Week+1+-+Adventuring+into+mathematics

__**Learning Activity 1.1: If mathematics were a food. . .**__

Brussel Sprouts - not everyone likes them, some love them. Sprouts grow with individual leaves layering on one another, just as in maths prior knowledge is needed as building blocks for future knowledge. Sprouts, like maths, are hidden where you don't expect them. Hidden under the gravy on the plate at the Christmas dinner table, just as maths is hidden in so much of daily life. Sprouts are nutritious and wonderful, but sometimes can be a little bit woody at the stalk, and sometimes slightly bitter if not cooked properly. Similarly maths is full of necessary information, just like a nutritious sprout, can be tough to palate at times, like a woody stalk, and frustrating when a concept is not fully understood, just like a bitter tasting sprout. - Suzanne W 30/05/2011

If mathematics we a food it would be broccoli, as it takes an acquired taste to really enjoy it, but it is full of richness and goodness that is essential in our life.- Ellen 30/5

Chicken Stock- On its own it's very basic, uninviting but when other ingredients are added, it adds another dimension making it inviting. Kendall Storey 29/5/11

Corn - It and its byproducts are in everything. Corn Syrup, Xanthan Gum and ethanol are examples. CHORY 29/5/11

Piece of cake - Some people find it easy. CHORY 29/5/11

If mathematics were a food it would be a pizza, it has endless possibilities, there is an large selection of choice and variety, but if you eat the whole thing you often are left feeling overwhelmed and sick. Sarah Wright - 30/5/2011

I see mathematics as a cake. Cakes are common, and are easy to find. They have varying degrees of difficulty; some are quite simple to make but others are more complex and require specific ingredients / recipes, or specific skills / tools. Generally, we need an understanding of how to make a simple cake before we can attempt a gateaux! Vicki 31/5/11

Mathematics is like seasoning (salt & pepper) – you always have to add it food to enhance the flavour.Adam 01.06.11

If Mathematics were food it would be a lasagne. Lasagne has multiple layers but is eaten as a whole. Achor 03/06/2011

If mathematics were a food it would be an orange as it can be cut into segments that represent fractions. Also an orange can be squeezedto extract its juice which may be measured to use in cooking. Kristy 03/06/11

If mathematics were a food it would be a passionfruit. If you have a passion for maths it will bear the fruits of your labour. It is hard on the outside but when you break through the surface you will be pleasantly surprised. The many seeds connect with the jelly to improve the flavour. Kerrie 4/6/11. Kristy sorry I have used your colour becasue I cannot find the tab to change the colour.

__**Learning Activity 1.2:** //**Donald in Mathmagic Land**//__

Found this one interesting, but only in some parts. Quite honestly, I found much of this repetitive and done in a manner that was beyond what I am assuming is its intended audience, being children. Really enjoyed how sports were portayed, in particular, the billiards with the angles. I found the golden rectangle a little hard to understand. The golden recatngle was a new concept to me, and I didn't find the explanation satisfactory in Donald in Mathmagic Land - I googled this one to get a better understanding. What I did appreciate about this though is how it is reiterated just how much maths is about us in our everyday lives. Two big things beyond the making of this short film that have happened in maths in the past 50 years - the landing on the moon and the change to decimal currency (as in introducing the dollar and no longer using the pound) - Suzanne W 30/05/2011

Donald in Mathmagic Land offered many interesting ideas of how mathematics is present in everyday life. It can be argued that Pythagoras was responsible for ideas including the golden rectangle. The golden rectangle can reproduce itself indefinitely. Pythagoras identified that the pentagram was full of mathematical aspects including the golden ratio and the golden rectangle which was admired for its beautiful proportions and qualities.

The golden section can be found in many of nature’s elements. Pythagoras believed that everything is arranged according to number and mathematical shape. Nature uses the pentagon as a mathematical way of forming many different flowers and star shaped objects including the starfish.

I personally found the video to be very interesting and I enjoyed how the ideas were presented in a fun and light manner. - Ellen 30/5

The Donald in Mathmagic Land movie presents mathematics in a positive light and is a great tool for opening discussions on mathematics related topics. It is an interesting film that captures the viewer's attention because of its use of cartoon and comedy, as well as presenting the relevancy of mathematics in people's everyday lives. CHORY 29/5/11

It opened my eyes to the many mathematical concepts that are prevalent in sports. Everything seems to have some sort of mathematical basis. Maths is much more than 1 + 1. CHORY 30/9/11

Not being a huge fan of maths and finding it quite difficult to understand the concepts of maths throughout my schooling, I find it strange to admit I found this clip, very informative and interesting. During my lunch break today I showed this clip to my work colleagues, it created a hot topic of discussion and brought to our attention how present mathematical concepts are in very day life.

I was very shocked to learn how Pythagoras created the scale of musical notes using a mathematical concept and I also particularly liked how the clip portrayed the use of mathematics in sport. Kendall 30.5.11

I enjoyed watching this clip as I felt like I could relate to Donald at the begining, maths was scary, the unknown and confusing, but that is all part of the journey. This small clip reminded me that maths really is in every aspect of life, it also taught me a few things I never knew. While I remember vaguely learning about Pythagoras theory in school I had no idea that Pythagoras was the father of maths and music, and that it was through maths the musical scale was created. I had also forgotten about the Golden Rectangle and that it can reproduce itself infinitely. As much as I despised maths at school, it has an interesting history behind it and can be found in anything from a section of a sphere which is a lense or the architecture of the Parthenon. Overall I enjoyed the clip, it was easy to sit and watch because it was light hearted and entertaining. Sarah Wright 30.5.11

I found several of the points raised from Donald’s adventures to be interesting. While I was aware that maths encompassed several aspects such as shapes and geometry, I hadn’t considered the influence it had on music. Learning that musical scales were developed from ratios was something I learned today. Vicki 31/5/11

There were many interesting facts (some of which I had forgotten about) about watching Donald in Magicland. As mentioned above the discovery of the musical scale by Pythagoras, the Pentagram and that it forms the golden rectangle and how this related to ancient and modern art and architecture as well as natural forms of pentagons / pentagrams in flowers, trees and shells helped form new approaches to maths and the natural world. Donald discovering how geometry and maths are paramount to succeeding in billiards was also interesting. Apart from having a good technique, a billard player calculates angles by using the markings around the edge of the table as a mathematical guide to find diamond pathways for hitting the desired shot. This footage highlights the need to relate maths to practical or real life experineces in order to help people to understand mathematical principles. Adam 01.06.11

I found the video to be quite educational and entertaining in that it shows children just how useful maths is and that you can find it in everyday things. This video can be used cross curriculums linking history and mathematics together for example. I am not quite sure what age group suits this video best because it does have a tendency to use hard words occasionally. I have learnt from the video the mathematical properties in basic shapes such as rectangles and pentagrams. I have also learnt that mathematics plays a part in games such as chess I always knew it was about probability but didn't really think anything of the actual board we play on. Achor 03/06/2011

Disney, W. (1959) // Donald in Mathmagic Land //. Retrieved from []

I really enjoyed watching this video. It was interesting to see how maths was used to develop the musical scale we use today. I also enjoyed watching the three cushion billards game and the mathematical logic that is behind it. The golden rectangle was a new concept to me and when I researched it on the internet I saw examples of it in both architecture and art. For example, the Parthenon in Greece fits into the shape of a golden rectangle as does the lady in the painting of "Mona Lisa" by Leonardo da Vinci (Obara, n.d.). I think students would enjoy watching this cartoon as it shows how maths is in everything we do every day. However, I sometimes have trouble understanding Donald Duck when he speaks. Students of today who have not grown up with Donald Duck may also have trouble understanding him at times. __References__

Obara, S. (N.D.). Golden Ratio in Art and Architecture. Retrieved from [|http://jwilson.coe.uga.edu/EMT668/]EMAT6680.2000/oBARA/eMAT6690/Golden%__20Ra[|tio/golden.ht]__

Kerrie 4/6/11.

Learning Log - Chory Tyrrell 09/06 No questions. ||
 * ** 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 should be fun and meaningful to learners lives
 * Computer games with a mathematical education as its focus can be of value
 * Social interaction amongst learners help build mathematical knowledge and understanding
 * Patterns and relationships within mathematics
 * Mathematics should be learned from easy concepts building up to harder topics || * Mathematics need concrete materials to aid in learning the subject, especially in the beginning because many of the ideas in mathematics are abstract
 * Problem solving should be incorporated throughout the learning of mathematics. Understanding should be emphasised over memorisation of facts
 * Being mathematically literate is very important in modern times ||
 * ** Questions I have and related things I do not understand from my reading **


 * Learning Log - Ellen 30/5 ||
 * **Ideas and examples that is familiar to me from my own experiences with mathematics learning and teaching** ||
 * Worksheets and content-driven teaching practice ||
 * **Ideas and examples related to mathematics learning and teaching that are new to me** ||
 * Learner-centred teaching ||
 * **Questions that I have and related things I do not understand from my reading** ||

**//Learning Activity 1.3 Record Chart: A first glimpse into mathematics education//** Sarah Wright 31/5/2011
 * **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** ||
 * * Story situations from the children’s lives to allow them to feel the solution process is personally developed and owned
 * Constructivism – the way in which the individual see’s and understands concepts based on previous experiences (previously learned knowledge) || * The most important use of materials in mathematics is to provide experiences that can be discussed and reflected on to allow the effects of the embodied actions to emerge as mathematical ways of thinking.
 * Understanding the relationship between mathematics and language, for example; knowing that ‘dia’ means across can help with the meaning of diameter, while I practice this I had never actually put thought into it ||

How anyone can say "If someone believes that mathematics ability is something one is born with, there really is little they can do to change the situation**."** (p. 32) I found reading this line horrific, there is much that can always be done. Situations can always be changed. Always. Suzanne 01/06/2011 ||
 * __**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** ||
 * * Teaching using that which is familiar to students
 * Students constructing their own knowledge
 * That one piece of mathematical knowledge is needed clearly before building upon it
 * That maths is essentially symbols with meaning attached
 * The use of ICT and other materials
 * The meaning of words such as tri, quad, etc || * How student centred the teaching is now and the encouragement of discussion ||
 * **Questions I have and related things I do not understand from my reading**


 * 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. ||
 * * Elementary mathematical ideas under pin the development of all mathematics
 * The major role of a teacher is to help children to create more powerful constructions and that developing autonomy and self-motivation is vital.
 * Discussion among peers is needed
 * Language is the key to all mathematical learning.
 * Having knowledge of counting words in Latin and Greek can help with understanding complex words in mathematics
 * Interactive white boards and digital content can transform mathematical pedagogy in a classroom.
 * It is much easier to make more mistakes on a calculator.
 * The internet has many sites where teaching materials can found.
 * || * When children write teen numbers back to front, because they generalise the pattern for other two-digit numbers and write the digits in the other in which they hear them.
 * If child were able to invent their own methods and explanations that showed up in patterns of errors, they would also be building their own understanding of appropriate ways of thinking rather than simply taking in a teacher’s explanation.
 * The importance of using materials when teaching mathematics.
 * Materials are not something to be used at the beginning of a mathematics teaching and learning.
 * A difficulty with many of the materials proposed for the classroom use is that they actually demand knowledgeable users.
 * Patterning is fundamental to mathematical thinking.
 * Games should be seen as an integral part of a balanced teaching program.
 * Games can also be used to explore new notions and to lay the foundations for concepts and processes that will be formalised later. ||
 * Kendall Storey 2.6.11 ||

**//Learning Activity 1.3 Record Chart: Achor 03/06/2011//** The whole concept of gender mathematics is new to me. It is really that different between boys and girls. We may mature faster than boys but I believe that it shouldn’t be based on gender due to our individual experiences and personalities are far more different from others. Can someone please help me to understand the concept of gender mathematics? ||
 * **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** ||
 * * Student participation is crucial
 * Scaffolding can enhance learning significantly.
 * Interactive lessons can have a greater outcome than those that are just all theory.
 * Mathematical Games on the computer are both educational and also keeps the mind more alert. || * Materials are best used later on in the lesson.
 * Teachers have to test the problem students are about to solve before they solve them ||
 * **Questions I have and related things I do not understand from my reading**

__**Learning Activity 1.4: A new gourmet restaurant**__

**Munching Mathematics Menu**

**On today’s menu – //The Infinite Triple Berry Cake//**

A multi layered cake with tempting layers of rich chocolate for enjoyment, followed by infinite layers of sponge cake nestled within a triple berry mix for nutrition, nurture, and nourishment.

The cake is layered with chocolate as mathematics can be as enjoyable as chocolate tastes, with berries that represent the nourishment, nurture, and goodness that mathematics has on our lives. - Ellen 30/5

__Munching Mathematics Menu__

Chef's Special!!!

2 minute noodles at a low price

This hearty meal will be prepared and served quickly to you from our kitchen to your chosen table. The noodles are delicious and fun to eat as you get through all the strands of noodly goodness. - CHORY TYRRELL 09/06

Choices Exquisite Pizza, At our restaurant you can choose how much pizza you would like, whether it be a whole, half or quarter, whatever will satisfy you without being too much to handle. We cater for all customers, whatever their needs. We allow for choice of variety, with the option for healthy and nutritional value or standard and classic options. You can be daring and explore new alternative ideas or stick the classic rules which we all know and love. You can add or subtract or don’t forget divide or multiply the amount of pizza you want to take home. This boutique style of exclusive service is second to none and prepared fresh for you every time. //**Why I chose Pizza **// I believe that like a gourmet pizza, maths has endless opportunities and opportunities. Maths gives answers where the only answer is infinite, and like a pizza what you have as a topping is only restricted by your imagination. Pizza likes maths can be over whelming, a heavy large family pizza for one person can be far too much in one sitting. Pizza like maths can be viewed by some as horrible, people who are intolerant to wheat avoid pizza altogether, like people who are intolerant to maths, to them this is unchartered water that they know they just cannot venture into. Sarah Wright 30/5/2011
 * Munching Mathematics Menu **

//“Build your own layer Cake”// This menu item allows you to build your own layer cake. The chef has listed some suggested some layers that may work well together, but the choice is up to you! Talk to our friendly staff about what some other guests have created.

This menu item facilitates a scenario for the guest to consider how to achieve the finished product, rather than being told how it should be done. The suggested chef options act as scaffolding in a constructivist environment, while the discussion with staff promotes social interaction. Discussing ideas, possible solutions, and outcomes are “integral to learning mathematics” (Booker, Bond, Sparrow, & Swan, 2010). Vicki 31/5/11

Hot Brick Steak with a Parfait of Julienned Vegetables

Guests are invited to cook their steak to their own liking. Our chef is on hand to provide you with a hot rock on which to cook your steak to your liking. Should you need guidance, our expert chef is on hand. Once your steak is cooked to perfection (according to your tastes), a side dish of perfectly cooked julienned vegetables, including carrot, snow peas, asparagus and leeks will be presented in a parfait style for your enjoyment.

The menu item in giving the patron the opportunity to cook their own steak is akin to a students creating their own learning. The steak is cooked to the liking of the patron as a student learns and creates what is right for them. The chef being on standby should the patron need assistance, is similar to the teacher being there to offer assistance, and guidance, being scaffolding. The julienne of vegetables, being presented parfait style (layered) represents the layering of mathematics - how one part must be learnt, or in this case, consumed, before reaching the next layer of vegetables, or learning.

Suzanne 01/06/2011


 * Munching Mathematics Menu **

Create and Make Sushi

Customers can choose various toppings or fillings for sushi, sashimi or sushi rolls. For example raw fish, pickled ginger and cucumbers, cooked chicken, avocado, sesame seeds, fried tofu etc can make numerous flavour combinations. In addition many shapes and sizes of the sushi can be created involving geometry, forms and shapes, measuring, fractions and counting. A delicious way of learning and involving mathematics. Adam 01.06.11

Munching Mathematics Menu We bring you the finest ingredients to make the best lasagne you have ever tasted. All alternating layers of delicious pasta sheets, cheese sauce and minced beef in Roma tomato sauce. Just like mathematics our lasagne has a lot of ingredients to make something a whole. We also have a vegetarian lasagne for herbivore friends instead of beef or Italian sausage they can have spinach. It may not be nice for some but for the people who know what’s’ good for you they will eat it. Just like maths if you know its good for you it will motivate you to learn it. Achor 03/06/2011

__**Learning Activity 1.5:** **Motivation in Mathematics**__

**The PowerPoint that was presented by Paul Swan shows a great example of getting students interested in mathematics by using tricks. These tricks are a great way of intriguing students and keeping them motivated by engaging in play. By doing this it makes the learning process fun. - Ellen 30/5**

The powerpoint presented by Paul Swan shows how you can attempt to achieve motivation in learners by delivering to the audience some interesting tricks that will lead to them to wonder how it was done. The activities are relatively short in duration which help in keeping the attention of the audience, especially one containing young learners. - CHORY TYRRELL 09/06

**Paul Swans PowerPoint displays as intriguing, entertaining and interesting way of implementing mathematical concepts. Mathematical tricks and games like these could be used as an introduction to a maths lesson, to regather the attention of students or to provide a break in a lesson. Kendall 30.5.11**

The Paul Swan powerpoint offers some good examples of how to get the attention of students. Particularly if it is a noisy class, or a hot day where concentration is lacking, something like this may be a great way to start the lesson. However, if this is simply done as a parlour trick and not followed up on, an opportunity for learning is lost. Booker et al, discuss how games can be useful as they promote abstract thinking, such as one that Paul Swan offers. Ultimately, students need to grasp the concept and create their own learning. Suzanne 01/06/2011

The Paul Swan motivational maths powerpoint helped to eliminate the anxiety from solving mathematical problems. It is a great approach for teaching primary mathematics as it incorporates games, puzzles, multi layed calculations, etc helping young students understand mathematics in a fun and entertaining environment. Adam 01.06.11

The Paul Swan power point breaks down the mathematical language barrier for children so it is easier for them to solve the presented problems. The games can help keep the children's mind sharp and help them to practice on their brain reflexes on how quickly they solve the problem. Visual aid especially in young children helps them to jog their memory as oppose to mindless textbook theory for hours on end. Achor 03/06/2011

__**FINAL SUBMISSION FOR WEEK 1, COMPILED AND COMPLETED**__

**Mathmates – Group 3 – Ellen Williams**

**Here is a start – feedback and further relevant points to be added by MathMates members before submission.**

//How do children learn Mathematics?//

Teachers of mathematics are encouraged to value that each learner has their own individual learning needs that must be met within a “lea r ner-centred” (Booker, Bond Sparrow & Swan, 2010, p. 5) environment. Children learn from being active within their own learning experiences and when children “construct their own mathematics, this knowledge is both personal and owned” (Booker et al., 2010, p. 12). When children have control over their individual learning these “experiences are empowering” (Booker et al., 2010, p. 13) to them and more likely to be retained.

Learners of mathematics need to be presented with “meaningful experiences that incorporate materials, patterns, language and symbols” (Booker et al., 2010, p. 26) in order to foster a mathematical way of thinking. These experiences must be built upon gradually, using “real life situations and concrete materials” and furthermore, giving the opportunity for children to “collaborate with peers in mathematical situations is crucial for learning” (Booker et al., 2010, p. 26).

**Reference** Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching primary mathematics// (4th ed.). Frenchs Forest, NSW: Pearson Australia. - Ellen 30/5 Hi Ellen, I think that your contribution is great, I would suggest paraphrasing rather than using direct quotes, however did not want to edit without approval for example editing the last sentance- When building upon experiences gradually, the use of materials and situations familiar to the students will aid in the children's comprehension of the affect on their reality. Additionally, through providing oppertunities for children to collaborate in mathematical situations children will extend their zone of proximal development and as such their learning experience will be enhanced. Otherwise, I simply edited a spelling mistake I saw. Lia Wrigley 1/06/11 Hi Ellen,

Here is a piece I wrote on the topic, which you may or may not want to use for this weeks contribution:

To effectively teach mathematics, consideration must be given to the child’s previous knowledge. The area of mathematics begins with simplistic ideas, such as recognising shapes, patterns, and numbers, before moving onto more complex ideas. As such, it is paramount that children have a solid understanding of mathematical basics, plus the required prior knowledge, before progressing to the next level. This can be demonstrated in teaching tasks such as addition or multiplication, where students must first have an understanding of numbers and their meaning, before being able to complete number tasks. Failure to accommodate this requirement makes it difficult for children to grasp the learning, make sense of it, or achieve higher order thinking (Booker, Bond, Sparrow, & Swan, 2010). Vicki 31/5/11

References:

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


 * Week 1 Contribution **

Co-operation within the classroom is important to ensure that children are able to develop mathematical concepts. This ensures social interraction, class participation which encourages learning through discovery, observations, and discussions about the task or activity required. Students apply reasoning which helps them to make sense of how the group formed their conclusions. This ultimately results in studenst forming mathematical meanings through the frmaework of learning co-operatively. Therefore the role of the teacher is not about verbalising information and organising mathematical worksheets rather they are the fascilitating learning and encouraging to scaffold ideas and create concepts through classroom integration and interactive discussion. Adam 01.06.11


 * References: **

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

A few points of how I believe children learn mathematics:

These are thoughts for encouraging children in learning mathematics, hopefully also thereby encouraging intrinsic motivation.
 * Discussion with peers/collaboration
 * Through constructivism (Piaget & Vygotsky's theories) with appropriate scaffolding given
 * Having maths placed in "real world" terms - that it is in every day life, shopping, street signs, nature
 * Through the use of material - be it pop sticks, blocks etc
 * By building upon previous knowledge.

Cheers, Suzanne 02/06/2011

Hi Everyone, Just reading through the responses and idea's that have been written for this weeks 500 word essay and it all sounds great. Doesn't look like there is anything that hasn't been covered when addressing the question of how children learn mathematics. Really great work, how are you going Ellen piecing it all together?

Sarah

[|Heidi187] just now

Within the domain of mathematics it is very important for all student's to be taught through real world examples. This aids the student in grasping the new content. Learners must have a safe and well functioning classroom environment which allows them to feel comfortable when asking questions or contributing to group discussion. The student will benefit from hands on activities rather than always completing written tasks.

References Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching Primary Mathematics//. Frenches Forest, NSW: Pearson Australia. Heidi

(03/06

HELLO EVERYONE!! THANKS FOR YOUR FEEDBACK, I WILL BE TAKING EVERYONES CONTRIBUTION INTO ACCOUNT. I HOPE TO HAVE IT UP TONIGHT FOR FINAL APPROVAL, THEN I WILL POST SUNDAY NIGHT. HOPE YOU ARE ALL WELL :) ELLEN - 4/06

Here it is...everyone's feedback and contributions were all collated in the best way I could. I've just had 6 months off, so this was a little tricker than I thought!! I hope you are happy with it .....Ellen :)))

ok i just reposted this as someone deleted it??? 5.52pm

<span style="background-color: transparent; color: #000000; font-family: serif; font-size: 17px; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">Group 3 MathMates – Contributed by Ellen Williams, Vicki Williams, ****<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">Suzanne Williams, ****<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">Lia Wrigley, ****<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">Heidi Wilkie ****<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">, ****<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">Sarah Wright ****<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">, ****<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">Adam Townsend **

Word Count - 485

<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">//<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-decoration: none; vertical-align: baseline;">How do children learn Mathematics? //

<span style="background-color: transparent; color: #000000; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">To effectively teach mathematics, consideration must be given to the child’s previous knowledge. The area of mathematics begins with simplistic ideas, such as recognising shapes, patterns, and numbers, before moving onto more complex ideas. As such, it is paramount that children have a solid understanding of mathematical basics, plus the required prior knowledge, before progressing to the next level.Booker, Bond Sparrow & Swan (2010) consider that teachers of mathematics are encouraged to value that each learner has their own individual learning needs that must be met within a “learner-centred” (p. 5) environment. Together the authors discuss that children learn from being active within their own learning experiences and when children “construct their own mathematics, this knowledge is both personal and owned” (p. 12). When children have control over their own individual learning these “experiences are empowering” (Booker et al., 2010, p. 13) to them and knowledge is more likely to be retained.It is essential that teachers are equipped with many teaching and learning strategies to foster a positive classroom climate including an understanding of constructivism. Teachers should aim to provide learners with a safe and well functioning classroom environment which allows them to feel comfortable when asking questions or contributing to group discussion and group activities. There are many effective strategies teachers should be familiar when considering teaching mathematics including how to keep children engaged and motivated within the learning process. In order to achieve high levels of motivation teachers should know as much information about their students as possible. Teachers should offer an individualised approach to their teaching methods by “personalising content by linking topics to student’s lives” (Eggen & Kauchak, 2010, p. 310). Eggen & Kauchak (2010) consider that that student-student interaction is a vital part in the learning process, as peers play a fundamental role in scaffolding learning. Activities that allow students to participate and be active in the construction of their knowledge show deeper and more meaningful learning experiences.Teachers can demonstrate effective teaching practices by teaching tasks such as addition or multiplication, where students must first have an understanding of numbers and their meaning, before being able to complete number tasks. Failure to accommodate this requirement makes it difficult for children to grasp the learning, make sense of it, or achieve higher order thinking.Booker et al., (2010) discuss that when learners of mathematics are presented with “meaningful experiences that incorporate materials, patterns, language and symbols” (p. 26) they are more likely to foster a mathematical way of thinking. Additionally, through providing opportunities for children to discover, observe, discuss and collaborate in mathematical situations children will extend their zone of proximal development and as such their learning experience will be enhanced.The role of the teacher is therefore not just about verbalising information and organising mathematical activities and worksheets but rather facilitating learning and encouraging students by scaffolding ideas and to create concepts through classroom integration and interactive discussion.

<span style="background-color: transparent; color: #000000; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">**<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">Reference **

<span style="background-color: transparent; color: #000000; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">Teaching primary mathematics //(4th

<span style="background-color: transparent; color: #000000; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">ed.). Frenchs Forest, NSW: Pearson Australia. <span style="background-color: transparent; color: #000000; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">Eggen P., & Kauchak, D. (2010). //<span style="background-color: transparent; color: #000000; font-family: 'Arial','sans-serif'; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">Educational psychology: windows on classrooms //(8th.

<span style="background-color: transparent; color: #000000; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify; text-decoration: none; vertical-align: baseline;">Ed.). French's Forest: Pearson

Ellen - this is good. Really good. Well written, well referenced, and clearly well thought out. The only thing, and it is a really small thing, that I would perhaps change is in the third paragraph. A number of times it is stated "teachers should...". Perhaps one of these could change to be 'teachers need to be aware of...." or "teachers need to aim to..." - just something like that to break it up a little. Like I said, a really small thing. It is the only thing I would possibly change, and if you don't want to change it at all, speaking for myself alone, I am perfectly happy for this to be on the DB as is. Cheers, Suzanne 04/06/2011

Yes I agree, Suzanne. Thanks Ellen for pulling this together for us. It looks good. Vicki 5/6/11

Thanks Ellen, looks great :D Lia 5/6/11

Mathematics is a crucial life skill that all children need to learn in order to get into the work force and contribute to society. Maths is one of the most useful subjects other than literacy; everything we do has to do with maths from driving a car to groceries shopping. The role of a teacher is to ensure that every student at least understands the fundamental math skills to help them in the future. It is also a teacher’s duty to assess their students and identify what is the best teaching approach when teaching the class to ensure maximum results. Achor 4/06/2011 References: Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). Teaching primary mathematics (4th ed.). Frenchs Forest: Pearson Australia.

Ok thanks ...again for the feedback, it feels like forever since i have wriiten in academic writing, so thanks for being kind!!! this is what I have gone with :)

**<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Group 3 MathMates – Contributed by Ellen Williams, Vicki Williams, ****<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Suzanne Williams, ****<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Lia Wrigley, ****<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Heidi Wilkie ****<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">, ****<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Sarah Wright ****<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">, ****<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">Adam Townsend and Achor Zhou. **

<span style="color: #ff00ff; font-family: 'Arial','sans-serif'; font-size: 16px;"> //How do children learn Mathematics?//

<span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">To effectively teach mathematics, consideration must be given to the child’s previous knowledge. The area of mathematics begins with simplistic ideas, such as recognising shapes, patterns, and numbers, before moving onto more complex ideas. As such, it is paramount that children have a solid understanding of mathematical basics, plus the required prior knowledge, before progressing to the next level. <span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">Booker, Bond Sparrow & Swan (2010) consider that teachers of mathematics are encouraged to value that each learner has their own individual learning needs that must be met within a “learner-centred” (p. 5) environment. Together the authors discuss that children learn from being active within their own learning experiences and when children “construct their own mathematics, this knowledge is both personal and owned” (p. 12). When children have control over their individual learning these “experiences are empowering” (Booker et al., 2010, p. 13) to them and knowledge is most likely to be retained. <span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">It is essential that teachers are equipped with many teaching and learning strategies to foster a positive classroom climate including an understanding of constructivism. Teachers need to be aware to provide learners with a safe and well functioning classroom environment which allows them to feel comfortable when asking questions or contributing to group discussion and group activities. There are many effective strategies teachers must be familiar when considering teaching mathematics including how to keep children engaged and motivated within the learning process. In order to achieve high levels of motivation teachers should know as much information about their students as possible. Teachers are required to offer an individualised approach to their teaching methods by “personalising content by linking topics to student’s lives” (Eggen & Kauchak, 2010, p. 310). Eggen & Kauchak (2010) consider that that student-student interaction is a vital part in the learning process, as peers play a fundamental role in scaffolding learning. Activities that allow students to participate and be active in the construction of their knowledge show deeper and more meaningful learning experiences. <span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">Teachers can demonstrate effective teaching practices by teaching tasks such as addition or multiplication, where students must first have an understanding of numbers and their meaning, before being able to complete number tasks. Failure to accommodate this requirement makes it difficult for children to grasp the learning, make sense of it, or achieve higher order thinking. <span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">Booker et al., (2010) discuss that when learners of mathematics are presented with “meaningful experiences that incorporate materials, patterns, language and symbols” (p. 26) they are more likely to foster a mathematical way of thinking. Additionally, through providing opportunities for children to discover, observe, discuss and collaborate in mathematical situations children will extend their zone of proximal development and as such their learning experience will be enhanced. <span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">The role of the teacher is therefore not just about verbalising information and organising mathematical activities and worksheets but rather facilitating learning and encouraging students by scaffolding ideas and to create concepts through classroom integration and interactive discussion.

<span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">**Reference**

<span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching primary mathematics// (4th ed.). Frenchs Forest, NSW: Pearson Australia. <span style="color: #ff00ff; display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: justify;">Eggen P., & Kauchak, D. (2010). //Educational psychology: windows on classrooms// (8th. Ed.). French's Forest: Pearson