Tag Archives: Memory

One approach to introducing cold calling to the classroom

After reading Glen Pearsall’s Top 10 Strategic Questions for Teachers (concise, free ebook) recently I was really inspired to introduce cold calling into the classroom. I had also wanted to incorporate spaced repetition into my class as well, so I thought it would be a good opportunity to kill two birds with one stone. (note: I’ve just started in my teacher training placement school, I’ve taught 3 lessons there in previous weeks but today was the first day of a month taking two year 9 math classes full time).

The way I thought I’d implement cold calling, to use pop sticks with the student’s names on them, was inspired by watching Dylan William’s ‘The Classroom Experiment‘, but I was afraid of making kids feel too put on the spot by the questioning. How to scaffold their participation?

The first student question I wanted to pre-empt was, ‘Why are we doing this spaced repetition stuff?’ (I didn’t actually use that term, I’ve called it ‘Micro-revision’). I addressed that by showing them the following clip.

I asked students what they’d learned from the clip, and if anything surprised them. I then mentioned that at the start of every class from now on we’ll be doing ‘micro revision’, 3 questions to jog our memory on previous topics.

Then, to address fear of making mistakes and a feeling of being put on the spot, I showed this clip from Jo Boaler.

I then said, ‘remember those coloured pop sticks you wrote your names on the other day?’ (Last Friday I had asked them to write their name on a coloured pop stick and used them as exit cards). ‘Well, for each question on the micro-revisions, I’m going to be using the sticks to select someone to share their thinking with the class.’ I then flashed up the following slide.Screen Shot 2015-04-20 at 6.11.05 pm

Then we got stuck in, and I revealed the first 3 micro-revision question (I also added in a challenge question in-case any of the students were streaming ahead. I stated that I wouldn’t be going through that one with the whole class). I watched the class and walked around to gauge when most of them had done about as much as they were going to.

I had a few questions planned, 1: What is this question asking us to do? What does it relate to that we’ve learned before? (More on metacognitive questioning and practices here), 2: Why did you do that?, i.e., just basically get them to justify their mathematical thinking. I also encouraged them to use correct terminology. Then… the moment of truth!

Screen Shot 2015-04-20 at 6.25.21 pmThe first student I asked said “I didn’t do it”. I replied “That’s ok, if you were going to do it now, how would you do it?”, he went right ahead and solved it in front of the class (him talking, me writing on the board). The second student was really happy and excited to share as well, and the third student even used the terms ‘numerator’ and ‘denominator’ in their answer which blew me away! I’ll also note that I was careful not to say ‘What’s the answer?’ but instead used the two questions outline above along with ‘Can you share with us how you approached this question?’. The emphasis was on sharing approaches, not on answers.

In closing, I was really happy with how the whole exercise came off, and I look forward to keeping up with the micro-revisions. I’ve also just had the thought of making Fridays ‘Feedback Fridays’, where I’ll give them five questions on the micro-revision and ask them all to hand in their answers so I can get a more clear picture of how each student is doing (That’s ‘Formative Feedback Fridays’ in teacher lingo ; ), and to write on the back of the sheet any feedback that they have on my teaching.

 

Train: The last of the 5 steps of efficient learning

This is the fourth in the five steps of efficient learning that are outlined here

Train: Train/Practice/Review, all of these words mean the same thing. This last step of efficient learning can take as little or as much time as you like, it depends on what you want out of it. If you only want to remember the info for a multiple choice test tomorrow, your requirement for training will be minimal. If you want to remember it for life, this will be an ongoing process. This article first deals with why you should bother training then moves on to how to do it.

Why Train?

Training facilitates the following process, each of outcomes is discussed below1.

Screen shot 2014-09-12 at 3.35.53 PM

In the following I refer quite a bit to the importance of storing things in long term memory in order to make space in your working memory for thinking. If this doesn’t make sense to you yet. Read this article on how knowing things facilitates Critical Thinking.

From Short Term to Long Term Memory

This is the difference between remembering something for only a short period of time and having it available to call upon whenever you need it. As I explain in the critical thinking article I linked to above, without storing information in your long term memory you’ll be clogging up your working memory and be significantly compromising your ability to solve problems. Unless you’ve remembered it you simply don’t know it.

Making it Automatic

I remember one time when I was learning to drive I was travelling along the highway with my friend in the back seat and my mum suggested that I change lanes to take an exit. I checked my mirrors and started to do a head check when I felt the steering wheel move. I looked forward again and mum was holding the steering wheel. I glanced at my mate in the rear view mirror and he had a very worried look on his face. I had been veering off the road!

At this point in my learning-to-drive process I understood how to do it and I could physically drive. All the info of the process was stored in my long term memory, but the process wasn’t automatic for me yet. It took conscious concentration for me to drive and I’d have to go through the steps in my head. eg: when taking off:  “clutch in, turn car on, indicate, get the revs up, let the clutch of slowly till it bites, ease the hand break off, check mirror, shoulder check, move out onto road”. This was an attention consuming process and meant that if I got distracted by something my passengers were in a risky position!

This is the same for all learning. For something like maths, we want to make the basic rules of algebra automatic so that we can think about how to solve new problems without having our working memory clogged up with wether you need to divide or multiply both sides by 5 to isolate x.  Training to the point of automaticity is vital for taking your learning to the next level and especially for performing well in stressful situations.

Transfer

I mentioned transfer in step 3: Understand. Transfer occurs when you’re able to apply an idea or concept to an unfamiliar situation because you understand it well enough. Transfer can happen shortly after a concept has been transferred to long term memory, but training helps to cement it, and automaticity frees up working memory space so that you can think of new and more creative ways and apply the concept to novel situations.

Other than just being able to solve questions that we’ve never seen before, there are other ways that we can test for transfer. One way to test for transfer is to ask if we could think of a new situation in which the principle in question could apply, this new situation could be just  an example, or it could be in the form of an analogy.

eg: If your english class has just been exploring the concept of Irony*, the teacher may ask ‘can anyone think of any new examples of ironic situations?’. A student may reply, ‘You’re walking to work then a piano falls on your head’ . If this is the case, you could conclude that this student hasn’t quite grasped the concept solidly enough for transfer to occur. If, however, they suggest ‘You poke your eye out whilst putting on your safety glasses’ or ‘The ambulance set out to save the lady but ran over a man on the way’ it would be clear that transfer had occurred.

*Irony: A condition of affairs or events of a character opposite to what was, or might naturally be, expected; a contradictory outcome of events as if in mockery of the promise and fitness of things. (In French ironie du sort.) -Oxford english dictionary.

How to Train

Screen shot 2014-09-12 at 4.36.05 PMThe most important and most ignored principal of revision is to SPACE YOUR PRACTICE. This is the case for mental tasks. For physical tasks ‘cramming’ can often be effective because muscle memory is different to mental memory. The best way to space out your practice is by using Spaced Repetition Software. If you have read many of the articles on this blog before then you should be familiar with the software Anki by now. This article I put together about Anki is one of the first articles I ever wrote on this blog, and it remains one of the most relevant.

Once you’ve got your head around spacing your training effectively here are some other tips. These tips have been written with maths and physics type questions in mind, but they apply to many other scenarios too.

  • Practice with questions that have solutions so that you know you’re practicing the correct thing!
  • ‘Batch’ your practice. ie: Practice one type of question at a time. Make  sure you understand how to deal with that type of question before moving on to the next
  • Shorten Feedback loops: This is related to batching. If you practice a question that’s too long, by the time you get to the end of it you won’t remember what you were doing at the start. It can be helpful to do one section of a question at a time and check your progress before moving on.
  • Time yourself: In a test situation you have a limited time. You need to develop the ability to answer questions quickly so that you get through the test in time. Ideally the questions that you know how to do you should be able to do them under the time allocated to them to free up time in the test/exam for you to deal with questions that you haven’t come across before.
  • Practice questions multiple times: A trap for young players, I’ve often heard the comment ‘I’ve done this question before’. That’s great, but can you do it again? More importantly, will you be able to do it in the test? You really want to be training to the point of automaticity.

EXCELLENT. So now you’ve Surveyed the topic, Acquired the best possible information, Understood it (maybe already, maybe understanding will come later), Linked new info to things you already know and you’ve just Trained your skills to the point of automaticity. Now it’s time to work out how to perform under pressure (article to come soon).

References:

  1. See kindle Location 2074 of Daniel Willingham’s Why Don’t Students LIke School?

Memory 201: Mnemonics – Supercharging Your Memory

If you’ve already read the  articles Memory 101 and Memory 102 then start reading from the “Mnemonics” heading two paragraphs below this message. 

In the previous two articles in this memory series I wrote about how, in order to remember something new, it’s necessary to link new knowledge to existing knowledge. We called this existing knowledge ‘memory anchors’. There are two main ways that we can link new knowledge to old knowledge. The first is anchoring for meaning and the second is through using mnemonics. This article addresses the latter.

Anchoring for meaning is a much stronger way of building memory connections than mnemonics is. Anchoring for meaning means we logically connecting ideas in ways that reflect how those concepts are actually linked in the real world. However, there will be times when anchoring for meaning isn’t possible (see the bottom of the anchoring for meaning article for examples) In times like these a Mnemonic are your best bet.

In this mnemonic, knuckles represent months with 31 days and spaces in-between knuckles represent months with 30 days (except for Feb of course)

In this mnemonic, knuckles represent months with 31 days and spaces in-between knuckles represent months with 30 days (except for Feb of course)

Mnemonics

Mnemonics are an array of memory techniques that can be used to memorise something. They can be linked to something on your body, someone you know, or something you’ve imagined. One of the key things to be sure of when you’re making a mnemonic is that the thing you’re attaching the new info to isn’t going to disappear (ie: it’s a good memory anchor), eg: tThe hands in the above picture aren’t going anywhere… hopefully. Here are some of the key mnemonic methods.

  • Acronyms: This is when you create a word where each of the letters of that word is the start of another word. An example of this would be S.A.(U).L.T. This acronym stands for Survey, Acquire, Understand, Link, Train, and is the one that I use to remember the five steps of efficient learning. When making an acronym, it’s ideal to make it in such a way that the word that’s the basis of the acronym (S.A.(U).L.T) is easy to remember itself (this one looks like SALT, with a bowl of salt ‘U’ in the middle). These are great for remembering combinations of words or concepts.
  • The Link Method: The link method is when you link various things together in any way you like, often this works best if you visualise them being linked together. This is a great way to remember lists of objects. For an example of the link method in use see this article.
  • Method of Loci, aka: Journey Technique: Method of Loci is a fantastic method for remembering things such as speeches or essays. You think of a location that you already know well, such as your house, and you attach different points from the speech or essay to different locations in the house. For an inspiring example of this see Joshua Foer’s TED Talk on it.
  • Stories are pretty self explanatory. This is a good one for teachers. If you are looking to teach your lesson in the format of a story, the four key components of a good story are  causality, conflict, complications and strong characters (the 4 Cs). How to make this work is a bit harder than it sounds and for those interested in exploring storytelling further, Daniel Willingham in suggests the book:  Druxman, M. B. (1997). The art of storytelling: How to write a story.
  • Songs: Awesome! put the info you want to remember into a song : )
  • Analogies: I leave analogies at the end here because they’re half way between anchoring for meaning and mnemonics. They’re finding an example of something that we already know where some key characteristic/relationship reflects a key characteristic/relationship in the new thing that we’re trying to learn. Analogies are a powerful way of understanding difficult concepts and I discuss them in more detail in this article about understanding.

Mnemonics require creativity to come up with. Perhaps you struggle writing songs, so maybe that isn’t a good one for you, perhaps you have trouble visualising things, maybe the link method isn’t going to be that useful. Regardless, successful use of mnemonics is something that is going to take time and practice to develop. I must stress, mnemonics can be anything. It’s simply a creative way of linking ideas together in such a creative, funny, emotive, sad, etc way that you’re not going to forget it!

You can often find mnemonics that others have found helpful such as SOHCAHTOA or ELI the ICE man. That said, mnemonics that you make up yourself are more likely to stick in your head batter.

Once you got a mnemonic for a concept the next step is to practice it frequently enough that you remember it! This brings us to the last of the 5 steps to efficient learning, Train.

 

Link: The fourth of the 5 steps of efficient learning

This is the fourth in the five steps of efficient learning that are outlined here

Ever understood a concept in class but the next day it was just as much of a mystery as before your revelation? This is because you didn’t Link your new knowledge to something you already knew. Once we’ve gained understanding of a concept (or whilst we’re trying to gain an understanding of a concept) we need to explicitly link it to something we already know so that our newly acquired knowledge doesn’t just float away.

In Cognitive Science, linking new information to old is referred to as “Anchoring” (we can connect the concepts of ‘Link’ to an ‘Anchor’ by thinking about how anchors are usually on the end of chains that are made of links). For a more in-depth discussion of Anchoring you can read this article, Memory 101: Memory Anchors-The Basis of Remembering. 

If this concept intuitively makes sense to you then you can move straight on to exploring HOW to anchor information.

There are two ways to anchor a memory in your mind. You can either attach it to previous knowledge in a way that is logical and reflects connections in the real world. This is called “Anchoring for Meaning“. If this isn’t an option then you can link the new knowledge to old in a way that doesn’t make sense necessarily but that is memorable. This is called “Anchoring via a Mnemonic“. To explore these two concepts, check out the links below.

After you’ve got a hold of step 4: Link, you can move on to the final of the 5 steps of efficient learning, Train.

 

Understand: The third of the 5 steps of efficient learning

This is the third of the five steps of efficient learning that are outlined here

Understand: Some things you’ll understand straight away and the ‘understand’ step will easily fit in right between acquire and link. But sometimes this is a huge challenge. This is the step where we often are challenged in moving from concrete to abstract ideas, or the other way around. We can think of understanding the lynchpin or keystone of learning. It needs to be there otherwise learning hasn’t really taken place.

Screen shot 2014-09-12 at 11.17.01 AM

But sometimes  it’s unrealistic to expect understanding to come straight away. Sometimes the content is just so hard that it’s going to take a while to sink in. In this kind of a scenario we may have to be patient and follow through with the next two steps (link and train) before we truly understand. Regardless, there are things we can do to boost our chances of understanding, and make it happen faster. This article details some excellent methods.

But first, Here’s my top tip for understanding: DON’T LIE!!!

DON’T LIE!!!

This may sound like a strange place to start when we’re discussing understanding but it really is the basis. What I’m talking about here is lying to yourself or to your teacher. If you tell yourself that you understand before you do, or tell your teacher that you understand before you do, then the next piece of content will be moved on to and that just doesn’t help anyone.

I can’t stress this enough. It’s a lesson that has taken me a long time to learn. But not for myself, It’s never made any sense to me to lie about whether I understand or not. But it appears to be pretty common for lots of people*.

As a teacher I’ve been in the following situation countless times: I’ll explain a concept and a student says ‘aha‘ or ‘oh, I get it now‘ or ‘yeah, that makes sense‘. I think ‘great, we’ve really had an aha moment!’, only to discover that they fail the test and when I ask them ‘what happened’ they tell me they didn’t really understand in the first place.

As such, now if a student says ‘aha’ or another such exclamation I’ll say ‘great, now you explain it to me’…. 

Half the time, that’s what I hear. Which is great. It’s honest feedback. We can’t learn without honest feedback. If you tell me you don’t understand then I can take a different tack and approach explaining it from a different direction. Honesty: This is the first and most crucial step to understanding! 

*I’ve learnt that students behaving this way is probably because they have are performance goal orientated student rather than a mastery goal orientated student. This means that they are more concerned about other peopling thinking that they understand than they are about actually understanding. Therefore they’ll go to lengths to keep up the charade that they understand, even to the detriment of their education!

What is understanding?

Good question!!! At this point it’s important for me to comment on the connection between step 3: Understand, and step 4: Link. In many ways understanding is simply linking new things that you learn to things that you already know in a way that is going to help you remember. More links to things you already understand represents deeper understanding. Here’s an example.

-In year 10 you may learn about the derivative. You learn that the derivative tells you the slope of a line, and that for a straight line, the derivative is only a number.
-Then in year 11 you might learn that the concept of the derivative is more broad, it actually gives you the slope of the original function (whether it be linear or quadratic, etc) for any x value (don’t worry if you don’t know what I’m talking about, just keep reading).
-Then in year 12 you do a physics unit and find out that the derivative links displacement to velocity, and that acceleration is the derivative of velocity!
-Then years later someone points out to you that the formula for the surface area of a sphere is actually also the derivative of the formula for its volume! WOW!!!

Screen shot 2014-09-12 at 11.19.18 AMPerhaps in year 10 you did understand the derivative as it was taught to you, but every additional link that you made to other things you knew about (velocity, displacement, area, volume, etc) represented an increase in your understanding of the concept of a derivative. It broadened your understanding and increased your ability to transfer. Transfer is the ability to apply the concept to new situations where you haven’t seen it used before. This is the basis of creativity and is one true tests of understanding.

This concept map of derivatives can be found  on Darylin Barney’s page here. My derivative analogy can be found here

How do I get understanding?

As mentioned, linking is understanding, but sometimes the concepts that you’re trying to understand are so foreign that your brain doesn’t manage to naturally make any links. In situations like these there are a couple of things you can do.

Find an Analogy:

Maybe you’re trying to understand electrical circuits and you find it helpful to think of them as rivers, maybe you’re trying to understand what goes on in an atom and you think of how the planets orbit around the sun to try to understand how electrons orbit around the nucleus. Analogies are powerful tools for understanding. You can find analogies by googling ‘analogy for electrical circuit’ or ‘analogy for the atom’ and this can set you on track to better understanding. A good teacher should help you out with this! A good teacher or tutor can also introduce you to helpful analogies. Click here for a bit more info about analogies and to see an example of how analogies can be used to understand a complex concept like the derivative.

The Pokemon Card Method:

This is to be used when you’re really clutching at straws (as I have been many times). The idea of the pokemon card method is that when you’re a kid (and assuming you collected pokemon cards) you don’t really know why certain pokemon are good, or why they would make a good addition to playing deck, you just know that they’re good. You know they’re good because you’ve probably heard it from your friends (maybe they even tricked you, sorry younger brother…). So you do your best to collect a card of that particular ‘good’ pokemon. Over time you collect more and more pokemon and you learn how they can work together to win pokemon battles. Through the relations that you see between the cards (link), and how they interact with each other you get a better understanding of why the cards you collected in the first place were good (or you realise you were fooled!). In this analogy pokemon cards represent facts or phrases that you know are important, but you just don’t understand yet. So that’s basically the pokemon card method. You collect up key bits of info, even though you don’t understand them yet. As an example, here are some pokemon cards (key phrases) that I collected when I was trying to understand Wave Mechanics at Uni.

-Probability density: Is the probability of finding a particle at a given position. It is the wave function multiplied by the complex conjugate of the wave function
Eigenfunctions are: Solutions to the Time Independent Schrodinger Equation (TISE)
Eigenvalues are: allowed total energy values that are possible in conjunction to solns to the Time Independent Schrodinger Equation
Any linear combination of wave functions: is also a solution to the Time Independent Schrodinger Equation

Now, I can guarantee that when I wrote these things down I only knew 2 things. 1: It was important. 2: I had no idea what it meant. Then I went away, and I tried to get these phrases in my head**, I also brought them along with me to lecture (along with about 100 more of them) on my computer and when the lecturer said one of those words (eg: eigenfunction’) I could use the search function in my word document to pull up that line. Over time my brain started to see the words such as ‘eigenfunction’ as cues to bring up phrases such as ‘solution to the TISE’. As I began to internalise these ‘facts’ my brain began to automatically build connections between the concepts. This happened till eventually I was able to explicitly talk about the connections between these concepts, at which point I began to feel like I was ‘understanding’ wave mechanics!  At the end of the semester, I understood enough for transfer to occur. Ie: I was able to apply the concepts that I now ‘understood’ to situations that were unfamiliar… questions in the exam! Understanding success!

Since that time I’ve come to a better understanding of why this method actually worked. It’s because facts are the foundations of critical and scientific thinking.

**What I was doing to memorise them at the time was to print out two lists of them. One was the complete list and the other was a list with just the parts in bold on it. I’d staple the only-bold-bits page in front of the complete-sentences page and try to recall the full sentence from the cues on the only-bold-bits page. This method was pretty effective, but at the time I hadn’t heard about Anki. If I had have I would have used it to get these phrases into my head as it’s much more efficient.

Conclusion

Don’t lie, and keep trying! Ideally you’ll begin to understand after steps 1: Survey and 2: Acquire. But if you can’t, try to use the analogy or the pokemon card method, or just move straight on to step 4: Link then 5: Train. Understanding WILL come later if you keep on working and following through with the process. In the words of the great Physicist Erwin Schrödinger.

“In an honest search for knowledge you quite often have to abide by ignorance for an indefinite period… The steadfastness in standing up to [this requirement], nay in appreciating it as a stimulus and a signpost to further quest, is a natural and indispensable disposition in the mind of a scientist.”

Check out the next of the five steps, Link.

Memory 102: Anchoring for Meaning-How you Think Determines How you Remember

Anchoring for Meaning

In the previous article to this one I wrote about how, in order to remember something new, it’s necessary to link new knowledge to existing knowledge. We called this existing knowledge ‘memory anchors’. There are two main ways that we can link new knowledge to old knowledge. The first is anchoring for meaning and the second is through using mnemonics. This article addresses the former. Anchoring for meaning is a much stronger way of building memory connections than mnemonics is. Anchoring for meaning means we logically connecting ideas in ways that reflect how those concepts are actually linked in the real world*. For example, if you’re trying to learn about derivatives by exploring how velocity is related to displacement, that’s great, because in real life velocity is the derivative of displacement. But if you’re trying to understand the derivative through a mnemonic that you’ve made up about tweedle dum and tweedle dee, it might not stick as well. Hyperphysics Example *The most effective way that I’ve come across of explicitly anchoring for meaning is through the use of concept maps. Above is an example of how the website Hyperphysics helps its visitors to anchor for meaning when learning about Quantum Physics. Hyperphysics is an amazing site and whenever I want to know anything about Physics (eg: Newton’s Laws) I usually just type into google  “Newton’s Laws Hyperphysics” and there’s a high chance of getting a great summary.  But it’s not just sticking power that makes it important to anchor for meaning when possible. It’s recollection power. In order to store your memories in a way that they’ll get cued at a relevant time, it’s really helpful to store them in a logical way, and the most logical way is by meaning and logical connections. To expand upon our derivative example above, if you learn about the derivative as linking displacement and velocity, then when you come across a question asking you to explore how velocity and acceleration are linked, you’re more likely to think that the derivative may have something to do with it (and you’d be right!), but if you’ve managed to get the derivative concept stuck into your brain via the tweedle dum and tweedle dee mnemonic, the ‘relate velocity to acceleration’ question will more likely leave you in wonderland… This fact, that anchoring for meaning means that your memories will be cued at the optimum times is part of a bigger principle. This principle is encapsulated by Daniel Willingham with the phrase “How You Think Determines How You Remember”

How You Think Determines How You Remember

Let’s play a game! Try to remember the objects in capitals (not bold) from the following 3 violinistsentences

  • The violin player lugged the heavy PIANO up the stairs.
  • The car salesman took a bite of a juicy APPLE.
  • The WALKING STICK was leant upon by the retired sword fighter.
  • The boy cracked the EGG when he fell off the fitness ball.
  • The vampire was passed right through by the GHOST.

Below I’ve provided 2 sets of clues to remind you of the key words in the list above. Scroll down so you can no longer see the above list and start by reading the first set of clues. Try to use them as a basis for remembering the 5 objects.

Clue set 1: An instrument, something red, something long and straight, something round, something scary

How did you go?  Maybe you got all 5? If you did, well done! If not, maybe this second list will help a little bit more…

Clue set 2: Something that’s heavy, Something that’s juicy, Something you lean on, Something that cracks, Something that can pass through other things.

If the above example 1 worked well then you will have found the second list much more helpful. Perhaps the first set of clues even made you remember a wrong word from the list! Whilst the first set of clues were all valid clues, the clues didn’t mirror the way that you thought about the objects in the first place (ie: the way the sentences described them such as a juicy apple rather than a red apple). This is because as anything makes its way from short term to long term memory, the way that it’s thought about whilst in that transition phase influences how it’s remembered/encoded and thus, what brings the memory back.

There is one key lesson in this for teachers. When we’re designing a lesson plan, and trying to spice it up for students it is VITAL that we ask ourselves ‘what is this activity actually going to make the students think about‘. If we try to teach students about the history of aviation by getting them to make model airplanes, chances are what they’ll remember from the lesson is who they managed to hit with their plane rather than who the Wright brothers were. As teachers, our goal is to get students to think about meaning. It’s important that, when we can, we introduce content in a way that emphasises its meaning.

What to do when Anchoring for Meaning isn’t Possible

There are times when it simply isn’t practical to anchor for meaning. This could be if:

  • You’re starting a learning project into an area where you don’t know anything at all yet – eg: If you start to learn a language that seems extremely detached from you own, like Chinese.
  • You haven’t built up the required background knowledge to make links in a logical way yet, and/or you simply don’t have time to do it – maybe you’ve been slacking off all semester and the test is coming up!**
  • If there simply isn’t a logical reason why the piece of information is the way that it is – eg: you meet someone and you want to remember their name. (There’s usually no logical reason why a person has a certain name, and even if there was one for their parents, there’s no guarantee that it will seem logical to you!)

In cases like these we need to revert to a secondary way of anchoring. Mnemonics! Mnemonics refers to a whole suite of memory techniques that can be used when, for whatever reason, you can’t manage to Anchor for Meaning. Learn about mnemonics in the next article in the memory series, here.

**BEWARE. Often we can use mnemonics to cut logical-learning corners, but in the long run this only serves to handicap us. The more genuine facts you know about a topic, the easier it is for you to learn more about that topic. If you get into the habit of linking things that you learn to your prior knowledge in abstract ways, you’re rate of learning is going to be compromised further on down the track. When you’re dealing with subjects where there are logical connections to be made (Maths, Physics, etc)  it really is in your best interests to take the time to lay down solid foundations and to REMEMBER those foundations.

Notes:

  1. Inspired by the example in Why Students don’t Like School by Daniel Willingham. Kindle location 1092.
  2. From Why Students don’t Like School by Daniel Willingham. Kindle location 969.

Are Facts more Important than Critical Thinking?

‘Factual Knowledge Precedes Skill’

This is the ‘guiding principal’ in chapter 2 of Daniel Willingham’s Why Students Don’t Like School. I’ll start by pointing out that this title for Willingham’s book is a bit misleading and the subtitle ‘A cognitive scientist answers questions about how the mind works and what it means for the classroom’ gives readers a much better idea of the book’s content.

Willingham’s book is an excellent overview of 7 crucial cognitive principals that are of great value to anyone who is interested in teaching and learning. In fact, the book in large part inspired this set of posts (of which this is the first) for me and I’ll be going over each principle in detail in the coming weeks.

Of all of the lessons in the book, this one was for me the most profound.Why? For many years I have been of a certain mind that “we are wasting our time teaching kids facts at school, what we need to be teaching them is how to learn and how to think critically!” Whilst I still firmly believe that learning how to learn and critical thinking are… critical, this chapter helped me to realise that:

“Data from the last thirty years lead to a conclusion that is not scientifically challengeable: thinking well requires knowing facts, and that’s true not simply because you need something to think about.The very processes that teachers care about most—critical thinking processes such as reasoning and problem solving—are intimately intertwined with factual knowledge that is stored in long-term memory (not just found in the environment).”-kindle location 552

…It’s all to do with working memory.  Here’s (my elaborated version of) “Just about the simplest model of the mind possible” that Daniel introduces in Chapter 1. Let’s talk through it

This is what your mind looks like

When we begin to solve a problem, 3 windows of our mind are engaged, The environment, our working memory, and our long term memory. The environment is where the question is posed, it’s also where we have access to other information like youtube clips, formula sheets, the working of the kid sitting next to us, and so on. Long term memory is where we store all of the stuff that we’ve already learned. Working memory is where the processing happens. So when we solve a problem we can draw both from our long term memory and from the environment to come up with the solution. If that’s all there is to it then theoretically we should be able to solve any problem as we have access to a seemingly limitless amount of information, but there’s a catch, your working memory only has about 7 slots. 7 precious slots with which you can work*. The reason why long term memory (knowing stuff) is so important is that by remembering stuff you can compress many individual pieces of information and concepts (represented above as pink blocks) in such a way that they only take up one slot in working memory (ie: 1 blue block=many pink blocks). This process is called Chunking and it frees up working memory space for additional info and processing facilitating higher order and more complex thinking. This has important implications for teaching/learning techniques such as the use of formula sheets and scaffolding.

* (7 plus or minus 2 slots covers the majority of the population)

For an example of this please see the bottom of this page.

This information has completely changed my view of what it means to ‘learn’ something…

“I don’t have to memorise anything because I can just put it onto my formula sheet.”

This was my mindset throughout the majority of my undergraduate degree in Physics. See the picture below for an example of one of these such sheets (which we were permitted to take into exams).

Final Cheat Sheet Photo, page 1

After reading this chapter of Willingham’s book I now better understand why I found some parts of my degree as challenging as I did. My ‘I’ll just put it onto my cheat sheet’ mentality was actually preventing me from taking my Physics to the next level. The 7 slot limit of my working memory was being overwhelmed. I hadn’t memorised important facts and info sufficiently for me to ‘chunk’ them, which was limiting my ability to combine concepts in creative ways to solve problems. This conclusion has opened my eyes to the importance of storing things in long term memory and from now on I’ll be making a more concerted effort to use programs such as Anki to do just that! (also the reason why I’m changing my Wot-I-Got blog post format and will be introducing more mnemonics to help readers/my self to better remember blog post content in future).

Conclusion

So, are facts more important than critical thinking? Well… it’s more that facts are a precursor to critical thinking. Knowing facts frees up the processing power of your brain to analyse new information as it comes in.

But this isn’t the only reason why learning facts is super important. Another reason is because knowledge is like money, the more you have the easier it is to get. This is the topic of the next post in this series (coming soon).

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An example of how we’re limited by our 7 slots.

Let’s consider the importance of knowing stuff with an example.

Q: If the nightly revenue of a restaurant is represented by R=-20c2 + 200c + 1920 (where c is no. of customers per night) use calculus to find the maximum nightly revenue.

Without being too exhaustive let’s list some of the things that someone would need to know to answer this question. (think of each number as a pink block)

  1. How to read
  2. What a restaurant is (etc, etc, etc with the really obvious stuff)
  3. what revenue is
  4. that c2 means that it’s a quadratic
  5. that a quadratic equation has a gradient
  6. That the turning point of a quadratic is when the gradient = 0
  7. How to take a derivative
  8. How to set a derivative, R’, equal to 0
  9. Basic algebra to isolate C once you’ve set R’ equal to 0
  10. That that’s the number of customers that would generate maximum revenue
  11. that the R equation relates the number of customers to the revenue associated with that many customers
  12. That you can sub C into the R equation to calculate to find the maximum nightly revenue possible

Now, to me that looks like more that 7 pink blocks. For pretty much all students we can conclude that they have combined pink blocks 1 and 2 (ie, all the obvious stuff) into a blue block, but after that it’s still clear that other stuff must be ‘known’ in order for them to successfully complete the problem, especially if one of their 7 working memory slot is being taken up with a “I can’t do this, I’m confused” mantra.

From the above it’s hopefully clear that for a student to successfully solve this problem they must have stored at minimum 6 of the above bits of info in their long term memory.

 

Memory 201.1: Mnemonics – The Link Method

chainThis post is part of a series of posts on cognition that can be found here

By the time you finish reading this post you will have greatly expanded your ability to remember a whole bunch of items. This is interactive so get ready!

You will need: a piece of paper and a pen.

This exercised can be used with students and I’ve included a printable PDF below for instant use in class. Just ask students to fold along the lines (to make a kind of pamphlet so they only see 1 list at a time) and to not look at the list fore each round before you start the timer!

Round 1:

Open this online 1 minute stopwatch (or use your own) in another tab, start it going and remember as many of the following words as you can within 1 minute. When the time runs out, write down as many of the objects as you can  (the timer makes a sound when time’s up).

1. Spoonspoon
2. Bottle
3. Scarf
4. fingernail
5. Candle
6. Ice cube
7. Slipper
8. Hammer
9. Watch
10. Needle
11. Stop sign
12. T-shirt
13. Book
14. Rubber duck
15. Shovel

 

Now, your working memory (article to come) only has about 7 “slots”, ie: you should be able to hold only about 7 discrete things in your mind at any one time. If you got more than 7 items from the above list you’re doing a great job.

So how are we supposed to remember all 15 things on the list? There are many memory techniques that can help you do this. One branch of memory techniques is called mnemonics, and one type of mnemonic is The Link Method.

The Link Method is when you link objects together with stories, images, anecdotes or the like. Links can be as creative as you like but the main point is to try to use visuals and imagery.

Round 2:

So let’s try it! Below is a <1 minute recording of me (if you can’t see it there, view this post in your browser) using the link method to link another list of 15 random items together in a way that will hopefully help you improve upon your round 1 score! Listen to the recording and visualise the situation as I describe it (easiest if you close your eyes). When the recording is over, immediately try to write down all 15 items. (if you’re reading this somewhere where you can’t use sound you can read the story at the very bottom of this post. But ideally you’ll just listen and visualise).

 

bookmark1. Bookmark
2. Car
3. Rubber band
4. Tire swing
5. Pen
6. Boat
7. Photo album
8. Toothpaste
9. Tissue
10. Cookie
11. Nail
12. Drill
13. Chalk
14. Thermometer
15. Shoe

 

How did you go? I will note that taking someone else’s mnemonic is never going to work that well, the real value is in the thinking process that you yourself engage in to make the mnemonic. By making a mnemonic yourself the links references you use will be relevant to you. Furthermore, if I was to make a mnemonic for myself for the above it probably wouldn’t be associated with that many words, it would be more in the form of pictures, shapes and objects morphing and interacting in strange ways. Unfortunately I couldn’t adequately describe this in a 1 minute recording so had to go with the more conventional “story” in the above.

As such, the mnemonic above isn’t ideal for you to remember the round 2 list, so I don’t expect your results from round 2 to be revolutionary. I do hope they were a slight improvement on round 1. Now, for round 3, try to use the link method to link this new list of objects together! This is the test!

Round 3:

Here’s that timer again. Now it’s your turn. You have 1 minute to use the link method to make up your own creative way of linking the following 15 items together, again, when the timer goes, test yourself and see how you went!

1. Ballball
2. Cheese
3. Rock
4. Cigarette
5. Coin
6. Badge
7. Paper Plane
8. Tap
9. Watch
10. Camera
11. River
12. Beer
13. Plate
14. Beanie
15. laptop

 

How many did you get?

Surprise! Round 4:

The real value of memory techniques isn’t always immediately obvious. And making mnemonics is a skill that needs practice so perhaps you didn’t do as well in round 3 as you might be able to if you practiced some more. But hopefully this exercise will show that the mnemonics actually stuck the objects from rounds 2 and 3 in your head much better than just holding things in your working memory.

For this round, get out a fresh piece of paper. Draw three columns, label them round 1, round 2 and round 3 and get going writing down as many of the objects as you can from each round. Take as long as you like and let us know in the comments below how many you can remember from each round!

Conclusion

The Link Method is a powerful mnemonic technique for remembering very large lists of things but it has one main weakness, the chain is only as strong as its weakest link! You may have noticed that with the above mnemonics, if you forgot one of the links* it was hard to recover from there and you might miss several items before you made it back to your list. In some extreme cases maybe you couldn’t remember the first item and then you were stuffed!** This is because the memory anchor***  to which you affixed the item was another item that wasn’t lodged very well in your brain in the first place. The next article in this series, Memory 201.2: Mnemonics-Method of Loci  will introduce a way to get around this ‘weakest link’ problem in the link method.

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*eg: the link between cookie and nail wasn’t particularly strong in the mnemonic that I made, so perhaps you were left thinking… what comes after cookie?

**this is why I included a pic of the first item for each round ; )

***a memory anchor is something you already know that you can attach new knowledge to.(article to come!)

Here’s a printable version of this exercise for use in the classroom. For the surprise round 4 just ask students to flip the piece of paper over and write on the other side.

Here’s the story from round 2:

 

bookmark is jammed in the door of a car. The car has a rubber band in place of one of its tyres because the tyre’s being used for a tyre swing. The tyre swing has a pen pierced right through it and balancing on the tip of the pen is a boat. On the other end of the pen is a photo album and all of the photos are stuck on with toothpaste. You try to clean up the photo album with a tissue but then you  give the tissue to a kid who’s eating a cookie. You look up and realise the tyre swing only attached with a nail, you decide to use a drill to attach it. So you mark the spot on the tree with chalk but change your mind and decide to attach a thermometer. You attach the thermometer but it falls off into a shoe.

The most efficient way to remember anything!-Spaced Repetition Software

My current (primary) personal learning project is learning Mandarin. I started last November (2013) and I’m planning to travel to China this coming November. The goal has been to learn, within a year, to speak sufficiently well to hold a 20 minute conversation with a native speaker. But how to do it?

One of my matras is “ask someone who knows”, so I went onto a bunch of language learning websites* and asked a few people whom I knew had learnt languages before (and quickly) how best to approach it. One answer was unanimous; “SRS” or Spaced Repetition Software.

I much prefer to explain this kind of stuff by talking rather than writing, so watch this clip below to see the why, how and what of SRS.

Anki is definitely worth the (small) time investment to familiarise yourself with the software. It will revolutionise your learning!

For a summary of the research on spaced repetition, see this article on Gwern.

Update: Just found this great guide on how to use anki from Alex Vermeers. Check it out!

*fluent in 3 months ,  hacking chinese, and FluentU are all great! Also check out this blog post for an incredibly innovative way to learn the characters (I’m currently following it : )

Edit: See this great page for some info on SRS research: http://tiny.cc/srsresearch