Application of Matrices in real life. Presentation on application of matrices
CCC-M F2F meeting_140326
1. Creating, Collaborating
and Computing in Math
Enhancing the teaching and learning of
mathematics using technology
Riverside School Board and McGill University- March 26, 2014
2. 9:00 - 9:45 Review of CCCM Project Goals
9:45 - 10:15 Formative Assessment
10:15- 10:30 Break
10:30-12:00 Formative Assessment
12:00- 1:00 Lunch
1:00 - 3:00 Small Focus Groups
3:00 - 3:30 Wrap up
Plan for the Day
3. 1. Student success in mathematics
2. Digital literacy
3. Focus on the transition from elementary to secondary
4. Professional learning network
5. Use of data to monitor and orient practice, inquiry,
and learning
Key Themes of CCC-M project
4. 1. Foster a community of practice in mathematics
teaching and digital tools
2. Develop collective understandings of the situation
3. Develop practice in terms of using digital tools for
ourselves and for students
4. Sharing, reflection, and inquiry
Objectives for Year 1
6. Teacher beliefs and practices
• Assessing beliefs on
1) Mathematics as a subject (M)
2) Mathematics learning (L), and
3) Mathematics teaching (T)
• Three orientations in beliefs and practices
7. Three orientations in teacher’s beliefs
• Transmission (T) views Mathematics as a series of “rules
and truths” that must be conveyed to students and
teaching as “chalk and talk” followed by individual practice
until fluency is attained.
• Discovery (D) views Mathematics as a human creation and
encourages students to learn through individual
exploration and reflection, while the teacher adopts a
reflective, facilitating role.
• Connectionist (C) views mathematics as a network of ideas
that teacher and student must construct together through
collaborative discussion.
12. Reflection happens in different ways
Fluid, informal
Deliberate, recorded, traceable
Individual and collective
What is Reflection?
13. Teacher reflection
Reflective practitioners (Schön, 1983)
a) Reflection in action: Developing
an awareness if decisions in
practices
b) Reflection on action: Developing
an interpretive critique of practice
Reflective teachers identify problems, generate and evaluate
solutions, thereby build a professional knowledge base
constructed through experience and a consciousness of
professional action.
14. A multilayer model for reflection
Layer 1: Technical
• Critique of Lesson Development & Delivery
Layer 2: Deliberative
• Interactive journal writing
• Video-based lesson analysis
Layer 3: Inquiry
• Topical Seminar discussions
* Reference: Etscheidt, Curran, & Sawyer (2014)
15. Various approaches for reflection
Case-study / Autobiographical / Action research
Self-reflection / Collaborative reflection (e.g., support
group; critical friends; peer reflection)
Verbal reflection (e.g., audio recording) / Written
reflection (e.g., teacher diary or journal; reflection
blog)
17. According to Hattie (Hattie Ranking: Influences And Effect
Sizes Related To Student Achievement)
Formative Assessment ranks as the third greatest
influence on student achievement and Micro Teaching
ranks fourth.
What research says
18. Using data day to day to:
Formative Classroom Assessment
Cycle
Plan
Teach
Reflect
19. Summative
Assessment
Data about
people, practices and
perceptions
Benchmark Common Assessments
Formative Common Assessment
(1-4 times per month)
Formative Classroom Assessments
(daily or weekly)
The Data Pyramid
e.g. student self-assessments, descriptive
feedback, use of rubrics/criteria, student
products that check for understanding
(checklists), Gizmos
Math problems of the week, vide
understanding
20. Before Instruction During Instruction After Instruction
Find out what student
knows
• Pre-assess
• Anticipate
confusions and
misconceptions
To monitor and adjust
teaching and learning
• Check for
understanding
• Make student
thinking visible
• Give students
specific, description
non-evaluative
feedback
• Regroup and
reteach
(differentiate)
To reflect and plan
next steps
• Establish quickly
who exceeds, meets
and no yet
• Analyze student
work according to
rubric
• Identify
misconceptions,
errors and confusion
• Plan to re-group, re-
teach or extend
The Cycle in Action
21. Formative assessment means simply using an
assessment to inform instructional adjustments
Formative assessments is used to inform the next
step needed for students to succeed
It is assessment FOR learning
Continuous Assessment
22. Types of Formative Assessment
Pre-Assessment or during the learning cycle
Reflections or self-assessments
Response systems (or paddles)
Ticket-in or Ticket-out
Engineered discussions
Tasks
Activities
Quiz
Peer checking (correcting)
24. Supportive Classroom Climate
Conveyed Unit Targets
Continuous Assessment
Student Self-Direction
Flexible Student Groups
Data-Informed Instruction
Differentiation of Student Work
Key Strategies for Differentiated
Classroom
25. What technological tools are at your disposal to
implement formative assessment?
What types of formative assessments have you used?
Let’s share!
Technology and Formative
Assessment
26. You have identified the following:
1. Transfer of knowledge
2. Decoding Application Questions and Situational
Problems
3. Student Engagement and Motivation
Student Learning Problems
27. Choose one of the identified student learning
problems to focus on this afternoon in small groups.
1. Transfer of knowledge
2. Decoding Application Questions and Situational
Problems
3. Student Engagement and Motivation
Focus Groups
29. Reflect and record current practices
Develop further questions to explore
Online exploration Google Scholar
Identify key strategies identified in research to
address issue
Plan for further meetings
Group Exploration
Related to Goal 3 “Develop practice in terms of using digital tools…”; in an integrated way with other types of knowledge.A broader perspective on digital literacy: e.g., for own reflection.
Zero sum percentages. Confirms what what has been observed in other contexts.
We have lready started sharing, in f2f and EdModo.Now is the time to start engaging in “reflection” in a more deliberate way.
