An interesting read - one caution I have about the examples are none... or very few of the "corrections" actually showed what to do or stages of working to find the answer. Most were simply the correct answer - which will not help the student get it right next time. I wonder what the results might look like had the student showed in example 1 a series of cancellings with the division step written above and below each stage eg: 36/54 - 18/27 - 2/3.
The simplifying example looks like the student would benefit from some negative number practice and some SSDD on index rules and collecting like terms - This topic is always a tricky one (in my opinion) if there is wide spread difficulty
Finding the correct answer is all about using understanding of concepts to find the logical sequence of step by step processes to engineer a route from the clues in the question to the solution.
THEN there is the question of efficiency of process... hence why a one size fits all copied model solution actually fails the majority!
However, if the logic and sequence of steps is made explicit in the written process, and efficient shortcuts explained - better understanding for all is possible [I frequently need to use multiple colours for explanations, not just one]
The above examples all demonstrate something that should be strikingly obvious: low quality learning corrections lead to low levels of progress. The students in each case above have copied down the answer, presumably doing so without any thinking as evidenced by the subsequent lack of understanding in future questions. This does not mean, however, that all learning corrections are therefore invalid. Learning corrections can happen in many more ways than the simple 'copy down the correct answer' examples above. For example, peer-to-peer conversations and subsequent corrections completed, workings and steps adequately detailed in a different colour following a whole class review, or a subsequent example of a similar question with different values independently completed in a different colour alongside an incorrect question to demonstrate progress. To tar all learning corrections with the same brush misses the nuance of different approaches to completing learning corrections. The article is correct, however, to question the assumed validity of learning corrections and challenge the lack of progress that poor quality learning corrections can mask. Like any skill in teaching, learning corrections can be broken down into several categories, all with varying degrees of impact and effectiveness as evidenced by subsequent attempts at similar questions at a future time.
While the article raises a valid point about the ineffectiveness of green pen corrections, it misses a crucial aspect of learning - the need for active engagement and struggle in the correction process. It's a given that passively copying down corrections, as dictated by a teacher, won't enhance learning. What's important is that pupils should actively engage with their errors, understanding why they made them and how to correct them. This process, which aligns with Willingham's principle that we learn what we think about, demands a struggle on the part of the pupil. It's not about the color of the pen but the cognitive process behind the correction. Using a different color pen, whether green or any other, serves only to distinguish the correction from the original work, making it stand out. The key is ensuring that pupils are mentally wrestling with their mistakes, not just passively rewriting them.
As a teacher of too many years experience, corrections, and copying down examples only have value if they are acted on and used. E.g. corrections are useful when the student then fully understands the mistakes they've made, and can then correctly apply the method to a follow-up question. If it is just green-penning for green-penning sakes (i.e. for Ofsted/ SMT/ that's how we do it here), pupils will not make further progress.
I appreciated the article on copying down examples. Examples can be useful in books for revision, but over the years, I now minimise copying examples, and lesson objectives and instead provide mind-maps of topics for revision with worked examples. 35 mins lessons are too short for wasting time on copying down LO's and examples. I would rather the students/pupils were actively practising/learning in the lesson. Thanks Craig, always a good read!
An interesting read and I agree that simply copying a correct answer won't lead to learning. One thing I like to do do is encourage my children to use their purple (in our case) pen to write a sentence about why they got it wrong. I work within a primary school so this is often things like: I did the right method but made a mistake here; I added when I should have multiplied; I didn't line up my digits in the right place columns. Sometimes they simply write 'I don't know' and then I know that the concept needs more support.
The issue isn't the colour of the pen used for the correction, but the understanding that students have of a topic. Clearly, in the examples provided, the students lack basic fundamentals (e.g., multiplications; divisions; manipulation of number bonds; identification of common denominators; proportions), don't have a feel for the intellectual process (no workings) and its rigour (where are the equal and equivalent signs?), don't seem to grasp what they need to solve, and don't seem to know how to check their results. So, do they really understand what they are doing and why? Often, examples of how these problems translate in the real world will give students not only a good-enough reason to learn the subject, but will enable them also to translate theories and some very dry exercises into something that makes sense and is relatable. Sadly, few teachers are able to do this, when they simply apply the curriculum or when their grasp of a topic is theoretical rather than being also practical. In conclusion, teach the subject better, focus on what needs to be solved (understanding what needs to be achieved and how demonstrates command of the concepts), use practical examples, and the students will become better.
An interesting read - one caution I have about the examples are none... or very few of the "corrections" actually showed what to do or stages of working to find the answer. Most were simply the correct answer - which will not help the student get it right next time. I wonder what the results might look like had the student showed in example 1 a series of cancellings with the division step written above and below each stage eg: 36/54 - 18/27 - 2/3.
The simplifying example looks like the student would benefit from some negative number practice and some SSDD on index rules and collecting like terms - This topic is always a tricky one (in my opinion) if there is wide spread difficulty
Finding the correct answer is all about using understanding of concepts to find the logical sequence of step by step processes to engineer a route from the clues in the question to the solution.
THEN there is the question of efficiency of process... hence why a one size fits all copied model solution actually fails the majority!
However, if the logic and sequence of steps is made explicit in the written process, and efficient shortcuts explained - better understanding for all is possible [I frequently need to use multiple colours for explanations, not just one]
The above examples all demonstrate something that should be strikingly obvious: low quality learning corrections lead to low levels of progress. The students in each case above have copied down the answer, presumably doing so without any thinking as evidenced by the subsequent lack of understanding in future questions. This does not mean, however, that all learning corrections are therefore invalid. Learning corrections can happen in many more ways than the simple 'copy down the correct answer' examples above. For example, peer-to-peer conversations and subsequent corrections completed, workings and steps adequately detailed in a different colour following a whole class review, or a subsequent example of a similar question with different values independently completed in a different colour alongside an incorrect question to demonstrate progress. To tar all learning corrections with the same brush misses the nuance of different approaches to completing learning corrections. The article is correct, however, to question the assumed validity of learning corrections and challenge the lack of progress that poor quality learning corrections can mask. Like any skill in teaching, learning corrections can be broken down into several categories, all with varying degrees of impact and effectiveness as evidenced by subsequent attempts at similar questions at a future time.
At last, someone who has taken the time to do some evaluation of this wasteful, rote, stereotypical classroom practice. Thank you!
Maybe the answer in Maths questions are not important.
The correction should probably be a short sentence regarding the difference between a successful vs unsuccessful attempt.
While the article raises a valid point about the ineffectiveness of green pen corrections, it misses a crucial aspect of learning - the need for active engagement and struggle in the correction process. It's a given that passively copying down corrections, as dictated by a teacher, won't enhance learning. What's important is that pupils should actively engage with their errors, understanding why they made them and how to correct them. This process, which aligns with Willingham's principle that we learn what we think about, demands a struggle on the part of the pupil. It's not about the color of the pen but the cognitive process behind the correction. Using a different color pen, whether green or any other, serves only to distinguish the correction from the original work, making it stand out. The key is ensuring that pupils are mentally wrestling with their mistakes, not just passively rewriting them.
We all know it's true, we just need someone like you to come along and say it
As a teacher of too many years experience, corrections, and copying down examples only have value if they are acted on and used. E.g. corrections are useful when the student then fully understands the mistakes they've made, and can then correctly apply the method to a follow-up question. If it is just green-penning for green-penning sakes (i.e. for Ofsted/ SMT/ that's how we do it here), pupils will not make further progress.
I appreciated the article on copying down examples. Examples can be useful in books for revision, but over the years, I now minimise copying examples, and lesson objectives and instead provide mind-maps of topics for revision with worked examples. 35 mins lessons are too short for wasting time on copying down LO's and examples. I would rather the students/pupils were actively practising/learning in the lesson. Thanks Craig, always a good read!
An interesting read and I agree that simply copying a correct answer won't lead to learning. One thing I like to do do is encourage my children to use their purple (in our case) pen to write a sentence about why they got it wrong. I work within a primary school so this is often things like: I did the right method but made a mistake here; I added when I should have multiplied; I didn't line up my digits in the right place columns. Sometimes they simply write 'I don't know' and then I know that the concept needs more support.
The issue isn't the colour of the pen used for the correction, but the understanding that students have of a topic. Clearly, in the examples provided, the students lack basic fundamentals (e.g., multiplications; divisions; manipulation of number bonds; identification of common denominators; proportions), don't have a feel for the intellectual process (no workings) and its rigour (where are the equal and equivalent signs?), don't seem to grasp what they need to solve, and don't seem to know how to check their results. So, do they really understand what they are doing and why? Often, examples of how these problems translate in the real world will give students not only a good-enough reason to learn the subject, but will enable them also to translate theories and some very dry exercises into something that makes sense and is relatable. Sadly, few teachers are able to do this, when they simply apply the curriculum or when their grasp of a topic is theoretical rather than being also practical. In conclusion, teach the subject better, focus on what needs to be solved (understanding what needs to be achieved and how demonstrates command of the concepts), use practical examples, and the students will become better.
Do both. Then check out Snorkl. Bots are almost here as an extra set of eyes.
This may be tricky, but.....is there a place for passive activity in learning?