Standard 1: Know students and how they learn
1.1 Know physical, social and intellectual development and characteristics of students
Below I cite an example of my ability to know students and how they learn, and more specifically my understanding of how students’ physical, social and intellectual development and characteristics are catered for in my teaching.
Research shows that students learn best by having opportunities to explore content in a variety of ways, and according to Bruner’s (1985) principle, teachers will get a better result from all students if they combine concrete, pictorial and symbolic presentations of the material. This theory reflects the tenets of personal constructivism, which according to Piaget (1954) is where students make meaning from, and start to see patterns within, the content they are shown. Additionally, research shows that students’ learning is enhanced when they are presented with meaningful material which relates to their worlds, and according to Vygotsky (1987) teachers need to help students build upon their knowledge and understanding of the content from their zone of proximal development (ZPD)– the zone at which an educator can assist a learner through teaching and scaffolding to higher levels of understanding and skill. This ZPD reflects the learner’s intellectual development and their characteristics for learning, and according to mathematics educators Swan and Marshall (2010) the use of concrete materials and manipulatives in mathematics teaching is an effective way to teach content, particularly for young children who need sensory representations and experiences of concepts.
The Year 1 Australian Curriculum: Mathematics (ACARA, 2016) encompasses a wide range of skills and concepts, however one of the most relevant strands to the students’ lives is that of Money and finance. The financial concepts introduced at this early stage involve exploring the Australian coins and becoming familiar with each coin and denomination: Recognise, describe and order Australian coins according to their value (ACMNA017) (ACARA, 2016). On my recent practicum in Year 1, I was responsible for teaching a Money unit of mathematics and I implemented the theory about how children learn with the curriculum content I was required to teach into my lessons.
Below: Australian Curriculum ACMNA017 content descriptor and link. Credit: Australian Curriculum.
Below: Teaching program for Year 1 Money Maths. Image credit: Author.
This is my brief Money Unit program for the six Year 1 mathematics lessons on money. The students started with exploring the money and coins and then adding the values . Credit: Author.
In order to teach the children about the coins, I provided each student with opportunities to handle real Australian coins and role play with them in their groups. I then moved onto the explicit teaching of each coin and referred to a large poster of each coin and it’s identifying features, as well as the physical coins. During these lessons students were required to physically pick up the appropriate coins and relay back to me some of the features I discussed on the posters or ask questions and discuss about various features of the coins, such as the numeral, the date and the country of origin. I taught a number of sessions and provided opportunities for the students to explore and identify the coins both symbolically and physically, and after most students had shown evidence of knowing each coin, we moved onto adding the values of the coins.
Below: Whiteboard demonstration of coin adding. Credit: Author.
This activity was completed whilst the students were at the mat. Individual students came to the front to think aloud and tell the class how they 'made' each value of money written on the side of the board. Credit: Author
To make the learning more authentic and meaningful for the students, I taught the adding lessons in the context of a class shop. Through related ‘shopping’ activities, the students added firstly with physical coins with my guidance and scaffolding as a class and then in small groups and pairs on a cut-and-paste worksheet in which the students needed to find combinations of coins which would amount to a certain amount of money, as stated on the worksheet in numerals. During the worksheet activity (pictured below) I observed students working out the totals by counting on their hands and discussing with their peers, and I could see that each child was definitely building on their understanding that money can be added and subtracted, and that knowing the values of the coins makes this process much more effective.
Work samples. Image credit: Author
Overall, through hands-on activities with real coins, symbolic representations and numeral representations of money, the students were all able to successfully identify the values of Australian coins and appreciate the values in a real-world context. The students benefited from the different representations of money in which they were able to construct knowledge from both authentic and direct learning experiences.
This activity engaged the students and provided them with an opportunity to explore combinations of coins to become the sum of a monetary value. Credit: Author
This activity engaged the students and provided them with an opportunity to explore combinations of coins to become the sum of a monetary value. Credit: Author
References
Australian Curriculum, Assessment and Reporting Authority [ACARA]. (2016, August 15). Australian Curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1#level1
Bruner, J. (1985). Models of the learner. Educational Researcher, 14(3), 5-8.
Piaget, J. (1954). The Construction of Reality in the Child. New York: Basic Books.
Swan, P., & Marshall, L. (2010). Revisiting mathematics manipulatives materials. Australian Primary Mathematics Classroom, 15(2), 13-19.
Vygotsky, L. (1987). Thinking and Speech. New York: Plenum Press.