This the problem and are thus more likely

This semester, I learned various
approaches and theories behind knowing and
learning in math and science.  The class and I were able to
categorize the class content into three categories: cognitive development, learning
environments, and learning theories. Each category contains the essential
aspects that I learned from this course to become an educator.

Learning theories describe how a learner understands, handles, and retains knowledge. The
four theories are behaviorism, constructivism, cognitivism, and connectivism. Behaviorism was the only approach that
used behavior as a learning tool. Behaviorists first measured the current
behavior, trained it with conditioning,
and trained the subject to produce that preferred behavior. Classical
conditioning uses automatic response behavior to some stimulus while operant
conditioning uses consequences to shape voluntary behavior. 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. Cognitive development has so much information and research
that it is a separate category. The most recent theory is connectivism because it incorporates learning with technology. It assists learners to use
online resources and the community. Although there are advantages and
disadvantages for each theory, a balance between the four theories serve as a
solid foundation of learning.

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Cognitive development is the study of cognitivism. It had four pioneers: Piaget,
Vygotsky, Erikson, and Kolb. Piaget
was a psychologist who established the first cognitive theory. He created the Stages of Cognitive Development, which
consisted of the sensorimotor, pre-operational, concrete operational, and
formal operational stage. The sensorimotor stage starts with newborns
and toddlers; they gain knowledge by playing with objects. The pre-operational
stage is when the child can speak and can understand a word’s meaning, which
happens between ages two and seven. At the concrete operational stage, kids not
only think symbolically, but they think more logically too. However, they
sometimes fail to understand abstract concepts like conservation. From
adolescence and into adulthood, people are able to see alternate solutions to
problems and think more scientifically about the world. The other parts of
Piaget’s contribution were schema and adaptation. Schemas are
grouped pieces of knowledge that help us to interpret and understand while adaptation is the process of adjusting a schema because of new knowledge. Adaptation includes assimilation,
accommodation, and equilibrium.  Assimilation
incorporates a new situation into an existing schema while accommodation either adjusts an existing schema to fit the new
situation or creates a new schema. When new information goes through
assimilation without any difficulties, it is called equilibrium. Cognitive dissonance, which is discomfort stemming from two
conflicting beliefs, occurs during disequilibrium. 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

In contrast, Vygotsky thought the community played a bigger role on a cognitive
development. His sociocultural theory
explains that learning is interactive and impacted by a culture. One cultural
tool that comes from his theory is private
speech. It first begins when kids talks to themselves, which makes their thinking
visible. One way he sees the community furthering a child’s learning is
offering aid to them. The zone of actual
development is what the learner cannot do alone while the zone of proximal development is what
they can accomplish with assistance. Scaffolding
is the assistance from a knowledgeable person that closes the bridge between
those two zones. Erikson, on the
other hand, was a pioneer in psychosocial development. His eight stages of
psychosocial development spanned over a person’s lifetime. In each stage, a
person faced challenges about their identity and inner conflicts. Rather than
focusing on oneself, Kolb created a
cycle that was applicable to learning. The four steps in the cycle are concrete
experience, reflective observation, abstract conceptualization, and active
experimentation. Throughout the cycle, you would experience something new,
review what happened, try to learn from it, and apply it to a new situation.
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. These psychologists had differing views on
whether a child’s development was based on their own intelligence or the
environment. This was the nature versus
nurture debate—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. Although it was a contrast between the
community and the learner, learning environments focus on how they can balance
them and incorporate learning.

Learning environments are settings that stimulate learning. The four domains are
learner-centered, knowledge-centered, assessment-centered and
community-centered. Learner-centered
environments tend to the learner’s attitudes, ideas, and beliefs. No one
can assume what learners know because they come from different backgrounds. It
is also important to figure out what they do not know. The way to approach this
dilemma is through three principles of learning: pre-existing knowledge, active
learning, and metacognition. Pre-existing knowledge (prior knowledge) is what the
experiences and interpretations learners first have. Thus, it is important for
teachers to challenge misconceptions and present factual knowledge. Active
learning lets students test their conceptual understanding. Lastly, it is
crucial for students to develop metacognition
in order to extend (transfer) their
knowledge to a new context. Metacognition also involves thinking about one’s
own thinking process such as monitoring their progress, 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 first math proficiency is conceptual
understanding. It makes sure students are able to comprehend the math concept
and formulas. Procedural fluency is the learner efficiently using the
appropriate methods. Strategic competence is the student translating the given
information into an equation in order to solve the problem. Adaptive reasoning
is the student understanding why the method they used worked. Productive
disposition is seeing math as meaningful and applicable in the real world. 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 gives students real data to justify rather than depending on hypothetical data.
Inquiry instruction gives students a
scenario to solve with only their prior knowledge. Another form of inquiry is argument-driven inquiry (ADI). Students
form an argument that supports their findings and solution using claim, evidence, and reasoning (CER). The
claim of their finding is a statement that answers the research question. The evidence
backs up the claim with scientific data. The reasoning ties the claim to the
evidence that supports it. 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
lower and higher level questioning is what contrasts an expert versus a novice. Experts have greater factual knowledge, a deeper
understanding, and a more organized knowledge because they made mental patterns
and connections. They start by being novices and gain those characteristics
through experience. That is the ultimate goal—for students is to gain
meta-cognitive abilities to self-assess, reflect and rethink for better

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 in the classroom. Another
way to create a community-centered environment is to have a laughter in the classroom. It has
social benefits like reducing conflict, increasing communication, promoting
creativity, and lightens up the room. Having a community-centered environment
provides support and collaboration.