Week+6+-+2-dimensional+shapes+&+spatial+reasoning


 * __LEARNING ACTIVITY 6.1: Booker et al - p.404-417 - Deeper exploration into how children learn shape/space concepts.__**

-only some visual clues noticed || -can view shape as whole, but not properties (holistic?) || - acknowledge attributes and properties || -can observe interrelation of properties || -use deduction to prove statements  ||
 * Van Hiele proposed levels of geometric understanding (from Reys et al, 2009):**
 * **Level 0** || Prerecognition
 * **Level 1** || Visual
 * **Level 2** || Descriptive/analytic
 * **Level 3** || Abstract/relational
 * **Level 4** || Formal axiomatic

Implications of Van Hiele levels of understanding (taken from Booker p. 405):
 * Information: through experience students familiarized with content/language of shape & space
 * Guided orientation: explore objects/investigate relationships
 * Explication: explanation, talking, discussion using maths language
 * Free orientation: problem solving
 * Integration: reflection on how learning connects with/builds on other knowledge

General strategies and principals for teaching geometry:
 * explore and investigate
 * experience a variety of activities
 * see range of sizes and orientations
 * use a wide range of materials
 * describe activities and relationships


 * __LEARNING ACTIVITY 6.2: Booker et al - p.417-441 - Further exploration of 2D shape__**s
 * 2D shapes can be sorted into 3 groups: straight sided, curved, mixed.

PLRs: (all quotes and page references taken from booker et al)
 * how to teach geometry - implication of Van Hiele - top of p. 406 - 'Children need to engage in mathematical thinking by exploring an activity or situation, and then, with the explicit aid of the teacher, reflect and think about what they have done and found out.'
 * importance of reflection on the teaching of geometry - bottom of p. 407 - 'reflection and discussion with a teacher is vitally important in developing understandings and knowledge embedded in the activity.'
 * activities provided 408-413 - to address misconceptions/support learning of 2D shapes

// 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 6
 * 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**

The Van Hiele model provides a guide to the most effective method of teaching geometry (Reys, 2009). As with any subject, the teacher is assisted by an understanding of the way in which children learn. The van Hiele model provides this insight, proposing that children move through 5 stages in their geometrical understanding. In addition to this, attainment (how to guide students through each level) is specified by Booker et al (2009), allowing teachers to best initiate the theories of van Hiele into the classroom. In my learning, this will only be of benefit to me as a teacher, allowing me to plan lessons based on researched methods of best teaching children geometry.

Another reading in this week's activities (Booker et al, 2009, p.401-441) also concerned teaching geometry to students. As well as explaining the ways in which children best learn new concepts (exploration/reflection/variety of materials etc.), the text suggested activities to demonstrate the concepts, taking into account Van Hiele's levels of geometric understanding. For instance, Booker et al (2009, p. 419) suggest a card sorting game to consolidate the properties of the 3 basic forms of two dimensional shapes (straight-sided, curved and mixed). This utilizes several of the proposed guidelines for teaching mathematics; use a variety of materials, exploration and investigation, the opportunity to verbalise findings using mathematical language (van Hiele, 1986).

Although constructivism (the building of new knowledge upon previously learned information) has been a constant topic throught my learning thus far, the mportance of reflection has not been emphasised in recent weeks. This week, the text (Booker et al, 2009, p.407) reiterated the importance of importance of reflection on the teaching of geometry; 'reflection and discussion with a teacher is vitally important in developing understandings and knowledge embedded in the activity.'


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

The Van Hiele model enables me to understand how children best learn geometry. As a teacher, understanding that geometric experiences have the greatest influences on the advances through Van Hiele's levels (Reys et al, 2009) will allow me to plan effective geometry lessons, which increase my students' learning. Experience is essential; 'Children need to engage in mathematical thinking by exploring an activity or situation, and then, with the explicit aid of the teacher, reflect and think about what they have done and found out' (Reys et al, 2009).

This quote from Reys et al. (2009) also emphasises the importance of reflection, and subsequently, its role in constructivist lessons. Without a structured summation of learning, a lesson is left open. By recapping the points of the lesson, a teacher is reiterating them, and making sure each student has learned the intended knowledge from the lesson.

Booker et al. (2009) not only provides an overview of Van Hiele's levels of geometric understanding, but also suggests way in which to introduce them smoothly into lessons. For instance, Booker et al (2009, p. 419) suggest a card sorting game to consolidate the properties of the 3 basic forms of two dimensional shapes (straight-sided, curved and mixed). This utilizes several of the proposed guidelines for teaching mathematics; use a variety of materials, exploration and investigation, the opportunity to verbalise findings using mathematical language (Van Hiele, 1986).

REFS: booker reys