My ‘Classroom Behaviour Management’ strategies have been fashioned by my experiences as a corporate trainer and by the educational values inculcated in me by my parents and grand-parents. It is an on-going learning process influenced by cultural values, experiences – both good and bad, opinions of theorists, etc. The most important thing I’ve had to remember at all times is ‘that one size does not fit all’ i.e. strategies will change depending on each individual student and it is important to be fair at all times however angry I am with a situation.
I have used Skinner’s ‘The ABC’s of Behavioural Learning’ theory to understand the importance of basing consequences of behaviour on antecedents or past influences. I have used Professor Ramon Lewis’ categorisation of students based on their behaviour because it helps me to know how to change their actions. The basis for such behaviour is explained by me using Rudolph Dreikur’s theory.
What is classroom behaviour management?
A teacher would answer by saying, “Classroom Behaviour Management is when I can have one day of productive class work without facing any form of defiance from my students”. Or as Cruickshank, Jenkins and Metcalf (2005) said, “…teachers are expected to be good classroom managers. Administrators often equate control of students with good teaching”. But, that as we know is ‘wishful thinking’ and is ‘undemocratic’ and ‘unfair’ to students.
For me, “Classroom Behaviour Management is the effective use of different behavioural theorists’ strategies in day-to-day learning situations so as to ensure that disruption within and without the classroom is averted”. This is done to ensure a positive learning environment for all students.” Or as Marsh C, (2008) says, “The over-arching skill is to be able to recognise what is happening in the class and to be able to use coping strategies that are needed immediately, before major problems arise.”
As a pre-service teacher I have faced behavioural problems ranging from excessive talking, tardiness and culture-based remarks. A comprehensive way of representing them is to cite Charles, 2004 and Remboldt, 1998 who have categorised them as:
•aggression
•immoral acts
•defiance of authority
•disruptive behaviour
•off-task behaviour
In Australian primary schools, Australian researchers have stated that the most common “troublesome student behaviours are
•students being easily distracted
•students not listening to directions
•students talking out of turn
•students hindering other students” (McDonald & Wilks 1994; Little 2005; Edwards & Watts 2004)
Previously, I asked myself, “Why should I concentrate on classroom misbehaviour”? “Why can I not think about surviving through each hour of the day - of the term”? I gawked at the research done by behaviour management theorists. I even wondered at the feasibility of some theories. “Why are researchers looking into these aspects of classroom behaviour management”?
I believe it has to do with the doors education opens for people. My parents told me “education is the means to a better life”. In India, for every one job there are 10,000 or even more applicants. When I applied for my first job in 2001 as a ground staff at the Chennai airport, there were 8000 applicants for 4 vacancies. I got the job because of my communication skills and my Master of Tourism Administration degree. In India, we believe education helps us to improve the country’s economic and our living standards.
However, if students face the problems that are cited above, then they will discontinue their education. Marsh C, 2008 says “Teacher drop-out rates in some education systems are increasing and, to a large extent, teachers seem to be leaving because of negative behaviour experiences that they have had with specific students”.
It’s important we understand and use the strategies to prevent classroom misbehaviour so that students as well as teachers remain in the educational system. These strategies are not mere ‘spouted hot air’ but are ‘tools to increase learning’. As I said earlier, ‘education is a door to a better life’ and it’s my ‘Duty of Care’ to ensure that all students have the opportunity to find that ‘door’.
It’s important to address behavioural issues in the classroom since unresolved issues can result in resentment. However, how can I handle them? Are there positive conflict resolving techniques? How can I not fall into the trap of using sarcasm and aggression?
DeCecco & Richards, 1974 state “Studies have shown that most conflicts among students are usually not effectively resolved”. Behavioural theories help a teacher to resolve issues effectively. These theories help to reduce ‘unproductive classroom time’ or ‘off-task behaviour’ (Marsh C, 2008). Marzano, Marzano & Pickering, 2003 state “effective management techniques can enable classes of students to achieve at up to 20 percentile points higher than classes where effective management techniques are not employed”. Infantino and Little, 2005 note “up to 76 per cent of secondary school teachers’ time in Australia is taken up with controlling the disruptive behaviour of students and therefore greatly reducing the on-task time available”.
As a teacher, I need to ensure that controllable factors are addressed before using behavioural theories to handle ‘off-task behaviour’ (Marsh C, 2008). The three controllable factors are:
(Source: Bull and Solity, Classroom Management: Principles to Practice, 1987, Taylor and Francis Books Ltd.)
I believe the impact of ‘Behavioural Theories’ in decreasing ‘off-task behaviour’ (Marsh C, 2008) and increasing ‘on-task behaviour’ (Marsh C, 2008) can be figuratively shown as follows:
How are students categorised in terms of behavioural issues? Is it fair to categorise them?
Lewis R, 2010 says there are four categories of students:
It's important I recognise student behaviour categories. I use them to improve students’ classroom behaviour and to not label my students based on the categories. Also, I know when to back-off with a Category D student. I will explain ‘why it’s important’ later on.
Knowing the student categories has helped me to use Professor Ramon Lewis’ strategies for each category. Instead of re-inventing the wheel, I have been able to incorporate his strategies and turn students away from messy situations.
Why should one understand Skinner’s the ABC’s of Behavioural Learning Theory to be fair with handling behavioural issues?
Skinner M, 1950 the ABC’s of Behavioural Learning Theory helps me look closer at the antecedents of a behavioural issue rather than just the behaviour. Carolyn Orange, 2000 in “25 Biggest Mistakes Teachers Make and How to Avoid Them” says “Alas, words and deeds that cut deep to the tender core of the inner self, leave scars on the soul that can last a lifetime”.
Often, we refuse to look at what caused a behaviour to be manifested. Instead we punish students with consequences based on the behaviour. Skinner M, 1950 stated there are antecedents that will influence a student’s behaviour in a classroom. Based on those antecedents, we as teachers need to choose the consequences for the behaviour. I would represent this as follows:
Skinner M, 1950 referred to ‘motives’ as ‘Antecedents’. I have quoted Rigby, 1996 to elaborate on them. Skinner M, 1950 stated ‘Antecedents’ will influence the ‘Behaviour’. I have quoted Marsh C, 2008 to elaborate on the possible behaviours. For ‘Consequences’, I have quoted those used in Banyule Primary School.
I like what Mrs. Sharon Marmo – Principal and Miss. Selena Varghese – Mentor/Preparatory Teacher say, “Never let the consequences go outside your classroom”. In other words, ensure your students never have to go into another classroom or to a higher authority.
As a teacher, it is important that I get to the crux of an issue. It’s easier to do this in Australia than in India where there are 60 students in each class. Here I can provide ‘one-on-one support’ to my students. So, if there were disruptive behaviour in the class, I can find out what instigated that behaviour.
While volunteering at Banyule Primary School, two Preparatory students were disrupting the numeracy group by laughing loudly. It was the last day of the term and they were looking forward to the term-break. But this was preventing other students from working effectively. I knew I had to handle this. I remembered what my lecturer, Mr. Greg Powell said, “Students will go where their belongings are”. I moved one of the student’s things away. Lo and behold, he moved and got down to working on the activity. I based the consequence on the students’ actions but kept in mind what was causing the behaviour – the fact that they were going on term-break.
As teachers it is important we never base our strategies on a misguided judgement of children. Every child should be given the ‘benefit of the doubt’ and given a clean record every day, every week, every month and every year. Also, as teachers we need to remember Irving & Martin, 1982 statement, “Correction of every misbehaviour is not necessary”.
What is Dreikur’s Theory? How can I use this theory to improve classroom atmosphere so as to introduce a positive learning environment?
Knowing Skinner M’s, 1950 theory helps us to concentrate on the impetus/antecedent. Dreikur R, 1968 explains this very well by stating “all misbehaviour reflects children’s decision about how they can most effectively belong to, or be recognised by the group”. So, students will behave based on how they feel about their role in their groups. If a student is comfortable with his/her group, he/she will actively participate in class without exhibiting ‘behavioural issues’. However, if a student were to feel isolated or unaccepted by his/her peers, he/she will exhibit behaviour that will garner attention.
Dreikur’s theory is apt in today’s world where everyone looks for acceptance by peers. For this, students will exhibit behaviour such as - causing disturbances in class, not turning in home work, refusing to take part in class activities, questioning teachers, etc.
As a teacher I need to channel their need to be accepted into positive behaviour. This can be done by following Dreikur’s theory:
(SOURCE: Lewis, R. (2010). EDU4PIB [Lecture Notes]. Melbourne, Australia, La Trobe University, Faculty of Education)
SM is a student at MacLeod College. From my first day of practicum, she questioned everything that I did. She was disruptive in class and even bit her classmate once. At first I could not understand her behaviour. However, talks with her made me realise this was based on a need to be accepted by her peers and teachers.
I noticed SM’s talent for the written medium when I read her essay. I got her to take part in an ‘Essay writing’ competition organised by the Darebin City Council. I cannot say I have made great in-roads into improving her behaviour in class, but it is a first step. My hope is that she will realise her true potential and will channel her energy into improving her skills for the future.
It’s good that I fought my first impulse to ‘throw in the towel’ and walk out of that classroom. For three weeks now I have worked with SM and her classmates. The first step to breaking SM’s barrier was to not give up on her. When she noticed that I did not judge her, she began talking to me about her family, the place where she stays, how unsafe she feels, etc. Also she showed me her ‘personal essays’. I encouraged her to concentrate on her talents.
However, I have done nothing about changing her mode of learning or her assessment activities. I realise I need to collect data about SM’s ‘mistaken’ goals so that along with my mentor teacher I can talk to her about realising her ‘primary’ goal. This will help her to improve her learning skills.
When should I give up as a teacher? Why is it important for me to know when to give up and step back from a behavioural situation?
Erik Erikson, 1963 warns that “unhealthy resolution of a developmental crisis can affect a person later in life”. Inspite of this, it’s important for me to know when to step back instead of getting too involved with students’ behaviour. I tell myself I cannot be their ‘buddy’ and I’ve a ‘life of my own’ too.
As a university guest lecturer in India, I had to mediate between two warring student factions. The situation got out-of-hand when two students lost their tempers and hurled abuses at each other. My first instinct was to step between them. But a stronger sense of self-preservation prevented me from doing that. Instead, I changed my tone of voice and told them they could take their fight outside the university if they did not know how to behave like adults. The situation could have accelerated and turned ugly. However it did not because I knew when to take a ‘step back’.
Any harm to other students or to me always rings bells in my mind. This is based on my understanding of the ‘Duty of Care’ towards students and to me. The decision to ‘let go’ has to be taken by each teacher some time in his/her life. This is based on the impact of the behaviour on students, other teachers and the teacher himself/herself, as stated in the VELS ‘Duty of Care’.
Conclusion
‘Classroom Behaviour Management’ is an on-going process that changes based on students, classroom environment, educational policies, social understanding of educational management, etc. As a teacher, I believe I cannot learn all the strategies. However, I can implement them based on my students’ requirements.
I will work on improving the learning standards and environment in my classroom. I will not be condescending with my students. It is important that when I use behavioural strategies I remember that each student is an individual and I would have to tailor them to suit each student.
Teaching’s a long and winding road that I have decided to take. There will be positive and negative moments, but I will continue to learn so that I can do my utmost. I will ensure my students get the best out of me. And as I said earlier, ‘Classroom Behaviour Management’ strategies are not ‘hot air’ but ‘stepping stones’ to a better classroom environment that will ensure learning happens.
My 'Buddha' Moment
This blog captures my Buddha moment: a 'journey of enlightenment' into the tools that will help me facilitate knowledge instead of just teaching.
Wednesday, May 4, 2011
Wednesday, April 20, 2011
‘Mathematical Philosophy’ - My beliefs on how to teach mathematics effectively
Mathematics is “not my cup of tea.” It was irritating to know that I would have to sit through a series of lectures that would improve my skills in teaching mathematics. My first thought was that I wouldn’t learn much from the lectures. How wonderfully wrong I was!
Mathematics is defined as ‘the study of the measurement, properties and relationships of quantities and sets, using numbers and symbols. (n.d. 2004) This definition is a classic example of people’s notion about mathematics – boring, scarey and only for ‘super-brains’.
For countless generations, “mathematics teaching and learning practices…centre on memorisation of facts, and practice of pre-set meaningless procedures, which promote a view of mathematics as lacking creativity, imagination, or critical thought.” Sandra, F., and Len, Sparrow,. (2007).
It was expected of students to not only learn by rote the times tables and equations but also to work on algorithms without really understanding the logic or reason behind what they were doing. Students were not allowed to ask questions as to why they learnt what they learnt and why there was no other way to do what they did. Any questions were either met with stoic silence or a curt ‘it’s always done this way’ remark. This was how I learnt mathematics during my primary as well as secondary education. No wonder, by the time I reached Higher Secondary, I didn’t understand anything about what I was doing in class.
I believe I would have continued hating mathematics if it weren’t for my tenth grade teacher who inspite of limited resources and no access to the latest teaching methodologies, still attempted to make math interesting, logical and realistic. I learnt more about area, time, angles and space from him than I ever did from all the other mathematics teachers both in primary as well as secondary school.
Marilyn Frankenstein has summarised several other people’s and my perception of mathematics in her article ‘Mathematics Anxiety: Misconceptions about Learning Mathematics’. She said that the features of current maths curricula are as follows:
- rote calculations
- memory dependence
- unmotivated exercises
- spurious applications of calculation strategies
- authoritarianism in mathematics education
- tests which assume mathematics can be divided into tiny water-tight compartments
(Frankenstein, M., (1989). pp. 183 – 186)
There are certain questions teachers will have to answer before understanding the teaching methodologies for mathematics and they are:
- Who are our students?
- What are their requirements?
- What are their skill sets?
- What are the learning tools available to them?
- How do they like to study?
- How are they influenced?
- What are the methodologies in which they can be taught?
- How would these methodologies help them?
Before we focus on the current teaching methodologies and resources available to pre-service mathematics teachers, it is of primary importance that we focus on who our students are. Times have changed and it does not make sense to live in the past. We as teachers need to understand whom we are teaching if we have to improve our methodologies.
Though most teachers would not like what I am about to say, I will have to emphasise that we need to look at teachers as ‘knowledge service providers’ and our students as ‘end-users’ or ‘customers’. I am well aware of education being a noble profession but I prefer to think of it as any other industry for quality management purposes. Like all industries governed by the 6 Sigma and Lean Toyota project for service and quality assurance, we will have to make changes to service levels so as to assure quality levels are effectively managed.
Our students are our customers and their world is very different from the one that we live in or grew up in. I liked what Sir Ken Robinson said in a Youtube video played during an Issues lecture, “what are we educating them for?” Their world is changing faster than our own. It is more multi-cultural, multi-lingual and global than ours. Beare predicts the future world of our students in his paper on “From an old world-view to a new” by looking at various factors such as demographics, economic growth, environment, consumer patterns, impacts of consumerism, resource availability, etc in the future. (Beare, 2001, pp. 11-17).
Based on Beare’s statement it is possible to understand that ‘the nature of what is to be studied has also changed’. (Booker, G., Bond, Denise., Sparrow, Len., Swan, Paul.,. (2010). p. 7). There are several reasons why students will have to be proficient in numeracy. These external reasons are as follows:
- intellectual advancement in several arenas requiring an understanding of numbers and their functions
- technological growth both in infrastructural and cyber development
- economical instability requiring better understanding of market figures and functions
- environmental degradation that requires numerical knowledge of replantation and natural resources management systems to circumvent the negative impacts
These are just a few areas where mathematics will play a major role in the future lives of our students. However, as teachers, we will have to ensure that students understand the pervasiveness of mathematics in all walks of life, i.e. ‘an innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg’s time’ (Steen, 1997)
Students learn differently from before. They have access to better learning management systems and the world of knowledge is literally at their finger tips. Everything that has been discovered or is in the process of being discovered is available to them at the touch of a finger tip. As teachers, we will have to improve our technical skills so that we can use the same tools as our students to teach numeracy.
There is a process to follow when teaching mathematics as stated by Alistair McIntosh in ‘When will they ever learn?’ (McIntosh, A., (1977).) These can be enumerated on as follows:
- Don’t start formal work too early: “It is the experience of many good teachers…it is found to be unnecessary before the sixth year has passed…to do any formal Arithmetic on slates” (Reports, 1895/6)
- Use learning materials and start from practical activities: “…examples of any kind upon practical numbers are of very little use, until the learner has discovered the principle from practical examples.” (Margaret Brown, 1977, p. 10)
- Give children problems and freedom initially to find their own methods of solutions: “If a child be requested to divide a number of apples among a certain number of persons, he will contrive a way to do it, and will tell how many each must have.” (Margaret Brown, 1977, p. 10)
- Children must have particular examples from which to generalise: “When the pupil learns by means of abstract examples, it very seldom happens that he understands a practical example the better for it; because he does not discover the connexion until he has performed several practical examples, and begins to generalise them.” (By a teacher of youth, 1840, p. IV)
- Go for relevance and the involvement of the child: “When children explore for themselves they make discoveries…” (Curriculum Bulletin No.1, 1965, p. 1)
- Go for reasons and understanding of processes. Never give mechanical rules: “…when children obtain answers to sums and problems by mere mechanical routine, without knowing why they use the rule…they cannot be said to have been…well versed in arithmetic.” (Margaret Brown, 1976, p. 16)
- Emphasize and encourage discussion by children: “When children explore for themselves, they make discoveries which they want to communicate to their teacher and to other children and this results in frequent discussion. It is this changed relationship which is the most important development of all.” (Curriculum Bulletin No. 1, 1965, p. 1)
- Follow understanding with practice and applications: “When the pupil learns…he does not discover the connexion until he has performed several practical examples, and begins to generalise them.” (By a teacher of youth, 1840, p. IV)
There are various methodologies for teaching mathematics and they depend on what is being taught. I would prefer to use the same teaching process as the one I used when teaching literacy to young adults/mature age students in India. I will start each lesson with a ‘Lead In’ activity that gives students an idea/clue of what the day’s lesson is all about. Based on this clue/hint, there is the ‘Mathematics for Gist’ activity that focuses on a broad over-view of the topic. The next ‘Mathematics for Specifics’ activity focuses on the appropriate area of learning for that particular day. The learning acquired is then determined on a daily basis through ‘Post specifics-activity tasks’. The assessment/work-sheet will help me to gauge the learning curve of each student in the class.
The one lesson that comes to my mind when thinking about the above process is the one regarding an introduction to algebraic expressions using the ‘Leap Frog’ activity. That was the first time I realised the potential behind teaching mathematics. I had so much fun coming up with the algebraic expression that I realised I would like my students to enjoy learning mathematics too. I had re-discovered the joy of learning mathematics as when I was taught by my favourite mathematics teacher. I believe that it is important for students to move from a general idea to a more specific understanding of the mathematical discipline that is being explored for the day.
Based on what I have just said, I can say that my beliefs are a combination of both ‘Content and clarity’ and ‘Content and understanding’ as stated by Beswick (Beswick, K., 2006, p. 19). I believe it is important to increase my knowledge about the subject. Also, it is important that I should constantly update myself about changes in teaching principles and methodologies. I believe that sequencing of information is important since there is a specific reason why we have been teaching basic algorithms first before moving onto fractions or algebraic expressions. However, I would be glad to hear about alternative solutions from students as well as teachers. I do know that students might not know everything and there will be times when the answers will have to be given to them.
I believe that it is mandatory that ‘pupils are aware of different methods of calculation and are able to choose methods in relation to their effectiveness and efficiency in solving a problem’ (Askew, M. et al, n.d). It is important that I emphasise ‘the complementary nature of teaching and learning and valued classroom activity, which involved pupils working together with other pupils and teachers to overcome difficulties and to reach shared understanding’ (Askew, M. et al, n.d).
The road to being an efficient and effective Mathematics teacher involves self-discovery, self-learning and self-proficiency. If this will enable even one student to love Mathematics and discover maybe the greatest ‘Primary Number’ or even a new method for teaching ‘Mathematics’ then I am willing to make the required changes. Hopefully no student of mine will ever dream about “the final test involves escaping from a nightmare, which is depicted as a lifetime of mathematics problems written on a blackboard” (Swan, Paul., 2004, p. 501) and instead will learn to love this subject as much as I have come to love it.
Mathematics is defined as ‘the study of the measurement, properties and relationships of quantities and sets, using numbers and symbols. (n.d. 2004) This definition is a classic example of people’s notion about mathematics – boring, scarey and only for ‘super-brains’.
For countless generations, “mathematics teaching and learning practices…centre on memorisation of facts, and practice of pre-set meaningless procedures, which promote a view of mathematics as lacking creativity, imagination, or critical thought.” Sandra, F., and Len, Sparrow,. (2007).
It was expected of students to not only learn by rote the times tables and equations but also to work on algorithms without really understanding the logic or reason behind what they were doing. Students were not allowed to ask questions as to why they learnt what they learnt and why there was no other way to do what they did. Any questions were either met with stoic silence or a curt ‘it’s always done this way’ remark. This was how I learnt mathematics during my primary as well as secondary education. No wonder, by the time I reached Higher Secondary, I didn’t understand anything about what I was doing in class.
I believe I would have continued hating mathematics if it weren’t for my tenth grade teacher who inspite of limited resources and no access to the latest teaching methodologies, still attempted to make math interesting, logical and realistic. I learnt more about area, time, angles and space from him than I ever did from all the other mathematics teachers both in primary as well as secondary school.
Marilyn Frankenstein has summarised several other people’s and my perception of mathematics in her article ‘Mathematics Anxiety: Misconceptions about Learning Mathematics’. She said that the features of current maths curricula are as follows:
- rote calculations
- memory dependence
- unmotivated exercises
- spurious applications of calculation strategies
- authoritarianism in mathematics education
- tests which assume mathematics can be divided into tiny water-tight compartments
(Frankenstein, M., (1989). pp. 183 – 186)
There are certain questions teachers will have to answer before understanding the teaching methodologies for mathematics and they are:
- Who are our students?
- What are their requirements?
- What are their skill sets?
- What are the learning tools available to them?
- How do they like to study?
- How are they influenced?
- What are the methodologies in which they can be taught?
- How would these methodologies help them?
Before we focus on the current teaching methodologies and resources available to pre-service mathematics teachers, it is of primary importance that we focus on who our students are. Times have changed and it does not make sense to live in the past. We as teachers need to understand whom we are teaching if we have to improve our methodologies.
Though most teachers would not like what I am about to say, I will have to emphasise that we need to look at teachers as ‘knowledge service providers’ and our students as ‘end-users’ or ‘customers’. I am well aware of education being a noble profession but I prefer to think of it as any other industry for quality management purposes. Like all industries governed by the 6 Sigma and Lean Toyota project for service and quality assurance, we will have to make changes to service levels so as to assure quality levels are effectively managed.
Our students are our customers and their world is very different from the one that we live in or grew up in. I liked what Sir Ken Robinson said in a Youtube video played during an Issues lecture, “what are we educating them for?” Their world is changing faster than our own. It is more multi-cultural, multi-lingual and global than ours. Beare predicts the future world of our students in his paper on “From an old world-view to a new” by looking at various factors such as demographics, economic growth, environment, consumer patterns, impacts of consumerism, resource availability, etc in the future. (Beare, 2001, pp. 11-17).
Based on Beare’s statement it is possible to understand that ‘the nature of what is to be studied has also changed’. (Booker, G., Bond, Denise., Sparrow, Len., Swan, Paul.,. (2010). p. 7). There are several reasons why students will have to be proficient in numeracy. These external reasons are as follows:
- intellectual advancement in several arenas requiring an understanding of numbers and their functions
- technological growth both in infrastructural and cyber development
- economical instability requiring better understanding of market figures and functions
- environmental degradation that requires numerical knowledge of replantation and natural resources management systems to circumvent the negative impacts
These are just a few areas where mathematics will play a major role in the future lives of our students. However, as teachers, we will have to ensure that students understand the pervasiveness of mathematics in all walks of life, i.e. ‘an innumerate citizen today is as vulnerable as the illiterate peasant of Gutenberg’s time’ (Steen, 1997)
Students learn differently from before. They have access to better learning management systems and the world of knowledge is literally at their finger tips. Everything that has been discovered or is in the process of being discovered is available to them at the touch of a finger tip. As teachers, we will have to improve our technical skills so that we can use the same tools as our students to teach numeracy.
There is a process to follow when teaching mathematics as stated by Alistair McIntosh in ‘When will they ever learn?’ (McIntosh, A., (1977).) These can be enumerated on as follows:
- Don’t start formal work too early: “It is the experience of many good teachers…it is found to be unnecessary before the sixth year has passed…to do any formal Arithmetic on slates” (Reports, 1895/6)
- Use learning materials and start from practical activities: “…examples of any kind upon practical numbers are of very little use, until the learner has discovered the principle from practical examples.” (Margaret Brown, 1977, p. 10)
- Give children problems and freedom initially to find their own methods of solutions: “If a child be requested to divide a number of apples among a certain number of persons, he will contrive a way to do it, and will tell how many each must have.” (Margaret Brown, 1977, p. 10)
- Children must have particular examples from which to generalise: “When the pupil learns by means of abstract examples, it very seldom happens that he understands a practical example the better for it; because he does not discover the connexion until he has performed several practical examples, and begins to generalise them.” (By a teacher of youth, 1840, p. IV)
- Go for relevance and the involvement of the child: “When children explore for themselves they make discoveries…” (Curriculum Bulletin No.1, 1965, p. 1)
- Go for reasons and understanding of processes. Never give mechanical rules: “…when children obtain answers to sums and problems by mere mechanical routine, without knowing why they use the rule…they cannot be said to have been…well versed in arithmetic.” (Margaret Brown, 1976, p. 16)
- Emphasize and encourage discussion by children: “When children explore for themselves, they make discoveries which they want to communicate to their teacher and to other children and this results in frequent discussion. It is this changed relationship which is the most important development of all.” (Curriculum Bulletin No. 1, 1965, p. 1)
- Follow understanding with practice and applications: “When the pupil learns…he does not discover the connexion until he has performed several practical examples, and begins to generalise them.” (By a teacher of youth, 1840, p. IV)
There are various methodologies for teaching mathematics and they depend on what is being taught. I would prefer to use the same teaching process as the one I used when teaching literacy to young adults/mature age students in India. I will start each lesson with a ‘Lead In’ activity that gives students an idea/clue of what the day’s lesson is all about. Based on this clue/hint, there is the ‘Mathematics for Gist’ activity that focuses on a broad over-view of the topic. The next ‘Mathematics for Specifics’ activity focuses on the appropriate area of learning for that particular day. The learning acquired is then determined on a daily basis through ‘Post specifics-activity tasks’. The assessment/work-sheet will help me to gauge the learning curve of each student in the class.
The one lesson that comes to my mind when thinking about the above process is the one regarding an introduction to algebraic expressions using the ‘Leap Frog’ activity. That was the first time I realised the potential behind teaching mathematics. I had so much fun coming up with the algebraic expression that I realised I would like my students to enjoy learning mathematics too. I had re-discovered the joy of learning mathematics as when I was taught by my favourite mathematics teacher. I believe that it is important for students to move from a general idea to a more specific understanding of the mathematical discipline that is being explored for the day.
Based on what I have just said, I can say that my beliefs are a combination of both ‘Content and clarity’ and ‘Content and understanding’ as stated by Beswick (Beswick, K., 2006, p. 19). I believe it is important to increase my knowledge about the subject. Also, it is important that I should constantly update myself about changes in teaching principles and methodologies. I believe that sequencing of information is important since there is a specific reason why we have been teaching basic algorithms first before moving onto fractions or algebraic expressions. However, I would be glad to hear about alternative solutions from students as well as teachers. I do know that students might not know everything and there will be times when the answers will have to be given to them.
I believe that it is mandatory that ‘pupils are aware of different methods of calculation and are able to choose methods in relation to their effectiveness and efficiency in solving a problem’ (Askew, M. et al, n.d). It is important that I emphasise ‘the complementary nature of teaching and learning and valued classroom activity, which involved pupils working together with other pupils and teachers to overcome difficulties and to reach shared understanding’ (Askew, M. et al, n.d).
The road to being an efficient and effective Mathematics teacher involves self-discovery, self-learning and self-proficiency. If this will enable even one student to love Mathematics and discover maybe the greatest ‘Primary Number’ or even a new method for teaching ‘Mathematics’ then I am willing to make the required changes. Hopefully no student of mine will ever dream about “the final test involves escaping from a nightmare, which is depicted as a lifetime of mathematics problems written on a blackboard” (Swan, Paul., 2004, p. 501) and instead will learn to love this subject as much as I have come to love it.
What power do I use as a teacher?
This morning I was speaking to my sister and she told me about an incident in a school at Geelong. An Indian boy, now aged 6 years, had been enrolled in a school at Geelong last year. The boy’s completed his kindergarten at an International school in Bangalore, India. His communication skills, numeracy understanding and literary skills are commendable for a child of his age. However, his parents have seen a marked decline in his social skills a year after joining this school. Though he was commended for his ability to take on leadership roles at his former school, they have been made aware of his unwillingness to interact with his peers or with his teachers. It was only after several sessions with the parents and a teacher from his current grade that they got to know about an incident that had happened last year in the school. The boy not knowing the exact words for excusing himself had wet his pants while in class. Not only did the teacher pull him up before the entire class for this but also asked him “Is this what you do in your culture in your country?”
I am placing my indignation aside and wondering what would I have done if I had been the teacher? How would I have handled the situation? Which power that I have would I have used? This is a situation that requires tact and skill at drawing attention away from the boy’s embarrassment. Do I have the knowledge and the expertise required to do this?
I am aware that the most relevant of all the powers to be used here would be referent power. However, how would one use the right words and actions to make this boy feel less awkward or guilty? How would one draw the other students’ attention away from a situation like this? And how much time did his former grade teacher have to build rapport and understanding with the boy?
I really would like input on this since I am desperately trying to help this boy get back his confidence and love of learning that he had before. I am trying to do what Jaime Escalante would have done, i.e. help a student believe in himself once again though the odds seem stacked against him.
I am placing my indignation aside and wondering what would I have done if I had been the teacher? How would I have handled the situation? Which power that I have would I have used? This is a situation that requires tact and skill at drawing attention away from the boy’s embarrassment. Do I have the knowledge and the expertise required to do this?
I am aware that the most relevant of all the powers to be used here would be referent power. However, how would one use the right words and actions to make this boy feel less awkward or guilty? How would one draw the other students’ attention away from a situation like this? And how much time did his former grade teacher have to build rapport and understanding with the boy?
I really would like input on this since I am desperately trying to help this boy get back his confidence and love of learning that he had before. I am trying to do what Jaime Escalante would have done, i.e. help a student believe in himself once again though the odds seem stacked against him.
An imaginative approach to learning
What would a person do if he/she were to win the lottery? Or, what would a child do if he/she were to get a box with the most fantastic toys imaginable in it? I guess that’s how I feel right now.
I have been reading ‘An Imaginative Approach to Learning’ by Egan and I feel like I have discovered a treasure trove. In this article are tools that are extremely useful for teaching English to Speakers of Other Languages.
It was an eye-opener to see how I could use tools such as stories, metaphors, binary opposites, rhyme, rhythm and pattern, jokes and humour, mental imagery, gossip (yes ‘gossip’), play and mystery to teach not only the usage of the language but also the use of the language.
I hope to use these tools in my country since it is of primary importance that students are comfortable with ‘oral skills’ before they can move onto learning the ‘theory’ behind the language. Egan says in this article “No one learns to speak alone – or to read and write or to think using theoretic abstraction”. I have always believed that students should be involved in group activities since two minds or more are better than just one. Egan says that learning occurs through shared knowledge or activities.
Also, he says “Be suspicious of the simple claim that young children and people in oral cultures are ‘concrete thinkers.” I have believed that it is important for students to use their imagination as much as possible so that they can improve their communication skills.
There’s so much that a student can learn by narrating a story or discovering the joy of writing a poem, or even creating a play that is a spoof of the latest movie that he/she has seen.
Where would we be if people hadn’t questioned the phenomena that occur in our planet everyday? I am looking forward to asking my students to write out their own story about ‘their’, ‘there’ and ‘they’re’. Who knows, maybe, I will have the next George Lucas or Luciano Pavarotti in my class?
I have been reading ‘An Imaginative Approach to Learning’ by Egan and I feel like I have discovered a treasure trove. In this article are tools that are extremely useful for teaching English to Speakers of Other Languages.
It was an eye-opener to see how I could use tools such as stories, metaphors, binary opposites, rhyme, rhythm and pattern, jokes and humour, mental imagery, gossip (yes ‘gossip’), play and mystery to teach not only the usage of the language but also the use of the language.
I hope to use these tools in my country since it is of primary importance that students are comfortable with ‘oral skills’ before they can move onto learning the ‘theory’ behind the language. Egan says in this article “No one learns to speak alone – or to read and write or to think using theoretic abstraction”. I have always believed that students should be involved in group activities since two minds or more are better than just one. Egan says that learning occurs through shared knowledge or activities.
Also, he says “Be suspicious of the simple claim that young children and people in oral cultures are ‘concrete thinkers.” I have believed that it is important for students to use their imagination as much as possible so that they can improve their communication skills.
There’s so much that a student can learn by narrating a story or discovering the joy of writing a poem, or even creating a play that is a spoof of the latest movie that he/she has seen.
Where would we be if people hadn’t questioned the phenomena that occur in our planet everyday? I am looking forward to asking my students to write out their own story about ‘their’, ‘there’ and ‘they’re’. Who knows, maybe, I will have the next George Lucas or Luciano Pavarotti in my class?
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