Week+3+-+How+children+learn+mathematics


 * __Learning Activity 3.1: Thinking about how children learn mathematics__**


 * //What are things I can do as a teacher to help children learn mathematics?// **


 * ** Give children a variety of concrete experiences from which they can build their conceptual knowledge on **
 * ** Relate the mathematics to the children's interests, e.g. a child who likes soccer can be shown how mathematics is used in soccer, and then expand mathematics to our everyday life **
 * ** Explain to children that many of their dream careers require mathematics **
 * ** Give children simple concepts and gradually introduce more challenge **
 * ** Encourage children to talk to their peers if they need help with their learning **


 * What are things I can do as a teacher to help children learn mathematics? **


 * 1:Explain to students that mathematics is all around them. Eg: when paying for items, counting pages in a book, playing hop scotch, or clapping to the beat of music. **
 * 2:Introduce mathematics by firstly looking at different patterns around the classroom or the school building eg: like the brick patterns in a wall. This will help them understand that mathematics found in different forms and is constant. **
 * 3: Use playing card or dice games eg: like snap or dominos as a way of allowing children to play games while still learning about mathematical symbols **
 * 4: Download or play songs which descibe counting or other mathematical terminolgy eg: There were 10 in a bed, 12 days of Christmas, Number Rumba etc. **
 * 5: Place students in groups then give each group a different counting tool eg: one group has an abacus, the other has a calculator, the other counters, and pick up sticks. The teacher read out excercises which asks them to add,or subtract numbers. Each group should all have the same answers using different equipment. Each group rotates so that each child experiences and understands the many ways of counting. Adam T 13.06.11. **

**What are the things I can do as a teacher to help childrenlearn mathematics ?**

**Kristy V 14.06.11**
 * 1) **Activitieswhere students work in groups with concrete materials to construct their ownknowledge of the task.**
 * 2) **Use mathematical games including computer programs for students to gain an understanding in maths in a fun way.**
 * 3) **Use formative and summative assessments throughout my maths lessons so that lessonplans are created to meet the individual needs of my students to ensure eachstudent is given the opportunity to learn maths.**
 * 4) **Provideactivities that relate to daily life activities so that students understand howmaths is used in the world around them.**
 * 5) **Createa positive learning environment where students feel motivated and excited tolearn maths. This would be created by my enthusiasm, making students feelcomfortable, questioning and feedback.**

**Learning Activity 3.1** **What I can do as a teacher to help students learn mathematics?**
 * 1) **Present problems using realistic examples to show students relevance to their own lives**
 * 2) **Demonstrate problems using interesting modes/mediums. E.g. – fractions with cut up fruit or pizza.**
 * 3) **Ensure there is always opportunity for questions, or that students are able to approach the teacher privately to avoid possible embarrassment.**
 * 4) **Conduct formative assessment and provide positive feedback to students also identifies students who need extra help.**
 * 5) **Be approachable, supportive, patient and understanding as every child learns at a different pace and each child will have different strengths and weaknesses. - Sarah Wright 14.06.11**

As a a teacher to help children learn mathematics:
 * 1) Always bring the learning back to the real world - show how the problems encountered are relevant in students day to day lives
 * 2) Use tactile learning where possible, ie blocks, pop sticks, charts
 * 3) Use ICT where possible in teaching and also for students to research mathematics
 * 4) Have students create their own learning, rather than by teaching by rote learning
 * 5) Allow for discussions and group work, rather than students working individually.

What am I learning: Glossary:

**Behaviourism:** the observation of a behaviour and the adaptation of this to be replicated in own life - stimuls and response

**Constructivism:** the making of own knowledge. Discovering a new concept, relating this back to existing knowledge, seeing how it fits in with prior knowledge, adapting exisiting schema.

**Zone of proximal development:** Giving a learner a task that they cannot do alone, but with sufficient scaffolding, can achieve

**Procedural knowledge:** the understanding of concepts and seeing relationships between concepts. The realisation also of when to use known procedural knowledge at apt moments.

**Multiembodiment:** The transfer of a concept across various models - ie a rectangle is a sheet of paper, a side of a building, the side of a wheelie bin.

**Metacognition:** The reflection on the way something is thought about - ie why do I think this way?

**Mathematics Anxiety:** a real issue in which people may get themselves into a state of anxiety over mathematics, believing (incorrectly) that they are not capable of success in the area, usually leading to lack of confidence in self regarding mathematics. Reassure person that frustration is normal with mathematics and praise progress.

**Learned helplessness:** When one believes they are truly not capable of success and doomed to failure. More often found in girls than boys as girls have a tendency to blame failure on self (McDevitt & Ormrod, 20110)

**Retention:** the ability to hold on to learnt knowledge - more likely to be retained if related back to everyday life, reviewed occasionally, children are hands on learners.

**Cognitive Development:** the development of thinking and reasoning skills

**Physical Development:** the development of the body, in particular gross and fine motor skills

**Social Development:** the development of skills that allow one to function effectively with others.

Suzanne 15/06/2011


 * <span style="color: #ff0000; font-family: Times New Roman,serif;">//What I am learning// chart **


 * behaviourism – A theory that emphasises the impact the environment has on human behaviour <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child stopped misbehaving because he was physically hit when he did. **

**constructivism – A theory which asserts that humans make interpretations in their environment and these form their own understandings <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child had a different understanding of the story to that of the teacher by the time the book had been read. **

**zone of proximal development – The distance between what a learner can do on their own and what can be done with the assistance of a more knowledgeable person <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the teacher assisted the child so he could complete a more difficult activity he couldn't do on his own. **

**procedural knowledge – The type of knowledge which concerns procedures, processes, and steps <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child had the procedural knowledge for a fire evacuation. **

**conceptual knowledge – The type of knowledge which concerns understanding the relationships and meanings a concept has <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child knew the importance of healthy eating. **

**multiembodiment – Refers to having more than one model with the purpose of improving a learners' sense making <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, an orange, pumpkin and orange flower were used to point out the colour of orange. **

**metacognition – Thinking about one's own learning <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). An effective practice in reflecting on one's strengths and weaknesses. For example, the child started asking the teacher questions when he realised through reflection that it helps him improve his learning. **

**mathematics anxiety – The uncomfortable feelings a person has towards mathematics, usually as a result of their past experiences <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child stopped doing any more mathematics exercises because they were too difficult for her stage of cognitive development. **

**learned helplessness – An attitude that it is too difficult for them to learn <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child feels it is impossible to learn because of their genetic make up. **

**retention – Refers to the capacity people have in remembering and applying what has been learned <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child had a good retention of knowledge because she wrote notes down during the lecture. **

**cognitive development – The growth in thinking and ways of learning <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child's cognitive development was helped by his school teachers. **

**physical development – The growth in physique and physical abilities <span style="font-family: Times New Roman,serif;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child's physical development was aided by the physically demanding exercises he was doing at the gym. **

**social development – The growth in social abilities <span style="font-family: Times New Roman,serif; font-size: small;">(Reys, Lindquist, Lambdim & Smith, 2009). For example, the child's social development had come along way from when he used to only babble and coo. - CHORY TYRRELL 11/06 **

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**What I am learning chart:﻿** <span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Mathematical anxiety –//** “a fear of mathematics or other negativeattitudes toward mathematics” (Reys, Lindquist, Lambdin, and Smith, 2009, p.17).Mathematical anxiety can be expressed as poor performance, misunderstandings,misbehaviour, not being motivated, does not like maths and not confident in ownability. For example a student misbehaves in class because they do notunderstand the task.
 * <span style="color: #008000; font-family: Arial,Helvetica,sans-serif;">What I am learning chart: **
 * Behaviourism: Skinner and other behavioual theorists believe that children learn emotional responses to certain motivations based on their unique experiences with those causes. For example: when a child is bitten by a dog they associate this experience to all dogs they see. **
 * Constructavism: The perspective of children actively creating rather than quietly absorbing knowledge. This is achieved as children construc t meanings in partnership with their peers or adults so that they increasingly obtain understanding and thinking processes both individually and through joint efforts with others. For example: A child building a billycart needs help from an adult to construct the product so that they can learn and develop their skills. **
 * Zone of proximal development: Tasks that a child can achieve only with assistance and support . Eg: A tennis coach teaching a student how to hit a backhand - the students needs the coach's knowledge and skill to perfect their technique .**
 * Procedural knowledge: is uses to solve problems and carry an action out - it can involve more senses such as hands-on experience, practice at solving problems, understanding of the limitations of a specific solution, etc. Eg: A student understands that they are to line up when going to assembly. **
 * Conceptual knowledge: is achieved by the construction of relationships between pieces of information or by the creation of relationships between existing knowledge and new information that is just entering the system. Eg: A student understands the real meaning of Christmas from reading and listening stories about the navtity. **
 * Multiembodiment: Using numerous examples to communicate the meaning of the subject matter being taught. Eg: Wheat, Dairy, Meat, Sugar, Timber etc are shown as examples of primary industries. **
 * Metacognition: Knowledge and belief about ones own cognitive processes as well as efforts to regulate those cognitive processes to maximise learning and memory. Eg: A child uses the process of proir knowledge of Italian songs to understand new Italian words taught in class **
 * Mathematics anxiety: is an intense emotional feeling that people have about their inability to understand and do mathematics. People who suffer from this feel that they are not capable of doing any course or activity requiring mathematics which usually stems from a past experience. Eg: A person refuses to attempt algebra due to the negative experineces they had at school learning maths. **
 * Learned helplessness: is a psychological state where people feel powerless to change their self or situation. This is primarily caused when people attribute negative things in life to internal, stable and global factors. A female gives up on persuing year 12 maths as she was told that females are not as good at maths as males. **
 * Retention: An ability to recall or recognize what has been learned or experienced through memory. Eg; The student remembered the days of the month through learning a simple rhyming song. **
 * Cognitive development: Systematic changes in reasoning, concepts, memory, and language. Eg: Puzzles, counting games, blocks, and cooking are examples of learning experiences that enhance cognitive development in young children **
 * Physical development: is concerned with the biological changes to the body and the brain. It includes genetics, growth of the fetus in the womb, the birth process and brain development and motor skills including behaviours which promote and limit health and environmental factors that effect physical growth. Eg: Learning to bounce,catch and throw a ball uses the learning of motor skills **
 * Social development:is learning the skills that enable a person to interact and communicate with others in a meaningful way. Children make friends, communicate, interact and share, take turns, which helps them to know how to behave and use appropiate language. Adam T 13.06.11 **

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Learned Helplessness –//** “the belief that the individual can notcontrol outcomes and is destined to fail without the existence of a strongsafety net” (Reys et al. 2009, p. 18). The main ideas include that it is oftenrelates to maths, girls are more vulnerable and students feel success is beyondtheir control. For example boys and girls being treated differently withinmaths lessons.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Retention –//** “reflects the degree to which students can holdonto and use what they have learned” (Reys et al. 2009, p.19). The main ideasinclude retention is an important element of learning and goal of maths,forgetting is an aspect of retention and particularly in maths, skills need tobe used regularly. For example at the beginning of a maths lesson what wascontained in the last lesson could be discussed briefly to assist withretention.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Procedural Knowledge –//** “is reflected in skillful use ofmathematical rules or algorithms” (Reys et al. 2009, p.20). The main ideasinclude that this knowledge allows students to successfully complete a processand allows students to answer precise questions. For example a student cancomplete a task that follows mathematical rules.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Conceptual Knowledge –//** “involves understanding whatmathematical concepts means” (Reys et al. 2009, p.20). The main ideas include students linking ideas to existing and new ideas and it also involves studentsmaking connections. For example when students are asked a question they canlink the answer to other mathematical concepts.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Constructivism –//** “Jean Piaget argued “that learners activelyconstruct their own knowledge” (Reys et al. 2009, p.21).The main ideas ofconstructivism include the focus on the thinking that students do and it doesnot only depend on the teacher but also how students build on their knowledge.For example students are given a maths problem to solve and the teacherfacilitates the lesson.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Behaviourism –//** “focuses on observable behaviours and is basedon the idea that learning means producing a particular response (behaviour) toa particular stimulus” (Reys et al. 2009, p.21). The main ideas includestudents learn skills from watching a teachers demonstration, not constructingtheir own knowledge, it does not require any thought process by the student andreinforcement can shape behaviour. For example a teacher demonstrates how tosolve a maths problem and students follow the same process.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Zone of proximal development –//** “range of tasks that one cannotyet perform independently but can perform with the help and guidance of others”(McDevitt & Ormrod, 2010, p. 214). The main ideasinclude new and challenging maths tasks can put a strain on working memory andvarious tools can assist students. For example a teacher will scaffold astudent through a task they are having difficulty with.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Cognitive Development –//** “has to do with how a child thinks andreasons. It also influences how the child learns new information” (Reys et al.2009, p.25). The main ideas can include Piaget’s cognitive stages ofdevelopment and how children develop and think at different rates. For examplea teacher may use questioning to encourage student thinking.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Physical Development –//** “has to do with the child’s muscles andmotor skills” (Reys et al. 2009, p.25).The main idea is that it must beconsidered when planning lessons. For example a teacher gives students ahands-on maths task.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Social Development –//** “has to do with how children interact withothers” (Reys et al. 2009, p.25). A main idea in the early years is to focus onothers besides themselves. For example a teacher places students within groupsto complete a task so students learn how to interact.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Metacognition –//** “refers to thinking about one’s own thinking(i.e., cognition about cognition) (Reys et al. 2009, p.27). The main ideasfocus on students being aware on their own abilities, behaviours, strengths andweaknesses. For example a student thinks about the way the solve mathematicalproblems.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**//Multiembodiment –//** “the use of perceptually different models.Multiemodiment helps students abstract or generalise appropriately” (Reys etal. 2009, p.27). The main idea is for students to experience mathematicalconcepts in more than one context. For example students learning that shapes come in different sizes but have similar characteristics.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">**__References__**

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">McDevitt,T.M., & Ormrod, J. E. (2010). //ChildDevelopment and Education//. Upper Saddle River, New Jersey: Pearson.

<span style="color: #808080; font-family: Arial,Helvetica,sans-serif;">Reys, R. E,Lindquist, M.M, Lambdin, D.V, & Smith, N.L. (2009). //Helping Children Learn// //Mathematics//.Hoboken, New Jersey: John Wiley & Sons, Inc.

**<span style="font-family: Arial,Helvetica,sans-serif;">Kristy V. 14.06.11﻿ **

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Learning Activity 3.2** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Metacognition - Thinking about ones thinking, self-reflection. For example students telling the teacher how they feel about mathematics, what they like and dislike.**
 * What I am Learning ||
 * Key Vocabulary || Definition ||
 * Behaviourism || Is an approach to teaching that focuses on external actions and observable behaviours, and the impact the environment has on this behaviour. ||
 * Constructivism || Is an approach to teaching that focuses on the thinking that student do and their ability to integrate new ideas with their experiences and what they already know. ||
 * Zone of proximal development || When a learner’s prior knowledge is increased by the support or scaffolding provided by a more skilled or knowledgeable other. ||
 * Procedural knowledge || The skilful use of procedures, processes instructions and steps ||
 * Conceptual knowledge || Understanding the meaning of concepts ||
 * Multiembodiment || The transfer of knowledge from one concept to another. Relies heavily on experience before they are able to make the correct generalisation. ||
 * Metacognition || Refers to having the ability to think about one’s own thinking. It involves children becoming aware of their own skills and thinking. Furthermore It involves observing what you do as you work and monitoring what you are thinking. ||
 * Mathematics anxiety || Otherwise known as mathaphobia, a fear of mathematics, or a negative attitude towards mathematics. Generally expressed as poor performance. ||
 * Learned helplessness || It is the belief that the individual cannot control outcomes and is fail. Includes the feelings of incompetence, lack of motivation and low self-esteem. ||
 * Retention || Reflects the extent to which students can hold onto and use what they have learned. ||
 * Cognitive development || How a child develops the skills to think and reason. ||
 * Physical development || How a child develops their muscles and motor skills. ||
 * Social development || How a child develops the skills to interact with others. ||

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Procedural Knowledge – Skilful use of knowledge, for example a student is able to successfully complete a process or sequence of actions by correctly using a rule.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Conceptual Knowledge – Understanding what mathematics concepts mean, students can see relationships between different pieces of information. The area of a rectangle can be used to find the area of a triangle.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Constructivism – Leaners actively construct their own knowledge. Learners use their past experiences in relation to what they learn and actively constructs their own understandings.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Behaviourism – Learning means producing a particular response (behaviour) to a particular stimulus (something external). Students learn by watching teachers demonstrate specific skills. The use of rewards and punishments are also used to shape behaviour.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Zone of Proximal Development – Lev Vygotsky describes the range of learning activities and experiences, For Example giving a child a task that is just outside their zone of proximal development but not so far that they are unable to complete it on their own.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Multiembodiment – experiencing a concept in a range of different contexts, for example learning about circles by seeing the pattern in shape between a coin, ring or pizza. This helps students to see the abstract or generalize appropriately. You can also provide varied examples of a single model.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Mathematics Anxiety – degree of anxiety associated with mathematics, fear of mathematics. For example a student who has negative feelings towards mathematics because they don’t see how it is relevant to their everyday lives and believe they will never use it.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Learned Helplessness – Repeat failure can lead to a downward cycle, the student believes that they cannot succeed and they lose motivation to try. Teachers need to have a positive attitude and make it clear that they believe all students can learn mathematics.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Retention – The ability of a student to hold onto what they have learnt and then apply it. For example remembering how to find a percentage out of 100, so when they go shopping if there is a sale they can work out how much cheaper the product is after the discount.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Cognitive Development – The maturity and progression of how a child thinks and how they reason their understandings. The change in a child's thought processes.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Physical Development – The growth and maturation of the child’s physical body, including the development of their fine motor skills and muscles. For example, a child can move from printing to using cursive writing as they gain greater control of the fine motor skills in their hands.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Social Development – The progression of a childs understanding of self, of others and how they interact with others in relation to their age.** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Sarah Wright - 14.06.11**

Behaviourism: This explains how children learn due to influences of their environment whilst they are being observed. Constructivism: explains that learners manipulate what is taught to them and create their own knowledge. Not just by remebering what they have been told. Zone of proximal development: When a learner is able to complete activities with assistance of another person, but they are not yet capable of completing the task by themselves. Procedural knowledge: Having the knowledge to do things. Conceptual knowledge: A mental picture that enables students to apply their knowledge. Multiembodiment: Using several different constructs to help children understand a new concept. Metacognition: How we as humans become aware of and are capable of using our brains processes. Mathematics anxiety: When a person dislikes the subject of mathematics or has negative feelings towards such as fear. Learned helplessness: When a student has a strong belief that they are unable to successfully accomplish a task. References. Eggen, P. Kauchack, D. (2010). //Educational Psychology: Windows on classrooms. Upper Saddle River, NJ: Pearson Education. (Heidi, 15/6)//

<span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">//What are things I can do as a teacher to help children learn mathematics?//
 * <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Establish a positive learning environment, where students are no scared to be wrong or ask questions
 * <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Teach authentic mathematics in its true original form something they will be able to use when they mature.
 * <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Incorporate different visual media into my teachings to enhance the learning experience
 * <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">I will execute different teaching techniques such as scaffolding or group work
 * <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">I will ensure I will cover the state curriculum and go above and beyond to ensure all my students are knowledgeable on the all aspects in mathematics according to their age Achor 17/06/2011

<span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">**Key vocabulary Achor 17/06/11** <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Behaviourism- A theory that explains learning in terms of observable behaviour and how they are influenced by stimuli from the environment <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Constructivism- A theory of learning suggesting that learners create their own knowledge of the topics they study rather than receiving that knowledge as transmitted to them by some other source. <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Zone of proximal development-A range of tasks that an individual cannot yet do alone but can accomplish when assisted by others <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Procedural knowledge- Knowledge of how to perform tasks. <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Conceptual knowledge-A mental construct or representation of a category that allows one to identify examples and non-examples of the catergory. <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Multiembodiment- Representation in variety of different context in a completely organized system <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Metacognition- Knowledge and beliefs about one’s own cognitive processes, as well as efforts to regulate those cognitive processes to maximize learning and memory. <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Mathematics anxiety- Feeling of tension, apprehension, or fear that interferes with math performance <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Learned helplessness- Where a person has learned to behave helplessly <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Retention-An ability to recall or recognize what has been learned or experienced; memory. <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Cognitive development- Changes in our thinking that occur as a result of learning maturation and experience <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Physical development- Systematic changes of the body and brain and age related changes in motor skills and health behaviours <span style="color: #862d31; display: block; font-family: 'Times New Roman',Times,serif; font-size: 120%; text-align: justify;">Social development-The advances people make in their ability to interact and get along with others.

**__Learning Activity 3.2: Conceptual and procedural knowledge__**

**1st example – Procedural and conceptual. The child displays an understanding of division and can show the computation needed to come to the correct answer.**

**2nd example – Procedural. The child mentions the steps needed to work out 25% of a number.**

**3rd example – Conceptual. I believe this is conceptual knowledge because the child described how to find the area of a rectangle. It is not procedural knowledge because she doesn't specify the steps involved.**

**Procedural knowledge – Steven multiplies 7 x 3 by going 7 + 7 + 7 to arrive at the answer of 21.**

**Conceptual knowledge – Chris knows what to look for when identifying a circle. - CHORY TYRRELL 11/06**


 * Example 1: Conceptual and procedural knowledge is used as firstly Steve understands the mathematical concepts to divide the lollies then he uses mathematical rules to problem solve **
 * Example 2: Procedural knowledge is utlised by Jill who solves both equations using mathematical equations **
 * Example3: Conceptual knowledge is used by Nancy as she uses the meaning of conceptual knowledge to help her problem solve. **
 * Procedural knowledge example: A half is equal to 1/2 and .5. A quarter is equal to 1/4 and .25. **
 * Conceptual knowledge example: A student knows the method of calculating long division Adam T 13.06.11 **

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Activity 3.2**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Slide 1 – Steve firstly uses conceptual knowledge by showing his understand of mathematical concepts. He then uses procedural knowledge to complete the problem by using a mathematical skill.** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Slide 2 – In both of these examples Jill uses procedural knowledge as she clearly identifies the steps taken to complete the problem rather than showing understanding of why.** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Slide 3 - In the last slide Nancy firstly uses conceptual knowledge to show she has an understanding of what she needs to do, find the area of the rectangle, which is how much space it covers. She then uses procedural knowledge to explain how she will do this.** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Conceptual Knowledge example - A student knows to identify a triangle as it has 3 sides.** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Procedural Knowledge - A student has the following problem - a + 5 = 10, they work this out by subtracting 5 from 10 to learn that a = 5.** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Sarah Wright - 14.06.2011**

Slide 1 - Conceptual knowledge. Steve shows knowledge of a previously learnt procedure and is applying the procedure to the appropriate circumstances. Slide 2 - Procedural knowledge. Jill knows the steps to get the desired result, but shows little knowledge as to why. Slide 3 - Conceptual knowledge. Nancy realises to get to a needed outcome she must apply a previously learnt procedure in the appropriate circumstances Suzanne 15/06/2011

Achor 17/06/2011 Slide 1- Steve displays **conceptual knowledge** by show by displaying the fact that he know mathematical concepts. Slide 2- Jill displays the concept of **procedural knowledge** an understanding of fractions and divisions by identifying the steps she must take to solve the problem Slide 3- Nancy uses **conceptual knowledge** by displaying an understanding the concept of how to find the area of a rectangle. After she uses **procedural knowledge** by identifying the steps she must take to find the area of the rectangle

**__Learning Activity 3.3: Clarifying constructivism as a theory of learning__**


 * CHORY TYRRELL - 11/06 **

**1.**
 * **When the groups of children were asked how they knew they were right, the reader was shown examples of constructed understandings as the explanations were different for each group. Many times the children suggested what they thought might work. Social interaction, a key tenet in constructivism was present in the case study. The children created new understandings the more they progressed in the activity.**

1: Each group of children were able to construct their own thoughts and reflections by calculating how to divide the 12 cookies amongst 8 people. The students created their own knowledge by using practical tools like paper, scissors and glue to illustrate how they calculated the results. Afterwards the groups wrote their findings down and presented these to the class detailing the methods they used. Overall they constructed meanings in partnership with their peers so that they increasingly obtained understanding and thinking processes both individually and through joint efforts within the group. Adam T

**2.**
 * **Homework from secondary school mathematics class applied principles of behaviourism as it got us doing drill and practice**
 * **When learning addition in primary school, it was taught in a sequential order**
 * **A mathematics project in high school required us to work in small groups, encouraging social interaction, a principle in constructivism**

2a: In secondary school, all our mathematical lessons were taught using behaviourist principals. I remember using our textbooks in every lesson with the teacher reading out each excerise on the page parroting the tasks required. 2b: At primary school my grade 3 teacher incorporated games as a way of learning our multiplication. The more times that you were correct they closer you were to win the game. 2c: There was atime when the teacher created a store environment where there were goods for sale and a shopkeeper with a cash register. We were learning about adding and substracting and rounding off numbers. This encouraged group interaction while working alongside our peers helping eachother calculate goods bought. Adam T

**3.**
 * **Behaviourism** || **Constructivism** || **Both** ||
 * ** · Strong focus on drill and practice **
 * · Skills learned in a specific order **
 * · <span style="font-family: Times New Roman,serif;">Rewarding students with correct answers **
 * · <span style="font-family: Times New Roman,serif;">'Shaping' children's efforts with rewards for each success they make in their learning, and gradually removing rewards until they can succeed on their own (Eggen & Kauchack, 2010). ** || **  · Practice is in the context of consolidating understandings of concepts and related skills **
 * · Use of manipulative materials to develop understandings of concepts and skills **
 * · <span style="font-family: Times New Roman,serif;"> Group work is encouraged ** || **  · Many current primary school mathematics textbooks because they present topics sequentially, but also often aim to use pictures and other images to develop understandings. **
 * · <span style="font-family: Times New Roman,serif;">Educational games can teach skills in a specific order, and then after this let the user manipulate objects on screen to construct new understandings ** ||

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Activity 3.3**
 * **Behaviourism** || **Constructivism** || **Both** ||
 * * Strong focus on drill and practice
 * Skills learned in a specific order
 * Children actively work for rewards. Eg to encourage good behaviour a teacher awards a certificate called "Student of the Day" to reward good behaviour throughout the day. || * Practice is in the context of consolidating understandings of concepts and related skills
 * Use of manipulative materials to develop understandings of concepts and skills
 * Constructing rather than absorbing knowledge eg: a primary student illustrates what underwater sea life looks like using self constructed conception || * Use a project based mathematical assignment to encourage group interaction while working alongside our peers helping eachother solve the tasks using skills learned from the mathematical equations learned. Adam T. ||

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**1) Have not been able to open this video yet, have posted a question for help on the DB.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**2)** <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Behaviourist – In primary school, Year Two, our teacher believed in learning our times tables by ‘parrot fashion’. We used to sit on the floor and she would yell out our name and throw us a big rubber dice and say a multiplication like 5 x 9, and you had three seconds to anser the question. The last person left won a prize.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Constructivist – In maths class in Year 11 & 12 our teacher would always do problems with us on the board. He would use us in the problem and make the problem related to our own lives, for example he said that we were going shopping and there was a discount on a handbag, how would we work this out. He sometimes used real life experiences such as cutting up fruit to demonstrate fractions so we could physically see halves, quarters and so on.**

<span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**3)**


 * <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Behaviourism** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Constructivism** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Both** ||
 * <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**B. F Skinner** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Jean Piaget** ||  ||
 * <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Focus on external actions and observable behaviours** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Focus on construction of new knowledge by reflecting on past knowledge.** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**What has the child learnt – results from tests, how did the child come to this conclusion? What method did they use and why did they use this?** ||
 * <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Clear instructional guidelines for teachers – students are shown what they need to do** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Children are encouraged to understand the processes based on what they know and what they have just been told** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Teachers show students algorithms then use them in meaningful experiences, students then discuss with each other why this algorithm works.** ||
 * <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Focus on parrot fashion type repitition of skills** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Many different contexts are used to promote a deeper understanding of the concept** || <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">**Student repeats times tables over and over at school, singing along to the songs. Students then have to represent multiplications of various objects and how they came to that conclusion.** ||
 * <span style="color: #ff7700; font-family: Arial,Helvetica,sans-serif;">Sarah Wright 14.06.2011 **

Own behaviourist experiences: All my early learning experiences of maths in my schooling years I would describe as being behaviourist. Early years it was rote learning constantly, reciting times tables as a class and lots and lots of pencil and paper exercises. Later secondary schooling, with the introduction of sine, cosine and tangent all I can recall again is lots of pencil and paper tasks for this. I do not once recall a teacher setting up a pretend shop, or ever working in groups in maths class unless it was time and distance measuring outside. (Sounds all doom and gloom, but I want to mention, I enjoyed maths in school right up until the end of year 10!)

Own constructivist experiences: Was not within a maths class, but an accounting class. When being taught to balance a ledger (pre-GST gasp!), the teacher gave us a few steps and then left us to see if we could work out the remainder to get to the correct conclusion.

Suzanne W 15/06/2011
 * **Behaviourism** || **Constructivism** || **Both** ||
 * * Strong focus on drill and practice
 * Skills learned in a specific order
 * Recitation of learnt skills ie chanting of times tables
 * Concepts introuduced one at a time without real explanantion other than 'this is the way it is done' || * Practice is in the context of consolidating understandings of concepts and related skills
 * Use of manipulative materials to develop understandings of concepts and skills
 * Discussion amongst students encouraged
 * Group work frequently used to share ideas || * Concept introduced by demonstration by teacher. Students then encouraged to go off in groups and see if they can recreate demonstration in a different way. ||

//Achor 17/06/11//
 * 1) The students in the video were able to construct their own solution to the problem by using different materials and using conceptual knowledge that dividing the cookies means to split it evenly as possible. The students were able to come up with a solution on their own without teacher assistance. The teacher played the role of the facilitator instead of being the instructor.
 * 2) I was not born in Australia, I migrated here at a young age so English was very difficult and school was even harder. I taught myself additions and the alphabet before year one by watching TV and using my abacus to learn additions. Constructing my own knowledge through interactions with my environment like trying to read a catalogue or count how many lollies I may receive. My mother taught me division using my favourite lollies in a jar if I was able to divide it right I got to keep the lollies to share at school. It was difficult learning English in a mandarin speaking household but because of my environment, but despite my environment my mother did a good job of facilitating me in my education so I wouldn't fall too far behind. Achor 17/06/11
 * 3) //Learning Activity 3.3 Record Chart: Behaviourism and Constructivism//
 * **Behaviourism** || **Constructivism** || **Both** ||
 * * Strong focus on drill and practice
 * Skills learned in a specific order
 * Constant praise and encouragement || * Practice is in the context of consolidating understandings of concepts and related skills
 * Use of manipulative materials to develop
 * understandings of concepts and skills
 * Discovering solution through experimentation || * Many current primary school mathematics textbooks because they present topics sequentially, but also often aim to use pictures and other images to develop understandings.
 * Both encourage group cooperation and the use of different medias and materials to solve problems ||

**__Learning Activity 3.4: The role of mathematics manipulatives__**

**[]**

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',serif; text-align: justify;">**Measuring the Area and Perimeter of Rectangles**

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',serif; text-align: justify;">**This manipulative teaches children to measure the length and width of rectangles to find their perimeter. The child uses a virtual ruler to measure the lengths of the shapes. At the bottom are input boxes where the child can insert the figures they have discovered. The area of the shape is determined by multiplying the length and width. The child submits their answers and immediate feedback is given, telling the child whether they got it right or not. The instructions proceed the game, giving the child the procedural knowledge required to complete the activity.**

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',serif; text-align: justify;">**This manipulative could easily be implemented in the physical world. Its real strength is in its immediate feedback it provides the learner upon submitting their answers. A teacher is recommended to guide the users, as well as explain why they are wrong. - CHORY TYRRELL 11/06**

http://au.ixl.com/math/year-1/identify-3-dimensional-figures

Identifying 3 dimensional figures is an interactive manipulative as it uses coloured 3D diagrams and gives the student 4 options to choose the correct shape. This game also has a sound icon so that students can hear the word as well as recognise the shapes visually. This is helpful with students who may be visually impaired asswell. Once you have selected all the correct shapes the student can finish and submit which then produces a score and gives the student the option to progress onto the next playing level. This manipulative is a great interactive tool which the teacher could download using an interactive white board and getting the whole class involved in answering and identifying the correct answers. Adam T

http://mathplayground.com/patternblocks.html The pattern blocks was chosen as it is an obvious way to show children different shapes. Students can have fun with this and be allowed to create designs with the blocks, as well as learn how these shapes fit with one another. For instance the triangle fits into the hexagon six times perfectly, which would then mean what sort of triangle is it? I could also potentially see students being given a picture on an a4 piece of paper, and asked to recreate it using the munipulative pattern blocks.

While there are positives, I can see negatives also. Size is not able to be manipulated with this virtual size - the size available is the only size for that shape.The pattern blocks do not flip, which makes manipulation a little difficult at times, and it also necessary to be very precise when placing the pieces if wanting them next to one another and not on top of one another. This then needs students whose fine motor skills are at a stage that they can accomplish this.

Suzanne 15/06/2011

[]

This activity allows shapes to manipulated so children are able to see them at many different angles, and learn how shapes can change. (Heidi, 15/06)

[] I reviewed something different from another site instead of mathplay playground. This link allows students to learn about manipulative with this virtual tool allowing students to learn about tangrams. Student can click on a shape template and use the 7 shapes to fit it into the shape template. The shapes can be rotated so they do not overlap. Though the activity is a manipulative the educational value is very little if it were to be applied to authentic mathematics education.

<span style="color: #ff7700; font-family: 'Arial Black',Gadget,sans-serif;">Learning Activity 3.4

<span style="color: #ff7700; font-family: 'Arial Black',Gadget,sans-serif;">Maths playground – I loved using the geometry board, thought it was a lot of fun and easy to use.

<span style="color: #ff7700; font-family: 'Arial Black',Gadget,sans-serif;">NVLM – Tried out the congruent triangles, which was also good, enjoyed the geometry board better though.

<span style="color: #ff7700; font-family: 'Arial Black',Gadget,sans-serif;">Weaknesses of virtual manipulative – While they are really enjoyable and fun way to learn using them often can make it hard to go back to teaching normally in the classroom, especially where there are certain topics where the emphasis on drill and practice is paramount. This can be boring then for the student. <span style="color: #ff7700; font-family: 'Arial Black',Gadget,sans-serif;">Strengths- Fun, innovative, fresh and allows students to connect with what they are learning in a way that they are familiar with. Sarah Wright

**__Learning Activity 3.5: Everyday Numeracy__**

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',serif; text-align: justify;">**What features were common to many of the activities?**
 * **Everyday objects the child can manipulate in their hands**
 * **Shapes, symbols and colours**

**Why do you think these features were evident?** **They are in the immediate environment, the home.**

**How might these activities help younger children in learning mathematics?** **They provide concrete learning experiences which can be built up so children can have abstract thinking and reasoning in their mathematics in later years. - CHORY TYRRELL 11/06**

<span style="color: #008000; display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;">**What features were common to many of the activities?**You can use any objects in the house which are associated with everyday routines like cooking, cleaning, playing games. Nearly all things around the home have mathematical themes like patterns, shapes, colours, weights, and time associated with them. <span style="color: #008000; display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;">**Why do you think these features were evident?**These features can be found all around the home and garden <span style="color: #008000; display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;">**How might these activities help younger children in learning mathematics?**These activities allow the child to construct their own experiences and meanings. With the help of an adult / older person, the child can learn new mathematicaal processes and relate these experiences to mathematics. Adam T 14.06.11

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',serif; text-align: justify;">**<span style="color: #008000; font-family: Arial,Helvetica,sans-serif;">References: ** <span style="color: #008000; font-family: Arial,Helvetica,sans-serif;">Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching Primary Mathematics// (4th edition). Frenchs Forest, NSW: Pearson Australia.

<span style="color: #008000; display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;">McDevitt,T.M., & Ormrod, J. E. (2010). //Child Development and Education//. Upper Saddle River, New Jersey: Pearson.

<span style="color: #008000; display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;">Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons.

<span style="color: #008000; display: block; font-family: Arial,Helvetica,sans-serif; text-align: justify;">Adam T 14.06.11

**__References__**
 * CHORY TYRRELL - 11/06 **

<span style="color: #ff0000; display: block; font-family: 'Times New Roman',serif; text-align: justify;">**Eggen, P. & Kauchak, D (2010) //Educational Psychology - Windows on Classrooms// (8th edition) Pearson: New Jersey**

**<span style="color: #ff0000; font-family: Times New Roman,serif;">Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //<span style="color: #ff0000; font-family: Times New Roman,serif;">Helping children learn mathematics //<span style="color: #ff0000; font-family: Times New Roman,serif;"> (9th ed.). Hoboken, New Jersey: John Wiley & Sons. **

// What can I do to help children learn mathematics? // Task 3.1 asks you to think about what you can do as a teacher to help children learn mathematics. After you have completed all the tasks (particularly the readings) revisit the question in your MathMates discussions. From this discussion submit a description of what you believe you can do to help children learn mathematics.
 * __FINAL SUBMISSION FOR WEEK 3, COMPILED AND COMPLETED__**

My two cents worth for this week's submission: Thanks, Suzanne 15/06/2011
 * Try to teach with a mixture of behaviouism and constructivism tendencies. There will be at times that behaviourism is the way to go, particularly when introducing new concepts. Try for a balance between the two, with an emphasis on constructivism.
 * Use positive reinforcers with students. In particular for those who may exhibit signs of maths anxiety
 * Have high expectations for students, and challenge all students equally (p.18, Reys)
 * Create a positive learning environment

Thanks Suzanne, I will compiling everything on friday night so if everyone could get their pieces in by then it would be appreciated. (Heidi, 15/6)

It is important that students construct their own learning within class groups which involve discussion and interactive behaviour. The teacher should encourage and lead the lesson by guiding students to find the solutions to mathematical tasks. This may be through providing tools for students to create their solutions eg: scissors, markers, paper, glue etc and communicating with them so that children are verballising and recording their findings. It is also important that children do practice their mathematical learnings as this creates the basis for them to enjoy new learning discoveries with a constructive learning environment. Adam T 15.06.11

Students construct learning through social interaction. Children construct meaning and understanding when they reflect on their own reasoning and the reasoning of others (Booker, Bond, Sparrow and Swan, (2010). Talking about ideas, concepts and processes helps them to make sense of this new information. Children also need mathematical aides becasue many of the ideas they learn are abstract ideas. the concept of numbers is an example of this. For instance, they cannot physically see the number four but can relate it to objects, for example four pencils. Too many mathematical aides to demonstrate a single idea can be confusing to children as they cannot link them to one concept. It is better to have one strong mathematical aide so that they are processing one concept in their minds. Mathematical aides that can be taken on to secondary school include the number line. When children reach secondary school this familar tool can be used to teach negative numbers. This enables children to build onto exsting knowledge about numbers that they learnt at primary school. Children also need to be active in their learning through play, interactive games and outdoor activities. There are many sites that have educational games for children and these includeThe Learning Federation and the Illuminations website.

__References__

<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 15px; line-height: 150%; margin-left: 36pt; text-indent: -36pt;">Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). Teaching primary mathematics. Frenchs Forest, NSW:Pearson Australia.

<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 15px; line-height: 150%; text-indent: -36pt;">DDisney, W. (Producer). (1959). Donald in mathmagic land [Video file]. Retrieved

<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 15px; line-height: 150%; text-indent: -36pt;">from []

<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 15px; line-height: 150%; text-indent: -36pt;">NNational Council of Teachers of Mathematics. (2011). Retrieved

<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 15px; line-height: 150%; text-indent: -36pt;">from []

<span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 15px; line-height: 150%; text-indent: -36pt;">TThe Learning Federation. (2010). Retrieved from [|http://econtent.thelearningfederation.edu.au] <span style="color: #808000; font-family: 'Arial','sans-serif'; font-size: 15px; line-height: 150%; text-indent: -36pt;">Kerrie Kerrie Wyer

It is important that student's are given the skills to construct their own knowledge so they can reach equilibrium in a way that is familiar to them. This will allow them to recall or solve problems in a more effective fact pace as oppose to contemplating for a long time. Incorporating different types of media or materials to assist students in constructing their own information is effective due to the fact students are playing a more active role in their learning as oppose to being spoon fed information by the teacher. I want my students to be able to complete given tasks with little assistance and much guidance instead. I want classroom to be an active learning environment where students are facilitated and encouraged to experiment with mathematical concepts. Achor 17/06/2011

Children must be allowed to paticipate is social learning situations in order to construct meaning that makes sense to them. Being allowed to work in a group situation with peers more advanced then them allows children to extend their zone of proximal development as they are able to be guided into a higher level of thinking. Additionally, children who are more advanced will often take on the role of "leader" in social learning situations and as such act a head taller then themselves. Providing materials that are relevant to the learner will assist in creating intrinsic motivation as well as make the learning real to the student, therefore mathematical aids should aim to be consistent with the children's real world experiences and be geared towards their likes and dislikes wherever possible. Lia 17/06

Final submission, Guys I have finished the submission. Please have any adjustments made by tomorrow as I will be submitting tomorrow night. (There is a reference list never fear, I just missed it in the copy and paste. Thanks (Heidi17/06).

**<span style="font-family: 'Arial','sans-serif';">Question ** **<span style="font-family: 'Arial','sans-serif';">What can I do to help children learn mathematics? **

<span style="color: #808000; font-family: 'Arial','sans-serif';">Within this essay there will be several points made about how teachers can help children to learn mathematics. The first issue is that of ensuring children are learning within a safe environment. The second point is that of teaching children developmentally appropriate content within the classroom environment. The third and final point is ensuring that children are actively involved in their learning.

<span style="color: #808000; font-family: 'Arial','sans-serif';">A safe environment is one of the most important aspects of learning for all children. When a student does not feel comfortable or respected in their class, they can become withdrawn and are less likely to be productive learners. To ensure students are in a positive environment teachers must endeavour to have the room arranged in a way that allows all children to see the front of the room easily so they can be involved in teacher, student discussion and easily see directions written on the board (Reys. Lindquist, Lambdin & Smith, 2007). Students need to be able to work in small groups and participate in discussion so they feel like a valued member of the class (Eggen & Kauchack, 2010). The use of positive reinforcement by the teacher can also encourage students to be proactive when it comes to learning maths. Praising students for “critical thinking and problem solving” (Reys et al, 2007) will encourage them to further their knowledge of mathematics. <span style="color: #808000; font-family: 'Arial','sans-serif';">Developmental domains are an important part of a student’s life. children that are in different stages of development are capable of learning different concepts which means that all content that is being taught must correlate with the development of the child. Tasks must challenge children and encourage social interaction. By implementing small group tasks children can work together to learn new content and work within their “zone of proximal development” ( Eggen & Kauchack, 2010, p47.). This ensures that learners can complete activities successfully that they would not be able to do alone (Brady, 2003). <span style="color: #808000; font-family: 'Arial','sans-serif';">Children must be actively involved in their mathematics education so their knowledge is maximised and they are able to continue through successfully to high school mathematics topics. To ensure learners are actively engaged in their learning teachers must introduce different media such as tactile objects to symbolise number problems and digital media such as resources found on the internet that can allow students to manipulate shapes or complete mathematical problems. Attempting to use real world examples in an educational context is a great way to develop learner understanding and prepare students for their future in a world where mathematics is used every day (Booker, Bond, Sparrow & Swan, 2010). <span style="color: #808000; font-family: 'Arial','sans-serif';">By being actively involved in every students learning journey teachers can make the learning environment used by their students safe and productive, while also teaching students mathematical information that appropriate for their age. The use of many different learning tools allows the subject to become real and interesting; this will encourage students to develop a valid interest in the mathematics subject.(Heidi17/06)

Sorry Heidi, I did mean to respond to what you wrote. No matter what, it is posted and thanks for doing it :)

I had read it this morning and didn't think it really needed any changes particularly. I lost track of time and have only just gotten around to it now. Suzanne 18/06/2011 Hi Suzanne, that is not a worry you were the first to post your ideas anyway. thanks for letting me letting me know (Heidi, 18/06)