Week 1: What is Mathematics?

Big Ideas


Mathematics is a universal language that is not just used inside the classroom. It is used in facets of everyday life whether an individual is aware or not. When helping children to understand the language of mathematics, teachers can use the four levels of the mathematics language model, which allows them to assist children to go from a material, to a symbolic understanding of mathematics.


Concept, Skill, or Strategy: The Language Model

The framework of the language model is useful for educators as it can aid in the planning and implementation of mathematics activities, that help children progress through the four levels of the framework. It is important to us materials and language that match the developmental stage a child is up to, as they need to progress through each stage in order so they move through familiar and concrete material first, and then progress towards abstract materials (Jamieson-Proctor & Larkin,). This is because to completely understand a mathematical concept, children need to be able to demonstrate their knowledge at all four stages not just one or two (For example, a child cannot completely comprehend a concept at the symbolic stage, if they do not have an understanding of the materials stage).




(Jamieson-Proctor, 2021)


Misconception

A common misconception about mathematics is that it is only about numbers, symbols, shapes and rules (Jamieson-Proctor & Larkin). This misconception may come about when students only understand, or are taught procedural knowledge (rules and algorithms) and not the conceptual knowledge (deeper understanding and making connections) (Reys et al., 2020). As a teacher, I need to remediate this by helping students establish connections and understand relationships within concepts, and not just be teaching a set of ‘rules.’


ACARA

The first mention of mathematics in the Australian curriculum, is in the foundation year in the number and algebra strand:

(ACARA, 2021)

Scootle

This scootle resource is suited to children in foundation and year one who are developing understanding of numerals and quantities. It would be useful for children to practice counting and number patterns, and includes different levels of difficulty to cater for more than one stage of learning.

This resource could be used for children at the student language stage as it used familiar objects of a train and only uses numbers not symbols. However, some of the carriages display number as ones units/counters even in the first level of the game. Therefore, it could be argued that this wouldn’t be appropriate unless children were up to the materials stage.


Number Trains - Click Here!
(Education Services Australia, 2016)


Teaching resource

This worksheet can also be used for students in the foundation year to practice counting and the sequence of numbers (ACMNA001). It can be used for counting both forwards and backwards, and can be edited to include larger numbers if a child has moved on from 1-20.

(Teach Starter, 2021)



References

ACARA. (2021). Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Jamieson-Proctor, R. (2021). EDMA241. Mathematics Learning and Teaching 1: Week 1 Part 1 (slide 9) Brisbane, Australia: Australian Catholic University.

Jamieson-Proctor, R. (2021). EDMA241. Mathematics Learning and Teaching 1: Week 1 Part 1 (slide 19) Brisbane, Australia: Australian Catholic University.

Jamieson-Proctor, R., & Larkin, K. (unpublished). “Mathematics as a language”: A theoretical framework for scaffolding students’ mathematical understanding. https://leo.acu.edu.au/pluginfile.php/4397494/mod_book/chapter/317089/Maths%20Language%20Model.pdf?time=1580788580219

Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Cooke, A., Ewing, B., & West. J. (2020). Helping children learn Mathematics (3rd Australian ed.). Milton: John Wiley & Sons.

Education Services Australia. (2016). Number trains. https://www.scootle.edu.au/ec/viewing/L2317/index.html

Teach Starter. (2021). Caterpillar place value ordering numbers worksheet. https://www.teachstarter.com/au/teaching-resource/caterpillar-place-value-ordering-numbers-worksheet/




Comments

Post a Comment

Popular posts from this blog

Week 11: Measurement

Image
Big ideas This week was all about the concept of measurement. Measurement is of important significance in our everyday lives, with Reys et a. (2020), identifying measurement as the concept from the primary mathematics curriculum that is used the most directly in students’ lives. We use measurement for areas such as time, temperature and money, and other real-life situations, like finding the number of tiles needed to cover a bathroom. The concept of any measurement is counting units. Teaching sequence for measurement: 1. Identify the concept and make sure students understand the attribute they are measuring e.g. area, length 2. Choose an appropriate unit of measurement for the attribute being measured 3. Measure object using chosen unit 4. Record the number of units Concept A focus on length: This concept, like any other measurement concept, needs to be taught using the 4-step teaching sequence mentioned above. An appropriate unit of measurement should be chosen based on the stage of t...
Read more

Week 7: Number and Place Value

Image
Big Ideas This week in lectures and tutorials, we covered a large array of content. We firstly looked at number sense, numeration and mental computation. Numeration and mental computation was linked back to our content from weeks 2-5, and we were reminded of the big 7 thinking strategies across addition, subtraction, multiplication and division.  We then moved on to place value, which I found to be a much larger concept than I expected. This week I learnt that there is not just the ‘ones, tens, hundreds, thousands’ or the base 10 system. I found it really interesting to learn about other bases such as base 5 and base 3, and to see them modelled for me, as I was only ever taught the base 10 system at school. As a teacher, I will need to ensure I emphasise the importance of place value to my students and incorporate it into every area of mathematics. This is because place value is “one of the cornerstones of our number system” and is part of all work with whole numbers, the metric sy...
Read more