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Module 4- Curriculum Planning, Design, and Assessment, Curriculum…

- - - - Introduction (setting the scene) - exploration and informally highlighting key concepts
      - Exploration (mucking about) - explore content used to build, connect, and retrieve mathematical understandings
      - Analysis (Going Deeper) - connecting ideas between concepts and representations through the use of carious conceptual situations and examinations
      - Synthesis (Looking Across) - recognizing core ideas across multiple situations
      - Abstraction (Going Beyond) - reflect on knowledge gained in order to consider and reason what else
  - - - Mathematical Processes: Problem solving, communication, connections, representations, reasoning and proof
      - Resulting framework for views of these processes (Listed from low level to high level): participatory, experiential, sense-making
      - Results and new questions:
        
        Many participants shared the processes standards as something do DO rather than how students LEARN.
        
        Provides a framework for a deeper interpretation of NCTM's Standards of Mathematical Processes.
        
        How do teachers and teacher educators develop an understanding of the mathematical processes? How might developing a trajectory for learning to teach mathematics with the process standards look?
  - - - What aspects of teachers' abilitiy to enact high-quality mathematics instruction are captured by IQA (Instructional Quality Assessment) Mathematics rubrics for lesson observations and collections of students' work?
    - - IQA is needed to identify and improve the quality of mathematics education for all students.
      - Mathematical Tasks Framework was developed through various researchers observing over 300 lessons.
      - Classroom artifacts can enable the triangulation of self-report or survey data by providing direct evidence to assess or validate self-reported practices.
    - - Designed to be used reliably during live observations of classroom instruction.
      - Mathematical tasks:
        
        Influence student learning because working on mathematical tasks constitutes what students do during the majority of their time in mathematics class
        
        Different tasks provide different opportunities for students' learning
      - Task Implementation:
        
        Most significant impact on students' learning
        
        Importance of cognitively challenging instructional tasks and high-level cognitive demands are sustained
        
        Teachers can maintain opportunities for high-level thinking and reasoning embedded in cognitively challenging instructional tasks through questioning, encouraging conceptual connections, and holding students accountable for explanations
      - Explanations of mathematical thinking and reasoning:
        
        Mathematical discussion following students' work on an instructional task influences students' opportunities to engage in high-level thinking and reasoning
        
        Students should have opportunities to analyze, compare, connect and reflect upon the collective mathematical work
      - Teacher's Expectation
        
        Teacher's envisionings of what they expect to take place in the classroom play a major role in shaping what takes place
  - - - The study aimed to offer a way to implement Financial Pedagogical Content Knowledge (fmPCK) to include students' knowledge from different cultural backgrounds. The study also demonstrated the need to add Culturally Relevant Mathematics to foster more inclusionary practices in the classroom as this leads to greater student wellbeing and engagement in maths.
        
        The author looked at the difference between how financial literacy is understood in school compared to the cultural understanding of financial literacy in some parts of Africa and indigenous communities (e.g. Lobola, King Blacksmith and Indigenous knowledge system). the study examines the challenges teachers face when teaching some learners from different communities and cultures, ( current financial rules in on culture versus a dollar tomorrow, interest versus pay what you owe - zero interest).
    - - Learners are from different home backgrounds with much different understanding of financial literacy backgrounds and understanding ( as demonstrated by Lobola, Blacksmith, Zeroloans examples). Teacher knowledge needs to take into account the different understanding of the topic in order to value the context that the learner brings in order to validate and engage the learners.
        
        PCK is about transforming how knowledge of the subject matter is being taught and responding to the learner's needs
    - - Mathematics Training may be viewed as acquisition of mathematics or pure maths
        
        While Mathematical Education is educationn of the learner that becomes a part of one's cultural experience
        
        Teacher Knowledge and CognitiveActivation Model
        
        aka COACTIV Model --incorporates Cultural Responsive mathematics - helps minimize classroom disengagement and students feel valued that their culture has a place in the school. COACTIV will motivate some learners to feel respected as their cultural knowledge is represented in their learning
        
        Financial Mathematics fmPCK Framework
        
        Bridges home knowledge and school mathematics knowledge. It is recommended that resource people from the community are invited in to share cultural topics. Mathematics representation should look at - examples, non-examples counterexamples of concepts or topics to get all perspectives included