My little challenging group of year 10's can be quite difficult to engage at times. A real issue with their maths is getting them to read the question effectively. Completely out of character, they have loved exercises in the book Logic Mysteries by Jane Molnar. Although it misleadingly states grade 3-5 on the cover, the year 10 students have loved the idea of reading these problems and solving them. When I first introduced it, I abandoned the rest of my normal planned lesson as I had not seen these students this enthused and engaged since the algebra topic.
Each mystery has a story and is solved by eradicating options that do not exist. A grid is set up to record the findings as they go through the mystery.
Many great mathematical concepts can be investigated. For instance complementary events become obvious, if she has a bird - all the options in the bird column that are boys can be eradicated. Inequalities can be investigated through clues like Jane's age is less than Mary's. Sets can be investigated through concepts like Mary's item fits in a school bag... and so on..
The main thing is that it requires the students to read the clues that are not necessarily in order, requiring reading and re-reading until they are all done.
A similar book Quizzles or More Quizzles by Wayne Williams has proven very successful with my upper class of year tens. These logic puzzles are multi dimensional and can be quite difficult so be warned!
For these to be successful I invited students to attempt them themselves for 5 minutes then modelled how to complete a problem. Then the following day I gave another problem at the start of class.
Either way, improving comprehension and reading ability is more and more important in mathematics (the temptation to enter into a diatribe as to why we need to teach English in maths here is near on irresistible - I shall try though!). These three books have been some of the more enjoyable methods of developing literacy skills thus far.
Sunday, November 9, 2008
Ethical reasoning and streaming
Streaming is a difficult topic as it raises a number of questions regarding student capture, teacher judgement, assessment, and social justice.
Student capture for me is the most critical aspect of a classroom. Capturing a student's interest is a perpetual task, a combination of selling your subject and moving fast enough to keep their interest, yet slowly enough to allow them to fully grasp a subject. For some it can be done through connections with the teacher's personality, others through mathematics success, others through contribution to the class and others by connections with peers. If you can capture a student and get them to consistently have a positive attitude towards your subject then this is the first criteria met for a student to be placed into a difficult mathematics class. Streaming captured students into a class can greatly assist in improving possibility for success.
Teacher judgement is the next criteria. Does the student have the intellectual horsepower to complete the work? No amount of mathematics tutoring will assist a student that has extreme difficulty in reading a question, has too many holes in their skill base or takes too long to understand a new skill. A teacher needs to be able to identify that bit of extra practice that will move the student from being able to use a skill when directed, to be able to apply a skill undirected, to be able to identify the right skill from a range of available skills. It is possible that having to continuously assist a student on a continuous basis will destroy the flow of a class and disadvantage all within it especially in upper range classes.
Assessment is the next criteria. Assessment supports teacher judgement not the other way around. To stream purely on assessment is a recipe for disaster. This is especially true for students riding the end of their ability curve and coasting or loafing. These students, when they hit the wall and finally need to study can be hurt, confused and looking for those to blame for their lack of performance. If these students have not been properly coached before the 'big drop' in results, they can drop morale in a class at a rapid rate. Sometimes (especially in this case or the case where students are having external difficulties) it is best to ignore assessment and use the first two criteria to stream students.
Social justice is the final criteria and it has to be very carefully applied. An injudicious use of social justice to students when streaming will produce weak streams and deprecate the benefits of streaming. Just because a student has a legitimate reason for underperforming does not mean that in time a student will perform. Some say that streaming a class is a social justice issue in itself but watching students being unable to complete work that the rest of the class is working on and suffering self esteem issues or dumbing a class down to the lowest common denominator is not a solution to my mind.
The hardest part of establishing a stream is that it is not an exact science. A student performing at an optimum level with one teacher may not perform at all with another (this is especially true with boys). When creating a stream (especially in small class sizes) team dynamics play a large part - if you can create a team of peers and the teacher anything is possible. It's why I think traditionally the upper classes have been sought after - despite requiring the most skill to make work - they are the ones where there has been most flexibility in construction.
Student capture for me is the most critical aspect of a classroom. Capturing a student's interest is a perpetual task, a combination of selling your subject and moving fast enough to keep their interest, yet slowly enough to allow them to fully grasp a subject. For some it can be done through connections with the teacher's personality, others through mathematics success, others through contribution to the class and others by connections with peers. If you can capture a student and get them to consistently have a positive attitude towards your subject then this is the first criteria met for a student to be placed into a difficult mathematics class. Streaming captured students into a class can greatly assist in improving possibility for success.
Teacher judgement is the next criteria. Does the student have the intellectual horsepower to complete the work? No amount of mathematics tutoring will assist a student that has extreme difficulty in reading a question, has too many holes in their skill base or takes too long to understand a new skill. A teacher needs to be able to identify that bit of extra practice that will move the student from being able to use a skill when directed, to be able to apply a skill undirected, to be able to identify the right skill from a range of available skills. It is possible that having to continuously assist a student on a continuous basis will destroy the flow of a class and disadvantage all within it especially in upper range classes.
Assessment is the next criteria. Assessment supports teacher judgement not the other way around. To stream purely on assessment is a recipe for disaster. This is especially true for students riding the end of their ability curve and coasting or loafing. These students, when they hit the wall and finally need to study can be hurt, confused and looking for those to blame for their lack of performance. If these students have not been properly coached before the 'big drop' in results, they can drop morale in a class at a rapid rate. Sometimes (especially in this case or the case where students are having external difficulties) it is best to ignore assessment and use the first two criteria to stream students.
Social justice is the final criteria and it has to be very carefully applied. An injudicious use of social justice to students when streaming will produce weak streams and deprecate the benefits of streaming. Just because a student has a legitimate reason for underperforming does not mean that in time a student will perform. Some say that streaming a class is a social justice issue in itself but watching students being unable to complete work that the rest of the class is working on and suffering self esteem issues or dumbing a class down to the lowest common denominator is not a solution to my mind.
The hardest part of establishing a stream is that it is not an exact science. A student performing at an optimum level with one teacher may not perform at all with another (this is especially true with boys). When creating a stream (especially in small class sizes) team dynamics play a large part - if you can create a team of peers and the teacher anything is possible. It's why I think traditionally the upper classes have been sought after - despite requiring the most skill to make work - they are the ones where there has been most flexibility in construction.
Labels:
mathematics,
streaming,
teaching
Saturday, November 8, 2008
If that's culture.. you can have it.
Today I sat through Aida. Normally I can handle a little live Opera. I'm sorry, act three of Aida should be classified as grade A torture. Forty minutes to say the army is over there, get caught for treason and be sentenced to being buried alive. Three hours for the whole thing. It felt like forty years.
Want to get someone to talk? Need to know where that bomb has been hidden? Easy peasy.. Stick them in front of that dull as dishwater, repetitive, boring Verde nightmare. By the end of it they would be trying to poke their own eyes out and have their arm buried to the elbows in both ears.
I'd rather eat my own leg off than see it again.
Want to get someone to talk? Need to know where that bomb has been hidden? Easy peasy.. Stick them in front of that dull as dishwater, repetitive, boring Verde nightmare. By the end of it they would be trying to poke their own eyes out and have their arm buried to the elbows in both ears.
I'd rather eat my own leg off than see it again.
Wednesday, November 5, 2008
Teacher turnover, teamwork and classes for 2009
The generation of school spirit comes from the school, focuses through teachers and into students. Harmony between teachers is a key component to the generation of that aura of success in a school.
Part of this is ensuring that there is balance between the needs of students and the needs of teachers. At this time of year tension arises between staff regarding the classes teachers would like to teach to further their careers and what is in the best interests of students. What is in the best interest of students is not always the best option. This takes some courage to say, as it has always been my position that students come first - but I think it is naive to think this is always the case.
In the real world, knowledge management issues of a revolving staff are well documented. When staff leave it does not only cost in terms of vetting and rehiring staff but also in the content knowledge loss, training investment and organisational understanding that is only gained through experience with customers.
Teaching is no different. Reduce turnover and the school benefits. An organisation that considers the needs of staff to progress successfully in their careers is an organisation that cares for its staff. To do this staff members needs to have their progress clearly illustrated and documented.
In mathematics, this means careful consideration of the new level 3 MAT and MAS courses. If there are a number of teachers vying for these classes it may be a number of years before teachers are given access to them. Being offered these classes (or knowing that a course has your name on it two years hence) can be a clear motivating factor in staying with the school and fully embracing PD opportunities until that time.
Conversely not being offered these courses or seeing the courses offered to those 'less worthy' can be a demotivational factor. Similarly being continuously asked to take lower school or low ability senior school classes can be disheartening for those seeking to enhance their skill base or for those seeking rapid promotion.
This ties very close to timetabling as many promotional opportunities rely on staff having access to senior school classes. Timetabling can often make or break the way a teacher sees their classes. Teaching out of area, sharing classes with other teachers, large class sizes, behaviourally 'difficult' classes can all be contributors to negative staff morale.
For a maths team to be successful they have to work as a team, support each other and find new and innovative solutions to student behavioural, content delivery and motivational issues. When class distribution for the following year is being considered, it means that careful thought has to be made as to what will satisfy the majority of the team, motivate members and ultimately prevent turnover.
Part of this is ensuring that there is balance between the needs of students and the needs of teachers. At this time of year tension arises between staff regarding the classes teachers would like to teach to further their careers and what is in the best interests of students. What is in the best interest of students is not always the best option. This takes some courage to say, as it has always been my position that students come first - but I think it is naive to think this is always the case.
In the real world, knowledge management issues of a revolving staff are well documented. When staff leave it does not only cost in terms of vetting and rehiring staff but also in the content knowledge loss, training investment and organisational understanding that is only gained through experience with customers.
Teaching is no different. Reduce turnover and the school benefits. An organisation that considers the needs of staff to progress successfully in their careers is an organisation that cares for its staff. To do this staff members needs to have their progress clearly illustrated and documented.
In mathematics, this means careful consideration of the new level 3 MAT and MAS courses. If there are a number of teachers vying for these classes it may be a number of years before teachers are given access to them. Being offered these classes (or knowing that a course has your name on it two years hence) can be a clear motivating factor in staying with the school and fully embracing PD opportunities until that time.
Conversely not being offered these courses or seeing the courses offered to those 'less worthy' can be a demotivational factor. Similarly being continuously asked to take lower school or low ability senior school classes can be disheartening for those seeking to enhance their skill base or for those seeking rapid promotion.
This ties very close to timetabling as many promotional opportunities rely on staff having access to senior school classes. Timetabling can often make or break the way a teacher sees their classes. Teaching out of area, sharing classes with other teachers, large class sizes, behaviourally 'difficult' classes can all be contributors to negative staff morale.
For a maths team to be successful they have to work as a team, support each other and find new and innovative solutions to student behavioural, content delivery and motivational issues. When class distribution for the following year is being considered, it means that careful thought has to be made as to what will satisfy the majority of the team, motivate members and ultimately prevent turnover.
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