Week 12: Geometry

The Big Idea:

Geometry is known as one of the earliest forms of mathematics. It is an organised, logical and coherent system which involve the study of shapes, space and measurement. It is the study of 1D (lines), 2D ( planes) and 3D ( solids) shapes. Teaching geometry is central to mathematical processing and understanding as well as this it provides us with real life problem solving opportunities.


Concepts, Skills and Strategy:

Concepts- an organised, logical and coherent system for the study of shape, space and measurement.

Skills- the skills needed in geometry are communicating, drawing, naming, the ability to recognise similarities and differences, reading and navigating maps, visualising, modelling, thinking and reasoning.

Strategy- useful strategies for geometry include: sorting and classifying shapes, modelling, creating a net of a shape, drawing and building shapes with play dough, clay or any other material.

Misconceptions:

There is one common misconception when it comes to geometry and that is the understanding that a piece of paper can be mistaken for a 2D shape when in fact it is known to be a 3D shape because of it's depth and thickness. Furthermore, a paper is not a rectangle although it can be described as having a "rectangular shape" it is a " prism".

Resources:

According to the Measurement and Geometry section in ACARA Geometry is found in the Foundation Year and is described as " sorting and describing squares, circles, triangles, rectangles, spheres and cubes" along with this students will need to be able use spatial reasoning to visual 2D and 3D shapes as stated in the elaboration. This falls under the Scootle resource as ACMMG009.

Sourced Teaching Strategy:

( Jamieson-Proctor, R. 2019 Powerpoint presentation )

Textbook Concepts, Skills and Strategy:

In Primary mathematics it is important to understand the attributes and relationships of different geometrical objects. Throughout their early childhood and through to their primary years, students continue to describe and sort different objects. In doing so it will help them develop their thinking stage at Level 1 of Hiele's theory and move onto Level 2 of his theory. Children need to be able to recognise geometric shapes as objects used in the real world, they should also be able to list the names of common shapes including: triangle, square, rectangle, circle. As well as this they should also be familiar with other words that are associated with the shape such as a centre, radius, diarmeter  or circumference. Models play a key role in geometry, face models can easily be made with construction paper and edge models can be made with pipe cleaners or toothpicks that is connected with clay or tape ( Reys, R. 2012).


References:

Australia, E. (2018). Search - Scootle. Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMMG009

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406597&chapterid=190039

Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?year=11751&year=11752&strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&capability=Literacy&capability=Numeracy&capability=Information+and+Communication+Technology+%28ICT%29+Capability&capability=Critical+and+Creative+Thinking&capability=Personal+and+Social+Capability&capability=Ethical+Understanding&capability=Intercultural+Understanding&priority=ignore&priority=Aboriginal+and+Torres+Strait+Islander+Histories+and+Cultures&priority=Asia+and+Australia’s+Engagement+with+Asia&priority=Sustainability&elaborations=true&elaborations=false&scotterms=false&isFirstPageLoad=false

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 517,518,521,537,538). Milton, QLD: John Wiley & Sons.

Week 11: Measurement

The Big Idea:

This weeks focus was on the concept of Measurement, which begins in the Foundation Year. Knowing measurements are essential to everyday life such as knowing money or time. There are clear links to number knowledge to spatial situations such as different measurements including: volume, area, length and angles. Measurement is crucial in problem solving and it also connects mathematics to with different curriculum areas (english, arts, science). There are 4 main steps in the sequence of measurement:

1. Identity the Attribute - introducing and understanding the concept, this involves use of children language and non standard traits to measure ( pens, phones, blocks- counting units). 
2. Appropriate unit of measurement for attribute being measured- firstly, the use of non-standard units for measurement and secondly, using standardise units of measurements ( rules cm/m or protractors) 
3. Measure the object using the chosen unit- apply the number concept, matching the unit of measurement to the object through counting, comparing, ordering or sequencing.  
4. Report the number of units- represent the data with numbers, graphs or pictures. 

Concepts, Skills and Strategy:

Concepts- Knowledge of counting is essential in measurement as they will need to know numbers and how to count before they attempt to measure. Counting unit measurements such as km,m,cm,mm, l as well as any other useful units of measurement.

Skills- A few basic skills needed when learning measurement besides knowledge of number and counting is knowing what is countable and what is not countable. Being able to record the count as well as write the numerals is also important as it is a part of the 4 main steps outlined above. The proper use of equipment such as scales, weights, measuring tape, ruler as well as other measuring devices is also crucial.

Strategy- In measurement is it important to have the knowledge of multiplication and the times tables. Another useful strategy in measurement is the knowledge of all formulas ( eg. perimeter = L xW)

Misconceptions:

A few misconceptions when it comes to measurement for children is that all measurements should be the same if the piece of paper is the same. However, this is not the case as there are different types of paper with different lengths therefore it can not be assumed at all pieces of paper have the same length and width. Making a direct comparison is also a misconception as items of different sizes does not necessarily mean that the item will be heavier, it may be the opposite and weigh lighter even though it is a bigger book.


Resources:

According to ACARA, under the heading Measurement and Geometry for the Foundation Year students need to be able to compare both objects directly against one another using metric units to measure and estimate. As well as this it states that the suitable language used during the Foundation Year are: heavy, heavier, holds more, holds less, tall and taller are just a few examples given by ACARA as to the children's language that is used when describing the measurement of objects. Furthermore, comparing and ordering durations of events is also useful in the Foundation Year students will need to know and identify the days of the week on the calendar using sequencing to familiarise themselves with time order.  


Sourced Teaching Strategy:


( Youtube: https://www.youtube.com/watch?v=q8o7n-A0SC0)


Textbook Concept, Skills and Strategy:

The key ideas in measurement which are outlined in the textbook is that students start to explore the relationship between area and perimeter. Apply the concept and skills learnt in the pattern and relationship to find the result and lastly to create reasoning by explaining the possible solutions. According to the textbook measurement is can also be known as the notion for all concepts- number, pattern, geometry and data. Measurement can be brought into other subjects as it overlaps into many subjects. Measurement is known as a process in which a object is given a number to be associated with. As measurement is a process used in the " real world" it is important for children to measure objects outside of classroom materials, they will also need to develop their estimation skills as well as further develop their number sense ( Reys, R. 2012). Overall, measurement is crucial in their mathematical understanding as it is brought further into the context of the real world and it is for this reason and others that it should be taught in the Foundation Year.

References: 

Introduction to Nonstandard Measurement for Kids: Using Paper Clips to Measure. (2015). Retrieved from https://www.youtube.com/watch?v=q8o7n-A0SC0

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406594&chapterid=190032

Mathematics. (2019). Retrieved from https://australiancurriculum.edu.au/f-10-curriculum/mathematics/?year=11751&year=11752&strand=Number+and+Algebra&strand=Measurement+and+Geometry&capability=ignore&capability=Literacy&capability=Numeracy&capability=Information+and+Communication+Technology+%28ICT%29+Capability&capability=Critical+and+Creative+Thinking&capability=Personal+and+Social+Capability&capability=Ethical+Understanding&capability=Intercultural+Understanding&priority=ignore&priority=Aboriginal+and+Torres+Strait+Islander+Histories+and+Cultures&priority=Asia+and+Australia’s+Engagement+with+Asia&priority=Sustainability&elaborations=true&elaborations=false&scotterms=false&isFirstPageLoad=false

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 558,583,607). Milton, Qld: Wiley.

Week 10: Early Algebra part 2

The Big Idea:

This week further reinforced our understanding in the importance of Algebra. The main concept similar to last week is Algebra is a statement of a relationship between two variables. Algebra begins in the Foundation Year where children are taught to create and explore new ideas and key processes. There are two different types of patterns which relate to Algebra being: Geometrical Pattern and the Number Pattern, both of which begin in the Foundation Year and are carried through to Primary and Secondary school. It is important to note the difference between Formula and Formulae while a Formula is an equation a Formulae however is a statement of relationships between two variables.

Concepts, Skills and Strategies:

Concepts- It is the process of building and describing a pattern as well as this the concept of algebra also includes pattern, sequencing and generalisation which simply stands for a statement of relationship as mentioned previously. Further concepts also include Equivalence and Equation where the sign "=" stands for a point of balance, where one side has to be equal to the other for a state of balance to be met.

Skills- There are a number of skills used to help understand and work through algebraic equations. Skills such as: recognising patterns, growing a pattern, the process of repeating and describing a pattern.

Strategies- The use of materials or other manipulative can help with the process of solving an equation. Materials such as MAB blocks or balancing scales are useful in visualising the equation.

( ACU LEO: http://leo.acu.edu.au/mod/book/view.php?id=1238194&chapterid=36561)

Misconceptions:

As algebra is a complex concept to grasp there are many misconceptions that can occur. A common misconception among children is the difference between an Expression and Equation. An expression does not have a statement of equality or equal sign although it is a part of an algebraic equation, an example would be 7n + 3x-1 ( this would be a form of an expression). An equation however, has an equal sign a form of an equation would be 4x +5=2x+13.

Resources:

Stemming from last weeks post ACARA's description of Algebra in the Foundation Year under the subheading "Patterns and Algebra" can be defined as classifying familiar objects and explain the classifications. Furthermore, specific references to numeracy should be provided with understanding of patterns and the relationship within these patterns.

Sourced Teaching Strategy:

(Jamieson-Proctor, R. ( 2019) Powerpoint presentation ) 

Textbook Concepts, Skills and Strategies:

Following last week, the textbook outlines Algebra and Algebraic thinking in Chapter 15 when it states that it is: a study of patterns and relationship, a way of thinking, it is characterised by order and consistency, used to define terms and symbols and it is a tool. Primary students learn to develop algebraic thinking through modelling, generalising and justifying by explaining their reasoning or thinking behind their answers. Algebra is an essential part of the curriculum in the Primary years, as it builds on their understanding of Problems, Patterns and Relations.

References: 

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406589&chapterid=190027

Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&priority=ignore&year=11751&elaborations=true

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 485,487,488). Milton, Qld: Wiley.

Search - Scootle. (2018). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005

Week 9: Early Algebra

The Big Idea: 

The concept of algebra is introduced in the foundation years through recognising patterns, shapes and symbols, being able to build and describe the patterns created. At this stage in early algebra children may familiarise themselves with the words: Isolating, getting on its own and strip it down as it is the terms used in the Children's language stage when describing algebra. Algebra is a statement between two variables. An algebraic equation needs to be consistent all the way through. Simply put, algebra is the ability to understand patterns and order.


Concepts, Skills and Strategy:

Concepts- It is multiplicative, using bases 2 and 10. Although it is often Base 2. Algebra is referred to as an abstract number understanding, it consist of repetitive patterns, relationship equality and equilibrium ( balance). In algebra letters take the place of numbers and are represented as such these are often based on a repeating pattern. All patterns in algebra have to be consistent for it to be defined as a pattern.

Skill- The importance of pattern and order in Mathematics is vital in the understanding of algebra. A skill needed is to be able to recognise patterns and words ( letters) relating to the pattern, creating basic sentence problem to find a missing element or to grow a pattern. For example:

3XS+1=N.S

3 X number of sticks + 1= Number of sticks


Strategy- Useful strategies used in Early Algebra can include summing, multiplication as it is key to algebra, knowledge of patterns and sequences, the ability to problem solve independently and understanding symbols.

Misconceptions:

It is easy for misconceptions to occur especially when learning algebra. It is automatically presumed that algebra will make mathematics more complex as it combines both numbers and letters as well as different operations to find the total. As well as this a very early misconception that occurs when beginning to learn algebra is that students' may confuse the letter " X" with the variable " x". Finally,  another misconception combining non-like terms in an equation can further confuse a student for example : 5x + 4= 9x. This may confuse them as mentioned previously at this stage as they are not yet familiar with " x" being used as a variable.


Resources:

In ACARA under the Foundation Year Mathematics section subheading " Patterns and Algebra" the content description discussed how early references to algebra should be taught in the classroom with specific references to numeracy to be able to recognise and use patterns and relationship by observing natural patterns in the world around us and describe these patterns through material, sound, movement and drawings.

Sourced Teaching Strategy:

( Pintrest: https://www.pinterest.com.au/pin/157626055681170752/ )

Textbook Concept, Skills and Strategy: 

The main concepts in algebra which the textbook discusses is that algebra is the study of patterns and relationships, it is a way of thinking, it is characterised by order and internal consistency, it is known as a language that is carefully designed to define terms and symbols and lastly algebra is a tool. The skills that will be essential in the early years when students start to develop algebraic thinking and being to progress are the abilities to understand patterns in numbers, using language and symbols appropriately. Finally being able to work out problems, understand patterns and relations are all critical in early and primary school mathematics. A general strategy that applies to algebra is to number the terms, this can help students' to recognise and generalise a pattern ( Reys, R. 2012)  

References:

Jamieson-Proctor, R. (2019). Learning Environment Online: Log in to the site. Retrieved from https://leo.acu.edu.au/mod/book/view.php?id=2406589&chapterid=190027

Mathematics. (2019). Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/?strand=Number+and+Algebra&strand=Measurement+and+Geometry&strand=Statistics+and+Probability&capability=ignore&priority=ignore&year=11751&elaborations=true

Reys, R. (2017). Helping children learn mathematics (2nd ed., pp. 485,487,488). Milton, Qld: Wiley.

Search - Scootle. (2018). Retrieved from http://www.scootle.edu.au/ec/search?accContentId=ACMNA005