into next year. It has not only opened my eyes to the complexities surrounding the 'Number and Algebra' strand and 'fractions and decimals' sub-strand of the Australian curriculum but to the way each year of schooling supports one and other and the way each strand is reliant of each other in terms of the application of skills and students thought processors.

I have found working with the wiki a little frustrating in terms of formatting and copy and pasting from word. On most occasions the formatting will change from word to wiki. This has made it hard for work to appear well presented.

Matt.