This semester, I learned the
different approaches and theories behind knowing
and learning in math and science.  The class and I were
able to categorize the class content within three branches: cognitive
development, learning environments, and learning theories. They contain the essential tools to become
effective educators.

Learning theories describe different perspectives on how a learner understand, process, and
retain knowledge. The four theories are behaviorism, constructivism,
cognitivism, and connectivism. Behaviorism
emphasized that
learning is the production of desired behaviors[MS2] .
Behaviorists measured,
changed, and trained the behavior [MS3] of
subjects through conditioning. Classical
conditioning uses behavior that occurs as an automatic response to some
stimulus while operant conditioning uses voluntary behavior that is
shaped by consequences. Constructivism focuses
on the learner owning the knowledge through personal experiences and their
reflections of them. I like that the students are in charge of figuring out the
problem and are thus more likely to understand. They can reflect, extend and
transfer ideas based on what they experienced. Cognitivism
focuses on the mind and the mental processes like thinking, knowing, memory,
and problem solving. Lastly,
Connectivism is a learning theory that
provides insight into learning skills and tasks needed for learners to flourish
in a digital era. Technology has
reorganized how we live, how we communicate, and how we learn. We use
connections within networks, online resources, and the online community to
obtain knowledge[MS6] .
Although there are advantages and disadvantages for each theory, a balance
between the four theories serve as a solid foundation of learning.   

Cognitive development is the study of cognitivism. There are four pioneers: Piaget,
Vygotsky, Erikson, and Kolb. Piaget
was a clinical psychologist who established the first cognitive theory. One
aspect of his theory was the Stages of
Cognitive Development, which consisted of the sensorimotor,
pre-operational, concrete operational, and formal operational stage. The sensorimotor stage explained how infants and toddlers acquire knowledge
through motor and sensory experiences and manipulating objects. The pre-operational stage starts from age two to age seven; it occurs
when the child learns to speak and can think about things symbolically. At
the concrete operational stage, kids begin to think more logically,
but they tend to struggle with abstract concepts[MS9] .  From adolescence and
into adulthood, people
become capable of seeing multiple potential solutions to problems and think
more scientifically about the world around them. The other parts of Piaget’s contribution
were schema and adaptation. Schemas are
categories of knowledge that help us to interpret and understand the world while adaptation is the
process of adjusting a schema because of new knowledge. This
process includes assimilation, accommodation, and equilibrium.  Assimilation
is using an existing schema to deal with a new object or situation while accommodation occurs when the existing
schema does not work, and needs to be changed to deal with a new object or
situation.  Equilibrium occurs when a child’s schemas can deal with most new information
through assimilation. However, disequilibrium occurs when new information
cannot be fitted into existing schemas. Cognitive
dissonance is the feeling of discomfort that results from holding two
conflicting beliefs. But the child can restore equilibrium by either creating a
new schema or ignoring the new information. Overall, Piaget’s theory mainly focused on the specific
learning development a child goes through from birth to adolescence.

Vygotsky, on
the other hand, emphasized the influence of culture, peers, and adults on the
developing child. His sociocultural
theory explains that community plays a central role in the process of
“making meaning” for children. One cultural tool that stems from his
theory is private speech. It is the
use of language for self-regulation of behavior. Vygotsky sees private speech
as a means for children to plan activities and strategies and develop. He
believes cognitive development also occurs when a child uses mediatory tools to
facilitate the learning process. The zone
of proximal development the difference between what a learner can do
without help (zone of actual development)
and what they cannot do. Scaffolding is
the assistance from a knowledgeable person that closes the bridge between those
two zones.

Erikson was a pioneer
in psychosocial development. His eight stages of development theory revolved
around conflict and identity. In each stage, the person confronts new
challenges. Each stage builds upon the successful completion of earlier stages.
His theory is unique because every individual experiences these stages, from
birth to death. Kolb, however, developed
his experiential learning style theory based on its cycle and learning styles.
He believed effective learning is seen when a person progresses through
concrete experience (having an experience), reflective observation (of the
experience), abstract conceptualization (learning from the experience), and
active experimentation (trying what you have learned). Kolb also incorporated
learning styles to his two continuums based on the cycle. A learning style is a person’s preferred
method to gain knowledge. Each learning style represents a combination of two
preferred styles. A major controversy in cognitive development has been nature versus nurture: whether cognitive
development is determined by a person’s innate qualities (nature) or by their
personal experiences (nurture). At first, it swung towards nature because of
scientific discoveries of nature. During post World War I, evidence seemed to
support the connection between social class and intelligence. After the last
World War, people thought there is a balance between nature and nurture.

Finally, the major topic from class
revolved around learning environments,
which are environments that best promote learning. The four interdependent aspects
are learner-centered, knowledge-centered, assessment-centered and community-centered.
Learner-centered environments pay
careful attention to the knowledge, skills, attitudes, and beliefs that
learners bring to the educational setting. Since learners come from different
kinds of background, an educator cannot assume what the learner knows. Therefore,
it is important to understand what they know and do not know. The three
principles of learning is pre-existing knowledge, active learning, and
metacognition. Pre-existing knowledge is prior
knowledge learners bring with them because of their experiences and own interpretations.
Active learning lets students take control of their own learning. It is
important for the teacher to present factual knowledge and conceptual
understanding to challenge a learner’s misconceptions. Otherwise, they affect
their capability to remember, reason, solve problems, and learn new concepts. Lastly,
it is crucial for students to develop metacognition.
It helps students monitor their progress and improve on transferring, or extending, their knowledge to a new context. Metacognition
also involves thinking about one’s own thinking process such as study skills
and memory capabilities. Memory is the
mental capacity to encode, store, and retrieve information. Dyslexia hinders the memory process of
encoding words as meaningful information. However, with proper accommodation,
students can excel in learning despite it. Chunking is a way to organize and
store information into smaller manageable pieces. Two effects of memory are the
primacy and recency effect. The primacy
effect states the beginning of a list is remembered because it occurred first,
whereas the things remembered at the end of the list is called the recency
effect. Once the learner knows their starting point, they learn how to progress
and handle information.

Knowledge-centered environments provide numerous of ways to comprehend knowledge, as well as
acquire problem-solving skills. Educators need to promote literacy in the classroom. Students have to be literate (able to
understand, utilize and comprehend the subject’s language) to create,
communicate and compute with others. Math and science have jargon and symbols
that differ from the English language. For example, mathematical and scientific
literacy consists of mathematical & scientific knowledge, methods, and
processes applied in various contexts in metacognitive ways. In order for
that to happen, students need to follow the math and science proficiencies. The math proficiencies have five
components: conceptual understanding (comprehension of concepts, operations,
and relations), procedural fluency (carrying out procedures efficiently and
appropriately), strategic competence (formulating, representing, and solving
problems), adaptive reasoning (capacity for logical thought and reflection),
and productive disposition (seeing math as meaningful). The science
proficiencies are similar except its problems are not always computational; they
do not include procedural fluency and emphasizes more on scientific
explanations of the world. Although reading
strategies seem only useful in English class, they can be used in any
subject, especially math and science to teach students text comprehension. They
can increase students’ conceptual understanding of math and science. Once
students obtain the necessary information, they need a method. Fortunately,
there are student-driven approaches to solve a problem. One example is modeling, which involves either a
teacher demonstration (scaffolding) or a visual representation of the problem. A
specific case is a model eliciting activity
(MEA). MEAs pose as open-ended problems and challenge students to build models
in order to solve complex, real-world problems. MEAs encourage students to
invent and test models, which makes their thinking visible.  Another problem solving method is anchored instruction (AI). Like MEA, it
is a form of context-based learning designed to encourage students and teachers
to pose and solve realistic problems. Inquiry
differs from the rest because it is an active learning
process in which students answer research questions through actual data analysis. Inquiry instruction involves students in a form of
active learning that emphasizes questioning, data analysis, and critical
thinking. Another form of inquiry is argument-driven inquiry (ADI). It attempts to develop an argument
that provides and supports an explanation for the research question using claim, evidence, and reasoning (CER).
CER helps students learn
how to determine if available data are relevant, sufficient, and convincing
enough to support their claims. Overall, a knowledge-centered environment
builds a strong foundational structure for students to further their learning.

Assessment-centered environments provide frequent formal and informal opportunities for
feedback focused on understanding. There are two types of assessments:
formative and summative. Formative
assessments are used to provide feedback on where to improve teaching and
learning, whereas summative assessments
measures what students have
learned at the end of some set of learning activities. Both assessments
consist on questioning students to
see what they have learned. However, most classrooms ask lower cognitive
questions (fact, closed, direct, recall, and knowledge questions). These types
of questions consist of the two lower levels of Bloom’s taxonomy, knowledge and
comprehension. Bloom’s taxonomy is a
framework for categorizing educational goals.
The higher levels are applying, analyzing, evaluating, and creating. The
ultimate goal for students is to gain meta-cognitive abilities to self-assess,
reflect and rethink for better understanding.

Community-centered environments foster norms for people learning from one another, and
continually attempting to improve. Within a community, students are encouraged
to be engaged, constructive participants in a non-threatening environment and
to make mistakes. Accountable talk assures
responsibility to the community, accurate knowledge, and rigorous thinking. Students
should listen and be respectful to others