Week+2+-+School+mathematics+in+today's+world

__**complLearning Activity 2.1: Preparing yourself for effective learning**__

[] Kendall Storey 5.6.11

http://vels.vcaa.vic.edu.au/maths/index.html Adam T 07.06.11

http://www.qsa.qld.edu.au/7296.html - CHORY TYRRELL 09/06

[] – SACSA maths framework [] - AU curriculum maths - SuzanneW 09/06/2011

[] - Sarah Wright 9.6.11

[] - Kerrie Wyer 11/6/11

__**Learning Activity 2.2: School mathematics in a changing world**__ Ideas and examples that are familiar to me include; Maths is a requirement when dealing with every day situations. As levels of education progress, the content of the mathematics subject becomes more complicated. Students must have a sound knowledge of previous learning to be successful learners.( Heidi. 03/06)

Ideas that are new to me include; Children being assessed to increase their mathematics knowledge. The fact that what is taught may differ due to curriculum, the individual and the outer environment.

Questions. I know that all children can learn mathematics, but how do I implement the correct strategies for each individual student?( Heidi, 03/06)


 * Idea and examples thatare new to me: **

Mathscurriculum was influenced by the beliefs about how children learn, and ultimatelyabout how they should be taught

Mathematicalproficiency describes what it means to learn mathematics successfully

Takeadvantage of professional development opportunities.

Agood teacher who is willing to work with you is an invaluable resource


 * Ideas and examples thatare familiar to me: **

Mathematicsis about numbers

Toteach maths teacher must know more than just maths

The web can provide resources

Doingmaths and teaching maths are 2 different things

Kendall Storey 6.6.11

Achor 07/06/2011
 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * * Mathematics is a study of patterns and relationships
 * Mathematics is a tool useful in everyday life.
 * Younger children’s experiences with numbers commence with counting followed by fractions || * The guidelines on how to teach mathematics differ in response to different state curriculums. ||
 * **Questions I have and related things I do not understand from my reading**If schools are to be held accountable for students learning, what role should the parents play in teaching maths. ||

**//Learning Activity 2.2 Record Chart: School mathematics in a changing world//** Interactive white boards || Adam T 07.06.11
 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * Learning addition and subtraction || Understanding how mathematical equations work rather than memorising them.Understanding the multiplication theories rather than memorising the tables Calculators were not used in primary school when I was younger
 * **Questions I have and related things I do not understand from my reading**I don't understand why computers and calculators have the same weighting over working out equations using pen and paper and counters. ||

Learning Log // – CHORY TYRRELL 09/06 //
 * ** Ideas and examples that are **// familiar //** to me from my own experiences with mathematics learning and teaching ** || ** Ideas and examples related to mathematics learning and teaching that are **// new //** to me ** ||
 * * The many resources available to support the teaching, learning and assessment practices
 * Principles and standards available for guiding educational authorities planning
 * Concrete experiences with mathematics
 * Learning from simpler concepts and building on them to more difficult ideas || * Needs of the subject, needs of the child, needs of society
 * The different ways you can view mathematics as a subject, whether a tool, a language, or something else. ||
 * ** Questions I have and related things I do not understand from my reading ** Nothing. ||


 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * * The need to incorporate practical and real world experiences when teaching
 * Mathematics is its own language
 * Consider the needs of the child when teaching mathematics
 * That texts provided for students may not always be the optimal learning material, take them with a grain of salt and consider what the needs of the student are
 * That mathematics and the use thereof is empowering || * The five mathematical process strands: problem solving, communication, reasoning and proof, connections, representations
 * Considering the needs of society and the subject, not just the needs of the child.
 * Mathematics has changed as society has changed ||
 * **Questions I have and related things I do not understand from my reading**-Nil- Suzanne W 09/06/2011 ||

**Learning Activity 2.2**

**Questions I have and related things I do not understand from my reading?** **I know that showing students how maths is relevant to their everyday lives will help them understand its necessity, but how exactly can I show them that certain things are relevant, what exercises or methods can I use?** **SARAH WRIGHT 9.6.11** **Please refer to DB as I cannot paste table into wikki for some reason. Kerrie Wyer 11/6/11.**
 * **Ideas and examples that is familiar to me from my own experiences with mathematics learning and teaching.** || **Ideas and examples related to mathematics learning and teaching that are new to me** ||
 * * **Mathematics is a tool**
 * **The best way to teach mathematics is to use real world activities and examples.** || * **We need maths in everyday life, from the simpliest of tasks to the most complicated.**
 * **What determines the mathematics being taught – needs of the subject, needs of the student and needs of society.**
 * **Topics have been taught in isolation – should be taught showing how they are related to each other and how they are relevant in every day life**
 * **Previously thought not all students can learn mathematics** ||

__**Learning Activity 2.3: School mathematics from the Australian Curriculum: Mathematics and in your local context**__ Key mathematics content; NSW, Working mathematically, number patterns and algebra, measurement and data, space and geometry. Aus, Number and algebra, Statistics and probability, measurement and geometry

Proficiencies and processes AUS, Understanding, Problem solving and reasoning. (ACARA, 2010) NSW, To read, ask questions and describe. (nsw board of studies, 2009).

Key principles (Heidi 03/06)

NSW curriculum:• collecting, analysing and organising information• communicating ideas and information• planning and organising activities• working with others and in teams• using mathematical ideas and techniques• solving problems• using technology || Achor 07/06/2011
 * **Key mathematics content in each**Australian curriculum: Mathematics provides students with essential mathematical skills and knowledge in Number and Algebra, Measurement and Geometry, and Statistics and Probability.NSW curriculum: Working Mathematically, and the five content strands, Number, Patterns and Algebra, Data, Measurement, and Space and Geometry. ||
 * **Key mathematics proficiencies or processes in each**Australian curriculum: * Are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens
 * Develop an increasingly sophisticated understanding of mathematical concepts and fluency with processes, and are able to pose and solve problems and reason in Number and Algebra, Measurement and Geometry, and Statistics and Probability
 * Recognise connections between the areas of mathematics and other disciplines and appreciate mathematics as an accessible and enjoyable discipline to study.
 * **Key principles related to mathematics learning, teaching, and assessment in each**NSW Curriculum: As children engage in daily life they construct mathematicalunderstanding that is often enhanced by planned mathematicalexperiences in prior-to-school settings. ||
 * **Key aspects of the role of technology in mathematics learning and teaching in each**NSW Curriculum: Information and Communication Technology (ICT) has been developed with the significant utilisation of mathematics, and a range of opportunities exists within the teaching and learning of mathematics to utilise ICT. Forexample, spreadsheets can be used to record, organise and manipulate numbers in Number, Patterns and Algebra,and Data. ||

CHORY TYRRELL - 09/06 • Knowledge and understanding • Thinking and reasoning • Communicating • Reflecting. AUS: **Understanding ** Students build a robust knowledge of adaptable and transferable mathematical concepts. They make connections between related concepts and progressively apply the familiar to develop new ideas. They develop an understanding of the relationship between the ‘why’ and the ‘how’ of mathematics. Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and when they interpret mathematical information.
 * ** Key mathematics content in each ** QLD: Number, Algebra, Measurement, Chance and Data, Space.AUS: Number and Algebra, Measurement and Geometry, Statistics and Probability ||
 * ** Key mathematics proficiencies or processes in each ****QLD: Students use the essential processes of **Ways of working **to develop and demonstrate their ****Knowledge and understanding**. They develop their ability to work mathematically and build on their prior understanding by individually and collaboratively planning and conducting mathematical investigations; by posing and solving mathematical questions, problems and issues; and by challenging the reasoning and perspectives of others. They reflect on their learning and transfer their thinking and reasoning to a range of real-life and purely mathematical situations.

Fluency
Students develop skills in choosing appropriate procedures, carrying out procedures flexibly, accurately, efficiently and appropriately, and recalling factual knowledge and concepts readily. Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, when they choose appropriate methods and approximations, when they recall definitions and regularly use facts, and when they can manipulate expressions and equations to find solutions.

Problem Solving
Students develop the ability to make choices, interpret, formulate, model and investigate problem situations, and communicate solutions effectively. Students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.

Reasoning
Students develop an increasingly sophisticated [|capacity] for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising. Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false and when they compare and contrast related ideas and explain their choices. || **Critical and creative thinking ** * **Equity ** * **Cross-curriculum ** * **Sustainability ** * **Ethical behaviour **
 * ** Key principles related to mathematics learning, teaching, and assessment in each **** QLD: Having difficulty finding this. **** AUS: ** *
 * **Personal and social competence **
 * ** Key aspects of the role of technology in mathematics learning and teaching in each ** QLD: Students select and use tools and technologies, including information and communication technologies (ICTs). They routinely demonstrate an autonomous and purposeful use of ICTs to inquire, create and communicate within mathematical contexts. <span style="font-family: Times New Roman,serif;">AUS: Students develop ICT competence as they learn to use ICT effectively and appropriately when investigating, creating and communicating ideas and information at school, at home, at work and in their communities. ICT competence allows students to solve problems and readily perform previously onerous tasks. Calculators of all types, from the simple four-operations versions to more complex graphical and CAS calculators, can be used to make calculations, draw graphs and interpret data in ways that have previously not been possible. Digital technologies, such as spreadsheets, dynamic geometry software and computer algebra software, can engage students and promote understanding of key concepts. However, there will be occasions where teachers will ask students to undertake tasks without using technology. ||
 * **Questions I have and related things I do not understand from my reading of the textbook and my examination of the curriculum documents**None. ||
 * **Questions I have and related things I do not understand from my reading of the textbook and my examination of the curriculum documents**None. ||

**Key mathematics content** **Vi c: ** numbers, space, measurement, chance & data, structure, working mathematically ** Aust :** numbers and algebra, measurement and geometry, and statistics and probability.

** Proficiencies and processes **

**Vic:** students sort, count and compare concrete objects, and draw, arrange and manipulate simple shapes and objects. They use and describe basic measurement concepts related to themselves or familiar objects. Students begin to recognise the structure of number and develop cognitive understanding of number as an object in its own right, and extend their number knowledge and representation of mathematical processes beyond their immediate environment. They can recognise and work with simple patterns in number and space and recognise the use of mathematics in daily life. **Aust:** //Understanding// includes connecting names, numerals and quantities, //Fluency// includes counting numbers in sequences readily, continuing patterns, and comparing the lengths of objects directly, //Problem Solving// includes using materials to model authentic problems, sorting objects, using familiar counting sequences to solve unfamiliar problems, and discussing the reasonableness of the answer, //Reasoning// includes explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparison of length.

**Key principles related to mathematics learning, teaching, and assessment**

**Vic:** //Structure// does not begin as a dimension with explicit standards until Level 3, the precursor aspects of mathematical structure, that is what students should know and be able to do, in relation to //set//, //logic//, //function// and //algebra// are naturally embedded in the other dimensions at Levels 1 and 2. As noted in the introduction to the Mathematics standards: Mathematical reasoning and thinking underpins all aspects of school mathematics, including problem posing, problem solving, investigation and modelling. It encompasses the development of algorithms for computation, formulation of problems, making and testing conjectures, and the development of abstractions for further investigation. Computation and proof are essential and complementary aspects of mathematics that enable students to develop thinking skills directed toward explaining, understanding and using mathematical concepts, structures and objects. They provide a framework for the development of mathematical skills and techniques exemplified in the use of algorithms for computation and for the development of general case arguments.

**Key aspects of the role of technology in mathematics learning and teaching**

**Vic:** The role of technology in the Mathematics domain of the VELS is clearly outlined in the overview of each of its five dimensions, and is highlighted in the following excerpts: Number - Principal operations for computation with number include various algorithms for addition (aggregation), subtraction (disaggregation) and the related operations of multiplication, division and exponentiation carried out mentally, by hand using written algorithms, and using calculators, spreadsheets or other numeric processors for calculation. Space: representation, construction and transformation by hand using drawing instruments, and also by using dynamic geometry technology. Measurement, chance and data: Various technologies are used to measure. Data-loggers for direct and indirect measurement and related technologies for the subsequent analysis of data, Structure: and technology-assisted calculation and symbolic manipulation by calculators, spreadsheets or computer algebra systems, Working Mathematically: mental and using technology-assisted methods Adam T 07.06.11

AU: AU: AU: AU:
 * **Key mathematics content in each****SACSA:** * Exploring, analysing and modelling data
 * Measurement
 * Number
 * Pattern and algebraic reasoning
 * Spatial sense and geometric reasoning
 * Number and algebra - the understanding of the number system and their functions. Used to "investigate, solve problems and communicate their reasoning" (ACARA, n.d.)
 * Measurement and geometry - dealing with size and shape, area, speed and density
 * Statistics and probablility - the analysis of data, the drawing of inferences from data and making judgements based on the probablilty of data ||
 * **Key mathematics proficiencies or processes in each**SACSA: * problem solving
 * reasoning and proof
 * communication via mathematics
 * connections - that is, building upon previous knowledge and the understanding of connections between different mathematical ideas
 * representation - organising and recording
 * Understanding
 * Fluency
 * Problem solving
 * Reasoning ||
 * **Key principles related to mathematics learning, teaching, and assessment in each****SACSA:** * That learners have the "ability to understand, critically respond to and use mathematics in different social, cultural and work contexts" (SACSA, 2001). Teachers have as a result the responsibility to teach children to be able to do this
 * Assessment is based upon the Department of Education and Children's Services (DECS) guidelines for reception through to year 10. This advises teachers to take into account the diverse needs of students, the differing needs of individuals and groups and to base assessment around these as a beginning point. The amount of assessment, whether summative or formative is decided by the teacher, culminating in a report twice yearly where students are graded with an A-E level.
 * Periodic sampling of students work for National Assessment Program (NAP)
 * Preparation of students for NAPLAN testing
 * Twice yearly reports for parents/carers showing student achievement (not clear as to how this is shown, whether by percentage, letter grade, pass/fail etc)
 * Ongoing formative and summative classroom testing as set by the teacher ||
 * **Key aspects of the role of technology in mathematics learning and teaching in each****SACSA:** * SACSA integrates into the curriculum wherever possible the use of ICT - whether for research, presentation, and the use of computer software in order to create appropraite graphical representation of work (ie charts, graphs etc). The use of ICT is not clear whether this includes calculators
 * Use of ICT integrated into curriculum for research, creating ideas, communication, and graphical representation of work. AU currciulcum also makes mention of the use of calculators, which students may be asked at time to put aside in order to do 'pencil and paper' type work. ||
 * **Questions I have and related things I do not understand from my reading of the textbook and my examination of the curriculum documents****-Nil-**SuzanneW 09/06/2011 ||
 * Learning Activity 2.3 **
 * Key Mathematics content in each **
 * NSW – **
 * Mathematics involves the development of students’ thinking, understanding, competence and **
 * confidence in the application of mathematics. The five broad strands of Mathematics are: **
 * ** Working Mathematically **
 * ** Number **
 * ** Patterns and Algebra **
 * ** Measurement and Data **
 * ** Space and Geometry **
 * AUSTRALIAN – **
 * The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in // [|Number] and Algebra//, //Measurement and Geometry//, and //Statistics and Probability.// **


 * Key Mathematics proficiencies or processes in each **
 * NSW – **
 * • collecting, analysing and organising information **
 * • communicating ideas and information **
 * • planning and organising activities **
 * • working with others and in teams **
 * • using mathematical ideas and techniques **
 * • solving problems **
 * • using technology. **


 * AUSTRALIA – **
 * ** are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives and as active citizens **
 * ** develop an increasingly sophisticated understanding of mathematical concepts and fluency with processes, and are able to pose and solve problems and reason in //[|Number] and Algebra, Measurement and Geometry, and Statistics and [|Probability]// **
 * ** recognise connections between the areas of mathematics and other disciplines and appreciate mathematics as an accessible and enjoyable discipline to study. **


 * Key principles related to mathematics learning, teaching and assessment in each **
 * NSW **
 * ** Set out a clear picture of the knowledge, skills and understanding that each student should develop at each stage of primary school. They encompass, at a level broader than syllabus outcomes, the nature (key concepts and content) and scope (breadth, depth and rigour) of learning in Kindergarten to Year 6. They do not add new content or concepts to the K–6 curriculum **
 * ** Provide an answer to the question ‘What must be taught?’ in all schools. Using them you can be confident that you are delivering the most important learning for students. They place an emphasis on the fundamental skills needed to succeed at and beyond school, particularly in the areas of literacy and numeracy **
 * ** Give you the freedom to focus on the diverse learning needs of your students. Describing what must be taught in this way will ensure that important concepts and content such as Australian history and democracy, scientific investigation, cultural diversity, Aboriginal history and culture, and safe and healthy lifestyle are included in teaching and learning programs. By focusing on the statements you can be sure that you are meeting the common curriculum requirements in each key learning area **
 * ** Guide you in planning to meet the needs of students with varying ability levels and learning needs. You can select and use the syllabus outcomes and content that best suit the learning needs of your students and adjust teaching strategies and what it is that you ask students to produce **
 * ** Provide a basis for assessing, reporting and discussing student progress. **


 * AUSTRALIA **

** The curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently. ** ** The Australian Curriculum: Mathematics ensures that the links between the various components of mathematics, as well as the relationship between mathematics and other disciplines, are made clear. Mathematics is composed of [|multiple] but interrelated and interdependent concepts and systems which students apply beyond the mathematics classroom. In science, for example, understanding sources of error and their impact on the confidence of conclusions is vital, as is the use of mathematical models in other disciplines. In geography, interpretation of [|data] underpins the study of human populations and their physical environments; in history, students need to be able to imagine timelines and time frames to reconcile related events; and in English, deriving quantitative and spatial information is an important aspect of making meaning of texts. **

** The curriculum anticipates that schools will ensure all students benefit from access to the power of mathematical reasoning and learn to apply their mathematical understanding creatively and efficiently. The mathematics curriculum provides students with carefully paced, in-depth study of critical skills and concepts. It encourages teachers to help students become self-motivated, confident learners through inquiry and active participation in challenging and engaging experiences. **

** Key aspects of the role of technology in mathematics learning and teaching in ** ** NSW ** ** Students will be able to partake in ICT (Information, Communication Technology) which has been developed with the significant utilisation of mathematics. ** ** AUSTRALIA ** ** Digital technologies are facilitating this expansion of ideas and providing access to new tools for continuing mathematical exploration and invention. The curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently. SARAH WRIGHT 9.6.11 **

**Please refer to DB as I cant past into this wikki. Kerrie Wyer 11/6/11.**

__**Learning Activity 2.4: Using technology in mathematics learning and teaching**__ In the illuminations website, I learnt that Euler’s formula enables one to calculate the number of faces, edges, and vertices of geometric solids. The formula is: //faces// + //vertices// = //edges// + 2 Shown as: //F// + //V// - //E// = 2. This formula could be used for spatial reasoning, or problem solving lessons.

I found the Ask Dr Maths website a wealth of information. I like that it offers different responses to the same question, highlighting different ways of looking at things. As a teacher this will be useful to accommodate student diversity and allow lessons to be catered to the individuals. Vicki 6/6/11

1.On the illumination website I have learnt about semi regular and regular tessellations. The lesson is aimed at 6 to 8 yr. olds. A regular tessellation is made up of congruent polygons. A variety of different polygons is called a semi regular tessellation. Tessellations are named by how many sides it has for example a three polygon will be identified as 6.6.6 because each has 6 sides. A semi regular tessellation with 2 triangles and 3 squares would be identified as 3.3.4.4. Because the triangles have 3 sides each and the squares have 4 sides each. 2.Unable to log into Learning Federation at present time. 3.Dr. Math is a very user friendly website that allows students from primary school well into when they are in university or finished school. The explanations are easy to understand so the student that is asking the question would not have to re-ask the question. Students can also search questions and answers according to maths subject. This website is a useful tool in teaching because it incorporates the use of technology and maths. Students can play a more active role in their learning by reading the answer to their question. Achor 07/06/2011

The illuminations website had some great games and lesson plans for maths related geometry. The lesson plan I found interesting was "I've seen that Shape Before". The geometric realted activity I enjoyed was "Geosolids" although I must admit that I wouldn't have known about polyhedrons as a primary school student. The polyhedron looks at the relationship between the number of faces, vertices, and edges it has. Adam T 08.06.11

NB# Did not know how to log on to the learning federation site to find L9994

Ask Dr Math has a wealth of information regarding teaching topics, lesson plan ideas as well as online and practical games/activities. This website offers support and can help teachers formulate maths related lesson plans from primary through to secondary school. Adam T 08.06.11

<span style="color: #ff0000; font-family: Times New Roman,serif;">Locate an activity or lesson that is focused on an aspect of primary school geometry that you want to review or learn more about.

Interactive Geometry Dictionary: Areas in Geometry

This java applet is a short, interactive activity where the user can discover the essential elements that are identified and used when measuring the area of a parallelogram, rectangle and triangle. The brief for this activity mentioned the interrelation that the three shapes have with one another in working out the area. “You can find the area of a triangle using the area of a parallelogram, which in turn can be found using the area of a rectangle.” This activity encourages exploration in geometry. Sourced from: []

The Le@rning Federation

I found this learning object to be extremely fun and engaging. The viewfinder: flip side is a colourful, interactivity activity that enables the user to explore visual perspectives of solids such as cylinders, cones and cuboids. It is suitable from year levels 4 to 9. This would fit in the Space content strand for most curricula. I like how there is a glossary incorporated in the learning object, allowing the user to research immediately any words they do not understand.

Ask Dr. Math.

I loved using this online resource. It is helpful for all people interested in mathematics, whether they be teachers, students or mathematicians. The website has been around on the internet for a long time, and it contains a large wealth of information that would surely be of value to many people. Questions can be answered quickly from my experience. Be aware that your question may have already been answered.- CHORY TYRRELL 09/06

**Learning Activity 2.4** **On the Illumination website - I learnt something I had forgotten, how to find the area of a parallelogram using what I know about finding the area of a rectangle. Very useful for both student and teacher.**

**Had trouble logging into Learning Federation - will try again.**

**After jumping on the Dr. Math website, I found questions asked by students, teachers and teachers who were teaching a class by asking Dr. Math. I think the most valuable point here is an insight into the perspectives that students have of the maths questions they are asking. Their own personal interpretation of a question that to a teacher may seem black and white, to a child can be misconstrued or misunderstood. That misunderstanding could come from previous idea’s they had, or that they did not understand the instructions correctly. SARAH WRIGHT**

Illuminations - activity chosen: A Tale of Two Stories (http://illuminations.nctm.org/LessonDetail.aspx?ID=L294) This was a good recap on what a Venn diagram was. This is something that I had forgotten since my primary mathematical learning years.

Learning Federation: like others having difficulty with log in. Will continue to try this over the coming week.

Ask Dr Math: I looked at the query of why multiplyin by zero is always zero ie 0x0=0, 1x0=0 etc. The answer to the query was very thorough by Dr Math. While the answers to questions are quickly responded to, and are helpful, I was surprised at just how much focus I needed to concentrate on parts of the answer - it's been a long while since my brain has looked at proofs in this way, and it does make sense, but it means that my own understanding of queries such as these need to be up to date and comprehensible. This is not the type of answer I can give to a primary class, but it is the type of answer I can use to brush up my own understanding and bring the answer to a student who may have asked this in simpler terms. It's easy to foresee that this site will be a useful resource in the years to come.

Suzanne 12/06/2011

__**FINAL SUBMISSION FOR WEEK 2, COMPILED AND COMPLETED**__ Hi Everyone, I am compiling this weeks submission. This weeks question is:

// The mathematics curriculum. // <span style="background: none repeat scroll 0% 0% yellow; color: black; font-family: 'Calibri','sans-serif'; font-size: 13px; margin: 0cm 0cm 10pt;">Each of you will have a different curriculum to view due to your different locations. However the //key principles related to mathematics learning, teaching, and assessment// will have many common links across each state. After completing task 2.3 discuss amongst your MathMates your ideas of what the key principles are and then compile a list of 3 main principles related to learning, teaching and assessment.

__ Can you please provide me with your 3 principles, and the reason why, so I can compile our submission. If possible can you provide your input by Thurs night, as I will post a draft here for review on Fri, before submitting to db on Sun. Below is my individual contribution: __

I see the key principles for a mathematics curriculum as: focused, coherent, and well articulated. The first principle, focused, requires the curriculum to present concepts that are relevant and suitable to student’s grade, and age (Reys, Lindquist, Lambdin, & Smith, 2009). The New South Wales (NSW) curriculum achieves this by introducing basic mathematical concepts in early stage 1, before moving to more complex ideas in later stages. The second principle, coherent, ensures that mathematical ideas are effectively integrated together (Reys et al., 2009). Doing so enables students to apply their mathematical learnings in multiple contexts, which is a factor influencing the NSW mathematics curriculum rationale (Board of Studies New South Wales, 2006). Finally, a well articulated curriculum allows students to build on previous knowledge. Again, the NSW mathematics curriculum accommodates this principle and demonstrates consideration of Piaget’s learning theories (Eggen & Kauchak, 2010). Vicki 6/6/11.

References

Board of Studies New South Wales. (2006, May). //K-6 Mathematics syllabus//. Retrieved from Board of Studies New South Wales: [|http://k6.boardofstudies.nsw.edu.au]

Eggen, P., & Kauchak, D. (2010). //Educational psychology - Windows on classrooms (8th ed.) - Pearson international edition.// New Jersey, USA: Pearson Education.

Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons.

The Victorian Essential Learning Standards (VELS) state that "Mathematical Reasoning and Thinking" underpins all aspects of school mathematics, including problem posing, problem solving, investigation and modelling. Reasoning encompasses the development of algorithms for computation, formulation of problems, making and testing conjectures, and the development of abstractions for further investigation.Computation and proof are essential and complementary aspects of mathematics that enable students to develop thinking skills directed toward explaining, understanding and using mathematical concepts, structures and objects. These provide a framework for the development of mathematical skills and techniques exemplified in the use of algorithms for computation (Victorian Essential Learning Standards, 2009). Assessment should be designed to make student thinking visible. While it is important to monitor student progress, consideration should be given to developing a classroom culture that encourages and rewards risk-taking and experimentation. When developing assessment tasks, students should also demonstrate that they are assessing concepts and higher order thinking rather than just memorizing and recall (Department of Education and Early Childhood Development, 2009). Adam T 08.06.11

**References**

<span style="color: #008000; font-family: 'Arial','sans-serif'; font-size: 13px;">Department of Education and Early Childhood Development. (2009). Office of Learning and Teaching. Curriculum Planning Modules Presentation. East Melbourne, NEALS. Retrieved June 8, 2011, from []

<span style="color: #008000; font-family: 'Arial','sans-serif'; font-size: 13px;">Victorian Curriculum and Assessment Authority. (2009). Victorian Essential Learning Standards VELS. East Melbourne, NEALS. Retrieved June 7, 2011, from __[|www.education.vic.gov.au/management/elearningsupportservices/www/classroom/curriculum.htm]__

One of the major principles of the NSW curriculum is to ensure "continuity" (NSW board of studies, 2006, p6) is evident in primary school education. This gives the student's the right knowledge for their future secondary scondary education. The curriculum is also constructed in stages which allows teachers to cater student learning to a particular stage such as adolescent or middle childhood (Eggen & Kauchack, 2010, p48). Doing this allows student's to be taught the appropriate knowledge for their level of understanding ( Reys, Lindquist, Lambdin & Smith, 2007). Within the principles of teaching and assessment the curriculum is structured so that students are challenged with new knowledge that will develop their mathematical skills. It is imperitive as class time should not be used to teach topics that are to easy or too difficult. As teachers assess student's current knowledge they are able to initiate revision if student's are ahving difficulty and also move to new topics if the class has mastered the new skill (Reys et al, 2007). References. Eggen, P. & Kauchack, D. (2010). //Educational Psychology: Windows on classrooms.// Upper Saddle River, NJ: Pearson Education. NSW Board of Studies. (2006).//K-6 Mathematics Curriculum. Retrieved from:// []

Reys, R. Lindquist, M. Lambdin, D., & Smith, N. (2007). //Helping children learn mathematics.// Hoboken, NJ: Wiley. (Heidi, 09/06)

In Queensland, the QCAR Essential Learnings curriculum documents emphasise three major principles (Queensland Studies Authority, 2010). Queensland students are helped in their skill development so they can, apply their knowledge and skills to solve familiar problems, solve specific problems in novel situations, as well as use open-ended inquiries to investigate problem situations (Queensland Studies Authority, 2010).

Booker, Bond, Sparrow & Swan write about the importance of understanding and comprehension in today's mathematics education so that learners can come to find solutions to new problems (Booker, Bond, Sparrow, & Swan, 2010). Also in support of the major principles provided by the Queensland Studies Authority, is the assertion by Booker et al., that problem solving should be seen to happen throughout mathematics learning, and not simply something that happens at the end of studies (2010).

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). Teaching primary mathematics (4th edition). Frenchs Forest, NSW: Pearson Australia.

Queensland Studies Authority. (2010). //Mathematics.// Retrieved from http://www.qsa.qld.edu.au/7296.html

- CHORY TYRRELL 09/06

That learners have the "**ability to understand, critically respond to and use mathematics in different social, cultural and work contexts**" (SACSA, 2001). Teachers have as a result the responsibility to teach children to be able to do this - This pretty much sums it up for me what the South Australian curriculum (which is actually a framework as opposed to a strict curriculum like other states, including the National Curriculum) **key principle** is.

The only other think I would possibly comment on is the assessment within the national curriculum and NAPLAN - how this kind of assessment potentially affects students and schools with the level of expectation.

With so many curricula to take into consideration, including the national, I think this week's 500 word piece is rather a challenge! All the best with it and looking forward to reading what you come up with :) Suzanne W 09/06/2011

**Hi Vicki,**

**I think this is sort of a broad question as it covers principles related to learning (how students learn & why), teaching (what we teach, how we teach based on what knowledge, syllabuses, curriculum) and assessment (how we assess children, during class and lessons, what form of assessment we use and across the board (state/naplan). So I feel for you as I think this is pretty hard as there could be lots of sets of 3 principles for each individual aspect. Just looking over some things, If instruction in assessment, teaching and if curriculum is set in a coherent way this will in turn 'set out a clear picture of the knowledge, skills and understanding that each student should develop** **at each stage of primary school' (Foundation Statements, NSW).**  **I think everyone has pretty much covered a lot for you to try and squeeze in to 500 words. Good Luck! Sarah**

Hi everyone, Thanks for your contributions. I think I picked a bad week, this one was not easy to consolidate!! But, here is my first draft. Let me know if you have any feedback, so I can amend this copy and post the final one to db on Sunday night. **__SUZANNE__** **-** **If possible can you please give me the reference for the SACSA so I can just add it into the reference list?** ** Thanks - ** Have added it into the reference list for you :) Suzanne 11/06/2011

Vicki

**__Word Count:__** 549

**__Contributors:__** Adam Townsend, Heidi Wilkie, Chory Tyrrell, Suzanne Williams, Sarah Wright, Ellen Williams, Kerrie Wyer, Lia Wrigley, Vicki Williams,

With each of the different state’s curricula to take into consideration, including the Australian Curriculum, there were many principles relating to mathematics learning, teaching, and assessment identified by group nine. Analysis of these curricula highlighted that they were each student centric, designed to achieve optimal learning outcomes and allow students to apply their learnings in everyday life (Board of Studies New South Wales [BOSNSW], 2006; South Australian Curriculum Standards and Accountability Framework [SACSA], 2001; Queensland Studies Authority [QSA], 2010; Victorian Essential Learning Standards [VELS], 2009). As a result, teachers have the responsibility to teach children to be able to do so. To support teachers in achieving this goal, Reys, Lindquist, Lambdin, & Smith (2009, p. 5) note three principles which should be present in a curriculum for effective mathematics outcomes: 1. “Focused”, 2. “Coherent”, and 3.”Well articulated”.

The first principle, focused, requires the curriculum to present concepts and ideas that are suitable to student’s grades, and ages (Reys, Lindquist, Lambdin, & Smith, 2009). The New South Wales (NSW) curriculum achieves this by introducing basic mathematical concepts in early stage 1, before moving to more complex ideas in later stages (BOSNSW, 2006). Assessment is an important factor of this principle, as teachers must first assess student’s current knowledge before moving onto new skills (BOSNSW, 2006; Reys et al., 2009). During assessment, students should demonstrate higher order thinking skills, rather than just memorizing and recall (Department of Education and Early Childhood Development, 2009).

Secondly, the principle of coherent refers to the inclusion of mathematical ideas that are both meaningful and effectively integrated together (Reys et al., 2009). The use of meaningful content assists students to apply their mathematical learnings in multiple contexts. The South Australian Curriculum discusses some of these contexts as socially, culturally, and vocationally (SACSA, 2001). In short, the use of meaningful content shows students ‘why’ they need the knowledge (Reys et al., 2009). Underpinning this is the need for mathematical content to be effectively integrated. Successful content integration provides students with the skills of ‘how’ (Reys et al., 2009). Accordingly, the Australian Curriculum has been written to ensure there are clearly defined links between mathematical ideas (Australian Curriculum Assessment And Reporting Authority, n.d.). The Victorian Essential Learning Standards (VELS) states that "Mathematical Reasoning and Thinking" underpins all aspects of school mathematics, including problem posing, problem solving, investigation, and modelling (VELS, 2009).Booker, Bond, Sparrow, and Swan write about the importance of understanding and comprehension in today's mathematics education, so that learners can come to find solutions to new problems (Booker, Bond, Sparrow, & Swan, 2010).

Finally, a well articulated curriculum allows students to build on previous knowledge. This principle enables students to be taught the appropriate knowledge for their level of understanding, and be challenged with new knowledge to develop mathematical skills (Reys et al., 2009). As teachers assess student’s current knowledge, they are able to initiate revision or move to new topics once mastery is achieved (Reys et al., 2009). Evident within this principle is the consideration given to Jean Piaget and Lev Vygotsky’s learning theories relating to learning, teaching, and assessment (Eggen & Kauchak, 2010). The use of stages in the NSW mathematics curriculum accommodates this principle well, by requiring students to achieve learning outcomes in their current stage before moving onto the next (BOSNSW, 2006).

References

Australian Curriculum Assessment And Reporting Authority. (n.d.). //Mathematics rationale//. Retrieved from The Australian Curriculum: []

Board of Studies New South Wales. (2006, May). //K-6 Mathematics syllabus//. Retrieved from Board of Studies New South Wales: [|http://k6.boardofstudies.nsw.edu.au]

Department of Education and Early Childhood Development. (2009). Office of Learning and Teaching. Curriculum Planning Modules Presentation. East Melbourne, NEALS. Retrieved from []

Eggen, P., & Kauchak, D. (2010). //Educational psychology - Windows on classrooms (8th ed.) - Pearson international edition.// New Jersey, USA: Pearson Education. Queensland Studies Authority. (2010). //Mathematics.// Retrieved from []

Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons.

__SA curric -__ Department of Education and Children's Services (2001), //South Australian Curriculum Standards and Accountability Framework (SACSA),// retrieved from http://www.sacsa.sa.edu.au/index_fsrc.asp?t=LA

<span style="color: #008080; display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">Victorian Curriculum and Assessment Authority. (2009). Victorian Essential Learning Standards VELS. East Melbourne, NEALS. Retrieved from [|www.education.vic.gov.au/management/elearningsupportservices/www/classroom/curriculum.htm]

This looks great Vicky, I am working on maths today and tomorrow and will have my contribution then, sorry its no help as you have done such a great job already :) - Ellen 10/06.

**<span style="font-family: 'Times New Roman','serif';">Week 2 ** //<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">In regard to the Mathematics Curriculum, what are the key principles that guide teaching, learning and assessment? //

<span style="color: #ff00ff; display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: justify;">It is essential that the mathematics curriculum consists of “more than a collection of isolated skills and activities” (Reys, Lindquist, Lambdim & Smith, 2009, p. 5). It is discussed by Victorian Essential Learning Standards [VELS] (2009) that mathematics is crucial “in enabling cultural, social and technological advances, and empowering individuals as critical citizens in contemporary society and for the future.” Therefore a “focused, coherent and well articulated” (Reys et al., 2009, p. 5) curriculum must be implemented. The implementation of key learning areas including “number, space, measurement, chance and data, structure, and working mathematically” (VELS, 2009) will ensure a “focused” (Keys et al., 2009, p. 5) curriculum. <span style="color: #ff00ff; display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: justify;">Teachers of mathematics must foster meaningful experiences for students “including problem posing, problem solving, investigation, and modelling” (VELS, 2009) to name a few. When mathematics is presented in a meaningful way to students, this will ensure that the curriculum is applied in a “coherent” (Reys et al., 2009, p. 5) manner. <span style="color: #ff00ff; display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: justify;">Only when students can prove their “thinking skills that are directed toward explaining, understanding and using mathematical concepts, structures and objects” (VELS, 2009) may students progress. This will ensure that the curriculum is “well articulated” (Reys et al., 2009, p. 5) as knowledge and growth will occur in a progressive manner. **<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Reference ** <span style="color: #ff00ff; font-family: 'Times New Roman','serif'; font-size: 16px;">Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons.

<span style="color: #ff00ff; font-family: 'Times New Roman','serif'; font-size: 16px;">Victorian Essentail Leaning Standards. (2009). //Mathematics – Standards//. Retreived From http://vels.vcaa.vic.edu.au/vels/maths.html

Here is my contribution for the week, I understand that you have already finished your submission, please dont feel obligated to change it in any way unless you feel the need to, you have done a great job, thank-you- Ellen 10/06

Hey there Vicky, like Ellen I see you have already completed this weeks task and agree that you have done a great job. I am sorry but due to child/work commitments this was the first time this weeks that I have been able to do Maths work- unfortunately this will not be an uncommon occurance with me as the weekends are usually when I can study.

I particularly agree that building upon the knowledge that the student(s) have already gained is essential and thus accurate assessment of skill is necessary. I am also of the opinion that catering for the needs and requirements of the individual is not only required but of significant importance and adjustment of instruction, assessment and technique may be necessary to do this with accuracy (Eggen & Kauchak, 2009). Additionally, the importance of presenting children with information relevant to their world is a //must// regardless of subject as the application of the learning in the real world and achieving higher level thinking is the goal when teaching any information. In regards to NSW curriculum, there is emphasis on progressing through the heirarchal stages with a consistancy; each step is aimed at laying the framework for the next stage (NSW Board of Studies, 2006). Planning objectives, creating a lesson plan, determining assessment techniques and how review will be done are all crucial elements of ensuring appropriate application of curricula.

Eggen, P. & Kauchack, D. (2010). //Educational Psychology: Windows on classrooms.// Upper Saddle River, NJ: Pearson Education.

NSW Board of Studies. (2006). //Foundation Statments.// Retrieved from: [|http://k6.boardofstudies.nsw.edu.au]

Thankyou for your submission.

Lia 11/06

Hi Vicki,

Like Ellen and Lia I notice that you have already completed the submission. You have done a wonderfull job. Like Ellen I have work and childcare commitments during the week and complete most of my study on weekends. Here is my contribution which looks like it has already been covered.

According to the Victorian Essential Learning Standards mathematical reasoning and thinking underpins all aspects of school mathematics (VELS, 2010). This includes problem solving, problem posing, investigation and modellng. Computation and proof are also seen as important aspects of mathematics (VELS, 2009). They enable students to develope thinking skills directed towards understanding the mathematical concepts.

__References__

Victorian Essential Learning Standards. (2009). Mathematics - Standards. Retrieved from:http://vels.vcaa.vic.edu.au/vels/maths.html

Kerrie Wyer 11.6.11.

Hi Everyone, Looks like no-one had any changes to make (yay) so I will post our submission.

**Ellen, Kerrie, Lia** - Thanks for your input, I have added your names to the contributors list. Sorry I finished this before getting your input. I thought at the time it might have been a bit pushy for me to ask for this by Thurs, but I have committments over the weekend so I had to get it done on Fri. Ah, the joys of managing study with work, kids, and life!

**Suzanne -** thanks for the reference!

Cheers Vicki 12/6/11