A summary of the structure of knowledge

In the final term of this year, I completed an online course on “Theory of Knowledge” from the University of Oxford’s department for continuing education. As part of this course, I have to submit two assignments. The first, which is a summary of the structure of knowledge and limited to around 500 words, was due on the 5th June and I am posting a copy of it below.

A summary of the structure of knowledge

According to Pritchard (2014), we can distinguish between two types of knowledge: knowledge of something or knowledge of how to do something also referred to as propositional knowledge and ability knowledge respectively. It is the first of these that we are interested in in this summary.

Knowledge is valuable because knowledge has instrumental and non-instrumental value. Having knowledge is instrumentally valuable in the sense that it helps us achieve our goals, but it is also non-instrumentally valuable in the sense that having knowledge enriches our lives in and of itself.

To claim to know something is to make a claim or a proposition that a) you believe something and b) that your belief is true. If I claim that it is raining in London while I am living in Lausanne, and assuming that I have no ill intent to deceive those I am talking to, I am making a proposition which I must ultimately believe – how could I claim it was raining if I didn’t ultimately believe it to be so? Intuitively it seems that we cannot claim propositional knowledge if we don’t first believe it.

The claim that we know something “aims at” truth, to use Pritchard’s (2014) phrase. Claiming knowledge intuits at the truth of reality. We don’t normally count someone who holds a false belief as holding knowledge of something. For example, in a pub quiz, someone could be said to be knowledgeable of the topic in question if they hold what is commonly accepted as the “correct” or truthful response. Someone who incorrectly or falsely believes the answer is another proposition cannot be said to know the answer.

Thus, we can say that truth and belief are necessary conditions of knowledge. However, a guess (like a bet) that gets to the truth of the matter (that turns out to be true) is also a claim that contains truth and belief but is not considered knowledge. Under normal circumstances, someone who wins at roulette with the number 29 can’t be said to know that 29 was the correct number, but they did have a true belief that 29 was the number.

Therefore, to count as knowledge, a claim needs have more than truth and belief, it also needs to be justified. Knowledge has historically been counted as justified true belief. All three of these elements are necessary conditions for knowledge but on their own, they are not sufficient conditions for knowledge.

For example, Gettier cases show us that justified true belief isn’t always enough for knowledge. By luck, some agents can still hold true beliefs that are justified but that we would not normally count as knowledge. In the case of an agent who “knows” the time by looking at a stopped clock, if they look at the clock at the “correct” time even though the clock has stopped they will have gained a justified true belief, but they will have done so by luck. If they had looked at the clock five minutes later or five minutes earlier they would have acquired a false belief (Pritchard, 2014).

So, we also need more than justified true belief. We still need to consider the type of justification that is used when combined with true belief. More specifically we need to consider what supports our beliefs in order for them to be justified. There are normally three ways of considering this: a) beliefs do not need to be grounded on anything b) beliefs can be founded on an infinite chain of justifications c) beliefs can be grounded on a circular chain of beliefs. The different schools of thought of infinitism, foundationalism and coherentism offer different responses to this trilemma.

Justification and the support needed for belief is closely linked to rationality. Normally only rational beliefs would be considered knowledge. We can think of a judge who reaches their decision either by weighing up the evidence presented or on the basis of their emotional or prejudice. A judge who rationally weighs up the evidence to reach a verdict can be justified in their true beliefs but a judge who doesn’t, can’t be. However not all rationality is linked to finding the truth and to justify our beliefs we should be concerned with having epistemically rational beliefs. Pascal’s wager is a good example of the difference between epistemically and non-epistemically rationality. In the same vein, we need to consider whether agents can or should be held responsible for their beliefs.

Are people responsible for paying attention to how their beliefs are formed? Can we count a belief as knowledge if the agent in question has not considered how they have formed their belief?

References

Pritchard, D. (2014) What is this thing called knowledge? 3rd edition. Routledge.

 

My reads by year

Through the threshold library

My reads by year

A list of the all the books I have read each year.

2018

  1. What is this thing called knowledge? – by Duncan Pritchard. Read as part of Oxford Universities online CPD course – theory of knowledge
  2. Epistemology: Contemporary readings – edited by Michael Huemer
  3. What if everything you knew about education was wrong? – by David Didau – my review.
  4. Cleverlands – by Lucy Crehan
  5. Seven myths about education – by Daisy Christodoulou
  6. Making good progress? – by DaisyChristodoulou
  7. Why knowledge matters: rescuing our children from failed educational theories – by E.D. Hirsch
  8. Ouroboros –  by Greg Ashman
  9. What does this look like in the classroom? – by Carl Hendrick and Robin MacPherson
  10. The Sword of Honour Trilogy – Evelyn Waugh

2017

  1. Raising babies – by Steve Biddulph
  2. A brief history of everyone who ever lived – by Adam Rutherford
  3. Patient H.M. – by Luke Dittrich
  4. The Serengeti rules – by Sean Carroll
  5. Battle hymn of the tiger teachers: the Michaela way – edited by Katherine Birbalsingh
  6. American Gods – by Neil Gaiman
  7. Neverwhere – by Neil Gaiman
  8. How the Marquis got his coat back – by Neil Gaiman
  9. Stardust – by Neil Gaiman
  10. The ocean at the end of the lane – by Neil Gaiman
  11. Anansi boys – by Neil Gaiman
  12. The rise and fall of D.O.D.O – by Neil Stephenson and Nicole Galland
  13. What every teacher needs to know about psychology – by David Didau and Nick Rose
  14. How to stop time – by Matt Haig
  15. Why don’t students like school? – by Daniel Willingham
  16. Coraline – by Neil Gaiman
  17. The graveyard book – by Neil Gaiman
  18. Fragile things – by Neil Gaiman
  19. Smoke and mirrors – by Neil Gaiman
  20. His Dark Materials: The complete trilogy – by Philip Pullman
  21. Trigger Warning – by Neil Gaiman
  22. Norse Mythology – by Neil Gaiman
  23. Good Omens – by Neil Gaiman and Terry Pratchett

2016

  1. How to raise an adult – by Julie Lythcott-Haims – my review.
  2. What is the point of school? – by Guy Claxton
  3. Making thinking visible – by Ron Richhardt – my review.
  4. Aping mankind – by Raymond Tallis
  5. Getting Darwin wrong – by Brendan Wallace
  6. The problems of philosophy – by Bertrand Russell
  7. Why evolution is true – by Jerry Coyne
  8. Faith vs fact – by Jerry Coyne
  9. Seven Storey Mountain – by Thomas Merton
  10. Seveneves – by Neal Stephenson
  11. Never let me go – by Kazuo Ishiguro
  12. What is the point of school – by Guy Claxton
  13. Being Mortal: Illness, Medicine and What Matters in the End – by Atul Gawande
  14. Religion for Atheists – by Alain de Botton
  15. The Remains of the day – by Kazuo Ishiguro
  16. Fireflies – by Shiva Naipaul
  17. The Young Atheist’s Handbook: Lessons for living a good life without God – by Alom Shaha
  18. The vital question: why is life the way it is? – by Nick Lane

2015

  1. The brain at school: educational neuroscience in the classroom – by John Geake
  2. Classroom-based research and evidence-based practice – by Keith Taber
  3. Ways of learning: learning theories and learning styles in the classroom – by Alan Pritchard
  4. Pedagogy of the oppressed – by Paolo Freire
  5. Visible learning for teachers – by John Hattie
  6. Thinking, fast and slow – by Daniel Kahneman
  7. Raising girls – by Steve Biddulph
  8. Full catastrophe living – by Jon Kabat Zinn
  9. The moral landscape – by Sam Harris
  10. A Universe from nothing – by Laurence Krauss

2014

  1. Good work – by Howard Gardner, Mihaly Csikszentmihalyi, and William Damon
  2. Intelligence reframed – by Howard Gardner
  3. Contemporary theories of learning – by Knud Illeris
  4. Teaching as if life matters – by Christopher Uhl
  5. Nonviolent Communication – by Marshall Rosenberg
  6. The last child in the woods – by Richard Louv
  7. The sixth extinction: an unnatural history – by Elizabeth Kolbert
  8. Neanderthal man – by Svante Paabo
  9. The serpents promise – by Steve Jones
  10. The language of life – by Francis Collins
  11. Creation: the origin of life/the future of life – by Adam Rutherford
  12. Your inner fish – by Neil Shubin
  13. Life Ascending – by Nick Lane
  14. The Baroque cycle (3 books) – by Neal Stephenson
  15. The magic of reality – by Richard Dawkins

Earlier

  1. Bad Science – by Ben Goldacre
  2. Thirteen things that don’t make sense – by Michael Brooks
  3. The immortal life of Henrietta Lacks – by Rebecca Skloot
  4. The rational optimist – by Matt Ridley
  5. Quantum evolution: the new science of life – by Johnjoe Mcfadden
  6. The diversity of life – by E.O. Wilson
  7. Impossibility – by John Barrow
  8. Collapse – by Jared Diamond
  9. The self illusion – by Bruce Hood
  10. The selfish gene – by Richard Dawkins
  11. Genome – by Matt Ridley
  12. The secret life of trees – by Colin Tudge
  13. The man who mistook his wife for a hat – Oliver Sacks
  14. The Handmaid’s tail – by Margaret Atwood
  15. The Inheritors – by William Golding
  16. The Baroque cycle – by Neal Stephenson
  17. The greatest show on earth – by Richard Dawkins
  18. The song of the Dodo – by David Quammen
  19. The lives of a cell – by Lewis Thomas
  20. Fifty ideas you really need to know – by Hayley Birch
  21. The violinists thumb – by Sam Keen
  22. All the Evelyn Waugh novels and travel writing
  23. Game of thrones

What I learned about teaching biology this year 17-18

In 2016 I wrote this blog post. My answer to that question is now decidedly, yes. Content is King.

In this post, I want to explore why this is the case and outline what my ideas are now in relation to teaching biology.

The importance of content?

First, I should point out that a re-reading of my 2016 article makes me realise that I never concluded by suggesting content wasn’t king. Like all good questions, the article title helps to stimulate thought and a discussion about where we are at in our beliefs and in defending those beliefs. Really, the argument I was making was that teaching is not all about teaching content, but about teaching content AND encouraging critical thought with that content matter.

Content underpins everything. It underpins thinking. You can’t think without something to think about. It underpins understanding. You can’t understand something that is not represented as a propositional claim at a basic level. You can’t develop “skills” that aren’t grounded in some form of understanding.

When I am talking about content, I am referring to facts or propositional knowledge, statements that are thought to be true and are about the way the biological world is.

Propositional knowledge then must have primacy in teaching biology. To my mind, currently, propositional knowledge can be broken up into facts and concepts. Facts cannot be understood, they can only be known. Whereas concepts can be known and understood.

I think that to achieve deep, flexible, biological knowledge (flexible in the sense that it can be thought about in the abstract and applied in new situations) students need to achieve a conceptual understanding of the major themes in biology.

To do this they must first meet domain-specific examples. From those examples, they can then begin to pull out the commonalities to allow the mind to achieve an understanding of an abstract concept. My post here outlines how I went about this when teaching natural selection this year.

Learning domain-specific facts cumulatively builds to domain-specific conceptual understanding which accumulates in the learner being able to think in terms of these concepts and apply them elsewhere.

The importance of presenting content in the “right” sequence

Related to the idea of sequencing teaching so that we build up to conceptual understanding from specific examples, is the idea that we need to sequence teaching to avoid cognitive overload. To do this we need to think about which areas of the curriculum provide just enough challenge to engage students but not so much so they are overwhelmed.

In teaching biology, I think this is best achieved by teaching those areas with the least new propositional knowledge for the learner. Once the learner achieves mastery of this new knowledge then we can begin to add more.

In this sense, when trying to teach the understanding of the relationship of structure and function we may wish to look at studying the function first of any new example, before looking at the structures that support that function. Developing knowledge of the function of something might contain less instances of “facts” than the discrete structures that build up that function.

Once we have looked at lots of examples of, say, the relationship between surface area and diffusion, students will build up to the understanding of the relationship generally, and hopefully be able to apply this in new and novel ways.

Retrieval practice embedding content for the long-term

Drill and kill, right? Apparently not. My reading this year has convinced me that giving students the chance to practice retrieving information, not only builds their confidence that they can perform, and therefore reduces stress but also improves their ability to retrieve that information and therefore improves its storage in long term memory.

The same goes for learning the language of the subject and so now I try to begin my lessons with a fun low stakes retrieval practice activity. Low stakes in the sense that I do not record results and store them; students are not graded. For this I have prepared a deck of quizlet terms for the DP biology course and I alternate between using these or simply giving students a series of MCQ’s from last lesson, last week, last month and last term.

Interleaving & spaced practice – what might this look like in biology?

A year ago, on the Facebook AP/IB Biology teachers group, I first asked the question of what interleaving might look like in a biology course. I had been hearing a lot about interleaving during meetings and inset training from our DP Coordinator who is a Maths teacher. It seems that interleaving has been studied quite a bit in mathematics education.

When I asked the question, hardly anyone was aware of this concept amongst the biology teachers and I was stumped. I now have some ideas.

Interleaving or spaced practice is the idea that instead of learning all the content for a particular topic at once or in a set of continuous lessons, you space out the learning over time, revisiting topics over time.

In my experience, I have always taught a topic like cell structure and then moved onto the next topic, maybe membrane structure followed by membrane function – and I think that this is true of most biology courses.

In an interleaved curriculum these topics would be spaced out in time. Let’s imagine you have a 60min lesson every day with the same class, so five lessons a week. In an interleaved curriculum you may devote Mondays to cell structure, Tuesday to metabolism, Wednesday to plant physiology, Thursday to animal physiology and Friday to retrieval practice.

You would then teach the content of these units side by side over a number of weeks. It sounds a bit crazy but it has been demonstrated to improve long-term retention of learning and I am also excited by the possibility for the conceptual links you can make by teaching in this way.

 

The guidance bookshelf

Through the threshold library

The guidance bookshelf

Useful books that I use for university guidance.

How to raise an adult – by Julie Lythcott-Haims – my review.

There is life after college – by Jeffery Selingo

College (un)bound – by Jeffery Selingo

Colleges that create futures – by Robert Franek

So you want to go to Oxbridge? Tell me about a banana – by Oxbridge Applications

Thinking skills: Critical Thinking and Problem Solving (CIE) – by John Butterworth (I bought this for students planning on taking the TSA).

Looking beyond the Ivy league – by Loren Pope

Colleges that change lives – by Loren Pope

HEAP Guide – updated each year

Fiske Guide to Colleges – updated each year

Good university guide – updated each year

Strength finder 2.0 – by Tom Rath

Global Nomad’s Guide to University Transition – by Tina Quick

What should I do with my life (card game) – by the school of life

Sequencing facts before concepts: natural selection

I have spent a fair amount of time this year reflecting on the application of cognitive science principles in my own biology teaching. There has been plenty written about concepts like interleaving and sequencing in sciences and maths but very little that I have found about how these concepts may apply in biology teaching.

Specifically, I have written up some of my thoughts on sequencing my DP biology curriculum based  on these discussions here.

Some of what I have learned suggests that solid conceptual/abstract understanding can only be developed when novice learners have embedded factual or propositional knowledge in their own mental schemas. In addition, I have tried to think about how principles from cognitive load theory may apply in terms of biology teaching and the sequencing of content.

One example of this has been how I approached the teaching of the concept of natural selection this year for my Y12/G11 mixed SL/HL IB biology class. In the IBDP biology syllabus, this is topic 5.2 and I sequence it after 5.1 “Evidence for evolution” and before 1.5 “The origin of cells”.

I finish the evidence for evolution section by looking at the peppered moth and the changes within the populations studied by Dr Ketterwell, through this online simulation.

In the past, I have taught natural selection by going over the concept of natural selection and then looking at specific examples of it that are mentioned in the syllabus which are antibiotic resistance in bacteria and changes in the beaks of the finches of the Galapagos island of Daphne Major.

This year I sequenced the topic into three lessons (which unintentionally appear to have been interleaved as we are also doing the internal assessment at this point in time and one lesson a week is given over to just the HL students anyway) and taught specific examples of natural selection before finally generalising from these examples to the abstract concept of natural selection.

Lesson 1 – Antibiotic-resistant bacteria

We started with retrieval practice of previous material using a google slide presentation which contained four questions: one using material from the last lesson; another from last week; another from last month and another from the last term. I then asked the students to draw and label a prokaryotic cell. Something that they covered six months ago.

Once completed we moved on to watch some news reports about antibiotic-resistant infections and I asked students to discuss and articulate back to the class what they thought the key message of each of the videos were. These prompted discussion about the general nature of antibiotic resistant bacteria and I used questioning to continue this discussion amongst the class. We also discussed what antibiotics were and why they were used to treat bacterial infections as this was a concept we met when studying the immune system two weeks prior. I highlighted the possible area of confusion for students between the words antibiotic and antibody which I had picked up from examining the previous May session of exams, before going on to explain how bacteria have become resistant to antibiotics.

I then gave the class a past paper question to complete the topic and we reviewed the key points of this question from the mark scheme.

Lesson 2- Finch beak changes on Daphne Major

Again we started with retrieval practice in the same format as in lesson 1. We then conducted a physical simulation as outlined in this practical, where students mimic being finches and collecting food. This was followed by a discussion of the trends we found in the simulation and what this might tell us about birds collecting food in the wild.

We then moved onto exercise 3 from this page and when students had finished the video and quiz I asked them to summarise what happened to the finches in the film.

Lesson 3 – the concept of natural selection

After retrieval practice, we reviewed the definition of evolution we had covered in 5.1 “evidence for evolution” and I highlighted that natural selection was a mechanism by which evolution could occur. I then asked students to think back and name the three examples of natural selection that we had considered in the last few lessons. Once they had written their answers down, I went through those examples and placed them on the board. I then asked students to discuss in pairs the details of each of these examples, before snowballing into a class discussion of the details of each of the three examples: peppered moths, antibiotic-resistant bacteria and changes in finch beaks. While we discussed these I wrote down the key points from each one on a second board with each example in a column so that similar elements from each example ended up in the same row. I then discussed with the students what these key features of each of the examples were and related this to the concept of natural selection. We finished with an example question asking students to describe the process of natural selection using examples.