Response to:
Relational Understanding and Instrumental Understanding
by Richard R. Skemp
Relational Understanding and Instrumental Understanding
by Richard R. Skemp
Quote 1: "Instrumental understanding I would until recently not have regarded as understanding at all."
Response 1: I find it funny that he says this as I have witnessed the struggles of an 'instrumental learner'. Anyone looking to learn in this way has to evaluate why they want to learn in the first place. Otherwise, it very well might be a 'memorizing exercise' in futility. Someone with a poor memory must understand rationally or they won't have any skills to problem solve.
Quote 2: "If it is accepted that these two categories are both well-filled, by those pupils and teachers whose goals are respectively relational and instrumental understanding (by the pupil), two questions arise. First, does this matter? And second, is one kind better than the other?
Response 2: In many ways, there's two types of teachers; those who have learned about these learning/teaching styles and those who haven't. I feel it's important to appreciate both, even though having a relational understanding is more complete.
Quote 3: "He was a very bright little boy, with an IQ of 140. His misfortune was that he was trying to understand relationally, teaching which could not be understood in this way."
Response 3: I was a student who was trying to understand relationally what my grade 2 teacher was teaching instrumentally. Thankfully, since then I've been met by a plethora of like-minded teachers; relational thinkers, who could teach the way I learn.
Quote 4: "Just because less knowledge is involved, one can often get the right answer more quickly and reliably by instrumental thinking than relational. This difference, is so marked that even relational mathematicians often use instrumental thinking."
Response 4: When concepts get so difficult often times analogy & instrumental techniques are needed to solve difficult problems. In this way, it helps with the ultimate goal of relational understanding. This is an interesting relationship between the two.
Quote 5: "One of these is whether the term 'mathematics' ought not to be used for relational mathematics only."
Response 5: I don't think this distinction is so important, so long as a teacher is conscious of the two styles and how it affects the learning outcome. Instrumental math, which is how we all started learning, is still math.
In conclusion, it's important to make very clear the difference between the two learning/teaching styles, but not to discredit either of them. Instead, we must fuse these two styles together, harmoniously, so that our students can benefit from both. We must recognize students for their individual learning needs, cater to them, and not to forget why they're there.
Response 1: I find it funny that he says this as I have witnessed the struggles of an 'instrumental learner'. Anyone looking to learn in this way has to evaluate why they want to learn in the first place. Otherwise, it very well might be a 'memorizing exercise' in futility. Someone with a poor memory must understand rationally or they won't have any skills to problem solve.
Quote 2: "If it is accepted that these two categories are both well-filled, by those pupils and teachers whose goals are respectively relational and instrumental understanding (by the pupil), two questions arise. First, does this matter? And second, is one kind better than the other?
Response 2: In many ways, there's two types of teachers; those who have learned about these learning/teaching styles and those who haven't. I feel it's important to appreciate both, even though having a relational understanding is more complete.
Quote 3: "He was a very bright little boy, with an IQ of 140. His misfortune was that he was trying to understand relationally, teaching which could not be understood in this way."
Response 3: I was a student who was trying to understand relationally what my grade 2 teacher was teaching instrumentally. Thankfully, since then I've been met by a plethora of like-minded teachers; relational thinkers, who could teach the way I learn.
Quote 4: "Just because less knowledge is involved, one can often get the right answer more quickly and reliably by instrumental thinking than relational. This difference, is so marked that even relational mathematicians often use instrumental thinking."
Response 4: When concepts get so difficult often times analogy & instrumental techniques are needed to solve difficult problems. In this way, it helps with the ultimate goal of relational understanding. This is an interesting relationship between the two.
Quote 5: "One of these is whether the term 'mathematics' ought not to be used for relational mathematics only."
Response 5: I don't think this distinction is so important, so long as a teacher is conscious of the two styles and how it affects the learning outcome. Instrumental math, which is how we all started learning, is still math.
In conclusion, it's important to make very clear the difference between the two learning/teaching styles, but not to discredit either of them. Instead, we must fuse these two styles together, harmoniously, so that our students can benefit from both. We must recognize students for their individual learning needs, cater to them, and not to forget why they're there.
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