PRINCIPLES AND STRATEGIES IN TEACHING MATH

Module 2
Teaching Perspective

Teaching Perspective
There are two predominant schools of thought when it comes to teaching and
learning, and these are behaviorism and cognitivism. Reflecting on the different
theories on teaching and learning mathematics has implications that must be taken
into consideration. These theories are anchor on several principles.

What is the behavioral learning theory?

Behaviorism or the behavioral learning theory is a popular concept that focuses on

how students learn. Behaviorism focuses on the idea that all behaviors are learned
through interaction with the environment. This learning theory states that
behaviors are learned from the environment, and says that innate or inherited
factors have very little influence on behavior.

Behaviorism learning theory.

In the classroom, the behavioral learning theory is key in understanding how to
motivate and help students. Information is transferred from teachers to learners
from a response to the right stimulus. Students are a passive participant in
behavioral learning—teachers are giving them the information as an element of
stimulus-response. Teachers use behaviorism to show students how they should react
and respond to certain stimuli. This needs to be done in a repetitive way, to
regularly remind students what behavior a teacher is looking for.

Positive reinforcement is key in the behavioral learning theory. Without positive

reinforcement, students will quickly abandon their responses because they don’t
appear to be working. For example, if students are supposed to get a sticker every
time they get an A on a test, and then teachers stop giving that positive
reinforcement, less students may get A’s on their tests, because the behavior isn’t
connected to a reward for them.
Behaviorism learning theory.

Behaviorism and social learning theory

The behavioral learning theory and the social learning theory stem from similar
ideas. The social learning theory agrees with the behavioral learning theory about
outside influences on behavior. However, the social learning theory goes a step
further and suggests that internal psychological processes are also an influence on
behavior. Students or individuals may see things being done, but the social
learning theory says that internal thoughts impact what behavior response comes
out.

Behaviorism and social learning theory

Behaviorism doesn’t study or feature internal thought processes as an element of
actions. Social learning argues that behavior is much more complicated than the
simple stimulus and response of behaviorism. It suggests that students learn
through observation, and then they consciously decide to imitate behavior. There
are underlying emotions like peer pressure and a desire to fit in that impact
behavior.

Behaviorist teaching strategies.

Teachers can implement behavioral learning strategy techniques in their classroom
in many ways, including:
Drills. Teachers may practice skills using drill patterns to help students see the
repetition and reinforcement that behavioral learning theory uses.
Question and answer. Teachers can use a question as a stimulus and answer as a
response, gradually getting harder with questions to help students.
Guided practice. Teachers can be directly involved in helping students go through
problems to give them the reinforcement and behavior demonstration you want them to
follow.

Behaviorist teaching strategies.

Teachers can implement behavioral learning strategy techniques in their classroom
in many ways, including:
Regular review. Reviews are important to behavioral learning theory. Going back
over material and giving positive reinforcement will help students retain
information much better.
Positive reinforcement. Behaviorist classrooms utilize positive reinforcement
regularly. This can be in the form of verbal reinforcement and praise, reward
systems, added privileges, and more.

What is the Cognitivism?

Cognitivism is a learning theory that focuses on how information is received,

organized, stored and retrieved by the mind. It uses the mind as an information
processor, like a computer. Therefore, cognitivism looks beyond observable
behavior, viewing learning as internal mental processes. In this view, learners are
actively involved in the way they process information. Knowledge, memory, thinking,
and problem solving are areas for development.

Cognitive learning strategies.

While you may now have a basic understanding of what cognitive learning theory is,
it’s even more important to understand how to apply it in everyday life or the
classroom. There are many types of cognitive learning and a wide variety of
strategies you can utilize to help you maximize student achievement. Some of these
strategies include:

Cognitive learning strategies.

Some of these strategies include:
Asking questions.
Having opportunities to make errors.
Fostering self-reflection/self-questioning.
Thinking aloud.

Cognitive learning activities

Teachers can try some cognitive learning activities to increase learning
opportunities for their students. Some activities teachers can try are:
Make a game of memorizing poetry or facts
Write a journal entry that asks students to think about what they learned that day
or week
Students can demonstrate work in front of the class
Have students create their own learning game as they work to master facts or a
subject
Ask students to explain a problem to other students and teach it to them
Put a list of questions on the board and have students answer them to learn about
their thought process

What is the Constructivism?

Constructivism is based on the idea that people actively construct or make their
own knowledge, and that reality is determined by your experiences as a learner.
Basically, learners use their previous knowledge as a foundation and build on it
with new things that they learn.
Principles of constructivism.
Knowledge is constructed. This is the basic principle, meaning that knowledge is
built upon other knowledge. Students take pieces and put them together in their
own unique way, building something different than what another student will build.

Principles of constructivism.
People learn to learn, as they learn. Learning involves constructing meaning and
systems of meaning. For example, if a student is learning the chronology of dates
for a series of historical events, at the same time they are learning the meaning
of chronology.

Principles of constructivism.
Learning is an active process. Learning involves sensory input to construct
meaning. The learner needs to do something in order to learn, it’s not a passive
activity.

Principles of constructivism.
Learning is a social activity. Learning is directly associated to our connection
with other people. Our teachers, our family, or peers, and our acquaintances impact
our learning.

Principles of constructivism.
Learning is contextual. Students don’t learn isolated facts and theories separate
from the rest of our lives—we learn in ways connected to things we already know,
what we believe, and more.

Principles of constructivism.
Knowledge is personal. Because constructivism is based on your own experiences and
beliefs, knowledge becomes a personal affair. Each person will have their own prior
knowledge and experiences to bring to the table.

Principles of constructivism.
Learning exists in the mind. Hands-on experiences and physical actions are
necessary for learning, but those elements aren’t enough. Engaging the mind is key
to successful learning.

Principles of constructivism.
Motivation is key to learning. Students are unable to learn if they are
unmotivated.

Types of constructivism.
Cognitive. Cognitive constructivism focuses on the idea that learning should be
related to the learner’s stage of cognitive development. These methods work to help
students in learning new information by connecting it to things they already know,
enabling them to make modifications in their existing intelligence to accommodate
the new information. Cognitive constructivism comes from the work of Jean Piaget
and his research on cognitive development in children.

Types of constructivism.
Social. Social constructivism focuses on the collaborative nature of learning.
Knowledge develops from how people interact with each other, their culture, and
society at large. Students rely on others to help create their building blocks, and
learning from others helps them construct their own knowledge and reality. Social
constructivism comes from Lev Vygotsky, and is closely connected to cognitive
constructivism with the added element of societal and peer influence.

Types of constructivism.
Radical. Radical constructivism is very different from cognitive and social
constructivism. It focuses on the idea that learners and the knowledge they
construct tell us nothing real, only help us function in our environment. The
overall idea is that knowledge is invented, not discovered. The things we bring to
the table make it impossible for us to have truth, only interpretations of
knowledge. This theory was developed by Ernst von Glasersfeld in 1974.

Constructivism in education
In constructivist classrooms, the teacher has a role to create a collaborative
environment where students are actively involved in their own learning. Teachers
are more facilitators of learning than actual instructors. Teachers must work to
understand the preexisting conceptions and understanding of students, then work to
incorporate knowledge within those areas. Teachers will also need to adjust their
teaching to match the learner’s level of understanding.

Constructivist classrooms rely on four key areas to be successful:

Shared knowledge between teachers and students.
Shared authority between teachers and students.
Teachers act as a guide or facilitator.
Learning groups consist of small numbers of students.

Constructivism is a theory about knowledge and learning that is influenced by the

work of Piaget and Vygotsky. It is anchored on the following principles from
research on cognitive psychology:
Learners construct understanding. They do not simply mirror what they are told or
what they read.
To understand something is to know relationships. Bits of information isolated from
these structures are forgotten or become inaccessible to memory.
All learning depends on prior knowledge. Learners try to link new information to
what they already know in order to interpret the new material in terms of
established schemata.
Learning is enhanced by social interaction. Thoughts and ideas are enriched and
clarified when these are verbalized in the course of the learners’ interaction with
each other.

Questions?