Thinking about AI through the lens of Bloom's Taxonomy
Education is a field full of acronyms and I remember having a bit of a giggle to myself when I first saw these two. Lower order thinking skills (LOTS) or Higher order thinking skills (HOTS) are were made famous in Blooms Taxonomy, a model that really helps educators to create learning outcomes which are Specific, Measurable, Achievable, Realistic and Timebound (SMART)... there's another acronym. It gets especially confusing when we try to support our students as they develop lots of SMART HOTS.
But, as with many teachers, generative AI (artificial intelligence) has caused me to pause and rethink. And I don't generally think about AI that much beyond teaching my students to address the question of: (a) Should I use it? (b) How do I use it? and (c) Should I trust what it tells me? However, in this blog post, I wanted to explore something different. I wanted to explore my big fear - are students using AI to cheat? Or is there something else going on? And I wanted to base my thinking around Blooms taxonomy because this is where most teachers I thing develop their understanding of what constitutes lower and higher order thinking skills. I suppose the question I'm asking is, "Has AI changed the way we need to think about lower and higher order thinking skills?"
My Question: If (as implied by blooms taxonomy) memory/recall/information retrieval is the lowest order thinking skill, the thinking skill that forms the foundation off all other thinking skills and future learning, then has AI shaken the foundations of learning?
("Bloom's Revised Taxonomy" by Vanderbilt University Center for Teaching is licensed under CC BY 2.0.)
Back in the years before Google (BG) my fastest internet connection was provided by dial up modems - incredibly slow by modern standards but it was a thing that suddenly changed the amount of information I could access. I remember not being all that enthralled with it though because I was in my late teens/early twenties and hadn't needed it until that point. A few years later though, after being introduced to the world of teaching encountering new technologies like Technikal and Moodle and interactive whiteboards to more modern development of online assessment platforms like NUMBAS. Looking back I see how priviledged I was because, at the time, there were tools that only the wealthiest classrooms had access to. Over the years since I've watched different technologies emerge while others went out of fashion. What has always worried me was the way it can be used and/or abused in learning. But a major concern for me about AI in particular stemmed from the fact that I thought it detracted from the need to remember anything for, in traditional maths education, such a lot of the basic skills mathematicians teach require the recall of basic facts and formulae.
However, it makes me feel slightly hypocritical in saying that because, even when I use AI is used as a productivity tool, I don't really need to remember my key meetings, personal appointment, I don't need to summarise any documents or do any of that heavy lifing because my AI assistant will remind me or, even better, do it for me and quite often do it better than I can. It saves me time, energy and allows me to be more productive in the workplace. So, with that in mind, one might suggest that if AI is a work productivity tool, that students are going to encounter in the workplace, then shouldn't we be preparing them for that reality. But if we go down that road, one could begin to question the value of a teacher asking their students to memorise, define, or state the meaning of anything when technology exists that does the memory work for them?
For every maths teacher this is an eternal battle, addressing the question of whether we maths exams test memory or mathematical reasoning. So I find myself asking the question, is memory work even necessary? Hmm... time to dig deeper.
Thinking back to the very beginning of my career as a teacher I remember learning that 50% of the marks that were available in an exam were awarded for answering what was termed core level questions. In other words, a student who has done sufficient memory work with regard to remembering the basics and repeating those skill in parrot fashion could realistically expect to get a C grade pass in their final exams. So, by doing this, designing maths exams in a way that forced learners to engage in memory work, one could ask whether this is a test of memory or an example of power is exercised in the education system. What's more, the extension level question that were written in to the exam (the questions that involved solving more complex problems) were where learners could pick up the additional 50% of the marks allowing them to get potentially a B or A grade.
So, there were really two major implications here. The first is that, if students didn't do the memory work or had any learning barriers that impaired their memory, then these students had literally no chance of passing the exam. Secondly, by ensuring that memory work is built into the exam, it becomes possible to game the system by not presenting those students for exams that have shown any unwillingness or inability to do the required memory work.
Now this second point is something I have a major issue with. If a student has paid to sit a course at college (as was the case in my experience) then surely they have also paid for the right to at least experience what it's like to sit an exam. They have the right to experience what success or failure is like on their own terms. I remember a student that I worked with not long ago who was in my class and failed each of the core level assessments that I had administered to the class. I was perfectly within my rights too deny her the opportunity to sit the exam. After all, if we adopt the neoliberal view that sucecss or failure is a reflection of some deficit either on behalf of the teacher or the student, then by implication, her likely failure would damage my repututation as a teacher. However, I never subscribed to that view and allowed her to sit the exam. She passed with an A grade and is now a teacher herself. Now that's success in my book.
But more concerning is the narrative that teachers don't want students to fail and that, by not presenting students for exams somehow protects them. Does it? Is there not an equal chance that by allowing students to fail that they are afforded the chance to become more resilient? They get the opportunity to reflect on what went wrong, pick themselves up, dust themselves off and try again having learned undergone a valuable experience. Who knows, they might even learn that the need to do memory was more important than they realised.
However, this isn't about students being lazy or students having cognitive difficulties. It's about the issue of memory and whether it's still foundational in a world that being changed by technology. Strangely, as the world changed, teachers, lecturers and educators of all kinds around the world have had to deal with the fact that all of that information that students were, historically, expected to memorise is now available at the click of a button. Technology began to draw attention to the question of whether or not there was any need to do this memory work. How did math teachers deal with this problem? Thinking back, I would say we doubled down.
In the maths world we designed a whole exam system whereby students were forced to sit a non-calculator paper that accounted for 40% of the marks available in the exam. In hindsight, this seems odd because, as I finished high school and moved into HNC/HND level study my first class was computers and data handling followed by mathematical modelling with Mathlab, Statistics using GenStat etc. In a single year I went from being a school student and not trusted with technology to being a first year college student who was thrown in at the deep end with technology and software I had never heard of. Strangely, during my early years as a teacher, I remember conforming to these practices myself where if I was teaching in a computer lab, I had access to tools that allowed me to control the use of the internet and thereby prevent any online activity during class time at least ... that was until modern smart phones and mobile devices came along. And now we're looking at banning the use of phones in classrooms because... ?? They're a distraction? They're disruptive?
I've heard a number of arguments against the use of mobile devices in the classroom. My favourite is the, "back in my day", argument which doesn't seem to hold much weight beyond an uncritical replication of repeating how we as teachers were ourselves taught by the generation before us. A stronger argument might that of trauma informed practice whereby there is a recognition of toxic online behaviour or reducing the potential for cyberbullying. But when students step out of our classroom, the technology is still there, as bold and pervasive as ever. But, if we take vocational learning in simulated environments as an example, technical skills are taught in simulated real world environments in order to prepare students for their next steps into the real world.
Surely By removing the use of technology from the classroom, it's like the reverse, controlling the environment to protect students from the effects of the real world? Or, controlling the environment to ensure that students are better behaved thereby making our own lives easier? I don't see how this helps. In fact it reinforces the divorce between the academic environment and the world beyond. I'm even writing this blog post on my phone.
All that aside, here's the thing I don't get. Since the emergence of the internet and mobile devices, learners have been able to access huge amounts of data and information at the click of a button via phones or tablets, laptops or PCs. It's part of their world. So, don't we have a responsibility to guide learner's thinking and support them in critically engaging with the technology around them? As a lecturer who has worked in the field of literacies education, how can we help students to make sense of the world around them if we create an environment that doesn't reflect reality?
Yes, the internet and generative AI can be used to short circuit memory work. So can Google. But when used in this way, AI and other forms of technology become little more than glorified versions of wikipedia, or any other unreliable source of information which we educate against. This week my students even educated me against the use of AI pointing to the water that evaporates into the atmosphere to cool down the servers used for AI hardware arguing that AI can contribute to climate change. Every day is a school day!
So I find myself asking the question as to whether its the technology that's causing the problem or the way society uses it? Are students lazy for using the technology that helped them achieve the level of productivity that society expects of them? Are we as educators responsible for modelling the use of technology in ways that promotes technophobia over critical thought? Or has an emphasis on the political and economic realms of productivity brought us to the point where we don't need thinkers any more? As Althusser (1971) said:
"...I shall say that the reproduction of labour power requires not only a reproduction of its skills, but also, at the same time, a reproduction of its submission to the rules of the established order, i.e. a reproduction of submission to the ruling ideology..."
Does the use of technology replace the need for human thought? No. Narrative researchers the world over will tell you about the importance of memory and how it enables us to connect our past with our present and future. In fact studies have shown the effectiveness of using technology to create digital archives that enhance memory, transcending the embodied limitations that we all face as a result of human ageing. I would suggest that technology itself places greater responsibility on teachers and on the need to critically engage with technology, its use and its ability to detract from or enhance the learning experience. As soon as devices are taken away from students their recall has to come from within themselves forcing them to confront the high stakes binary of remember or fail. That's the easy bit. But is that education? Or an application of power? Why is it that student have to deal with high stakes assessment?
Returning to Blooms taxonomy, this heirarchical view of LOTS and HOTS (shown in the image above) suggests that memory is the foundation of all our higher level thinking. I've literally sat in classes where I've been told, "Don't try to understand, just remember and repeat parrot fashion! Understanding will come later." Personally, as a student I was never able to do that. If I couldn't understand why certain patterns occurred, or why certain techniques gave us the answer we needed, I found myself fumbling in the dark. I needed to understand - but that's level 2 of Blooms Taxonomy. Surely you can't go to level 2 before completing level 1 first?
My early years spent as a maths student studying for my standard grade were not happy ones. If I couldn't understand what I was doing or why I was doing it, on a purely pragmatic level, why would I remember anything I was being taught in maths class when I had no reason to? I was that stereotypical maths student who failed to see the point of maths when it amounted to little more than the manipulation of numbers and letters. Why should I care? At one point, I clearly remember being told by my maths teacher, "McIntosh, I don't know why you're bothering because you're never going to make the grade." This didn't do anything for my motivation and, to be fair, that year I got distinctly average results for my standard grade.
But I knew I wanted to be a teacher so I needed good grades in Maths and English. But because of my poor results at Standard Grade I wasn't allowed to sit my higher at school over a single year. I had to do a two year course instead. This really bothered me. It seemed like a waste of time - I wanted to teach music, not maths! But, since there was no option to resit standard grades back in those days, a series of modules in algebra and calculus was considered my to be my only option, followed by progression on to the higher program the following year. But that summer I discovered that my local college had a distance/flexible learning centre. Bingo!
I spent that entire summer at college studying algebra and calculus and this was the first time I encountered distance/flexible learning. That autumn I also signed up to do my higher maths in the evenings at the same college. So I was studying all day at school and an additional 2 nights per week at college. You might think that this was a lot for a 17 year old boy to take on. But in actual fact it was life changing because my evening maths lecturer was actually an engineer by trade. So for the first time I found myself talking about rate of change and understanding it's application in physics. I remember studying linear geometry and being able to apply it to closest approach problems. I studied the mechanisms of simple machines... In short, my teacher made learning experiential, relevant and interesting. By placing understanding and application before recall, the challenge of recall itself became easier for me. It was at that point I realised that people remember relevance.
What I found was that, for me it was more important to place understanding and application at the foundation of my learning because from there I was able justify the effort required to memorise and repeating a skill in order to master it. For me, memory and my ability to memorise was rooted in psychology. Relevance gave me a reason to care.
Rooted in the theory of conservation of resources from psychology, memory work was about finding a reason to commit the scarce resources in my brain to the learning of skills that were of value. Is that not the very reason our students give to us then they use AI or technology to short circuit the memory process? They're saying I'm not committing more resources than absolutely necessary to learn a skill that is of little or no value to me. I can just as easily have AI to do it for me. Now, as a teacher, I often find myself battling with students who have been labelled as "not good" at maths by some teacher they've encountered. Often they've internalised some sense of inadequacy, so why would they spend scarce resources and brain space to repeat an experience when they know the outcome will likely be failure? Unless we can offer them an alternative experience that changes their perception of the subject, an experience that changes their perception of themselves. Lets face it, if students have come to believe there's no value in learning a skill, then why would they give anything more than the minimum effort?
In my EdD studies I've come to understand that this theory of conservation of resources is related to the concept of trauma informed practice. It's the idea that each of us requires a certain amount of resources to function. I heard it once described as bucket and spade theory.
Imagine going to a beach to build a sand castle. You fill your bucket with sand. But there's a sign up that says you're not allowed to use more than 1 bucket of sand per day. And, being a responsible beach goer, you abide by the rules. But then your friend comes over and says they need to borrow some sand from you cos they've ran out. So, being a good friend, you give them some of your sand. Then your daughter comes up to you and says, "mummy, can I have some sand please?" So, being a supportive parent, you give them some of your sand. Then your partner says their bucket has broke and they lost all their sand. Expecting you to be a supportive partner, they say expectantly, "Can I borrow some of yours to get me by? I'll pay you back later?" Then your college lecturer reminds you that you need to have enough sand left in your bucket to practice with in order to prepare for the sandcastle building competition on Monday morning.
You can imagine this person's face as they look in their bucket and discover they have little to no sand left. The point is that each of us requires a minimum amount of sand to build our daily sandcastles.
Is it not the same with learning? If memory is sand then, according to Blooms Taxonomy, we need a minimum amount of it to perform the task of learning. There might be a lot of it around in the world, but our share of it is scarce - we only have one bucket! Often this is taken up with the important stuff, the things that we know we're going to need to deal with in the short term, so we need to prioritise how we use our sand just the same as we do with the money in our wallets. So unless we see the value in using some sand to compete in the sandcastle building competition, then it would be a very valid and logical decision to say, "I'm not going to give any of my sand to something that's not important to me."
I do wonder sometimes whether as teachers we put too much emphasis on how much sand our students commit to the activity of building sandcastles and not enough emphasis on giving them enough support they need to build a bigger bucket.
So what difference does memory make? If memory is simply the storage space that we visit in our brains when we attempt to retrieve information then surely that reduces the human condition to that of mere robots. In fact we would be less than robots because a robot can at least perform a task repeatedly to perfection. As humans we must accept that our memories are always partial, fallible and incomplete at best. When viewed through the lens of experience, what value do we assign to those memories? We each assign meanings to experiences that we have undergone in the past, whether that was living through some kind of significant event or undergoing the consequences of our own (or other people's) actions. Experiences allow us to place value on/in our memories and it is our memories of past events that very often often inform our actions in the present moment. When we think about memory, recall, or remembering in this way, is it really a lower order thinking skill?
What if we thought of memory as a lens through which we are able to evaluate the worth of our experiences? Then memory isn't a lower order thinking skill, but instead becomes integral to everything we do. Every mistake we make becomes integral in building experience, every conversation we have builds memories and builds experience, every event that we live through, all the good bits and all the bad bits... it all builds experience. And we carry that experience, whether good or bad into the future with us.
For me this is important because thinking of memory in this way takes the sting out of mathematics education. When learning maths goes beyond the number of ticks you get on your homework or your assignment and becomes a learning experience, then maths education becomes less about getting the most points in a homework assignment or a test and more about gaining experience of solving different types of problems and using a mathematical toolkit of techniques. An experiential lens turns our attention to the mistakes we make byviewing them as learning experiences that give us the chance to have a conversation about what happened and what we could have done differently in order to get a better result. Moreover, it de-gamifies the system because the whole subject becomes less about the metrics of success and more about the quality of the learning experience. But maybe that's the problem. For if no metrics existed to tell which school or college was good or bad, then how could we differentiate between the high performing schools/colleges/universities and those that aren't quite as good.
But instead of being critical of a system that is intentionally gamified by neolibleral rhetoric, what if we spent some time thinking about practical strategies that we could use that might be considered legitimate uses of technology in education. What about even designing in information retrieval activities in to our assessment activities.
- Could we suggest that students might use technology to create their own formula booklets?
- What if we asked students to investigate a problem and asked them to deliver their results in a short 5 minute presentation?
- Could we ask students to reflect on how frequently they use technology to complete their homework? And in what ways do they use AI to help them?
- What if we encouraged our students to write short text message like reflections about what they learned in class today on their mobile phones?
Does anyone else have examples of how AI or any other kind of technology could be used to enhance the learning experience in a maths classroom? I'd love to hear them. Equally, if you have different thoughts from me about the use of AI in maths education I'd be very interested to hear your views.
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