Week+1+-+Adventuring+into+Mathematics

//**LEARNING ACTIVITY 1.1:**//

//**If mathematics were a food, what would it be and why?**//
 * Prawns - messy, tricky, intricate. Takes careful consideration to navigate, requires full concentration. The finished outcome is very pleasing to some, others are put off by the effort, and some can't stomach it in any form!
 * A sensible food, like bran, or silver beet - we all know we need it, and that what we gain from it will be valuable to us, but that doesn't mean we enjoy it. We know that our bodies need vitamins to grow, but many of us don't enjoy those typically 'boring' foods, like brussel sprouts. Maths is similar, in that we know we'll have to use it at times in our lives, but we don't always enjoy the sometimes tedious task of learning it.

SHARE THE FOLLOWING ON THE TUTORIAL DISC BOARD:

Maths is something I view as requiring skill and know-how. While I excelled at maths in my younger high-school days, I seem to either have forgotten or lost my maths ability. Maths generally tends to conjure images of pi, //x,// algebra, pythagorus and equal-lateral-thingies. Although, if I truly consider the merits of maths, I regularly use simple sums in my daily life. For instance, I compare the prices of grocery items. This requires an understanding of basic maths, and a grasp of simple multiplication and division, including decimal points.

While I don't regard maths as one of my major skills, when required to, I can dust off my maths-hat and seem to have enough knowledge left to find the answers to my questions. This would lead me to believe that basic maths skills are important, as well as being useful and applicable in every-day situations.


 * //LEARNING ACTIVITY 1.2////:// //DONALD DUCK'S MATHEMAGICAL ADVENTURE//**


 * //PRE-VIEWING QUESTIONS://**
 * //Do you think maths can be fun? Give an example.//**
 * // As a teacher, I believe it is my role to, where possible, create enjoyment through learning. Therefore, dull theory can be broken up with practical activities. For example,student would have fun while learning during a game such as '[|buzz] ' (click link for explanation). //**


 * //How do you use maths in daily life?//**
 * // The foremost use of maths in my life is driving. I unwittingly use maths to calculate angles, reversing and judging distance when parking. The second most prominent example of maths in my daily life would be during the grocery shopping. I budget, which involves comparing size, price and quality, as seeing which products are best value for money. //**

//**What do you know about Pythagoras?**// // He had lots to do with triangles, discovered the the sides/angles were all equal. If you added up 3 angles of the equal-lateral triangle, you would always get 180 degrees? He had a theorem. //

//**Name any other mathematicians you know. Explain their work.**// // Einstein? Did he do stuff with apples or gravity? Or was that the other guy?No, he was a physicist. //


 * //Name examples of maths in sport, architecture, art etc.//**
 * // Examples include calculating angles when kicking goals, builders using maths to balance, measure etc, keeping score, statistics, betting. //**

What mathematical contribution did Pythagoras make?
 * //POST-VIEWING QUESTIONS://**
 * Discover octave had a ratio of 2:1, created musical scale. Pentagram - 2 shorter lines exactly equal third, 2nd and 3rd exactly equal 4th etc. 'Golden Section' & 'Golden Rectangle.' 'Everything is arranged according to mathematical number and shape (Pythagoras)' **

What is a golden rectangle? What's its importance in architecture and art? What do you see around you that's a golden rectangle?
 * Can be found in star, pentagram. Can mathematically reproduce itself indeintely (like folding a piece of paper in half) with exact proportions. 'Magic Spiral.' Greek Parthenon contains rectangles. Same of Greek sculpture. Cathedral of Notre Dame. Renaissance painters, Mona Lisa. Modern - skyscrapers. **

How is maths present in nature? Petunia, star jasmine, starfish, wax flower, shells, trees, pinecones.

Which games does Donald play, and how do they relate to maths? Give 2 more examples of games that utilize maths. Chess - calculated strategy on geometric board. Baseball - diamond. Score-keeping. Football - divided rectangle. Basketball - circles, spheres, rectangles. Hopscotch - multiple squares. Billiards - triangles, spheres, diamond. Angles. Technique (hitting the ball low so it spins backwards). Calculation.

My 2 example: Baseball (angles for pitcher/batter, diamond). Volleyball (aiming to hit the ball where your opponent won't be able to defend).


 * Give example of mathematical achievement that have occurred in the last 50 years.**


 * //LEARNING ACTIVITY 1.3://**

New ideas:
 * Focus is now learner-driven, rather than content-driven. This includes understanding how student learns.
 * Maths is more commonly known as 'numeracy' now. Numeracy allowing students not only to learn mathematics principles, but also how to use their mathematical knowledge in a constantly expanding world.
 * Numerate - competent in numeracy ('**to use mathematics effectively to meet the general demands of life at home, in paid [**//**sic**//**] work, and for participation in community and civic life**.' Australian Association of Mathematics Teachers, 1997'
 * '**The major role of the teacher is to create more powerful constructions and...developing autonomy and self-motivation is vital'** (Clements, 1997)
 * Materials (counters, 1s/10s/1000s blocks) can help to develop mathematical thinking by taking on potential meanings and allowing students to //experience// the maths
 * Maths - '**the study of patterns**' (Klaebe, 1986) including number, shape and arrangement
 * **'When mathematical ideas are communicated, particular care is taken in formulating language to keep track of what is happening with materials or representations which will eventually allow formal symbolic recording, mental operations or approximations to be conducted confidently'** (Booker 2010). Language is important, communication between students helps to develop language - regular opportunity to 'try out' the words promotes confidence in using them. Maths has a specialised vocabulary. '**Language is crucial to the learning of mathematics because it is through discussion that learners come to terms with mathematical ideas, develop ways of expressing concepts and processes, and take on the ways of thinking as their own'** (Booker, 2010).
 * Maths symbols mean nothing until meaning is given to them through understanding. A picture of a duck is meaningless until a child associated it with the yellow quack-quack animal; the meaningless outline on the page then becomes a duck.
 * '**As learners participate in the playing of instructional games, the manipulations of materials and verbalisations of actions, thoughts and interpretations assist in the construction of mathematical concepts' (Booker, 2010).**

Familiar ideas:
 * Maths teaching largely based on constructivism, reflective learning. **'Existing conceptions...guide the understanding of any new information or situation that is met'** (Booker et al, 2010). Not just concentrating on the solution, but an emphasis on how the solution was found. Rather than showing the answer, showing how to find it.
 * Words in maths have double meanings: average, product
 * Cooperative learning - group work, children working together to achieve a common goal. This is used to deepen understanding in maths. It promotes ability to communicate and reason mathematically, as well as other benefits of cooperative learning (higher motivation, accountability, increased learning).
 * The teacher-student role is significant to effective learning

Questions:


 * //LEARNING ACTIVITY 1.4 - Munching Mathematics Menu//**


 * //French Onion Soup with Gruyere Croutons://**
 * // A rich, flavoursome onion and beef-broth based soup, served with crunchy Gruyere-topped croutons. //**
 * Classic, historic, universal. We learnt the history of maths in the videos (origins, founders), and that maths has been around for a long time and has universal principles. The text also showed examples of relevant mathematical history (Greek word origins, contributions to maths over the years)
 * Can be the base for many other dishes, much in the same way that maths skills extend to other areas of life. I learned from the text that maths is not numbers and multiplication, but that the process of learning develops many other domains in life: problem solving skills, ability to reason.
 * The gruyere croutons represent a modern twist, to show that although maths is an old concept, it's still very much useful and relevant today.


 * //LEA//****//RN//****//ING ACTIVITY 1.5//**


 * //PLR 1//**
 * 1. Unit learning outcome(s) for which this item provides evidence of learning // (type these out in words; do not identify by a number only) //**
 * Identify, describe and apply effective teaching strategies for teaching mathematics.

2. **Description/outline of what you have learned and how this learning demonstrates the learning outcomes you have specified above** // **(This must be specific in that it includes examples and these examples are explicitly linked to your statements of learning.** **This is not just what 'you' as a person learnt - you need to write about the learning that should have occurred that week, whether you already knew it or not. What were the concepts that those tasks and readings were teaching you? Don't just describe the activity or say what you thought of it - the focus is on the 'learning.' You also need to assume I (as the reader) know nothing - if you use a term (eg. constructivism), you need to say what that is - don't assume I already know.** **What did I learn? Which Learning Outcome did it address? Which activities enabled me to learn this.** //  //** The text this week described a teaching strategy known as constructivism. This can be explained as a reflective technique that allows learners to assess new situations by using existing techniques (Booker, 2010). The constructivist teacher aims to guide student into finding their own answers. I had learned of constructivism earlier in my studies, but through the readings, have learned that constructivism is an effective mathematical teaching technique. Identifying constructivism, and learning that it is used successfully to teach mathematics will enable me to apply my pre-existing knowledge of this teaching strategy during planning of maths lessons. ** //


 * 3.** **How this learning relates to your development as an effective primary mathematics teacher.** //**This is where you must include practical examples for the classroom. How would you teach mathematics based on the learning from the week - this might be strategies, resources or activity ideas?** **You must include references as part of this section to support 'why' these stratgies are effective in teaching mathematics.** **How will I use the learning?** **Why will the learning help in my development as an effective primary mathematics teacher? What references support my claims to the question above?** //

// Constructivism has been shown to have many benefits, including ownership of learning, the ability to transfer learned constructivist principles to other situations, and the promotion of social and communication skills (Wilson, 2004). As a prospective primary school teacher, I could use my knowledge of constructivism in the classroom. An example of this may be explaining to a group of students in Grade 1 the rules of multiplying by 10. Students could be taught that to multiply a number by 10, a zero is added to the end. Upon learning this, students could then, hypothetically, multiply any number by 10. Constructivism is demonstrated, as instead of simply teaching the answer, the process of finding a solution is taught to students, increasing learning and understanding (Booker, 2010). By taking previously learned knowledge and applying it to mathematics teaching, I am aiming to master a teaching strategy that will aid my students' learning. //

//(References needed: (Wilson, 2004), (Booker et all, 2010)//

//**PLR 2**// // ** 1. Unit learning outcome(s) for which this item provides evidence of learning** //** (type these out in words; do not identify by a number only) **


 * Identify, describe and apply effective teaching strategies for teaching mathematics.

2. **Description/outline of what you have learned and how this learning demonstrates the learning outcomes you have specified above** // **(This must be specific in that it includes examples and these examples are explicitly linked to your statements of learning.** **This is not just what 'you' as a person learnt - you need to write about the learning that should have occurred that week, whether you already knew it or not. What were the concepts that those tasks and readings were teaching you? Don't just describe the activity or say what you thought of it - the focus is on the 'learning.' You also need to assume I (as the reader) know nothing - if you use a term (eg. constructivism), you need to say what that is - don't assume I already know.** **What did I learn? Which Learning Outcome did it address? Which activities enabled me to learn this.** //     //** The reading in the text suggest that maths has a specific vocabulary. Examples of this vocabulary are used in measurement: volume, area, circumference, diameter. Through discussion, students are familiarized with terms, which helps them to develop a deeper understanding, express ideas and and adapt to new ways of thinking (Booker et al, 2010). Understanding the importance of language will assist me in helping my students come to terms with new mathematical concepts. ** //

**3. How this learning relates to your development as an effective primary mathematics teacher.** //**This is where you must include practical examples for the classroom. How would you teach mathematics based on the learning from the week - this might be strategies, resources or activity ideas?** **You must include references as part of this section to support 'why' these stratgies are effective in teaching mathematics.** **How will I use the learning?** **Why will the learning help in my development as an effective primary mathematics teacher? What references support my claims to the question above?** //

When mathematical ideas are communicated, particular care is taken in formulating language to keep track of what is happening with materials or representations which will eventually allow formal symbolic recording, mental operations or approximations to be conducted confidently' (Booker 2010). Language is important, communication between students helps to develop language - regular opportunity to 'try out' the words promotes confidence in using them. Maths has a specialised vocabulary. 'Language is crucial to the learning of mathematics because it is through discussion that learners come to terms with mathematical ideas, develop ways of expressing concepts and processes, and take on the ways of thinking as their own' (Booker, 2010). In the classroom, I would promote use of maths language by facilitating class discussions, and providing students with ample opportunity to 'try out' their newly learned maths terms.

// **1.** **Unit learning outcome(s) for which this item provides evidence of learning**// **(type these out in words; do not identify by a number only)**
 * //PLR 3//**

//**2. Description/outline of what you have learned and how this learning demonstrates the learning outcomes you have specified above**// **(This must be specific in that it includes examples and these examples are explicitly linked to your statements of learning.** **This is not just what 'you' as a person learnt - you need to write about the learning that should have occurred that week, whether you already knew it or not. What were the concepts that those tasks and readings were teaching you? Don't just describe the activity or say what you thought of it - the focus is on the 'learning.' You also need to assume I (as the reader) know nothing - if you use a term (eg. constructivism), you need to say what that is - don't assume I already know.** **What did I learn? Which Learning Outcome did it address? Which activities enabled me to learn this.**

Mathematics has evolved to 'numeracy,' allowing students not only to learn maths principles, but also how to use their mathematical knowledge in several ways to address a constantly expanding world. This idea was introduced by the textbook, which suggests that numeracy is a 'natural tool for comprehending information' (Booker et al, 2010). This is in contrast to my preconceptions, which relate to maths being about numbers and calculations. An understanding of numeracy and its benefits to students will allow me to be a teacher capable of imparting useful life-skills to my students.

//**3. How this learning relates to your development as an effective primary mathematics teacher.**// **This is where you must include practical examples for the classroom. How would you teach mathematics based on the learning from the week - this might be strategies, resources or activity ideas?** **You must include references as part of this section to support 'why' these strategies are effective in teaching mathematics.** **How will I use the learning?** **Why will the learning help in my development as an effective primary mathematics teacher? What references support my claims to the question above**?

The text maintains that a numerate student is one who can 'use mathematics effectively to meet the general demands of life at home, in paid [//sic//] work, and for participation in community and civic life' (Australian Association of Mathematics Teachers, 1997). I have learned that numeracy is a wide-used ability, not a knowledge of numbers and what to do with them. As a teacher, I hope to incorporate my understanding of numeracy into teaching, with the aim of equipping my students with useful skills of reasoning, logic, and comprehension.