Module 4- Curriculum Planning, Design, and Assessment
READINGS
Big concepts
Arc of Leadership Edson et al
This research suggests that problem based curricula provides an avenue for promoting deep mathematical understanding and reasoning. The key is to understand the components the 'arc' framework and envision implementation from the perspective of the learner.
An Emergent Framework: Views of Mathematical Processes ::
Interview of 9 participants on how they view and understand NCTM's An Agenda for Action (1980) Mathematical Processes.
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?
Time for a Tune Up: Comprehensive Curriculum Evaluation
Comprehensive review model to include: Validity, Implementation, and Evaluation
Validity: Specify "enduring understandings" with focus group made up of multiple stakeholders including parents, instructors at local colleges, and local employers.
Implementation: relies heavily on trained educators that need regular reviews to ensure consistency. Evaluation on how enduring understandings are taught can be done by administrators, but even more effectively by students.
Evaluation: how well are students achieving key concepts? Cross-grade level teachers collaborate to design common assessments to use across all grades and possibly disciplines.
Thinking Quotes
"Nonetheless, it is not in the best interest of the students for educators to completely relinquish the power found in designing curriculum to those who do not intimately know the students" (Meyers, )
"A major hurdle for curriculum administration is solving the time dilemma." (Meyers,)
"Besides hearing about effective methods of instruction, the teachers heard again and again that the students desperately needed to be active participants in their own education" (Meyers, )
Arc of learning Framework:
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
Assessing Instructional Quality in Mathematics
Questions
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?
Background
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.
IQA (Instructional Quality Assessment)
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
Questions
Curriculum Development: Inductive Models F.C. Lunenberg
Towards Culturally Embedded Financial Mathematics PCK framework by J.P Makonye
J.P Makonye, 2020
"It is invaluable to incorporate mathematical ideas from the learner's culture in everyday mathematics teaching and learning. This addresses the rote learning of alien, meaningless mathematical Knowledge" ( page 102)
"Mathematical Content Knowledge framework embedded in learners' cultural background, I argue that such a framework encourages less alienation in the mathematics classroom. A culturally responsive curriculum is specifically designed not to perpetuate and enrich the culture of a people and equip them with the tools to become functional participants in society" (page 98)
" In the modern world, having learners from different countries, I'm surprised by that's, with different lunges and cultures in a school, has become the norm rather than the exception. The teacher needs to develop the knowledge and skills to respect learners' cultures. I argue that mathematics teachers need to embrace the diversity of knowledge that their learners bring to school, which would open new avenues on how to teach their learners" ( page 105)
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Weinstein and Fantini Humanistic model
- the curriculum is modelled on the learner's affect.
-Learners are identified based on age, grade level, and common culture; characteristics. then knowledge is based on one common characteristic and interest - school considers students concerns, needs and interest, self-image and self-concepts and the teacher develop strategies for instruction to meet learns needs and concerns
- content is organized based on life experience, attitudes and feelings and social context
- learning skills, self-awareness, learning how to learn and cognitive are central to evaluation and helping students progress
-teaching procedures match learning skills
Eisner Systemic Aesthetic Model
Has five detentions:
- Intentional: A need to decide on - What matters in school - teaching? Evaluative practices? Nature of our workplace?
- Structural: The school structure has not changed in the past 100 years. We start in September and end in June, with 30 students per class, taught by a single teacher. this structure has become too restrictive and needs to change
- Curriculum: Should be designed to engage students and pay attention to skills that count, ideas that matter and more interaction between students and programs
-Pedagogical:Quality of teaching must improve. Schools must serve teachers so that teacher can serve students
- Evaluative: move away from scoring students to finding out how we are doing to do better
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What is curriculum development (CD)? " Curriculum development can be defined as the process of planning, implementing and evaluating curriculum that ultimately results in a curriculum plan.
Models of CD for analysis by this paper
Hilda Taba - Instructional Strategy model (1962)
Geral Weinstein and Mario Fantini - Humanistic Model (1970)
Elliott Eisner - Systematic-Aesthetic Model( 1991)
Taba Instructional Approach.
-the content for each grade is organized around teaching-learning units, e.g social studies organized around the unit
- each unit is organized around 5 elements - objectives, content, learning experience, teaching strategies and evaluation measures
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Where do we go from here?
Edson et al, 2019
"A critical component of professional development is teacher experiencing a problem-based curriculum as leaners and reflecting on the emerging mathematical understandings and the realted pedagogy." (Edson et al., 2019)
"Teachers need to conduct mathematics classrooms that vary greatly from their own mathematical experiences. The challenge includes making sense of understandings from a problem-based perspective on the teaching and learning of mathematics.
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"Deep interpretation of [curricular processes] requires a common language," (pg. 98)
Cultural diversity and appreciation for the differences in the application of learning objectives
We need an understanding of our own philosophies and pedagogical content values in order to properly connect our curricular revision attempts.
HOW do we assess student curricular knowledge, when our own views of curriculum differ so greatly?
"Circle back" on own vision and processes, as well as depth of student connections of curricular concepts
Purpose of the Study
PCK for Financial Literacy Why Special Knowledge for Teaching Finacial Literacy
The Author makes a distinction between Mathematics Training vs Mathematical Education
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).
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
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
F.C. Lunenberg
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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
" the structural organization of school has not changed much in the past one hundred years. We start school in September and end in June: ...thirty students per class taught by a single teacher; grades are given several times a year, and students are promoted to the next grade. Such a structure is restrictive" ( page 7)
"the quality of teaching ou to be a primary concern of school improvement. To treat teaching as an art requires a level of scrutiny, assistance and support that any performing art deserves. Schools need to be place that serve teachers so that they can serve students" ( page 7)
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What can we add and adapt into our classrooms?
What can we propose to fellow faculty and school boards?
Why is it necessary to rethink the way schooling and the curriculum are structured and delivered in the technological age?