This document summarizes a professional development session for teachers on resources and tools for 21st century teaching and learning in mathematics. The session focused on enhancing students' learning through critical thinking, creativity, collaboration, and communication using various math activities, problems, and resources. Teachers were encouraged to utilize new technologies and strategies to foster these skills in students and continue their own professional growth through online tools and lifelong learning. The document provided examples of math tasks and lessons targeting these skills and reflected on how teachers can model and develop these abilities in their students.

1. Resources and Tools for 21st Century
Teaching & Learning in Mathematics
LAU/LEVANT Continuing Professional Development 2017:
“The 21st Century Skills across the curriculum: 4 Cs”
Jacqueline Burns
1 April 2017
Beirut, Lebanon

2. Session goals
• work through math activities
and problems through the lens
of the 4 Cs
• explore resources to enhance
students’ learning through the
4Cs
• inspire personal commitments
and stretch our abilities to utilize
21st Century tools, strategies,
resources and technologies

3. Warm-up
Suppose you have a list of numbers from zero to one
hundred. How quickly can you add them all up without
using a calculator?
HINT: There is a swift way to add these numbers. Think about how
the numbers at the opposite ends of the list relate to each other.
http://mathforum.org/k12/k12puzzles/critical.thinking/puzz3.html

4. What’s the solution?
The list contains fifty pairs of
numbers that add to 100
(100+0, 99+1, 98+2, 97+3,
etc.) with the number 50 as
an unpaired leftover:
50 X 100 + 50 = 5,050

5. The 4 Cs: Kitchen Cups
Suppose you need to measure exactly 1 liter of water. All that
you have in your kitchen are two containers. The smaller
container holds 3 liters and the larger holds 5 liters. How can you
use these two containers to measure exactly 1 liter of water?
http://mathforum.org/k12/k12puzzles/critical.thinking/puzz5.html

6. The Solution(s)
Kitchen Cups – possible solutions
Fill the three-liter container with water. Pour it into the five-liter container. Fill the
three-liter container again, and fill up the five-liter container. This will leave you
with exactly one liter of water in the three-liter container.
Fill the five-liter container with water. Pour three liters of the water into the three-
liter container. Two liters of water will remain in the five-liter container. Empty the
thee-liter container, and pour one liter of the two remaining liters from the five-
liter container. This will leave you with exactly one liter of water in each container
if there was no spillage during the pouring. if there was incidental spillage, there
will still be precisely one liter of water in one of the containers.

7. Got Milk?
The main purpose
of this task is to
get students to
practice adding or
subtracting two
digit numbers.
Critical Thinking

8. Got Milk?
Whole group:
• What do you notice in
the picture?
• What do you wonder?
What questions do
you have?
• Think-pair-share to
estimate and record
your answers.
Critical Thinking

9. Critical Thinking and Problem Solving
Reason Effectively
· Use various types of reasoning as appropriate to the situation
Use Systems Thinking
· Analyze how parts of a whole interact with each other to produce overall outcomes in complex
systems
Make Judgments and Decisions
· Effectively analyze and evaluate evidence, arguments, claims and beliefs
· Analyze and evaluate major alternative points of view
· Synthesize and make connections between information and arguments
· Interpret information and draw conclusions based on the best analysis
· Reflect critically on learning experiences and processes
Solve Problems
· Solve different kinds of non-familiar problems in both conventional and innovative ways
· Identify and ask significant questions that clarify various points of view and lead to better solutions

10. Reflections
• How can you model
communication skills for your
students?
• How can students be encouraged
to use technology to communicate
effectively and innovatively?
• How can you encourage students
to communicate their learning to a
varied and broader audience?

11. Students should be able to construct viable
arguments and critique the reasoning of others
Teachers must:
• provide opportunities for students to
listen to or read the conclusions and
arguments of others
• establish and facilitate a safe
environment for discussion
• ask clarifying and probing questions
• avoid giving too much assistance (e.g.,
providing answers or procedures)

12. Questions to develop mathematical thinking
• What mathematical evidence would support
your solution?
• How can we be sure that...?
• How could you prove that...?
• Will it still work if...?
• What were you considering when...?
• How did you decide to try that strategy?
• How did you test whether your approach
worked?
• How did you decide what the problem was asking
you to find? (What was unknown?)
• Did you try a method that did not work?
• Why didn’t it work?
• Would it ever work?
• Why or why not? What is the same and
what is different about...?
• How could you demonstrate a counter-
example?

13. Communication
Communicate Clearly
· Articulate thoughts and ideas effectively using oral, written and nonverbal
communication skills in a variety of forms and contexts
· Listen effectively to decipher meaning, including knowledge, values,
attitudes and intentions
· Use communication for a range of purposes (e.g. to inform, instruct,
motivate and persuade)
· Utilize multiple media and technologies, and know how to judge their
effectiveness a priori as well as assess their impact
· Communicate effectively in diverse environments (including multi-lingual)

14. Communication Task
This pre-algebra problem
targets concepts (ratios and
proportional relationships and
expressions & equations)
typically learned in grades
5-8 in an algebra readiness
course before students are
ready for formal algebra.
http://mathforum.org/pow/teacher/samples/MathForumSamplePreAlgebraPacket.pdf

15. Collaboration
· Demonstrate ability to work
effectively and respectfully with
diverse teams
· Exercise flexibility and
willingness to be helpful in making
necessary compromises to
accomplish a common goal
· Assume shared responsibility
for collaborative work, and value
the individual contributions made
by each team member

16. Collaborative Task: Fractions, decimals and
percents
Guidelines for Collaboration Suggested Lesson Outline
• Collaborative small-group work
• Forty minutes
• Calculate missing values on Card Set A
(Decimals and Percents)
• Once reaching consensus, give out
Card Set B (Areas)
• As groups continue to work, give out
Card Sets C (Fractions) and D (scales)
• Complete the blank cards so each
number is represented four ways
http://map.mathshell.org/download.php?fileid=1594

17. Solutions
http://map.mathshell.org/download.php?fileid=1594

18. Creativity and Innovation
Think Creatively
· Use a wide range of idea creation techniques (such as brainstorming)
· Create new and worthwhile ideas (both incremental and radical concepts)
· Elaborate, refine, analyze and evaluate their own ideas in order to improve and
maximize creative efforts
Work Creatively with Others
· Develop, implement and communicate new ideas to others effectively
· Be open and responsive to new and diverse perspectives; incorporate group
input and feedback into the work
· Demonstrate originality and inventiveness in work and understand the real world limits
to adopting new ideas
View failure as an opportunity to learn; understand that creativity and innovation is a long-term,
cyclical process of small successes and frequent mistakes
Implement Innovations
Act on creative ideas to make a tangible and useful contribution to the field in which the
innovation will occur

19. Creativity as Intellectual and Cultural Capital
Upon its independence on November
22, 1943, Lebanon adopted this flag.
Red symbolizes the blood of martyrs has
been shed in the revolution of
November 1943. The color white
symbolizes white snow that accumulates
on the mountains of Lebanon, a symbol
of purity and peace, and the cedar tree
that had been derived from Mount
Lebanon, it stands to holiness and
eternity and resilience of tradition.
https://en.wikipedia.org/wiki/Islamic_geometric_patterns

20. TASK: Replicate the flag of Lebanon
According to the Article 5 of the
constitution of Lebanon: "The
Lebanese flag shall be composed
of three horizontal stripes, a white
stripe between two red ones. The
width of the white stripe shall be
equal to that of both red stripes.
In the center of and occupying
one-third of the white stripe is a
green cedar tree with its top
touching the upper red strip and
its base touching the lower red
stripe".
Proportion 2:3
Adopted December 7, 1943
Design A horizontal tr-iband of red,
white (double height) and red;
charged with a green Lebanon
Cedar.

21. Creativity: Geometric Castle
The drawing shows a geometric castle. The main part of the
castle is a rectangular prism, and the four towers are, starting
with the front left: a square-based prism with a pyramid on top,
a cylinder with a hemisphere on top, a triangular prism with a
pyramid on top, and a cylinder with a cone on top. The smaller
drawing below shows you the castle from above. Now, my
challenge to you is to use the formulas for volume and surface
area to find the total volume and surface area of this castle!
I would suggest you do each geometric solid separately (of
course), show all your work, and keep them in an organized
fashion on your paper.
http://mathforum.org/sanders/creativegeometry/8.1morethreedeedraw.htm

22. Volume? Surface area?

23. Educators as Lifelong Learners
Tools for Professional Growth
• Twitter
• LinkedIn
• Edmodo
• Classtell
• Plickers
• Youtube
• WhatsApp
• Google Hangouts

24. Summary: Characteristics of 21st Century
teaching and learning of mathematics
• Learn new technologies
• Go global
• Smart phones and tablets
• Digital and paperless
• Collaborate
• eLearning
• Make connections

25. Reflection
What will you do to foster critical
thinking, creativity, collaboration and
communication in students?
How will you increase the effective use
of technology in your daily practice?

26. References and Resources
• http://www.nea.org/assets/docs/A-Guide-to-Four-Cs.pdf
• http://www.mathematicshed.com/uploads/1/2/5/7/12572836/81_fun_critical_t
hinking_activities.pdf
• http://www.criticalthinking.org/
• https://www.illustrativemathematics.org/practice-standards/3
• http://www.collaborativelearning.org/maths.html
• http://map.mathshell.org/download.php?fileid=1594
• http://mathforum.org/pows/

27. Processing, Next Steps, Reflections, Questions
The greatest sign of success for a teacher is to be able to say,
“The children are now working as if I did not exist.”
~ Maria Montessori, Educator (1870-1952)
Written reflection: Write one new tool or strategy will you make a
commitment to use in the immediate future.

28. Jacqueline Burns
USA | UAE
Jacqueline@globalmathconsultants.com
WhatsApp: +971 56 4166150
Twitter: @GlobalMath411