Week+9++-+Location,+arrangement+and+direction

-x and y axis -coordinate plotting -2 dimensional shapes -quadrilaterals -spatial reasoning
 * Group Summary -**
 * Mathematics concepts taught/consolidated:**

-Helps to tranfer mathematical concepts from the abstract into the concrete. -Allows area for collaborative peer and teacher learning, through discussion of shape names (Geoboard activity) -Appealing to students -Fewer limitations of physical manipulatives. Easier, faster, can easily alter/remove shape -Virtual manipulatives provide a resource for all abilities "to develop...relational thinking and to generalize mathematical ideas" (Moyer-Packenhamet al, 2008) -Immediate feedback for students, a form a reinforcement that encourages their learning
 * Strengths:**

-May not be appropriate as an introduction to a geometrics, but rather a skill consolidator after the initial learning
 * Weaknesses:**

Moyer-Packenham, P. S., Salkind, G., & Bolyard, J. J. (2008). Virtual manipulatives used by K-8 teachers for mathematics instruction: Considering mathematical, cognitive, and pedagogical fidelity. //Contemporary Issues in Technology and Teacher Education, 8//(3), 202-218. Available: []

Language of location: **
 * LEARNING ACTIVITY 9.1 -
 * Location:**
 * **over **
 * **next to **
 * **in front of **
 * **behind **
 * Direction: **
 * beside
 * forward
 * back
 * left
 * right
 * up
 * down

> Mathematics concepts taught/consolidated: -coordinate plotting -2 dimensional shapes -quadrilaterals -spatial reasoning **
 * LEARNING ACTIVITY 9.2-**
 * -x and y axis

Strengths: -Allows area for collaborative peer and teacher learning, through discussion of shape names (Geoboard activity) -Appealing to students -Fewer limitations of physical manipulatives. Easier, faster, can easily alter/remove shape -Virtual manipulatives provide a resource for all abilities "to develop...relational thinking and to generalize mathematical ideas" (Moyer-Packenhamet al, 2008) -Immediate feedback for students, a form a reinforcement that encourages their learning **
 * - Helps to tranfer mathematical concepts from the abstract into the concrete.

Weaknesses:
 * - May not be appropriate as an introduction to a geometrics, but rather a skill consolidator after the initial learning

LEARNING ACTIVITY 9.3:**** Harry’s Map Harry is a Pre-Primary student. Annotations: This is a map of Harry’s home. It doesn’t contain much detail, just his house, a road and some trees. The map is in an unlikely scale; the house is much larger in proportion to the trees. While the house is shown from a side-view, the road is from an overhead perspective. As a teacher, I can see that Harry is not very good with proportion, and doesn't notice much about his world that doesn't directly concern him. His concepts of location and direction has not yet developed.

Zoe’s Map Zoe is in a Year 1-2 class Annotations: Zoe’s map has many houses, and what appears to be her school. The road is shown from a birds-eye view, with the houses seeming to lie ‘on their back.’ Zoe's concept of spatial reasoning is slightly more developed than that of Harry's. she has shown awareness of her route to school, and the proximity of school in relation to her house, though not with much accuracy.

Aaron’s Map Aaron is in a Year 5-6 class. Some names (of roads) have been blacked out so that where Aaron lives or who he is cannot be identified. Annotations: This map is difficult to read, as the graphic quality is poor. It looks as though Aaron has attempted to draw a map to scale, including details such as parks, roundabouts and street names. Aaron has also used what seem to be measurement (metres).

Michelle’s Map Michelle is a Year 7 student. Some names have been blacked out so that where Michelle lives or who she is cannot be identified. Annotations: Michelle’s map is details and to scale. It shows the route from her school to her house. She has details street names, pathways, shops and her school. This map would be easy to follow.

Booker et al, p.465-469 Reys et al, p.347-349 **
 * LEARNING ACTIVITY 9.4:

1. Unit learning outcome(s) for which this item provides evidence of learning // (type these out in words; do not identify by a number only) //**
 * //PLR 9//
 * Identify, describe and apply effective teaching strategies for teaching mathematics.

2. **Description/outline of what you have learned and how this learning demonstrates the learning outcomes you have specified above**

While manipulatives have been widely discussed throughout the course, this week learning activity 9.2 asked for analysis of the strengths and weaknesses of three specific virtual manipulatives. Analysing the manipulatives, in conjunction with questions to further develop learning, showed how learning can be benefited by introducing virtual manipulatives.

Another task this week involved listing words used to describe location and direction. Prior to this, I hadn't considered that these two things were mathematical concepts. I realised a point that has been reiterated over the course - mathematics is a widely used skill, a series of skills and processes that extend to many everyday activities. Though I can't remember formally learning which words to describe the location/direction of things, it's something that becomes relevant several times a day: put that over there, look on top of the table, walk to the left etc.

The relevance of location was highlighted this week. From describing location, to plotting maths and reading maps, location and direction are a critical component of mathematics. Without the skills to identify and describe location, many tasks become impossible; following directions, describing where to find items, identifying properties of shapes and patterns.


 * 3.** **How this learning relates to your development as an effective primary mathematics teacher.**

By analysing virtual manipulatives, I was able to understand how visual representations demonstrate maths concepts. 'Teachers need to give students experiences in using a wide range of visual representations and introduce them to new forms of representations that are useful for solving certain types of problems' (NCTM, 2000, p. 284).

While I had 'read' that maths was a widely applicable area, this was one of the first time's it has been clearly demonstrated in a way that I comprehended. As Reys et al. (2009) maintain, 'Mathematics has become an essential part of our world, both in everyday life and in the workplace.' The learning activities this week allowed my definition of mathematics to be broadened.

Children's understanding of location is paramount to their understanding of the world: 'Examining location and movements gives children a way to describe their world and give order to their surroundings (Reys et al., 2009). Understanding this, and implementing it into lessons through the introduction of language will enable my students to build a sound understanding of location, and the ability to use it in their lives.

REFERENCES: //Principles and Standards for School Mathematics// (2000), NCTM

© State of Victoria (Department of Education and Early Childhood Development), 2007