Mi fractions homework sheet from roxanneatrak

Lesson Plan for MI Lesson

Masters l a lesson on multiple intelligences anonymous from roxanneatrak

Collaborative Approach to Learning - Multiple Intelligences Lesson

Collaborative Approach to Learning – Multiple Intelligences

Howard Gardener (1983), states that students should be given a choice on how to do something in order to help with their. If students are allowed to study a topic or subject in their own preferred learning style then they will learn better, retain the information and become better learners.

To put this theory to the test, my colleague and I planned a lesson (see appendix A) on adding, subtracting, multiplying and dividing fractions using the multiple intelligences, which was to be delivered to our own groups (B-D grade students). We felt that students would need some time to consider the different intelligences and to decide which was their preferred intelligence but did not want this to eat into our actual lesson time. As a result we used the last twenty minutes of the preceding lesson to explain the objective for the ‘MI’ lesson, explain the multiple intelligences and to recap over the four operations of fractions. Students were asked to consider their preferred MI and the MI that they would least likely use.

At the start of the ‘test’ lesson, I very quickly recapped over the key features and purpose of the lesson and have each student the homework task so that they knew what they were going to be assessed on. The intention here was to give them clear focus and understanding of what they would be required to demonstrate in their Homework, which would hopefully direct their learning within the lesson.

How did it go?

The students took a while to get into the lesson. That is to say that they seemed confused by what they had to do despite having had the instructions twice. They would ask ‘so what have I got to do?’, ‘how do I present it?’, ‘what kind of song?’.  I wonder whether the delay was due to the fact that this was a new style of lesson for the students. Would the outcome have been different if these activities were a staple part of their Mathematics diet?

Some students did very little in the way of presenting the methodology of at least one of the four operations of fractions. I feel that students required more structure and less of their own interpretation.

Most of the group, for their first MI, opted image smart and logic smart and hence set about making posters, mind maps , lists, bullet points etc… When they chose their second MI (their least preferred MI), some of the students really challenged themselves and went out of their comfort zone and tried ‘nature smart’, ‘sound smart’ and even ‘body smart’. The group of girls that chose ‘body smart’ created a dance to explain how to add and subtract fractions. Their creation was very impressive, well thought out and furthermore, made sense in the context of their task. As an observer, I would understand the method by watching their performance.

The other set (lower ability) had the same lesson delivered by my colleague and they struggled greatly to understand what they had to do. They didn’t manage a lot of work and tended to all opt for image smart, creating a poster.

Overall, I am not convinced that for a subject like Mathematics, this type of activity is particularly useful for new learning. Perhaps MI lessons have their place for example as an alternative revision lesson, a one off lesson or homework to act as a break from the ‘usual practice’.

The homework (See Appendix B) was testing facts. It was assessing the students’ ability to recall how to add, subtract, multiply and divide fractions based on the learning that took place in the MI lesson. The results from the homework are varied with very few obtaining full marks. That said, a lot of the students lost marks because they did not simplify their answer fully as opposed to not knowing the method of adding, subtracting, multiplying and dividing fractions.

When asked for their feedback on the lesson, with particular reference to its usefulness, the students were not overly positive. The group of girls who created a dance felt that they had really learned from the process and that they would now remember how to add and subtract fractions. Conversely, the vast majority of the group felt that they wouldn’t remember what they had learned and did not feel that this was an activity they would want to repeat. I wonder whether this is entirely because they are not used these types of lessons and would in fact need to be exposed to this style of collaborative learning more often and in all subjects? Would using MIs become more powerful if used regularly across the whole school?

A big question for me is, ‘Does this type of lesson work well for certain subjects but not others?’ Or are there certain MIs that work better for certain subjects?  When a similar styled lesson was delivered to a top set in year 9, they were able to get ‘stuck in’ immediately and were very resilient, reciprocal and resourceful. They all created some excellent work but again all students produced image smart work. Does this suggest that Image smart and logic smart are the obvious choices for Mathematics?

We will be running a short assessment under test conditions in a couple of weeks’ time to test the students’ ability to retain information and recall it after an MI lesson. Although we only have a relatively small sample size, to compare results and performance, we asked other colleagues to teach the four operations of fractions to the parallel sets in a more traditional teacher led, student practice manner. These groups were set the same homework and will sit the same assessment.

Session 1: Learning and Assessment (Surface and Deep Learning)

Learning and assessment go hand in hand in the modern day classroom. The learning is assessed at every level throughout each lesson and informs the planning for the next lesson. As teachers in the current educational climate, we often follow the same routines and procedures as our predecessors and our colleagues and find ourselves on an ever turning treadmill of assessing students, re-teaching concepts that have not been grasped and then re-assessing to see how much, if any, progress has been made since the last assessment. The question that we should really be asking is ‘what is learning?’ and more than that, ‘what is effective learning?’ and does effective learning involve so many assessments and intervention? To be effective teachers of learners, we really need to understand what it is we are trying to achieve and what the best approach is for our own individual subjects. Additionally, does one size fit all? Should all our lessons take the same format despite the class we are teaching? Or should there be a flexible and varying approach to our teaching according to the learners we have in front of us?

                So, what is learning? As quoted from the dictionary, learning ‘is the acquisition of knowledge or skills through study, experience, or being taught.’ That sounds quite simple. There are many times when I have stood at the front of my classroom and ‘taught’. I have discussed what we are learning, demonstrated how to ‘solve the problem’ or answer the question, walked through another example with pupils leading the method and then given students the opportunity to practise for themselves with an activity at the end that allows me to ‘assess’ how much the students have understood or indeed, how many of the students have understood. Quite often, after my plenary that allows me to assess progress, I leave the classroom happy that I have imparted my knowledge and skills, to say, solve an equation, successfully. I am relatively confident that the students would be able to answer a question just like the ones they did in class and get full marks, thus, allowing me to move on to the next step or the next concept at our subsequent meeting. It’s only really upon my reflection that I ask myself if being able to answer very similar questions means that students have understood, or if it means that they have acquired a skill that has been born from repetition and is then only useful when given conceptually similar questions as opposed to understanding why they are solving the equation, what that means, where it came from and how to apply it to varying situations. This thought leads me very nicely to discuss two different types of learning: Surface and deep learning.

                In their research of learning, Marton and Säljö (1976) categorised approaches to learning as either Surface learning or Deep learning. Surface learning can be described as memorising and recalling facts, acquiring new information and increasing the amount of information that can be regurgitated, and storing new facts, skills or knowledge that can be used time and again.  At the other end of the spectrum we have Deep learning, which can be defined as making sense of the concept and making links between that and other previously learned information, relating the new learning to real life and interpreting the information. zAccording to Ramsden (1988), Deep learning organises and structures content into coherent whole with the emphasis being internal, from within the student.

With this in mind, is my aforementioned example of one of my lessons allowing for deeper learning? My honest answer, if not disappointing answer, is no! Showing students how to do something and then expecting them to replicate the method is not encouraging deeper learning. Students are simply memorising and recalling a method by repetition. This is however, great when students are expected to pass an examination. Given the education system that we have in place in the UK, schools and therefore teachers are judged on how many students achieve grade C or above in their GCSE examination (amongst other measures), and more importantly for me, schools are judged on the performance of our students in Mathematics. If we are continuously assessed on our ability to ensure students achieve grade C+ in Mathematics, we are then bound to deliver the type of teaching that secures results in order to avoid failure ourselves. There are two issues at stake here. Firstly, I draw your attention to the fact that when we talk about ‘assessment’ we are not only talking about that of students, but we are talking about assessing ‘us’, the teachers, and schools. Is this the right thing to do? Nobody likes to fail and so giving schools and teachers rigorous targets to meet only encourages us to take the ‘shortcut’ to make certain that these targets are achieved. In Mathematics, the way to do this is by ‘rote learning’, repetition, memorising and recalling. Otherwise known as Surface Learning. This leads me quite nicely to my second point, which is that in Mathematics, teaching to the test (or more politically correctly put, ensuring students achieve grade C or above) is by far and away the most effective way of securing those targeted grades, given the time allowed in the curriculum. Investigating, exploring, linking Mathematics requires a great deal more time than we have available to us, or at least when we talk in relation to the looming GCSE examination. Furthermore, whilst I accept that there are certain mathematical concepts and topics that can be explored and discovered, there is also a need for repetition and recall. A prime example of this is knowing one’s times tables. We can show students why 2x2 is 4 by using counters etc…. but when you have done and said all, even as adults, we need to know our multiplication tables by heart in order to do calculations readily and without hesitation. As a practising teacher of Mathematics, I can say that it would be ideal to have more time to allow students to ‘explore Mathematics’ and to go into greater detail and discover where Mathematics came from and why, but it is important to be clear that we require both surface and deep learning to be able to process the information and apply it to new situations.

                Is good learning based solely on Marton & Säljö’s surface and deep learning? Howard Gardner (1983) suggested that there are ‘Multiple Intelligences’ where people are more proficient in some areas than others. We may be logical-mathematical; linguistic; musical; spatial; bodily-kinaesthetic; interpersonal and intrapersonal. As individuals, we are supposedly happier when we are learning according to our own natural intelligences. Relating these intelligences to my own teaching practice, I can understand why some students find Mathematics so hard, frustrating and even tortuous. If a student is not logical-mathematical at all, they will more than likely find that their reptilian brain takes charge causing them to enter into a fight or flight situation. This can be interpreted by poor behaviour as a distraction from their inability to grasp the concepts or even being passive in a lesson, ‘zoning out’. The limbic system validates learning and according to research, for this validation to take place, there needs to be an emotional connection to the learning, a personal link or goal. If learning is delivered in a way so that individuals’ natural intelligence is tapped into, could this be the emotional connection that is required to accelerate learning? I could consider facilitating learning in different ways to accommodate the different intelligences, but since a class of approximately 28 students will be made up of every single intelligence, my approach would only ever suit one style of learner. Hence, would the multiple intelligences be helpful when teaching a group of students? Perhaps if students were set according to their learning styles rather than their mathematical ability, this could pay dividends.

Claxton suggests that ‘good learners stick with things when they are difficult’ and know what to do when they don’t understand.  They are resilient, resourceful, reflective and reciprocal. This is the ideal student in Mathematics and indeed any subject. I quite often have conversations about how to get our students to ‘buy in’ to the idea of helping themselves by not giving up, finding the answers, revising their weaker areas and sharing their insight with others in a similar situation to reinforce their learning. Dare I say it, but these students are invariably the most mathematically able students. They can work independently but seek each other’s advice when they are struggling and only seek help from the teacher when they really have explored all options, they go home and look at the areas they have struggled with either in class, on a piece of homework or on a test and they form study groups and are prepared to help students less able than themselves. So the real question is how do we get ALL students to behave in this way? Perhaps some students would benefit from learning how to learn from other students. Maybe we don’t set on ability so that our more able students can support the less able not only in Mathematics but in their approach and attitude to learning. Maybe students only learn the subjects that they have an interest or affinity for. This I find to be an interesting idea, one which I’m sure will never be bought into, but one that allows students to excel rather than fail, build confidence rather than humiliation. Maybe we don’t assess some students or maybe we do assess but in a very different way than some of the more mathematical students. This latter comment brings me to my last point of reflection, Assessment.

                Why do we assess? As a teacher, I assess my students for a few reasons. Firstly, to allow me to see where the common misconceptions and areas of weakness are so that I may plan my subsequent lessons and any intervention that needs to take place. Secondly, so that my students can identify their own strengths and weaknesses and then hopefully go away and revise the areas that they have not performed so well on. Thirdly, to use the assessments as a benchmark to monitor progress of my students. As I have already alluded to in previous paragraphs, can assessment be more of a hindrance to some students than it is a useful tool? For some students (mostly the less able mathematicians), lots of assessments can just mean another opportunity to show how much they don’t know and quite often they demonstrate who does not possess Claxton’s four R’s. For these students, no amount of assessing and highlighting areas for improvement will encourage them to be independent learners or even reciprocal learners. In this case, I go back to my previous question. Should we assess all students? And if we should assess all students, should we consider how we assess a little more so that assessments are more sympathetic to the learners’ abilities and needs? As teachers we hope to help our students to make at least three levels of progress between Key stage 2 and 4, and in Mathematics this means that we need to teach our students specific skills and how to answer specific questions that will be asked on the GCSE paper that determines a grade, which determines if the minimum of three levels of progress has been made. This means our regular internal assessments need to test our students’ ability to recall these skills and apply them in an examination situation. Consequently, even now as I consider my own questions, I wonder how as individual teachers and schools, we can move away from the current model of skill testing test papers if the national benchmarking test is a paper that assesses the ability to recall, use and more now than ever before, but apply said skills. The new Mathematics GCSE is designed to assess understanding and application more than just the recall of skills. This is a pleasing turn of events since the examination focusses on students being able to recall, use and apply, which will only help students in the real world once they leave education. However, from a school teacher’s perspective, the new GCSE is very demanding of the lower ability students and causes a concern that these students will only end up failing more than they do currently. Once again, I revisit my question of ‘does one size fit all?’

                I could sit and ponder these questions and many more for a considerable period of time, but to conclude I will say this: under the current educational system in the UK, teachers can only do the best by their students if they teach in a manner appropriate to the students before them, adapting their practice as they go; assess the students within the guidelines of the examination that we are working towards but in a style that does not demean or deflate the learners; use the information highlighted by the assessment to ensure that students make progress; guide students to reflect on their own learning in terms of approach and performance; help students to become resilient, resourceful, reflective and reciprocal; encourage students to give their best and above all help students to become confident, competent, good learners and better young adults both in school and once they leave.

Session 1: Learning and Assessment (Surface and Deep learning)

Learning and assessment go hand in hand in the modern day classroom. The learning is assessed at every level throughout each lesson and informs the planning for the next lesson. As teachers in the current educational climate, we often follow the same routines and procedures as our predecessors and our colleagues and find ourselves on an ever turning treadmill of assessing students, re-teaching concepts that have not been grasped and then re-assessing to see how much, if any, progress has been made since the last assessment. The question that we should really be asking is ‘what is learning?’ and more than that, ‘what is effective learning?’ and does effective learning involve so many assessments and intervention? To be effective teachers of learners, we really need to understand what it is we are trying to achieve and what the best approach is for our own individual subjects. Additionally, does one size fit all? Should all our lessons take the same format despite the class we are teaching? Or should there be a flexible and varying approach to our teaching according to the learners we have in front of us?

                So, what is learning? As quoted from the dictionary, learning ‘is the acquisition of knowledge or skills through study, experience, or being taught.’ That sounds quite simple. There are many times when I have stood at the front of my classroom and ‘taught’. I have discussed what we are learning, demonstrated how to ‘solve the problem’ or answer the question, walked through another example with pupils leading the method and then given students the opportunity to practise for themselves with an activity at the end that allows me to ‘assess’ how much the students have understood or indeed, how many of the students have understood. Quite often, after my plenary that allows me to assess progress, I leave the classroom happy that I have imparted my knowledge and skills, to say, solve an equation, successfully. I am relatively confident that the students would be able to answer a question just like the ones they did in class and get full marks, thus, allowing me to move on to the next step or the next concept at our subsequent meeting. It’s only really upon my reflection that I ask myself if being able to answer very similar questions means that students have understood, or if it means that they have acquired a skill that has been born from repetition and is then only useful when given conceptually similar questions as opposed to understanding why they are solving the equation, what that means, where it came from and how to apply it to varying situations. This thought leads me very nicely to discuss two different types of learning: Surface and deep learning.

                In their research of learning, Marton and Säljö (1976) categorised approaches to learning as either Surface learning or Deep learning. Surface learning can be described as memorising and recalling facts, acquiring new information and increasing the amount of information that can be regurgitated, and storing new facts, skills or knowledge that can be used time and again.  At the other end of the spectrum we have Deep learning, which can be defined as making sense of the concept and making links between that and other previously learned information, relating the new learning to real life and interpreting the information. zAccording to Ramsden (1988), Deep learning organises and structures content into coherent whole with the emphasis being internal, from within the student.

With this in mind, is my aforementioned example of one of my lessons allowing for deeper learning? My honest answer, if not disappointing answer, is no! Showing students how to do something and then expecting them to replicate the method is not encouraging deeper learning. Students are simply memorising and recalling a method by repetition. This is however, great when students are expected to pass an examination. Given the education system that we have in place in the UK, schools and therefore teachers are judged on how many students achieve grade C or above in their GCSE examination (amongst other measures), and more importantly for me, schools are judged on the performance of our students in Mathematics. If we are continuously assessed on our ability to ensure students achieve grade C+ in Mathematics, we are then bound to deliver the type of teaching that secures results in order to avoid failure ourselves. There are two issues at stake here. Firstly, I draw your attention to the fact that when we talk about ‘assessment’ we are not only talking about that of students, but we are talking about assessing ‘us’, the teachers, and schools. Is this the right thing to do? Nobody likes to fail and so giving schools and teachers rigorous targets to meet only encourages us to take the ‘shortcut’ to make certain that these targets are achieved. In Mathematics, the way to do this is by ‘rote learning’, repetition, memorising and recalling. Otherwise known as Surface Learning. This leads me quite nicely to my second point, which is that in Mathematics, teaching to the test (or more politically correctly put, ensuring students achieve grade C or above) is by far and away the most effective way of securing those targeted grades, given the time allowed in the curriculum. Investigating, exploring, linking Mathematics requires a great deal more time than we have available to us, or at least when we talk in relation to the looming GCSE examination. Furthermore, whilst I accept that there are certain mathematical concepts and topics that can be explored and discovered, there is also a need for repetition and recall. A prime example of this is knowing one’s times tables. We can show students why 2x2 is 4 by using counters etc…. but when you have done and said all, even as adults, we need to know our multiplication tables by heart in order to do calculations readily and without hesitation. As a practising teacher of Mathematics, I can say that it would be ideal to have more time to allow students to ‘explore Mathematics’ and to go into greater detail and discover where Mathematics came from and why, but it is important to be clear that we require both surface and deep learning to be able to process the information and apply it to new situations.

                Is good learning based solely on Marton & Säljö’s surface and deep learning? Howard Gardner (1983) suggested that there are ‘Multiple Intelligences’ where people are more proficient in some areas than others. We may be logical-mathematical; linguistic; musical; spatial; bodily-kinaesthetic; interpersonal and intrapersonal. As individuals, we are supposedly happier when we are learning according to our own natural intelligences. Relating these intelligences to my own teaching practice, I can understand why some students find Mathematics so hard, frustrating and even tortuous. If a student is not logical-mathematical at all, they will more than likely find that their reptilian brain takes charge causing them to enter into a fight or flight situation. This can be interpreted by poor behaviour as a distraction from their inability to grasp the concepts or even being passive in a lesson, ‘zoning out’. The limbic system validates learning and according to research, for this validation to take place, there needs to be an emotional connection to the learning, a personal link or goal. If learning is delivered in a way so that individuals’ natural intelligence is tapped into, could this be the emotional connection that is required to accelerate learning? I could consider facilitating learning in different ways to accommodate the different intelligences, but since a class of approximately 28 students will be made up of every single intelligence, my approach would only ever suit one style of learner. Hence, would the multiple intelligences be helpful when teaching a group of students? Perhaps if students were set according to their learning styles rather than their mathematical ability, this could pay dividends.

Claxton suggests that ‘good learners stick with things when they are difficult’ and know what to do when they don’t understand.  They are resilient, resourceful, reflective and reciprocal. This is the ideal student in Mathematics and indeed any subject. I quite often have conversations about how to get our students to ‘buy in’ to the idea of helping themselves by not giving up, finding the answers, revising their weaker areas and sharing their insight with others in a similar situation to reinforce their learning. Dare I say it, but these students are invariably the most mathematically able students. They can work independently but seek each other’s advice when they are struggling and only seek help from the teacher when they really have explored all options, they go home and look at the areas they have struggled with either in class, on a piece of homework or on a test and they form study groups and are prepared to help students less able than themselves. So the real question is how do we get ALL students to behave in this way? Perhaps some students would benefit from learning how to learn from other students. Maybe we don’t set on ability so that our more able students can support the less able not only in Mathematics but in their approach and attitude to learning. Maybe students only learn the subjects that they have an interest or affinity for. This I find to be an interesting idea, one which I’m sure will never be bought into, but one that allows students to excel rather than fail, build confidence rather than humiliation. Maybe we don’t assess some students or maybe we do assess but in a very different way than some of the more mathematical students. This latter comment brings me to my last point of reflection, Assessment.

                Why do we assess? As a teacher, I assess my students for a few reasons. Firstly, to allow me to see where the common misconceptions and areas of weakness are so that I may plan my subsequent lessons and any intervention that needs to take place. Secondly, so that my students can identify their own strengths and weaknesses and then hopefully go away and revise the areas that they have not performed so well on. Thirdly, to use the assessments as a benchmark to monitor progress of my students. As I have already alluded to in previous paragraphs, can assessment be more of a hindrance to some students than it is a useful tool? For some students (mostly the less able mathematicians), lots of assessments can just mean another opportunity to show how much they don’t know and quite often they demonstrate who does not possess Claxton’s four R’s. For these students, no amount of assessing and highlighting areas for improvement will encourage them to be independent learners or even reciprocal learners. In this case, I go back to my previous question. Should we assess all students? And if we should assess all students, should we consider how we assess a little more so that assessments are more sympathetic to the learners’ abilities and needs? As teachers we hope to help our students to make at least three levels of progress between Key stage 2 and 4, and in Mathematics this means that we need to teach our students specific skills and how to answer specific questions that will be asked on the GCSE paper that determines a grade, which determines if the minimum of three levels of progress has been made. This means our regular internal assessments need to test our students’ ability to recall these skills and apply them in an examination situation. Consequently, even now as I consider my own questions, I wonder how as individual teachers and schools, we can move away from the current model of skill testing test papers if the national benchmarking test is a paper that assesses the ability to recall, use and more now than ever before, but apply said skills. The new Mathematics GCSE is designed to assess understanding and application more than just the recall of skills. This is a pleasing turn of events since the examination focusses on students being able to recall, use and apply, which will only help students in the real world once they leave education. However, from a school teacher’s perspective, the new GCSE is very demanding of the lower ability students and causes a concern that these students will only end up failing more than they do currently. Once again, I revisit my question of ‘does one size fit all?’

                I could sit and ponder these questions and many more for a considerable period of time, but to conclude I will say this: under the current educational system in the UK, teachers can only do the best by their students if they teach in a manner appropriate to the students before them, adapting their practice as they go; assess the students within the guidelines of the examination that we are working towards but in a style that does not demean or deflate the learners; use the information highlighted by the assessment to ensure that students make progress; guide students to reflect on their own learning in terms of approach and performance; help students to become resilient, resourceful, reflective and reciprocal; encourage students to give their best and above all help students to become confident, competent, good learners and better young adults both in school and once they leave.

Measuring Performance

This is really just a test to see that it all works as it should. Some initial thoughts.......
Does assessment and measuring performance hamper learning????

Schools are measured based on pupil performance at GCSE, A Level etc... As a result schools are under a whole lot of pressure to perform (get the grades out of the students), which in itself is wrong. Shouldn't we as educators be wanting to educate students? to give them a thirst for knowledge? to help them achieve THEIR potential? It seems we as educators may want to do that but are potentially driven more by the need to get above a certain percentage of A*-Cs. I digress!

Schools are under pressure to perform - teachers are therefore under pressure to perform (lessons can become exam driven) - kids are therefore under pressure to perform (get stressed, turned off because they are bored/ anxious/ not interested in the subject/ don't see the point because they don't want to do that subject) - teachers get cross/ stressed and therefore put more pressure on students - pupils get more stressed and back away even more - teachers get more .......

I could go on but I think we all understand what I'm getting at! If schools weren't measured on the number of A*-C then perhaps there would not be so much need to constantly assess in a test format. Perhaps lessons would become more pupil driven and therefore lessons would become more engaging, which hopefully means students would want to learn. If you could afford to go off piste and go into greater detail on a topic then perhaps we would inspire students to do some indepenedent research, which may encourage them to study further. If lessons were more about 'how' are we going to learn this and 'why' is this useful to you as an individual, then perhaps students would learn better and want to learn more.

If the brain values emotions more than higher order thinking and learners make emotional connections when there is a purpose to the subject that they have set, then surely our learners should be interviewed about their ambitions, strengths, desires and abilities (to do or not to do) before they are told that they have to do GCSEs in certain subjects?

I have lots of other questions, some rhetorical, some not. I do just feel that the education system is trying to be lots of different things and perhaps the current model is not what is best for everybody.

Why one state school and not different types that are aimed at different types of learners with different strengths?
Why at least 3LOP?
Why is English and Maths so important when not every child will need either subject (in the way they are studied for GCSE)?

Since learning is a different thing for different people at different times, should there be one size fits all?