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.

 

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.

 

Review: What if everything you knew about education was wrong?

This Easter holidays I read David Didau’s 350+ page compendium.

Basically, this book is an essential must read for any teacher. It is detailed and covers quite the range of ideas relating to classroom practice. On top of that, it is very well written, with clear and accessible language.

It is broken into four parts.

Part 1 “Why we are wrong” introduces the reader to a few general psychological concepts. Throughout the book, David references Daniel Kahneman’s work “Thinking, Fast and Slow” a lot and I think much of what is written here is sourced from that book, although, perhaps, simplified and certainly written in a much less head scratchy way. If you have read “Thinking, Fast and Slow” many of the ideas about psychological traps and biases will be familiar to you. Still, David is able to show how to apply these concepts succinctly to the classroom setting. He also provides an excellent explanation of effect sizes and the statistical techniques used to compare the effectiveness of classroom interventions before giving some real food for thought as to why this evidence might not be as robust as we think. His critique of Hattie’s work was quite surprising for me and I welcomed the explanation of a concept I had heard lots of people talk about, but nobody has ever explained.

Part 2 lays out what David refers to as the threshold concepts for learning to teach effectively. David unpicks many commonly held myths about classroom teaching and learning and makes an argument as to why many of these cherished ideas are wrong. The key idea here is that learning does not equal the same thing as performance in class. Learning is essentially an invisible process happening in peoples heads and by looking at performance in class we assume that this equates to learning in the mind of the student. Classroom observers look for evidence of “rapid and sustained” learning during class time, however learning, David makes the case for, is messy, non-linear and if it is going to be sustained cannot be rapid. Aside from the difference between learning and performance he covers concepts such the difference between novice and expert learners, the structure of our memory in terms of storage and retrieval strength and cognitive load.

After explaining our cognitive biases and how they apply in education before unpicking many myths about classroom practice held in educational circles, in part 3 David goes on to apply the cognitive concepts from part 2 directly to teaching practice. He gives a clear exposition of interleaving, the spacing effect, the testing effects and the effects of feedback. His writing will prompt you to think about these topics and how they may apply in your own planning and instruction – I know that they certainly have for me.

In the final part, he examines other pet theories in education that we could be wrong about. The first chapter deals with formative assessment and presents a surprising critique of Dylan Wiliams work, with a reply for Dylan Wiliam. There are also chapters on the problems of lesson observations, differentiation, praise among others.

One of the things that I was most surprised about and enjoyed reading was the critiques of the work by very established researchers. The work of both Hattie and Wiliam were picked apart at different points in the book. I am not sure I am fully convinced by the arguments but it was a pleasure to read something that was a little bit different in the sense that I have never come across critical reflections of these, much discussed, in schools at least, concepts before.

I also like the way the book is laid out. Now that I have read it through, I am able to easily go back and find relevant chapters for different concepts again.

This book has given me quite a bit to think about in terms of my curriculum planning and my classroom practice. Despite having just finalised my DP curriculum, I am already prompted by thoughts in this book to review it – particularly in line with David’s thesis that we should plan curriculums around threshold concepts. Doing that first involves identifying them which will probably be the springboard for my next CPD drive. However, I am fully aware that even the threshold concept of threshold concepts may turn out to be an unevidenced and unprovable claim made by education researchers and that my time here will be wasted. Only time will tell!

Where is the evidence for your ideology?

The International Baccalaureate® aims to develop inquiring, knowledgeable and caring young people who help to create a better and more peaceful world through intercultural understanding and respect.

To this end the organization works with schools, governments and international organizations to develop challenging programmes of international education and rigorous assessment.

These programmes encourage students across the world to become active, compassionate and lifelong learners who understand that other people, with their differences, can also be right. – IBO Mission Statement.

As I outlined in this post, I am an IB educator who really believes in the mission of the IB. I believe in developing inquiring, knowledgeable and caring young people who help to create a better world. I think these aims are laudable and, with enough schools, teachers and families on board, achievable.

However, as I have reflected on my own practice over the last few years I have begun to question some aspects of the IBs ideology. In this post I want to examine the IB’s approaches to teaching. These “main pedagogical principles that influence and underpin IB programmes” are:

Fairly innocuous? Why write a post that is critical of these statements and principles? Well, there is one general reason and some specifics which I will come to.

My problem with the approaches to teaching in general is the following: The IB is the only awarding body offering a truly international curriculum. There are others; IGCSEs spring to mind, and of course, some international schools do offer national curriculums but the IB really is one of a kind in the sense that it is the only qualification awarding body, that I know of, that is not rooted to a national system and is found in schools, both private and public, countries all over world. It has no competition.

The ITT that teachers from different countries and from within countries will vary widely. For example my school-based training, via the GTP, really offered nothing academic – no explanations or reasoning or evidence for why teachers have to plan their lessons a particular way – it was essentially a check sheet of fadish skills that I had to demonstrate I was doing. When I converted this to a PGCE I was motivated by a desire to get to understand the theory behind teaching. I have since come to reflect that those theories I was exposed to had little to no evidence to support them.

As someone who has completed a science degree and masters, when my someone explains a theory to me without evidence, it just translates into my mind as an idea, an unsupported hypothesis. And this is what the great many “theories” in education circles appear to be, whether you are talking about Vygotsky, Piaget, Freire, Bloom, Bruner or many others, ideas without evidence, or if they have evidence it is low quality, small-scale or anecdotal.

The IB admittedly was founded in the era when some of these ideas were being taken up seriously:

From its beginnings, the DP has adopted a broadly constructivist and student-centred approach, has emphasized the importance of connectedness and concurrency of learning, and has recognized the importance of students linking their learning to their local and global contexts. These ideas are still at the heart of an IB education today. – ATL website

But now the tide is changing and I wonder if the IB is willing to keep up with that. Robust, evidence from cognitive science is seriously beginning to shine a light on what works. Even better some of this evidence is being triangulated not just from laboratories but from classroom studies as well.

My general concern is, therefore, this: if national ITT systems vary inter- and intra- nationally then the IB has to do something to help get all its teachers on the same page. Becuase it lacks competition it also has quite the sole market on influencing the teachers of its programs. It must make sure that the teaching methods it advocates are backed up on solid evidence, not just on what feels good socially and culturally or what is simply a la mode.

Now to my issues with specific approaches to teaching:

A focus on inquiry

A lot has been written about the effectiveness or not of inquiry-based teaching and learning. The debate rages on but essentially some of the arguments against inquiry-based teaching are:

  1. It is inefficient – students simply cannot learn as much knowledge in the same amount of time as they can from guided instruction.
  2. It is inequal – students who have knowledge richer home lives bring far more to the table than their knowledge deficient partners (just think about EAL learners in that context for a minute).
  3. It generates misconceptions – students can easily discover wrong-knowledge which can be very hard to dislodge and unlearn.
  4. It can lead to the illusion of knowledge – this is when students think that they know something but lack deep understanding of the content.

Concept-based teaching

Is great so long as you teach the right concepts and don’t make the unproven assumption that skills and knowledge can simply transfer from one domain to another. They can’t. Skills are context and domain specific. Concepts are domain specific. We should focus on domain-specificc threshold concepts, which requires careful planning on a content rich curriculum. Once you know the content that needs to be taught then you can identify the threshold concepts in your curriculum and plan your teaching interventions appropriately. The arbitrary lists produced for the MYP nor the self-imposed “essential ideas” of the DP biology curriculum, which forces teachers to lump certain knowledge together, in what may not be the most appropriate way, will do.

Differentiation

The black art of teaching. There are so many issues with this I don’t know where to start. On one hand, you lower the boundary for some students, therefore making a value-based, subjective decision about what a student can achieve and potentially limiting their potential, on the other, school management have carte blanche to drop any student into your class and expect you as the classroom teacher to “differentiate” even if that student doesn’t speak English.

Yes, we are all individual and unique but as David Didau points out, so are snowflakes and those differences mean nothing when it snows. The fact is we all learn in broadly similar ways and we all have broadly the same ability. Differentiation assumes that ability is the cause of differences in what students learn in the classroom but it may well be that ability is the consequence of the student’s classroom experience. Therefore if you lower the bar, overtime you lower their ability.

Differentiation to the point of tailoring learning engagements for individuals students is a huge workload issue for teachers and at what opportunity cost? There also appears to be no evidence for the efficacy of differentiation, even some that may suggest it has a negative impact.

For more information see chapter 22 of “What if everything you knew about education was wrong?” by David Didau.

This much I know about EAL teaching

In my view, biology is a subject that is largely about language instruction. Of course, this doesn’t mean, to the exclusion of all other considerations. Yes, of course, there are facts and concepts that need to be learned and understood but, at its heart, it is a subject concerned with language acquisition.

And just like French, it is full of irregular verbs.

Personally, I remember the challenge of all the new vocabulary of the subject at A level, as being something that attracted me to it; I had the impression that by learning all these new words I would be entering another higher plane of existence.

So just imagine what this vocabulary is like for a new student, stepping into this level of biology and operating in their second or third language and perhaps with a very limited exposure to schooling in English. I am always surprised by the number of other adults, parents and administrators, who don’t seem to see this.

Parents, particularly, seem surprised when I bring up the issues of academic language acquisition

I have had some amount of experience teaching students who have started the subject with no English or very little English and this post will outline what I understand about teaching them today I fully recognise that  I am no expert.

James Cummins: BICS & CALP

My first foray into the realm of EAL teaching brought the work of James Cummins to my attention. To summarise, Cummins’ work postulates differences between basic interpersonal communication skills (BICS) and cognitive academic language proficiency (CALP).

Essentially, the former can be developed over a relatively short period of time (1-3 years) and is the language of peer culture. Children who have developed BICS may well sound fluent and indeed can communicate on a level using common everyday terms and phrases with their family and peers. The latter can take much longer, 5-7 years, and once developed allows the individual to think, manipulate and utilise complex academic concepts mentally. They can think with the language and they can think in very abstract terms.

It seems to me that the work of Cummins suggests that schools should resist simply placing older EAL students into secondary subject-specific classes and hoping that they will catch up. This may work with students going into grade 6 and 7 classrooms but could actually retard students progress in grades 9 and up.

Obviously, in the international context, students may well keep joining older classes (I once had a student who joined grade 10 directly from school in Israel. She has never been taught in English and yet was expected to just catch up in grade 10 biology) and so we can’t reasonably say don’t come to school. But the approach of some managers seems to be that students will just pick up the language.

These students need intensive English instruction first (if that is the language of instruction of their academic subjects) using methods that have been shown to have the largest effect size. Strategies in this category have the best hope of bringing the students learning forward faster and thus the best hope of bringing the time for students to acquire CALP down.

Isabel Beck: Tiered Model of Vocabulary Aquisition

More recently I have come across the work of Isabel Beck whose model of vocabulary acquisition places words into three categories:

 

  • Tier 1: These are the common, everyday words that most children enter school knowing already. Since we don’t need to teach these, this is a tier without tears!

  • Tier 2: This tier consists of words that are used across the content areas and are important for students to know and understand. Included here are process words like analyze and evaluate that students will run into on many standardized tests and that are also used at the university level, in many careers, and in everyday life. We really want to get these words into students’ long-term memory.

  • Tier 3: This tier consists of content-specific vocabulary—the words that are often defined in textbooks or glossaries. These words are important for imparting ideas during lessons and helping to build students’ background knowledge.

 

In biology instruction, it is the tier 3 words that all students are going to struggle with initially, but EAL students may also be lacking a good number of tier 2 words, which will make their comprehension the tier 3 words that much limited as these words often provide the context for the tier 3 words.

For example this year I can think of the words “coolant” and “yield” that came up as not being known by my grade 11 students. Many of these are students raised in English speaking families but have been attending Swiss public schools up until the start of grade 10 or 11. These aren’t words that come up in everyday conversation but are used across academic domains.

I am relatively new to the idea of Tiered vocabulary but it does seem, on first impressions, a useful way to think about words that EAL students may or may not have and to plan to help students bridge that gap.

Perhaps, one wider school aim could be to map out the tier 2 words that are common across subjects. Once a working list is compiled then students can be assessed for their knowledge of these words and interventions put in place.

Strategies

  • Identify and pre-teach complex vocab (tier 3 words) before starting the unit (I use Quizlet “learn” for this)
  • Get to know your suffixes and prefixes so that you can explicitly model your understanding of the terminology to students.
  • Keep new words on the board, clearly visible to students to use in their thinking, speaking and writing.
  • Encourage more reading and writing in your classroom. Encourage students to constantly use the new terms that they are being exposed to.
  • Use a reading age analysis to examine the tests and exams that students in your class are likely to sit – what is the level? What is the English reading level of your EAL students?
  • At the start of the course give students lots of opportunity for guided reading, ask students to identify words that they don’t know and keep a running list. Provide explanations for these words.
  • In line with the above, continue to identify Tier 2 word gaps in your student’s knowledge through reading exercises.
  • Perhaps try to list out common tier 2 words in your subject (this would take time) and compare with other departments. Check students understanding for these.