Week+5+-+2-Dimensional+Figures

__**Learning Activity 5.1: Exploring 2-dimensional figures**__


 * What is the role of free exploration in this lesson?

Allows the children to play with the material and get used to manipulating with it. The free exploration was given at the beginning of the lesson so as to allow children to familarise with the new concepts they were about to learn in geometry. Children will normally play with unfamiliar material before they try to make sense with it with the help of a teacher.

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 * What techniques were employed to engage students throughout the lesson?

Techniques used to engage the students included using an opaque bag requiring the children to put their hand in and describe the shape they were feeling in the hand. This was an exciting surprise for the children as they learn the attributes that make up shapes. The children drew on a small blackboard what they thought the shape they were feeling looked like. The questions used were interesting. The colourful pattern blocks that the children played with were fun. The partners the children worked with motivated them to learn more about the pattern blocks they were manipulating. - CHORY TYRRELL 17/06

The role of free exploration follows Vygotsky’s theory that children develop cognitively even when they are playing (Eggen & Kauchak, 2010). On their own the students were able discover patterns, shapes and even fractions. The lesson allowed students to work co-operatively in groups of two so they can also discover as a team the use of shapes and how they can be manipulated to create a new shape. The teacher engaged the students in the lesson by asking questions like “What have you learned?” or “Is there any other shapes you able to create?” Questions like this can launch class discussions or zone of proximal development for students who didn’t discover things on their own. Achor 24/06/2011 Eggen, P, & Kauchak, D. (2010). Educational psychology - Windows on classrooms New Jersey, USA: Pearson Education. : Pearson international edition.


 * What is the role of free exploration in this lesson? **

This was to help the students discover the nature of the new materials as well as discuss and create deign through playing and handling the shapes. This also helps to manage the class later in the lesson as the students have had a chance to handle the objects prior to completing the required tasks.

Initially Rose Christensen began the exporatory lesson by pairing students in 2, where they could create patterns, shapes, figures etc. The next excerise involved the entire class sitting on the floor where Rose would hold a paper bag so that students could take it turns to feel the the shape and its properties. The other students were required to draw what they were listening to and visualising how the shape was being described. Throughout the lesson Rose would pose questions eg: how many shapes can make a hexagon?, What is another word for a half a hexagon? etc. Due to the informal nature of the class discussion the students were comfortable speaking their thoughts and answering questions as the way they understood geometrical meaning. Adam T 27.06
 * What techniques were employed to engage students throughout the lesson? **

What is the role of free exploration in this lesson? Free exploration plays an integral and necessary part in this lesson. By being able to discover through play different shapes, their attributes and relationships to one and other, students are developing their own understandings. They are exploring through practice, play and experimentation how these shapes relate to one another, how they can be manipulated and constructed to form new shapes. This is deep learning in action as the students are constructing and developing their own understandings through free exploration with the guidance provided by the teacher. Free exploration allows the students to create their own understanding through physical activity and experience, rather than simply being told what they need to know.

What techniques were used to engage students throughout the lesson? The teacher provided students with shapes to experiment with and gave them the opportunity to free explore in pairs. This allowed for opportunity for personal discovery before she drew them back together as a group to ask questions that stimulated thought as to what they had just discovered. There was time here for discussion, questions and comments. The use of free exploration in pairs followed by discussion as a group allowed the students to discuss what they had learnt in their pairs and clarify this learning with the teacher and the group. Sarah Wright 28.6.11

//What is the role of free exploration in this lesson?// The free exploration allowed children to play with the piece and become familiar with them. The teacher recognised that the students would play with the pieces anyway, and so allowing them to have free play first provided a greater opportunity that they would stay focused on task during the lesson. //What techniques were employed to engage students throughout the lesson?// Vicki 1/7/11
 * Hand on experiences
 * Allowing students to have fun, free play
 * Interaction – group discussion, questioning, drawing shapes
 * Interesting activities (covering hexagon with other shapes), discovery learning.

__**Learning Activity 5.2:** //**Shape Maker**//__ Achor 24/06/2011
 * 1) 3 different ways to make a hexagon
 * 2) Yes to all of the questions you make a triangle from 2 to 6 pieces
 * 3) Yes, I found to ways to make a triangle
 * 4) No? I didn’t find the answer to this.
 * 5) Yes using 2 trapezoids and 2 triangles
 * 6) Yes, using 4 triangles and 2 trapezoids and 1 hexagon.
 * 7) Yes, you can make a non-regular with to 6 pieces.
 * 8) 4 Pieces to make a larger triangle
 * 9) 3 or 2 to make a larger rhombus
 * 10) None, I couldn’t find a way.
 * 11) Hexagon is equilateral shape it can only be formed using triangles. If you use only hexagons to make a shape, the only result you will find is tessellations.

__**Learning Activity 5.3: Children’s learning of 2-dimensional figures**__

**//Learning Activity 5.3 Record Chart: Children’s learning of 2-dimensional figures Achor 24/06/2011//** **//Learning Activity 5.3 Record Chart: Children’s learning of 2-dimensional figures - Adam T.//** Vicki 1/7/11
 * **Ideas and examples that are //familiar// to me from my own experiences with mathematics learning and teaching** || **Ideas and examples related to mathematics learning and teaching that are //new// to me** ||
 * * Visual cues are formed when handling and experimenting with shapes
 * With our first encounter with shapes we are taught what the shape is. Later we can identify what the shape is because we know its characteristics and its name
 * Geometry is a very practical subject it allows students to interact with one another and experiment with shapes || * Geometry also deals with locations such as coordinates.
 * Altitude is measured by what is specified at the base ||
 * **Questions I have and related things I do not understand from my reading**If children are given the names of the shape without being told or given the opportunity to explore. How do they eventually learn? Do we assess them without having to teach them about it? ||
 * **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** ||
 * Recognize and name shapes and relate these to everyday lifeDescribe the parts of a 2D shapeDrawing shapes and playing with different shapes || Transfornations and use symmetry to analyze mathematical situationsRelating ideas in geometry to ideas in numbers and measurementUsing 2D geometry in navigation ||
 * **Questions I have and related things I do not understand from my reading**Have educators tried to combine geometrical mathematics with other subjects like science or arts? ||
 * ** 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** ||
 * - Maths vocab should be built slowly. - Students need to see examples in different sizes and orientations || - Geometry engages children differently in performance and persistence than other maths topics. - Geometry is a topic where other maths can topics can also be taught - Many students are often only taught to recognise shapes and names. Need to move beyond this – to describing angles, sides etc and other properties of shapes. - Four levels of learning – from recognising shapes to proving statements about shapes. - Children first focus on the number of sides a shape has. - To teach relationships of shapes (i.e what makes a quadriliaterial etc) students must first verbalise the shapes properties. ||
 * **Questions I have and related things I do not understand from my reading** (See if any of your //Maths Mates Group// have any ideas for you in answering one of these questions.) ||


 * __FINAL SUBMISSION FOR WEEK 5, COMPILED AND COMPLETED__**

Hi Everyone,

I'm doing the submission this week, so if you could please try and get your contributions in by Friday it would be greatly appreciated.

Thanks

<span style="color: #ff8400; font-family: Arial,Helvetica,sans-serif;">Sarah Wright

Hi Sarah - just wanted to apologise for not contributing to this week's mathsmates question. It's been a rather interesting week for me. Good job with the first draft! - Suzanne


 * Free Exploration **

Mathematical learning occurs when there is a combination of activity and discussion. Through students' dialogue teachers gain insight into their views and knowledge, and see how these views are matched to those of the teacher inorder to check that the class is understanding meaning. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Free exploration in geometry provides a useful vehicle for developing logical thought and mathematical ways of working, such as classifying, hypothesising, justifying and generalising. <span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">Exporatory lessons help to build connected ideas and is important in developing spatial sense and in understanding geometrical concepts (Booker et al. p.410. 2010)<span style="font-family: 'Arial','sans-serif'; font-size: 10pt; line-height: 115%;">. Adam T 27.06

References: Booker, G., Bond, D., Sparrow, L, & Swan, P., (2010), //Teaching Primary Mathematics,// (4th Ed.). Frenchs Forest, New South Wales : Pearson <span style="display: block; font-family: Calibri,sans-serif; font-size: 11pt; height: 1px; left: -10000px; line-height: 115%; overflow-x: hidden; overflow-y: hidden; position: absolute; top: 1911px; width: 1px;">Building connected ideas rather than just remembering names and facts is important in developing spatial sense and in understanding geometrical concepts. Hi Sarah,

Good luck with this. I think it is a hard week to stretch out 500 words! Here is my blurb ...

The free exploration also served as a tool for the teacher, to ensure the students remained on task during the lesson. To achieve optimal outcomes, it is important for teachers to engage students through the provision of hands-on activities, in a group environment (Booker, Bond, Sparrow, & Swan, 2010). However, in a doing so, there is a risk that students may spend too much time talking and playing, and lose sight of the task at hand. In such a learning environment, it is important for teachers to ensure students’ attention is directed on the learning experience (Reys, Lindquist, Lambdin, & Smith, 2009). Therefore, by utilising free exploration at the beginning of the lesson where students could experiment or play, the students were less inclined to be distracted by the shapes when group learning was occurring.

References Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching primary mathematics// (4th ed.). Frenchs Forest, NSW: Pearson Australia. Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons.

Vicki 1/7/11

<span style="color: #e46c0a; font-family: Arial,Helvetica,sans-serif;">Hey Guys,

<span style="color: #e46c0a; font-family: Arial,Helvetica,sans-serif;">This is the first draft, and yes Vicki you were right struggled to pull out 500 words, this is about 460 at last count. Please let me know what you think, what I could change, any errors or anything I haven't included and I will edit and get a final copy to you asap!

<span style="color: #e46c0a; font-family: Arial,Helvetica,sans-serif;">Thanks, <span style="color: #e46c0a; font-family: Arial,Helvetica,sans-serif;">Sarah

<span style="color: #e46c0a; font-family: Arial,Helvetica,sans-serif;">FIRST DRAFT

<span style="color: #e46c0a; font-family: Arial,sans-serif; font-size: 12pt;">Free exploration or play, plays an integral role in the process of introducing new concepts to children. Free play should be the beginning of all learning, as this is how the would-be learner becomes familiar with the situation which he or she is confronted (Dienes, n.d.). This invaluable time gives children the opportunity to explore, discover and create their own understanding of a new concept. Free exploration can be used in numerous subjects including science and mathematics, where by using it learners are able to actively construct their own understandings (Eggen & Kauchak, 2010, pg. 43). This is particularly important in mathematics where exploratory lessons help to build connected ideas and is important in developing spatial sense and in understanding geometrical concepts (Booker et al. p.410. 2010)

<span style="color: #e46c0a; font-family: Arial,sans-serif; font-size: 12pt;">By using free play at the beginning of the class teachers are able to engage students through the provision of hands-on activities, in a group environment (Booker, et al, 2010). Teachers can then explore the learning the children have made in a group setting. Free exploration is just as valuable for the student as it is for the teacher, as it gives the teacher the opportunity to observe and understand how their students are forming their own understandings, what lines of thought they are using and it is exciting to see them actively using their minds.

<span style="color: #e46c0a; font-family: Arial,sans-serif; font-size: 12pt;">Zalton Deines introduced free play in his theory of levels of mathematical learning, where Free Play is the first stage of six; other theorists have also recognised the important role of free play. Brunner described this level as ‘enactive’ and describes it as firsthand manipulating, constructing, or arranging of real world objects, child is interacting directly with the physical world, (Reys, 2009, p. 23.) The recognition of the necessity to have this direct interaction with physical materials (Reys, 2009, p. 23) has contributed to the growth of constructivism (Reys, 2009, p. 23.) Free play promotes ideals of constructivism as it allows concepts to be taught in a social environment where children are able to construct meaning through the experiences they have with materials and problems, as well as through examining and reflecting on their own reasoning and the reasoning of others. This is such an important factor especially now with research confirming that “isolated” learning’s are not retained (Hiebert, 2003a, as cited in Reys, 2009). Without experience students will lack the direct concrete experiences they need to understand a concept (Eggen & Kauchak, 2010, p. 36).

<span style="color: #e46c0a; font-family: Arial,sans-serif; font-size: 12pt;">Free play is an invaluable tool for both teachers and students, it provides opportunity for individual learning and observation from the teacher, it allows students to use their own initiative to discover new concepts and build their own understandings.

<span style="color: #e46c0a; font-family: Arial,sans-serif;">Booker, G., Bond, D., Sparrow, L., & Swan, P. (2010). //Teaching primary mathematics// (4th ed.). Frenchs Forest, NSW: Pearson Australia.

<span style="color: #e46c0a; font-family: Arial,sans-serif;">Eggen P., & Kauchak, D. (2010). //Educational psychology: windows on classrooms// (8th. Ed.). French's Forest: Pearson

<span style="color: #e46c0a; font-family: Arial,sans-serif;">Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2009). //Helping children learn mathematics// (9th ed.). Hoboken, New Jersey: John Wiley & Sons.

<span style="color: #e46c0a; font-family: Arial,sans-serif;">Dienes, Z., //Zoltan Dienes’ six-stage theory of learning mathematics,// Zoltan Dienes’ Website, Biography, Math Games, Poetry and more//....// Retrieved from []

Hi everyone,

Here is my contribution. I noticed I am too late but will post it anyway. The draft looks great with lots of references.

Free exploration occurs when students are given concrete objects to play with. For example, in geometry children are given blocks of different shapes and during their exploration are able to discover the relationships between the shapes. Students actively make sense of their discoveries and this allows for deeper understanding. Students are constructing their own learning which is known as constructivism. According to Dienes (1960) in Reys, Lindquist, Lambdin, and Smith (2009, p. 24) children "...observe relationships, recognise patterns, and make generalisations and abstractions as they integrate new knowledge into thier existing mental structure." Free exploration allows students to do this. It allows them to actively make sense of what they are discovering and this allows for deeper understanding.

References

Reys, R., Lindquist, M. M., Lambdin, D.V., & Smith., N. L. (2009). Helping Children Learn Mathematics. Hoboken, New Jersey: John Wiley & Sons Inc.

Kerrie Wyer - 1/7/2011.

I am on next week for collating. I will collate next Friday night and have a draft posted Saturday morning for viewing. Hope this suits everybody. - Kerrie Wyer 1/7/2011. <span style="color: #ff8400; font-family: Arial,Helvetica,sans-serif;">

<span style="color: #ff8400; font-family: Arial,Helvetica,sans-serif;">Hey Guys,

<span style="color: #ff8400; font-family: Arial,Helvetica,sans-serif;">Does anyone feel there needs to be any changes? Or are there any other contributions? I haven't posted it yet, I will leave it for another few hours so if anyone thinks there needs to be any changes they can let me know... thanks! <span style="color: #ff8400; font-family: Arial,Helvetica,sans-serif;">Sarah