I found this discussion of prior knowledge very clarifying and informative, thank you. What stood out most for me the is the move towards engineering the prior knowledge which students actually use, rather than just assuming it’s there or hoping it becomes organised in the right way.
Dylan Kane’s point in the comments about component skills and 'linking structures' in maths feels especially concrete here. In practice, I'd be curious to hear how you think teachers can decide what counts as 'useful' prior knowledge to surface or build before a new topic, especially when students come in with such mixed or partial amounts of knowledge/experience?
Good question. Partly what determines useful prior knowledge is the structure of the subject itself. My subject (English) differs a lot from maths for example. For English the useful prior knowledge may be big concepts, vocabulary, fact systems etc. Understanding the knowledge needed for a subject and how it builds is crucial.
Absolutely, subject specific progression is very useful way of thinking about this. The horizontal evenly distributed prior knowledge base required for English is vastly different to the more hierarchical order of maths knowledge. Thank you for getting back on this
In math teaching I would get even more specific about two ways prior knowledge influences learning.
First, there are component skills. A component skill of finding the area of a circle is squaring numbers. For solving simple equations it’s fact fluency. For integer operations it’s visualizing positives and negatives on a number line. If students aren’t reasonably fluent in the component skill, that consumes working memory and makes learning more difficult.
Second there are links between skills, a is like b. Complementary angles are like solving the equation x + a = 90. Solving systems of equations by elimination is like column addition/subtraction. Solving the equation 3(x + 1) = 15 is like solving the equation 3x = 15, but with one additional step.
This isn't "knowing more about a topic helps you learn." It's much more precise and often feels surgical: there are very specific component skills to practice before learning a larger skill, and there are very specific connections I want students to make, and so my teaching is very carefully designed around those principles. I like the idea of advance organizers -- it falls solidly in that second category above. But the examples I see often aren't at this level of specificity where I have found thinking about prior knowledge most helpful.
This was a great post. Thanks for writing it. I've been discussing explanations and the role of the teacher recently whilst arguing about flipped learning. I keep finding myself saying that one of the key roles of a teacher is to organise the information and not just relay it. Would this align with the ideas you have been exploring?
Sarah, is this really a transfer issue then? In the sense that the learner may know something about a topic but for whatever reason may not bring this to mind when it would be useful to do so?
I found this discussion of prior knowledge very clarifying and informative, thank you. What stood out most for me the is the move towards engineering the prior knowledge which students actually use, rather than just assuming it’s there or hoping it becomes organised in the right way.
Dylan Kane’s point in the comments about component skills and 'linking structures' in maths feels especially concrete here. In practice, I'd be curious to hear how you think teachers can decide what counts as 'useful' prior knowledge to surface or build before a new topic, especially when students come in with such mixed or partial amounts of knowledge/experience?
Good question. Partly what determines useful prior knowledge is the structure of the subject itself. My subject (English) differs a lot from maths for example. For English the useful prior knowledge may be big concepts, vocabulary, fact systems etc. Understanding the knowledge needed for a subject and how it builds is crucial.
Absolutely, subject specific progression is very useful way of thinking about this. The horizontal evenly distributed prior knowledge base required for English is vastly different to the more hierarchical order of maths knowledge. Thank you for getting back on this
Really interesting! Makes me think about the implications with our ECTs...
Let's talk more...
Great post!
In math teaching I would get even more specific about two ways prior knowledge influences learning.
First, there are component skills. A component skill of finding the area of a circle is squaring numbers. For solving simple equations it’s fact fluency. For integer operations it’s visualizing positives and negatives on a number line. If students aren’t reasonably fluent in the component skill, that consumes working memory and makes learning more difficult.
Second there are links between skills, a is like b. Complementary angles are like solving the equation x + a = 90. Solving systems of equations by elimination is like column addition/subtraction. Solving the equation 3(x + 1) = 15 is like solving the equation 3x = 15, but with one additional step.
This isn't "knowing more about a topic helps you learn." It's much more precise and often feels surgical: there are very specific component skills to practice before learning a larger skill, and there are very specific connections I want students to make, and so my teaching is very carefully designed around those principles. I like the idea of advance organizers -- it falls solidly in that second category above. But the examples I see often aren't at this level of specificity where I have found thinking about prior knowledge most helpful.
This was a great post. Thanks for writing it. I've been discussing explanations and the role of the teacher recently whilst arguing about flipped learning. I keep finding myself saying that one of the key roles of a teacher is to organise the information and not just relay it. Would this align with the ideas you have been exploring?
Similarly, I think I heard Cavaglioli saying that teachers are information designers(?)
This is an amazing piece! Especially the mediators and moderators. I touch upon some of these in Daniel Willingham Reminded Me That Memory Is the Residue of Thought (https://harriettjanetos.substack.com/p/daniel-willingham-reminded-me-that?r=5spuf). Thank you!
Very interesting!
Sarah, is this really a transfer issue then? In the sense that the learner may know something about a topic but for whatever reason may not bring this to mind when it would be useful to do so?
Thank you Sarah
You might like to check out this post from David Didau https://open.substack.com/pub/daviddidau/p/missing-the-wood-for-the-trees-why?r=74sdm&utm_medium=ios regarding the Buchin study. Some substantial criticisms about how much it really offers.