- Explain the link between laying a good foundation of ‘pattern and structure’ and successful algebraic thinking
- Explain what a ‘repeating pattern’ is and give an example
- Explain what a ‘growing pattern’ is and give an example
- Clarify the difference between procedural and conceptual understanding
- Define ‘functional thinking’ and explain the relevance it has to teaching underlying concepts instead of focusing on the computational aspects
- Design a fun A4 poster for your class to explain the meaning of an ‘equals to’ sign
POE Activity 1: Knowledge and Content
“Learners who have deep understanding are able to think flexibly with and about things they understand. They can consider ideas form multiple perspectives, solve complex problems, arrive at reasoned conclusions and use their own initiative to guide their exploration of knowledge.” (Killen, 2015: 67).
Write 500 – 600 word academic essay in which you describe and discuss:
- The importance of encouraging learners to communicate mathematically and to build their metacognitive abilities as important components in building deep understanding
- The use of questioning by a teacher to engage learners in Mathematical thinking that facilitates deep understanding
- The importance of problem‐solving, generalising and justifying as part of the teaching process in teaching for deep understanding.
POE Activity 2: Pedagogical application (Marks: 50)
Planning and execution of lessons with a clear goal in mind are skills that you must use to develop into a successful Mathematics educator. Using all the knowledge and skills that you have accumulated throughout the duration of this module, complete the following:
Summary of Task
Create an interactive lesson focusing on any relevant topic for a grade 4 class. Your lesson plan should be completed in as much detail as possible and should be approximately 1 hour. You need to include all worksheets and activities that will be completed during your lesson. If any additional resources are used, please put effort into integrating your lesson with a theme/unit from another learning area.
While preparing your lesson, utilise the following to increase learner engagement and understanding:
• Visual representations.
• The utilisation of hands‐on activities and multiple representations to help learners to develop conceptual understanding.
All resources (including slides, visual aids, lesson plans and other) must be printed and submitted in hardcopy to be marked. Should you use physical objects, e.g., dice, please include a photograph of these. Correct referencing must be present wherever required. (refer to Covid19 Section for submission guidelines if the campus is under lockdown.)
Consider the following questions before writing your lesson plan:
• Why are you teaching this particular lesson or topic?
• What are the learning outcomes you want learners to achieve as a result of the lesson?
*REMEMBER BLOOMS TAXONOMY*
• How will you assess if learners have met these outcomes?
• What constraints will you have to consider when presenting this lesson?
• What content should the learners master to achieve the learning outcomes?
• What teaching strategy will you choose, so that learners achieve the outcomes most effectively? Why did you choose this teaching strategy?
• What resources will be needed for the lesson?
• What reflection questions could you (as the teacher), answer once the lesson has been taught, to evaluate the success of the lesson.
Answers to Above Questions
Answer 1: There is a direct link between laying a good foundation of pattern and a structure and successful algebraic thinking. This is mainly because most educators use pattern in order to promote generalisation as a pre-algebraic activity. As algebra is considered as a tool for expressing generalities, exploring patterns in the elementary level can be considered as the foundation to algebraic reasoning.
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