1. Creating, Collaborating
and Computing in Math
Enhancing the teaching and learning of
mathematics using technology
Year 2 (2014-2015)
Riverside School Board and McGill University- October 7th, 2014
2. Agenda
9:00 Introductions and Recap of year 1
Objectives and Activities for year 2
9:45 Tina and Kristie Sharing
10:30 Break
10:45 Teaching students to problem solve
12:00 Lunch
13:15 Survey
13:45 Formative Assesment
15:30 Planning for school visits
4. Key Themes of CCC-M project
1. Student success in mathematics
2. Digital literacy
3. Focus on the transition from elementary to secondary
4. Use of data to monitor and orient practice, inquiry,
and learning
5. Professional learning network
CCC-M Website: http://ccc-m.wikispaces.com/home
5. Objectives for Year 1
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
5. Consolidate a long-term partnership between RSB
and McGill
6. Identified Problem Areas in the
learning of mathematics
We have identified the following:
1. Transfer of knowledge
2. Decoding Application Questions and
Situational Problems
3. Student Engagement and Motivation
7. 1. Develop and test solutions based on collective
understandings of the situation
a) Design and implement video-based lesson studies
b) Develop practice of using digital tools for teaching and
learning math
c) Facilitate reflection and inquiry as well as sharing
2. Continue the professional learning network in
mathematics teaching and digital tools
3. Consolidate a long-term partnership between RSB and
McGill
Objectives for Year 2
9. Lesson Study
(Hart, L. C., Alston, A., & Murata, A. (2011). Lesson study research and practice in
mathematics education. New York: Springer.)
10. Lead Teachers
Lesson study: Kristie and Lindsay
Reflective practice: Monica and Caitlin
Inquiry teacher: Brad and Brandon
11. Sharing by Tina and Kristie
Planning for Situational Problems
12. Teaching students to problem solve
Three strategies:
Getting at the math question
Using a Bar model to represent a problem
Error analysis –How/why is it wrong? How
can you correct it?
13. Getting at the Math Question
Consider the following application question:
028
Name: __________________ Date: ______________
ACTION SITUATION
OP1 Operations
(Natural Numbers)
(8)
Observable
manifestations of
a level…
5 4 3 2 1
Evaluation
Criteria
Analyze
Choice
Application
Justification
The CN Tower has 4 observation decks for tourists. The higher one climbs,
the more spectacular the view is, especially when the weather is good. At
342 metres, there is an exterior observation deck with a glass floor… I
personally had the opportunity to walk on the floor and let me tell you it is
an incredible feeling!
Someone asked, is the glass really solid? The guide quickly told us that the
glass floor of the CN Tower can hold up to 14 hippos.
One male hippopotamus weighs on average 3 tonnes
One tonne is equivalent to 1 000 kg.
Human adults weigh on average 70 kg.
Calculate the number of people that the glass surface of the CN Tower can
support without risk of collapsing. Has this reassured you?
14. We can use a web diagram to pull out the important information
in the problem
At the centre of the web is the question we are working to solve
Problem Title: ___The Glass Floor______________
Surround the task with the important information from the problem. If there is information you won’t need, cross it out.
What is the problem asking?
One male hippo weighs 3
tonnes
Calculate the # of people the
CN tower floor can support.
Has this reassured you?
15. What’s the math question
The question in the text is not always a math question (ex.
Has this reassured you)
The math question is the final result/amount you are looking
for. Another way to think of this is to have students
consider “How will you know when you’re done?” – Which
calculation will you do that will give you your final answer?
What’s the Math question?
How many humans (70kg each) are equal to the weight of 14
hippos (3 tonnes each)?
16. Using a bar model
A bar model can be used to represent several
types of problems
It allows to visualize the know and unknown
values in the problem and the relationship
between them
http://www.youtube.com/watch?v=YeIN4Z1-KXc
17. Now list the steps…
Once the problem has been modelled, the steps needed to
solve it become more apparent
Determine the weight of 1 hippo in kg (3x1000)
Find the weight in kg that the floor can hold (weight of 1
hippo x 14)
Find out how many humans are equal to that weight (÷70)
OR
Find out the weight the floor can hold (14 hippos x 3 tonnes)
Convert that weight to kg (x 1000)
Find out how many humans are equal to that weight (÷70)
OR…
18. Analysing errors
The solution you are given is wrong (no guess work,
students can’t “opt out” by saying they think it’s
right)
How/Why is it wrong? What error did this student
make? Was it a minor error or a conceptual error?
What would you do differently to make it correct?
19. After a bit of guided practice, this strategy works well for
homework:
Answers are on the board as they arrive – quickly
circle/put a dot/etc. next to the ones that are wrong.
In a group of 2-3 discuss WHY they are wrong and how
you can fix them
The discussion is not about finding the right answer
(that’s on the board!). The purpose is to understand
what you did wrong and how to fix it.
20. Community of Practice
Choose a math problem (Sit Prob or Application) or a
POL learning target that you will be teaching in the near
future and do the following:
1. Think about conceptions and misconceptions
2. Share teaching strategies
3. Plan a lesson
4. Rehearse the lesson with your peers
22. Teaching practices and
impacts on student success
Recall Hattie’s ranking of influences and effect
sizes related to student achievement.
Do you remember which teaching factor has the
highest influence on student achievement?
http://visible-learning.org/hattie-ranking-influences-effect-
sizes-learning-achievement/hattie-ranking-teaching-
effects/
23. Common Formative Assessment
Guiding Instruction through common formative
assessments:
https://www.teachingchannel.org/videos/guide-instruction-
with-cfas
24. Continuous Formative Assessment
Assess
Plan
lesson
Convey
targets
Activate
learning
Assess
Provide
Feedback
Adjust
Activate
Learning
Pre-Instruction
(beginning of unit)
During Instruction
25. Types of Formative Assessment
Pre-Assessment or during the learning cycle
Reflections or self-assessments (e.g. checklist)
Response systems (or paddles)
Ticket-in or Ticket-out
Engineered discussions
Tasks (e.g. 3 minute paper or 1 sentence summary)
26. Types of Formative Assessment
(continued)
Activities in groups (e.g. observing peer work and
conversations)
Quiz (for feedback on learning not marks)
Peer checking (correcting)
Misconception Check:
Provide students with common or predictable
misconceptions about a specific principle, process, or
concept. Ask them whether they agree or disagree and
explain why. Also, to save time, you can present a
misconception check in the form of multiple-choice or
true/false.
28. Formative Assessment Activity
From the website The Teaching Channel:
1. Watch videos on FA
2. Tag a few of your favorites
3. Reflect on the type and the purpose of the
formative assessment shown in the video
4. Discuss why you like it and how you would
implement this strategy in your classroom
You will find a suggested list of videos on Edmodo
30. Edmodo and the community of
practice
Revisit the purpose of the community
Subgroups within the Edmodo community
App Sharing
31. Thank you and have fun!
Dr. Alain Breuleux: alain.breuleux@mcgill.ca
Dr. Gyeong Mi Heo: gyeongmi.heo@mcgill.ca
Karen Rye: karen.rye@rsb.qc.ca
Tina Morotti: tina.morotti@rsb.qc.ca
Sandra Frechette: sandra.frechette@rsb.qc.ca
Editor's Notes
Inquiry and reflection are anchored in the lesson study cycle.
Inquiry goes from simple informal tacit thinking about your practice to a more formal, structured data-based evidence-oriented process (a collaborative process).
