| Focus area 2.1 Content and teaching strategies of the teaching area Demonstrate knowledge and understanding of the concepts, substance and structure of the content and teaching strategies of the teaching area. Focus area 2.2 Content selection and organisation Organise content into an effective learning and teaching sequence. |
I taught a Year 7 mathematics class on my last placement, with mixed cognitive abilities ranging from A to D. I taught one lesson on ‘best buys’ (ACMNA174), planning it’s integration into a sequence of lessons across 4 weeks (2.2) (Australian Curriculum, Assessment and Reporting Authority, 2021). I considered strategies to effectively engage this group of 12-13 year-olds, taking into account interests, abilities, prior learning and potential mathematical misconceptions (2.1).
Even though the behaviour of the students was exemplary, I was conscious of engaging them emotionally and cognitively in the mathematics content (Duchesne & McMaugh, 2019). I considered their age, interests and prior learning from Year 6 (2.2), which included basic equivalent fractions, decimals and percentages (ACMNA131) (ACARA, 2021). I demonstrated alternative ways of thinking about rates by relating it to prior knowledge on equivalent fractions (2.1) (2.2). It is critical that concepts within mathematics are linked and that students are explicitly made aware of these links (2.1) (Goos et al., 2017).
To engage students, I chose concrete manipulatives that students could see and touch as the “hook” at the beginning of the lesson (2.1), as research has shown that creating authentic learning experiences using physical objects is important in engaging students and developing numeracy (Goos et al., 2012; Goos et al., 2017; Pendergast & Main, 2017). Lollies packaged in different sizes, with varying costs, were used to illustrate the concept of rate. Students played a guessing game of how many lollies were in each container, as estimation is a critical aspect of mathematical understanding and using a game for this age group is an effective strategy (2.1) (Goos et al., 2017). I also asked students to explain the strategy they used to estimate, giving these students the opportunity to justify their answer to enhance higher order thinking, and model to other students how to estimate (2.1) (Goos et al., 2017).
This was followed by a brainstorming activity where students indicated what they thought ‘best buy’ meant. This collaborative activity is an effective strategy in engaging students of this age (2.1) (Pendergast & Main, 2017). I provided scaffolding and questioning to assist students in linking ‘best buy’ with metalanguage and their own experiences (2.1), as shown in my lesson plan (Artefact 2a). Addressing misconceptions, such as thinking of the vinculum as a division operation, is critical for teachers to address (2.2) (Goos et al., 2017). I explicitly addressed this during the lesson (2.1), the importance of which was noted in my mentor’s feedback (Artefact 2b). I chose to cover ‘best buys’ before rounding decimals, as I wanted students to observe the issue with rounding when comparing irrational numbers (2.2). This served as a real life link to the next lesson on rounding decimals, amplifying its’ relevance (2.2). I observed significant emotional and behavioural engagement from the students, which was confirmed by my mentor’s feedback (Artefact 2c). I also called on individual students to answer questions, and this provided formative assessment of their cognitive engagement.
During my GTPA next semester, my goal will be to implement more concrete manipulatives, collaborative learning (Pendergast & Main, 2017) and real-life learning experiences related to mathematics (Goos et al., 2017). I’d also like to gauge the success of these measures by employing varied formative assessment. While I was able to observe individual student’s engagement in the activities, my aim will be to collect more evidence using varied formative assessment.
References
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2021). Australian Curriculum. F-10 curriculum Mathematics (Version 8.4). Retrieved October 3, 2021 from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
Duchesne, S. & McMaugh, A. (2019). Educational psychology for learning and teaching (6th ed.). Cengage Learning Australia.
Goos M., Dole S. & Geiger, V. (2012). Numeracy across the curriculum. The Australian Mathematics Teacher, 68(1). 3-7. https://files.eric.ed.gov/fulltext/EJ974975.pdf
Goos, M., Vale, C., Stillman, G., Makar, K., Herbert, S., & Geiger, V. (2017). Teaching secondary school mathematics: research and practice for the 21st century (2nd ed.). Allen & Unwin.
Pendergast, D., & Main, K. (2017). Quality teaching and learning. In D. Pendergast, K. Main & N. Bahr (Eds.), Teaching Middle Years: Rethinking curriculum, pedagogy and assessment (3rd ed.). 66-80. Allen & Unwin
