2. Through the experiences that teachers
provide, students learn mathematics.
Hence, the way students understand
mathematics, solve problems, and even
their disposition towards the subject are
being shaped by the mathematics
teaching they encounter in school
(NCTM, 200, p.16)
3.
4. Mathematics is one of the
subject that pervades life
at any age and in any
circumstance.
5. • Mathematics from K-10 is a skills subject.
• By itself, it is all about quantities, shapes
and figures, functions, logic, and reasoning.
• Mathematics is also a tool of science and a
language complete with its own notations
and symbols and “grammar rules” with
which concepts and ideas are effectively
expressed.
6. Twin goals of mathematics
in the basic education
levels, k-10, are Critical
Thinking and Problem
Solving
7. Critical thinking is the intellectually
disciplined process of actively and skillfully
conceptualizing, applying, analyzing,
synthesizing, and/or evaluating information
gathered from, or generated by,
observation, experience, reflection,
reasoning, or communication, as a guide to
belief and action.
8. EXAMPLE:
The decisions you make while picking a
particular stream to pursue a career in that
domain are crucial to critical thinking. For
instance, when a person wants to be a doctor,
they need to decide which area of specialization
to go for. Critically evaluating the factors
involves aspects of critical thinking.
9. EXAMPLE:
Students might apply critical thinking in their
Math lesson to work out the best way to
approach their group project. They make
decisions such as who will complete each task,
in what time frame. They solve problems like
how and where they will meet outside of school
hours to work together.
10. According to George Polya
(1945 & 1962)
mathematical problem
solving is finding a way
around a difficulty, around
an obstacle, and finding a
solution to a problem
11. “If you illustrated the problem,
then you already solve half of
the problem”
Example:
AB is one side of a rectangle
which measures 8𝑥. 𝐴𝐵 ∥ 𝐶𝐷.
BC is a diagonal of the
rectangle. What is the measure
of BC if the area of the rectangle
is 48𝑥2
?
12. There are five content areas in the curriculum,
adopted from the framework prepared by
MATHTED & SEI 2020
• Numbers and Number Sense
• Measurement
• Geometry
• Patterns and Algebra
• Probability and Statistics
13. Numbers and Number Sense
as a strand include concepts of
numbers, properties,
operations, estimation and their
application.
14. Measurement as a strand includes the use of
numbers and measures to describe,
understand, and compare mathematical and
concrete objects.
•It focuses on attributes such as length, mass
and weight, capacity, time, money, and
temperature as well as applications involving
perimeter, area, surface area, volume, and
angle measure.
15. Geometry as a strand includes
properties of two and three-
dimensional figures and their
relationships, spatial visualization,
reasoning, and geometric
modelling and proofs.
16. Patterns and Algebra as a strand studies
patterns, relationships, and changes
among shapes and quantities.
• It includes the use of algebraic
notations and symbols, equations, and
most importantly, functions, to represent
and analyze relationships.
17. Statistics and Probability as a strand is
all about developing skills in collecting
and organizing data using charts,
tables, and graphs; understanding,
analyzing and interpreting data;
dealing with uncertainly; and making
predictions about outcomes.
18. The specific skills and processes to be developed
are:
• Knowing and understanding
• Estimating, computing and solving; visualizing
and modelling;
• Representing and communicating;
• Conjecturing, reasoning, proving and decision-
making
• Applying and connecting
19. The following values and attitudes are to
be honed as well:
• Accuracy
• Creativity
• Objectively
• Perseverance
• Productivity
20. We recognize that the use of appropriate
tools is necessary in teaching mathematics.
• Manipulate objects
• Measuring devices
• Calculators and computers
• Smart phones and tablet PCs
• The Internet
21. The framework is supported by the following
underlying learning principles and theories:
• Experiential and Situated Learning
• Reflective Learning
• Constructivism
• Cooperative Learning
• Discovery and Inquiry-based Learning
22. Experiential Learning is the process of learning by
doing. By engaging students in hands-on
experiences and reflection, they are better able to
connect theories and knowledge learned in the
classroom to real-world situations.
Experiential learning activities can include, but are
not limited to, hands-on laboratory experiments,
internships, practicums, field exercises, study
abroad, undergraduate research and studio
performances.
23. Situated Learning involves students in cooperative
activities where they are challenged to use their critical
thinking and kinesthetic abilities. These activities should be
applicable and transferable to students' homes,
communities, and workplaces (Stein, 1998).
Examples of situated activities are as follows: Cooperative
internships that allow students to be immersed in the
workplace. Field trips in which students can experience the
work environment. Laboratory settings where students
actively participate in mock activities.
24. Reflective learning typically involves looking back at
something, a past experience or idea and critically
analyzing the event. By looking at successful and
unsuccessful aspects of an experience, reflection will help
students learn from their past experiences and turn surface
learning into deep learning.
An example of reflective learning is that of an athlete
learning a set of skills to succeed in their sport. As part of
reflective learning practice, the athlete can take time to
analyze what their strengths and weakness are, and how
they can use that knowledge to perform at a higher level.
25. Constructivism is the theory that says
learners construct knowledge rather than
just passively take in information. As people
experience the world and reflect upon those
experiences, they build their own
representations and incorporate new
information into their pre-existing
knowledge (schemas).
26. In cooperative learning, students work
together in small groups on a structured
activity. They are individually accountable
for their work, and the work of the group as
a whole is also assessed. Cooperative
groups work face-to-face and learn to work
as a team.
27. Discovery learning is an inquiry-
based learning method that takes a
constructivist approach to education,
where students are encouraged to
construct their own knowledge through
a self-directed learning process—
essentially “instructionless” learning.
28. Inquiry-based learning is a learning process that
engages students by making real-world connections
through exploration and high-level questioning. It is
an approach to learning that encourages students to
engage in problem-solving and experiential learning.
Examples of inquiry-based learning
include observational field trips, science
experiments, and hypothesis-based research
projects.
30. Answer the following questions and write your
answer in a one whole sheet of paper. (20 pts)
1. How can the twin goals of
mathematics be achieved?
2. What learning theory will you
apply most in your teaching as a
future teacher? Why?
