The Numerate Educator A3
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Curtin University *
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1021
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Mathematics
Date
Apr 3, 2024
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docx
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Uploaded by MasterResolveShark32
The Numerate Educator: Assessment Three
Weight: 50%
Due: Monday 25
th
of October
Part A
This assignment asked us to discuss the mathematical content knowledge outlined
throughout the unit this semester and relate it to the pedagogical content knowledge needed
to teach three concepts in early Number and Algebra. The concepts outlined in the report
are sorting and classifying, patterning and subitising and group recognition. Area One: Sorting and classifying
Mathematical content knowledge:
Sorting and classifying in mathematics is defined by the Australian curriculum as grouping
objects or people together according to their similarities. In foundation years students are
expected to be able to sort and classify familiar objects and be able to explain why they
chose to classify them in that way (ACMNA005). Reys et al (2020) mentions how classifying
is fundamental to learning in the real world and how it can extend much further than just
numbers. Once the concept is grasped children can use their knowledge to sort objects and
distinguish between thing and even people (for example grouping people based on eye
colour). Classification is essential to sorting as it allows people to reach and understanding
and agreement on what is to be counted in certain situations.
Lavitelli, (as cited in Platz, 2004) makes a distinguish between sorting and classifying by
stating that simple sorting is the beginning step to classifying, if a student is sorting then they
are often told the task and then proceed to carry it out by themselves, for example “give me
all the red pens.” However, classifying requires students to inquire about the characteristics
of an object and distinguish how they can be categorised, for example, “look at these pens,
how can be sort them into groups?”
Pedagogical content knowledge:
There are many ways in order to encourage students to sort and classify objects one of the
ways, as suggested by Reys et al (2020), is to use the well know concrete material of
attribute blocks or ‘logic blocks.’ These blocks usually come in the medium of wood or
plastic for the physical blocks or the app Hands-On Math Attribute Blocks App can be
purchased through the apple store for iPads for online usage. The attribute blocks are a good tool for students who are beginning classifying as they differ
in a number of things including colour, shape and size. Before doing this activity, I would
allow the students to have some free play with the blocks so that they could become familiar
with the blocks. Once the activity has begun I will be able to walk around the class and
observe how the student intuitively sort, classify and group the blocks in their own different
ways. A good example of sorting and classifying can be seen in Lakeshore Learning where a
teacher named Meghan talks about some activities she uses in order to teach students
different attributes of objects, she described this to her children as ‘words we use to describe
an object, such as its size colour or shape.’ An example of an activity she uses involves
three hoola hoops (or circles drawn on the pavement with chalk), paper and markers. In
each circle using the paper write down three colours (for example red, blue and yellow), the
students can be divided up into small groups and then go on a ‘classifying hunt’ around the
classroom to find objects that match the categories of each colour.
Area Two: Patterning
Mathematical content knowledge:
Patterning in mathematics, Year one, is defined by the Australian curriculum as being able to
investigate and describe number patterns formed by skip counting and patterns with objects
(ACMNA018). Reys et al (2020) defines patterning as the foundation of all mathematics,
stating that recognising, creating, constructing, copying, continuing and describing patterns
require problem-solving skills and constitute an important part of mathematics learning.
Reys et al (2020) describes how a pattern can fit into three different categories of attributes,
geometric attributes (shape, symmetry and structure), relational attributes (function,
sequence), physical attributes (size, texture, colour, number) and/or affective attributes
(appeal, sadness, happiness). Natural and manufactured concrete materials can be used as resources to help students
understand how patterns are formed, examples of object materials are wood or plastic cubes
or miniature animals, pattern blocks, food, people, leaves, almost any concrete material can
be used for patterns.
Pedagogical content knowledge:
There are many ways in order to encourage students to learn and make patterns. Reys et al
(2020), suggested that there are four main steps to how students learn how recognise,
understand and make patterns, they are coping a pattern, continuing the pattern and finding
the next one, extending a pattern and creating patterns.
Copying a pattern is conducted by showing a pattern to a student and getting
them to replicate it. For example, a student might be handed a piece of
string and be asked to choose the beads to copy the pattern modelled by
the teacher. With continuing the pattern and finding the next one
requires students to analysis the pattern and be able to tell what’s
required to continue it on its path, an example is shown in
figure one.
When extending the pattern, the student is shown a pattern
and asked to extend it and find the next object. For example, a simple stamp exercise can
be conducted where the student has to draw the next two animals in a pattern outlining the
following:
Sheep – Chicken – Dog – Sheep – Chicken – Dog – Sheep ____?_
____- ____?_
_____
Finally creating patterns, creating and understanding patterns is one of the fundamentals of
mathematics and students need to be comfortable in using concrete materials to do so. For
example, giving students natural, craft or everyday materials to create patterns, sometimes
the pattern will be complex and other times it will be simple, but it is essential to their
mathematical thinking. Area Three: Subitising and group recognition
Mathematical content knowledge:
When students are young, before they even begin to count they are aware of small groups of
numbers, such as two eyes, one mouth, two wheels on a bike etc. Studies show that
students entering school are able to identify quantities of groups of three or less without
needing to count on their fingers. Other techniques to use to identify groups of four or five
are objects such as dice or dominos (Reys, 2020, p.193).
Pedagogical content knowledge:
Research has shown that children find rectangular arrangements easiest, followed by linear
and then circular, with random arrangements being the most difficult, as the child will need to
break it up into recognisable parts (Reys, 2020, p.194). Compared to grouping or counting,
when dealing with subsidising real-life objects, such as animals, have been found to be
difficult for young children to subitise. Simple examples of activities to perform with students
could be rolling a dice and having to read the number shown without counting on their
fingers.
Figure one
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Part B:
This part of the assessment asks us to reflect on our own personal numeracy progress, this
includes, but is not limited to, aspects of Math space, LANTITE preparation, readings and
leanings from the topics. I will be focusing on how my understanding of mathematics has
developed, what I have learnt about teaching mathematics to foundation years and my
overall knowledge of the unit. Reflection:
This semester I have become much more aware of the great need to use concrete materials
when teaching students in the classroom, as pointed out in class, concrete materials are
essential for children because they help facilitate an understanding of mathematical
concepts. The understanding of how children learn in younger years has developed my own
personal break down and understanding of mathematics as simple things such as addition
and subtraction are taken for granted if you don’t know the breakdown of how it begins. Throughout this semester I attended almost every in class session however, didn’t use math
space as I found the in-class content beneficial enough, and if I had questions my tutor was
always more than happy to help. Overall, I found the unit extremely beneficial and have already been able to apply my
knowledge in a classroom setting as I work in a pre-primary class as an E.A, where we are
currently working on grouping and addition/subtraction. I found the initial analysis of the
Australian curriculum for assignment one rather daunting as it was unfamiliar to me, however
I now find the Australian curriculum extremely helpful and use it on a weekly bases with
other assignments.
Word count: 1,407
References:
Australian Curriculum Assessment and Reporting Authority. (n.d.). The Australian
Curriculum: Science
(Version 8.3), Foundation, All curriculum elements. http://www.australiancurriculum.edu.au/download/f10
Reys, et al. (2020). Developing meanings for the operations. Helping Children Learn
Mathematics (3rd ed., p. 183-194).