INDIVIDUAL HURDLE TASK 1: OUTLINE OF AN INQUIRY-BASED PEDAGOGICAL PRACTICE: TEACHING, LEARNING, ASSESSING, and JUSTIFICATION
Specific teaching/learning topic (Plan)
Lesson Plan
The choice of what to teach and how to link the teaching to the Australian Curriculum are very challenging choices that a teacher needs to make regularly (Wiske, Breit, & Franz, 2004). The learning topic I choose is Mathematics and the Lesson focus is on Place Value. I am planning to teach this lesson in grade one for a duration of 60 minutes. The lesson is embedded in a Unit of Work that takes place in Term Four, week 5-6 and it aims to expose students to two strands of the Australian Curriculum:
- Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (VCMNA087)
- Count collections to 100 by partitioning numbers using place value (VCMNA088)
The reason why I am choosing this topic is mainly to cover two strands of the Australian Curriculum but also to experience and use the Mathematical Content Knowledge and Pedagogical Content Knowledge acquired along the last two years of Master of Primary Teaching. Particularly, during EDMA504 with Matt Sexton and EDMA684 run by Belinda Beaman and the Annual Mathematics Conferences held at ACU.
Teaching, learning, and assessment cycle (Teach)
A well-planned lesson does not necessary lead to an effective learning experience as it depends what strategies are utilised to deliver the planned lesson (Killen, 2015). This Unit of Work employs a number of different teaching strategies because there is not a unique strategy to effectively teaching children (Killen, 2015). Some examples of teaching strategies adopted for teaching this place value lesson are: direct instruction, work in pair, small groups and whole class, more/less than, Part-Part-Whole, renaming 2-digit numbers, Problem Solving (Van De Valle, 2017). In the lesson plan chosen I use more than one strategy to differentiate and cater for a range of students offering enabling and extending prompts.
Diagnostic, Formative and Summative Assessment
It is essential to assess students in order to foster improvement among students and based on the judgement it is also crucial to promptly taking action to address the gaps in the students' knowledge (Tompkins, Campbell, Green, & Smith, 2014).
The content knowledge taught in classroom is assessed in three different moments and ways. Diagnostically at the very beginning of the unit of work to collect data about the students’ prior knowledge and fostering recalling. Throughout the unit of work, several formative assessments are run to identify and address knowledge gaps with the purpose to adapt the present and future teaching. During formative assessments the teacher gathers essential information to better understand which teaching strategies and approaches are more effective in that specific context.
Finally, summative assessment would be implemented at the end of the unit of work to collect data for reports, identifying if the success criteria are met and create a background for future units of work.
With the purpose of being as effective as possible, all the assessments are strictly linked with the planned success criteria, learning intentions and Australian Curriculum and also, they are carefully planned prior the first lesson or unit of work (Popham, 2008).
The theoretical teaching model
The pedagogical approach that underpins this unit of work sees the student in the centre of the learning process. Constructivism is the main teaching model in this unit of work. Instead of using explicit and direct teaching only, as ‘behaviourism’ would, the unit of work sets up the conditions for the students to build upon students’ prior experience, creating their own knowledge and generating self-motivation though curiosity. There are mainly three ways the constructivist approach takes place in the unit of work. Firstly, the five lessons are planned in a way that the students can connect their own experiences with the learnings. Each lesson begins with prior knowledge activation (e.g. how many do you have?) which is recognised as the best practice since prior knowledge is the basement for new knowledge construction (Lee, Coomes, & Yim, 2019). Piaget (1950) defined ‘assimilation’ the process which occurs when the students build upon their prior knowledge. Secondly, they have the chance to construct their knowledge as they are asked to produce and investigate different features of the informative text and perspective of the proposed topics. In fact, the lesson progression involves the development of a mini-lesson which consists of the teacher modelling the following task and directly teaching the main ideas of the learning intention. Children are not exposed to a full direct teaching lesson but they are rather supplied with direction for their learning. In fact, the teacher is not a mere knowledge dispenser, she/he is rather a thinking facilitator (Tompkins, Campbell, Green, & Smith, 2014). Finally, the intent of planning this unit of work is to self-motivated students who are going to be more successful learners. The students are asked to engage in a task in order to develop their thinking which involves a natural process of learning (Smith, 1971). The “vocabulary experts” activity is a clear example of self-motivating and thinking trigger that generates learning among students. The tasks are adapted for ‘gifted’ and ‘diverse’ learners to ensure that the cohort has the same pace and time to work on their task. Enabling and extending prompt are then included in the unit of work to support the teacher in delivering the lesson. Another important pedagogical component embedded in the unit of work is the “gradual release of responsibility model” which emerge from the progression planned for the four lessons. The teacher starts modelling the topic and the task (I do), then progress into doing together (we do) to finish releasing complete responsibility to the students (you do). The reason behind the use of this model is that it develops confident learners and craft the conditions for the students to take responsibility for their own learning (Fisher & Frey, 2008).
Literature review
Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning.
Journal of Mathematical Behavior 25(3), 208–223.
This article examines the development of students in terms of their functional thinking in primary setting environment. The authors describe the current evaluation and shift from the traditional approach of teaching algebra, inciting how this shift suggests that algebraic reasoning occurs in conjunction with arithmetic reasoning. The author aims to connect the gap between experiences in earlier years with patterns and through the progression of primary school to increase the exposure to abstract algebra by teaching within the domain of the students’ knowledge and experiences.
The author conducted a research teaching experiment within two classrooms with a total of 45 children, which comprised of four lessons. The lessons were designed to enhance the students’ ability to build mental representation in order to explore the use of function tables. The study shows that elementary students can both develop functional thinking and communicate this thinking both verbally and symbolically. In addition, the results show that the students had more difficulty with subtraction changes than addition changes. Thus, the lessons showed that depending on the context of a problem, a students’ ability to generalise the problem in inhibited.
Wilkie, K. J., & Clarke, D. M. (2015) Developing students’ functional thinking in algebra through different visualisations of a growing pattern’s structure.
Mathematics Education Research Journal, 28(2), 223-243.
This article examines the way in which upper primary school children visualize particular growing patterns and their level of generalisation. The authors describe the potential of student within the age brackets of upper primary in terms of their ability to visualise a pattern in a myriad of ways, and their ability to conjure more than one functional rule to their visualisation. Moreover, the author poses a need to consider the ways in which teaching and learning of algebra have been implemented and the importance of pattern generalisation.
The authors’ research focused on conducting an experiment with ten groups of teachers and student, in which the students were given a series of questions, with a particular focus on two tasks, the first was how the students choice of visualization relates to their ability to generalise and that individual students are able to visualise the same geometric structure in a myriad of ways. The study showed that the students answers and performance could be categorised into 4 methods, and highlighted that the design of these growing patterns had an effect on these students, to aid their ability to focus on the structure of an item in the pattern.
References
Lee, H. S., Coomes, J., & Yim, J. (2019). Teachers’ Conceptions of Prior Knowledge and the Potential of a Task in Teaching Practice.
Journal of Mathematics Teacher Education,
22(2), 129–151. Retrieved from https://search-ebscohost-com.ezproxy2.acu.edu.au/login.aspx?direct=true&db=eric&AN=EJ1211568&site=ehost-live&scope=site
Killen, R. (2015). Effective teaching strategies: Lessons from research and practice (Seventh ed.).
Piaget, J. (1950).
The psychology of intelligence. London: Routledge & Kegan Paul.
Van de Walle et al. (2017). Chapter 11: Developing whole number place value concepts (pp. 246-270)
Wiske, M. S., Breit, L. & Franz, K. R. (2004). Teaching for understanding with technology. San Francisco: Jossey-Bass.
Popham, W.J. (2008).
Transformative assessment. Alexandria, VA: Association for Supervision and Curriculum Development.
Tompkins, G., Campbell, R., Green, D., & Smith, C. (2014).
Literacy for the 21 st Century: A balanced approach
(2nd
Ed.). Frenchs Forest, NSW: Pearson Australia.
Angelo, T. A., & Cross, P. K. ( ) From Classroom Assessment Techniques, A Handbook for College Teachers, 2nd Ed.