The use of artificial intelligence in teacher development, part 1

In writing about artificial intelligence (AI) here I have decided to describe its existence as if it were one entity, rather than recognise the existence of and name several different entities. This has been done both for convenience and because I do not wish this article to serve as a review nor endorsement of any ‘product’, especially as I will be discussing one in particular.

Introduction

The debate about the use and usefulness of AI seems to now be a daily topic, and is one which appears to be in no danger of disappearing as it becomes ever more part of our lives in ways that we may not even be aware. It was inevitable that its use within education would be explored, from current directions on its implementation to allegedly reduce teachers’ workloads, to considering how it can assist in the education of others (including being a ‘copilot’ in the classroom), to vilification in its use by students for homework or coursework completion purposes. I suspect it is not an outrageous prediction that there will eventually be, to much attention, a widespread trial of it as a classroom teacher with additional adult(s) in the room, who may not be teachers let alone subject specialists, there only to support classroom management.

I have more than once experimented with its use for planning lessons, and these experiences have been frustrating. Following detailed prompts on what I wanted, what was produced initially appeared to pass my quality judgments only for me to quickly discover that there were deep issues with what was suggested, that if followed could lead to problems or bemusement within the classroom. Even worse, in some cases, the mathematics presented has simply been incorrect. I did not find it reduced workload, if we equate this with time spent; earlier this year when the school for which I was working provided developmental time for teachers to explore AI use in planning an upcoming lesson, I decided to set it the task of planning a series of lessons on the transformation of functions and their representative graphs. Very quickly there was a need for me to teach it or correct the necessary mathematics, at which point I decided that my time was better spent planning the lessons for myself rather than teach an artificial entity how to do it.¹

In these instances, the expertise of the AI was in doubt. How trusted, therefore, can its use be in the development of teachers?

My experience of the approach to the development of non-early career teachers at the school previously mentioned was almost entirely based around short half-termly ‘drop-ins’ by a member of the school’s leadership team at some point in a calendared week, where the observer’s focus would typically be non-subject specific and based upon the school’s teaching and learning model of routines. There would then be a conversation based upon this observation, which based upon logistics would usually be both short and take place many days after the observed lesson, and then a developmental target would be set based on the model. The school, not wishing to stand still in its practices and in considering the effectiveness of this current approach, decided to trial the use of AI for this purpose. I was thus one of a group of teachers who was invited to take part in a pilot scheme in the use of a particular package during the final term of the academic year. 

Given my misgivings, I doubt that it is surprising when I share I was incredibly sceptical about the use of AI for developing teaching practice. As a result, I readily accepted the invitation to be part of this group.

Next: practicalities of, and qualms about, the usage of artificial intelligence to provide feedback

¹I suspect it is inevitable that I return to the use of AI in planning in future writing, especially given I have had several conversations regarding its use by trainee teachers.

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©2025 David M. Lawrence.

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A Lesson Account, 1: Part 5

Part 1, Part 2, Part 3, Part 4

 <The next part of this lesson is being omitted in detail. The teacher repeats their process to find 1% of an amount, which they then demonstrate how to use in order to find 4%. The structure is as described before, although they do not move the class to independent work. They state that due to time constraints, this was just an introduction, and that there will be a recap and more time spent on this next lesson.>

Given there was apparently not enough time for the teacher to give as much depth to this section as they wanted, were they correct in moving to it? What else could have been done, or what could have been done differently, in this part of the lesson that related to what had come before? 

The teacher praises the class for their work today and states that before the class packs up, they want to do one final check for understanding of today’s work. The teacher says that, as usual, they will write a question on the board and the class is then to answer on their whiteboards, using the normal revealing procedure, and that once again they should remember to show all of their working out. They write ‘30% of 120?’ on the board; when students reveal their answers, the teacher comments that the vast majority of the class has the correct answer of 36.

So not all of the class obtained the correct answer; regardless, what does the teacher do with this information? What does it tell them about today’s lesson, and how does it inform their planning of the next lesson? What is the purpose of this final check?

The language of “as usual” implies that this check is done at the end of a majority of the lessons. Is it always done no matter what, and if so - why?

The teacher stated that they were checking “understanding”. Is that revealed to them here in this check? What does ‘understanding’ look like, and can it be accurately assessed with one question immediately at the end of a period of teaching and follow-up questions?

The teacher then deals with the administration of the students packing up and their dismissal. Before the students exit, two are asked by the observer to describe what, if anything, was different about today’s lesson compared to their other lessons; they both independently respond that nothing was different, and instead that “every” lesson is “exactly” like this one.

How may such a comment influence teacher and student perceptions? If this claim is correct, is this desirable? 

Reflection

I have posed a large number of questions here, far too many to process together at once; I will be exploring many in more depth in future writing. But I would encourage the reader to reflect on just how much was asked, and your reaction to these questions. Some may have been frustrating, some you may have felt were unimportant, some you may have felt were not valid to be asked, some you may have felt cannot be answered. You may have other questions I did not pose, and some other questions may occur to you (and me) later. I hope you found that some questions carried merit and have inspired further consideration, and that part of this consideration is why these particular questions resonated with you.

Once again, the point of these questions was never to judge; the point was in their asking. Learning and teaching are complex endeavours and a teacher who is in development is a teacher who is intellectually curious about both learning and their own practice. No matter the origin of a particular lesson plan nor, indeed, the particulars and decisions in its teaching2, there will always be a wealth of questions to be asked about the learning and teaching that (hopefully) took place.3 These questions may be posed by an external observer, but it is essential the teacher accesses their internal observer so that personally important questions can be marked for future further contemplation and hopefully also discussion with others. 

A teacher may find themselves in a situation where such potential personal professional growth and challenge is not supported or, worse, is actively discouraged in the aid of an apparent ambition for the vision of all lessons within a department or a school. If such a teacher is required to acquiesce to this, I would invite the teacher in question to consider the nature of their situation and what could happen to their practice in the long, and even the short, term and consider what is important to them and their identity as a teacher.

What type of teachers do students deserve?

2I have encountered many teachers who would instead have used the word ‘delivery’ here; what does that implicitly reveal about the practice of their lessons?

3Which is why as part of an observation/coaching process, having decided upon which of these questions may be most desired within a discussion, it is important that sufficient time is set aside for a timely, genuine, conversation

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A Lesson Account, 1: Part 4

Part 1, Part 2, Part 3

The teacher projects a series of questions on the board; the questions all have the form of those previously discussed, except for the last one which is ‘4% of 30?’. An instruction is given that students should copy the date and title down and then work through the questions in order, once again showing ‘full working out’, and it is repeated that this work should be done individually and in silence. A student is picked to repeat the instructions back and then the class is told how long they have for the task, and they state that this is a maximum amount of time.

What may the teacher’s previous assessment have provided to inform them of the suitability of the class working through a series of questions in this manner? Is it appropriate for every student to begin in the same place, to complete every question? Is there sufficient challenge for students here? Is there sufficient development of mathematical thinking for students here?

Is there any scope for the teacher to makie changes from their plan based on what they have observed and assessed, or do they stay with their plan regardless?

What is gained and what is lost by not allowing any discussion?

What is the desired outcome when a task is presented with the structure of questions described here? How many questions of a similar type are enough to present to students? How many is too much?

The teacher praises every student for starting the task and they then circulate among the students. The students they initially select for one-to-one attention are the three who displayed the equivalent of ‘I don’t know’ during the preceding work on whiteboards. After a brief amount of time spent with each, those students then appear to answer some of the questions independently.

Is this the best method to offer support to students in this situation? What other approaches could be utilised?

How likely is it that these students are often if not always the first or among the first to receive individual support? If that is the case, what may cause this to happen?

As the students complete the work, the teacher then circulates amongst them, looks over their shoulders at what they have and are writing down and stops to offer both support and ask questions of a few.

What may inform the teacher’s decision about how to move around the room and in which order they visit students? What decisions may influence which students they select to spend longer with - has this been determined before the lesson or by information gained during it? How much variety from lesson-to-lesson is there in which students are selected for individual attention?

As the teacher is talking with one student, conversations between students start in two different places in the classroom. One conversation is about the mathematics being undertaken, one appears to be about a football match. The teacher stops their own conversation, praises the majority of the class for working well and following instructions, and says they now expect this to be true of all of the class. The conversations quickly stop.

In a situation such as this, what may be the cause of conversations both “on” and “off” task, despite the teacher’s instructions?

A very short time later, whilst the teacher is still with the same student and well before the stated time for the task has elapsed, a student puts their hand up and then tells the teacher they have finished; a few other students also have put their pens down and are nodding. The teacher briefly says something to the student they are with and then tells the class to finish the question they are on whilst they go to the front and get the answers ready to project. A short time later, the answers are projected and the students are told to mark their own work. They are told that if they got any wrong answers, they should copy down the correct answer and try and work out where they made their mistake.

Based upon this description, to which students has the time given for this task been based upon? Does the teacher know that sufficient time has been provided for all? What message may this be sending to the class about how their lessons work and who they are for?

In this lesson, if students do not understand the work, where does responsibility lie? What strategies have been developed for this situation, and what may be witnessed or evident to make this clear?

How likely is it that students ask for help if they are stuck in a lesson such as this? What classroom culture facilitates this, and what signals are there that such a culture does or does not exist?

What has been done here to help build students’ confidence in themselves as mathematicians?

Next: lesson ending and final reflection

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A Lesson Account, 1: Part 3

Part 1, Part 2

After this second example is completed, another question is written on the board: 60% of 40? The teacher tells the class that they wish everyone, without exception, to answer the question on whiteboards and reveal in the usual way after a countdown. They tell them that everyone, without exception, must attempt this, and that all students must show working out exactly as written on the board. The teacher asks if anyone has any questions before they begin; two students put their hands up. The first student picked shares that they already know the answer, can’t they just write the answer down? The teacher shares that there are many reasons why we show our working out, including that it is important for examinations, that it will help them with harder questions, and that it will also make it easier for the teacher to help if needed.

Given that this is neither an examination nor - apparently - “a harder question”, are these valid reasons to present here? If the primary motivation for this working out is that the teacher can observe that students are apparently following and applying the method they have introduced, would this solely not be enough of a reason to present to students?

When do and when do you not show your methods when answering questions in mathematics? What is your motivation for doing so, or not doing so? What dictates the level of detail included?

The second student states that they ‘don’t get it’; the teacher responds that they should try their best and that they will help them soon. 

What strategies can students be encouraged to implement when they do not ‘get’ something? When is it appropriate to vocalise these, and when is it not? How could a mathematics classroom operate so this becomes second nature to the point the statement is less likely to be made?

The teacher then instructs the class to answer the question in silence, and tells them they have twenty seconds. When the time elapses, the teacher asks everyone to reveal their answers. The teacher’s head movements indicate that they are scanning the whiteboards, where it is evident to the observer that most students have reproduced similar working out to the teacher and obtained an answer. Three students have written the equivalent of “I don’t get it” or incomplete methods. The teacher thanks the students and tells them to put their whiteboards down, before sharing that the correct answer was 24 and that as they were happy with what they saw, the class is going to proceed to practice questions to be completed, in silence and individually, in exercise books.

After stressing the importance of working out, if the teacher then only emphasises attention on the 'correct answer' what are they implictily telling the class?

Is individual work moved to at this point because the teacher has assessed that “the class” is in a position to do so, or because the plan - whatever its source, as previously questioned - dictates this is the point to do so?

If this move is a result of the teacher’s assessment, what number (or proportion) of the students not displaying what they wanted is considered acceptable in order for this to still happen?

As will be described, the teacher goes to the three students to offer individual support at the outset of the next section. What other strategies could have instead been potentially implemented to support these students?

Next: individual work

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A Lesson Account, 1: Part 2

Part 1

My description below of how the teacher ‘presents’ the mathematics to their students has been left somewhat vague, as a deep focus upon that is not my motivation in writing this piece; subsequent lesson accounts will more directly address the mathematics under consideration. 

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After some administrative matters, the teacher describes the focus of today’s lesson and shares how they view it in relation to that which has come before and that which is still to come in their lessons. They share that the focus is on finding percentages of a given positive integer, without the use of a calculator, and the teacher shares with the class that they are going to build upon something most of them have just answered - finding 10% of 60.

Given that the teacher has observed that at least some students did not demonstrate that they were able to obtain the correct value to this question, what does the teacher then do with this information? How does it inform what they offer next, if it does? Is the identity of the students who did not display ‘6’ and/or the methods that the teacher may have been looking for retained for further action?

The teacher then demonstrates how to find 30% of 60, by writing a model solution on the board. They emphasise how they are laying out their working, that this is crucial and that they expect all of the students to produce similar when they attempt their own questions. This demonstration is completed without any interaction with the class, although the teacher is regularly turning from the board to make what appears to be eye contact with students and their eyes move in a way that suggests they are scanning over all of the students.

How has this demonstration been arrived upon - is it a method the teacher has arrived at themselves, is it a departmentally agreed upon strategy and wording that all teachers follow, is it following a ‘script’ from an external source that teachers are given to ‘deliver’? To what extent may the answer to this question have impacted upon the teacher’s thinking about the mathematics under consideration and their own teaching of it? Does this matter?

Whilst building upon how 10% of a positive integer is obtained, the mathematics here is presented as a set of rules to learn and follow. Is that true for how one obtains percentages of positive integers, or is this instead something students could have worked at potentially reasoning for themselves? Does the difference matter?

There seems to be an expectation here that students fully focus on what the teacher is saying, doing and writing - or that the teacher is convinced that this is happening - so that they follow in order to understand. Is this how understanding is derived - by following a set of instructions? Are questions or discussion thus a hindrance to be stopped rather than a potential aid to learning? 

With this example left on the board, the teacher then writes down an additional question: what is 40% of 70? They state that they are going to repeat the process with similar working out, but this time with the class’ help. Several hands go up; the teacher asks for the students to put their hands down and states that they instead want everyone to think about what the steps are and that they will then ask specific students what to do. The teacher then proceeds to do this, with their inputs to the students taking the form of “what do we do next?”. There are no questions posed as to why particular steps are undertaken, nor questioning on why particular results are obtained. The teacher’s inputs are generally posed to the whole class, with a few seconds passing before a particular student is picked to answer. If the teacher accepts what is said as correct, another student is asked to repeat it and it is then written on the board. If a student says that they do not know, another student is asked instead, and it appears that if they offer what the teacher wants, the initial student is asked to repeat. If this second student also states they do not know, the teacher refers back to their first example and asks directed questions to the second student with the aim that they share similar for the question currently being undertaken. If a student offers an answer the teacher does not accept, the teacher tells them they are mistaken, and seeks out an answer they find acceptable from another student with the first then asked to repeat.

What are the advantages and disadvantages of not allowing any students to volunteer answers? What is gained and lost by a teacher entirely deciding who they are going to call upon to answer? How do teachers in this position make decisions on who they are going to ask, and how much variety is there in their choices from lesson to lesson?

How may students feel in response to the knowledge that they may be asked to answer questions at any point, no matter how ready they feel? Does this matter?

In the scenario described here, if a student says that which the teacher wants to hear, can the teacher reach a conclusion about the student’s understanding? If a student repeats back another student’s words, what does that mean about their understanding? Is this different from a student repeating back a teacher’s words?

If a teacher hears what they want to hear, does that mean learning is happening?

Is there an implicit direction in the background here that students in the class are discouraged from asking questions about what they are learning, and their understanding of it?

Next: moving away from whole class teaching

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A Lesson Account, 1: Part 1

This ongoing series will offer descriptions of parts or entirety of lessons. These lessons may have been taught by myself, or be among those I have observed, or an amalgamation. The intention is not to pass judgment on that which is described, nor on myself as a practitioner or on others, but instead to question and learn. 

I offer the following account of a lesson, which was structured according to a template; the lesson focus was upon ‘calculating percentages of amounts’. My questions regarding what was offered and observed are in italics.

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The students arrive at their mathematics lesson, where the teacher awaits to greet them at the entrance to the classroom. On the board are projected six short questions, which have been selected from the curriculum the students have, in theory, already encountered. It transpires that one question is related to the focus of today’s lesson, the others are not.

Is it important what students immediately encounter upon entry to a lesson? What is the purpose of an initial, opening task (using whatever naming language is applicable)?

With this kind of opening, does it matter which questions are chosen, and when? Are these a standard set of questions which all students are set, irrespective of their class or teacher, or are they chosen by the teacher for the class in front of them? Do the questions chosen link to one another from lesson-to-lesson, or do they appear to the students to be a random unrelated selection? Does this matter?

There is an expectation that the students sit in silence and answer these questions, on something which can be used to reveal their answers later, without assistance from the teacher or from other students. This is a standard opening routine to every lesson. 

Are such routines important? Are they needed? If so, how and when - as similar as possible across the whole school, or across all lessons in a subject, or across all lessons by a specific teacher, or across all of the lessons by a specific teacher with a specific class? What if the teacher believes there is a need to deviate from this opening - are they automatically wrong?

What is the power of students working in silence in this situation? What is potentially lost by its insistence, and does this matter? What does a student do if they do not know how to approach answering a question, given they know no assistance is forthcoming?

After all students have arrived, the teacher takes the register and then circulates among the students. They have been praised for their efforts, or encouraged (it appears that the teacher attempts to do this discreetly) where required. The students are told how much time they have remaining to complete the task. Some students are not visibly writing, whilst others appear to be making themselves look busy.

Is it okay for students to ‘opt-out’ in this situation? Why might they be doing so?

When the stated time elapses, the teacher asks the students to reveal their answers as a class, one question at a time. As they proceed, the teacher offers brief feedback, in most cases either only providing an answer or a short instruction on how they obtained their answer. For two questions, after the teacher has seen the class' answers they comment that they will offer a fuller explanation after the answers to the rest of thel questions have been revealed. They do this, after apparently aiming to ensure all of the class are paying attention, spending a short period of time demonstrating how the answers are obtained. They do this without any interaction with any members of the class, with the exception of one student who after the demonstration puts their hand up and then shares that they still do not understand. The teacher explains this question does not relate to today’s lesson and that the student should not worry right now, but should aim to do some independent learning to ensure their understanding is improved.

What do the students gain and what do they lose from only knowing whether their answers are “correct” or not, along with at most only the briefest of explanation, and without any discussion with any other person about the mathematics? Is there an implicit belief on the teacher’s part that what is being offered should be nothing more than a reminder?

What might the teacher be looking for that allows them to reach a conclusion about how many and which questions deserve further consideration? Is this assessed during the revealing of answers or could it have been determined - or at least suspected - prior to the lesson? 

What is the purpose of a teacher explaining without any interaction initiated by students, versus explanations where such interaction is allowed or encouraged?

When does the teacher consider it “okay” for at least some students to not understand something that is offered here? What is the potential difference in perception of this between the teacher and the student(s)? What may a student take away from a situation like this regarding themselves as learners, the subject as a whole, and their teacher? Does this matter?

What influences decisions about when to further explore mathematics that is ‘tangential’ to the planned focus of the lesson? If the teacher does not want such a ‘distraction’, should they have set questions that are away from the main scope of the lesson and thus carry a higher probability of the students being provided with such distraction?1

Is it possible that, no matter what the teacher says or does, the students are at this point mentally focused upon a different area of mathematics than that which the teacher wants?

If instead of mathematics being addressed in a lesson, students are encouraged (or in this case, left) to pursue explanations or understanding in their own time, how often is there evidence of this happening?

If a student has been unable to answer a majority of the questions set, what feelings could have been invoked about themselves as a mathematics student before they then encounter any new mathematics in the rest of the lesson? Does this matter? 

What does this lesson opening implicitly tell students about how mathematics is learnt and its source? Does this matter?

Next: the main ‘focus’ of the lesson

1Mathematics has many beautiful aspects, one being that any prompt at all poses the opportunity for our minds to take us on journeys away from that which may be 'intended'!

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An Introduction, Part 4: My aims and guiding principles

 

Caleb Gattegno, whose wisdom is a touchstone. 

(Image courtesy of the Association of Teachers of Mathematics)

Part 1 Part 2 Part 3

We are all evolving beings, and if we are not currently satisfied with our performance or knowledge as a teacher it is important to realise that what we will be tomorrow can be greater than that we are today should we sufficiently work upon our selves, and who we were yesterday informs who we are today. A combination of ideas I possessed before I started my training to be a teacher, my experiences since, and the wisdom of my influences have led me to develop an ever-firming sense of what I believe as an educator. Working with the Association of Teachers of Mathematics (ATM) led me to greatly appreciate the existence of its aims and guiding principles, which it was said were the basis for all of its work as an entity. Similarly, in the background of everything I do and the work I produce here are a similar set of principles. The extent to which my work meets these has and does vary, but I measure myself on what it is I am working towards:

• Only awareness is educable (Caleb Gattegno, The Science of Education Part 1: Theoretical Considerations)

• Mathematics is a way in which we make sense of the world, and our human nature has us as natural mathematicians; our teaching should look to reach and develop this (following ATM)

• A questioning rather than accepting nature is fundamental to the development of both one’s self and one’s teaching, and this should be embraced. The same nature should be encouraged and developed rather than subdued within students

• In the most powerful classroom, teaching should be subordinated to learning and thus a fundamental operation of the practitioner is to assess and respond (following Gattegno)

• The mathematics classroom should always be about its learners, not its teacher

• Self-belief in learners should be encouraged and promoted; the notion that one “cannot do mathematics” should never be accepted, and intelligence-judging language or values should be contradicted

• Mathematics teaching should focus upon the “necessary” and seek ways to engage with and develop this (following Dave Hewitt)

• Teaching mathematics is not the same as teaching pupils to learn mathematics, and both must be attended to within a classroom (following many, particularly The Psychology of Learning Mathematics by Richard R. Skemp)

• Teaching takes place in time, learning takes place over time (Pete Griffin, Mathematics Teaching 126, following John Mason)

• Learning is often messy rather than neat and linear; planning and preparation must take this into account and the practitioner must battle the notion that their role is the delivery of packets of information irrespective of and formulated away from the needs of the learners in front of them

• Teachers should aspire to be the best versions of themselves by removing judgment and instead adopt a continuing developmental view of their own practice in response to their students’ learning, by engaging with themselves and with others

• The developing teacher never loses sight of themselves as a lifelong student, of their subject and its learning, and of their learners as human beings

• Collaboration is powerful for both learners and teachers: we always can learn from one another

• Whilst knowledge of current research and evidence is powerful and desirable, falling prey to solely that which is currently en vogue loses sight of the rich tapestry of research, writing and ideas from the past and instead leaves one open to merely following agendas

• The development of intuitive practice is desirable, as then is its deconstruction

As I end both this piece and my introduction as a whole, I realise that it will be of interest to look back upon in the future as my thinking further evolves to see how much of the above I would change or revise, what, if anything, I would remove, and what I would add. I also suspect that, in one way or another, this introduction has previewed everything I will ever write here.

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