In the movie Animal House, when Lawrence “Pinto” Kroger and Kent “Flounder” Dorfman walk past the statue of Emil Faber, founder of Faber College, we see that his motto is “KNOWLEDGE IS GOOD”.
Knowledge is good, but what about understanding and wisdom? (The editorial, Purpose of this Website, elucidates the difference between knowledge, understanding and wisdom.) In my formal education, and my perception of most academia (especially undergraduate university education), is they provide a breadth of knowledge (a little bit of knowledge of many things) to students because they do not know what jobs/careers the student will pursue (the depth of knowledge they may need).
In my case, I was not provided the depth of knowledge, or it was presented in a manner that was obfuscated by the teacher, the book being used for the class, or both.
Breadth of Knowledge
Breadth of knowledge (BOK) refers to the full span of knowledge of a subject.
Case in point, I do not remember being taught the following mathematical concepts in school, or they were not highlighted as essential for more advanced mathematics: PEMDAS, significant digits, rounding digits, or SOH CAH TOA. Did I need these? Yes! Why were they not taught? I do not think I will ever know why.
Depth of Knowledge
Depth of knowledge (DOK) refers to the extent to which specific topics are focused upon, amplified and explored.
Due to a limited amount of time for each math class, or any school subject, I sometimes think that DOK is sacrificed for BOK. However, DOK, as developed through research by Norman L. Webb in the late 1990’s, is defined as the complexity or depth of understanding that is required to answer an assessment question. The ThoughtCo website published two pages entitled Find Out What Depth Of Knowledge Is, and How Depth of Knowledge Drives Learning and Assessment. See these pages for details about DOK.
The problem I have with DOK is amplified by its very definition: “the complexity or depth of understanding that is required to answer an assessment question.” No! Learning IS NOT about answering questions, or memorizing information and then testing the student on what they memorized. Memorization is needed but not to the point that it is the only thing used to grade a student. (See Learn by understanding, not by memorizing.) DOK fits nicely into academia because it is structured, can be measured, teachers may be able to implement it, companies can package it and sell it to schools, and it sounds impressive.
Memorizing formulas is tedious and many wrongly associate it with math. Math is about understanding things. There are formulas in mathematics that no living soul could possibly remember, while their derivation is natural and can be done with some effort. All you have to do is think for yourself and not let people tell you to just accept mathematical statements. Ask them why.
kuco
Constructivism
As I was researching information for this commentary on knowledge, I came across the article: Constructivism as a theory for teaching and learning. I do not agree with all aspects of constructivism, but I agree with most of tenets presented in the article especially the sentence: “Constructivism’s central idea is that human learning is constructed, that learners build new knowledge upon the foundation of previous learning.” Yes, teaching should take into account what the individual student knows (origin), teach them the information they need to reach the goal (i.e., what is the knowledge they need to take away to advance to the next level even if that level is employment).
The following information is taken directly from portions of the article, I encourage you to read the theory with an open mind. These portions are to pique your interest in the topic and expose you to an alternative way of teaching.
What is constructivism?
Constructivism is ‘an approach to learning that holds that people actively construct or make their own knowledge and that reality is determined by the experiences of the learner’.
Knowledge is constructed, rather than innate, or passively absorbed
Constructivism’s central idea is that human learning is constructed, that learners build new knowledge upon the foundation of previous learning.
This prior knowledge influences what new or modified knowledge an individual will construct from new learning experiences
Learning is an active process
The second notion is that learning is an active rather than a passive process.
The passive view of teaching views the learner as ‘an empty vessel’ to be filled with knowledge, whereas constructivism states that learners construct meaning only through active engagement with the world (such as experiments or real-world problem solving).
Information may be passively received, but understanding cannot be, for it must come from making meaningful connections between prior knowledge, new knowledge, and the processes involved in learning.
All knowledge is personal
Each individual learner has a distinctive point of view, based on existing knowledge and values.
This means that same lesson, teaching or activity may result in different learning by each pupil, as their subjective interpretations differ.
What are the features of a constructivist classroom?
Tam lists the following four basic characteristics of constructivist learning environments, which must be considered when implementing constructivist teaching strategies:
- Knowledge will be shared between teachers and students.
- Teachers and students will share authority.
- The teacher’s role is one of a facilitator or guide.
- Learning groups will consist of small numbers of heterogeneous students.
| Traditional Classroom | Constructivist Classroom |
|---|---|
| Strict adherence to a fixed curriculum is highly valued. | Pursuit of student questions and interests is valued. |
| Learning is based on repetition. | Learning is interactive, building on what the student already knows. |
| Teacher-centered. | Student-centered. |
| Teachers disseminate information to students; students are recipients of knowledge (passive learning). | Teachers have a dialogue with students, helping students construct their own knowledge (active learning). |
| Teacher’s role is directive, rooted in authority. | Teacher’s role is interactive, rooted in negotiation. |
| Students work primarily alone (competitive). | Students work primarily in groups (cooperative). |
Critical evaluation
Strengths
Constructivism promotes a sense of personal agency as students have ownership of their learning and assessment.
Limitations
The biggest disadvantage is its lack of structure. Some students require highly structured learning environments to be able to reach their potential.
It also removes grading in the traditional way and instead places more value on students evaluating their own progress, which may lead to students falling behind, as without standardized grading teachers may not know which students are struggling.
References
McLeod, S. A. “Constructivism as a theory for teaching and learning.” 2019. Simply Psychology. http://www.simplypsychology.org/constructivism.html.
Mathematical Mysteries 