Teaching is not an easy job to do well. Math teaching is somewhat more difficult than teaching many other subjects because its the bogey-man of school topics. This suggests that we should work as hard as we can on making teachers jobs less difficult and, maybe, we should spend a little more effort on cutting teachers who have math in their portfolio a break. Logical and obvious, right? Instead what happens is that we assume problems with teaching are the fault of the teachers, punish them, and try and create rules that force them to do a good job. Occupy Math is a professor of mathematics with a research specialty in the creation of sets of rules for games and controlling systems — he is sure this cannot work. A set of rules that forces good behavior does not exist in a situation more complex than a game of Candy Land.
Evidence suggests that simply treating teachers as professionals and letting them teach will yield better results.
I don’t mean no checks on bad teaching are needed — but the checks we have are incredibly wrong-headed. Let’s start our examination of this problem by considering the infamous shoe bomb incident. An absolute lunatic packed plastic explosives into his shoe and tried to set them off over the Atlantic during a flight from Paris to Miami. The fact he was sweating inside his shoes meant the fuse wouldn’t light. He was restrained, the plane landed at Logan airport in Boston, and the lunatic was given three life terms plus 110 years. This is a starting point for an analysis of a common type of human illogic. We take our shoes off and run them through the scanner at many airports (but not at some others) because someone failed to detonate a shoe bomb. Once. The classic name for this is nailing the barn door shut after the horse has escaped. In general, when something bad happens, we way over-protect ourselves from the exact thing that happened and don’t bother to look much at other possibilities. If we were really worried about people smuggling things onto airplanes, large shoulder pads would be as important to run through the scanner as shoes.
What’s the scoop on teaching here? We have had a problem with declining test scores in North America for quite some time. A rational thing to do would be to look at countries that don’t have this problem, e.g. e.g. Finland, and see what they are doing right that we could imitate. You know, examine the system as a whole and try to improve it. Instead we try to figure out who to blame and, based on that, to put patches on the system. Let’s start with some of the causes of the problem.
- High stakes standardized testing that actually makes things worse. Since Occupy Math last wrote on this subject he has learned of Goodheart’s Law which says “When a measure becomes a target, it ceases to be a good measure.” This is a wonderful summary of why our use of standardized testing is a complete debacle. If you teach to the test, the test stops measuring what it is supposed to.
- Wildly counter-productive micro-management of teachers. In Occupy Math’s home province of Ontario, if the grades in a class deviate more than a modest degree from the expected distribution, the teacher must write a supplemental report explaining why. Occupy Math thinks this is an idiotic use of the teacher’s time and that it encourages teachers to turn in unreal grades. It also shows that educational policy is based on a pretty substantial misunderstanding of statistics.
- Teachers, by which Occupy Math means people who actually interact with students, have too small a role in the design of curricula. Educational theory is a jargon-riddled mess in which command of an arcane vocabulary trumps any ability to create an environment in which students will learn. The link is the Grade 1-8 Mathematics Curriculum for Ontario. Here’s a game: how many pages before the first thing that will get taught in a classroom is mentioned?
What are the causes of declining achievement?
There are a number of factors that help explain why things are getting worse. Occupy Math does not claim the following list is exhaustive, but these are some of the really big factors.
- Less parental engagement. Society and the economy both changed. There are more single-parent families and more families where both parents work. Parental involvement is one of the strongest predictors of a student’s academic success and parents are simply less able to be involved.
- Prescriptive teaching environments. This is the topic of this post — teachers are told what to teach and how to teach it in a manner that stifles creativity and kills job satisfaction. Someone who enjoys teaching will spend more effort on it and do a better job than someone who is having the joy and life sucked out of them by the system.
- Really bad curriculum decisions. This comes back to Goodheart’s Law and the goal of making math into a series of rituals to get good scores on standardized tests. The effect has been to reduce the amount of math taught and has driven the level of mind-numbing repetition way up. People do not learn as well with numb minds!
- Really bad tests. While Occupy Math is distinctly not a fan of standardized testing, some standardized tests are better than others.
- Excessive standardization. There is a general, correct belief that we should teach a standard set of skills to everyone. Not having basic skills is a huge handicap in later grades, in higher education, and limits the opportunities a person has throughout their life. This need for standards is, however, abused to justify academic strait-jackets on teachers.
This last point — excessive standardization — is a key one. Since we need to have equality of opportunity in our schools, having some schools teach more than others is viewed as unfair and elitist. This view is not entirely wrong, but it is counter-productive. If all schools meet basic standards and some go beyond them, yes, the schools that are going beyond will give their graduates an edge. The point that is getting missed is that society as a whole will benefit. Substantially. In addition, if the schools are trying different programs (all including those critical basics) they will discover techniques that can be shared. Insisting that schools all toe the same line also means that any special training and talents that individual teachers have are wasted or at least forced underground. The current system is one that encourages equality through intellectual poverty.
What could we do differently?
Suppose that, at each school, the academic departments get together each summer to look over the standards (a sensible list of skills and abilities that students in each grade are supposed to master). Knowing their community, the students in that community, and the parents, the departments select one of a variety of basic plans. They then augment the plan to address both local issues and their own talents and special training. Enrichment activities are added. Many of these are selected from a diverse portfolio of such activities. Some additional activities are devised by teachers and parent volunteers. Good activities are placed in the ever-growing portfolio which also has a place for user comments. Is this paradise? No, it is just one possible way to run a school system. Occupy Math has been a parent volunteer who would fit right into this system before moving to Canada.
Occupy Math lived in Iowa. There the individual school boards had substantial control over what was taught and how it is taught. The result was consistent top-three-in-the-nation performance with bottom-half-of-the-nation costs. From the Soviet Union to the Ontario Ministry of Education, we have endless evidence that detailed central control does not work. There is also evidence that treating teachers as professionals worthy of trust works much better than what we are doing now. The standard performance of respected teachers treated and paid as professionals is much better, but the system reacts to — and only reacts to — the worst case scenarios, especially those that make it into the media.
Why pick on the teachers?
This is actually an important question to discuss. Teachers are perceived as having far more control than they do and so are easy to blame. Passing a bunch of rules and implementing other forms of micro-management create the appearance of doing something at a very low monetary cost. If micro-management doesn’t work, it is really easy to claim the teachers have still not been brought to heel. All of this is aided and abetted by schools of education run by fad-driven blue-sky theorists with no time in the trenches. It is difficult to collect good evidence when the subjects of study are people’s children, but the correct response is not to completely avoid trying to gather evidence, and there is some progress in good directions.
The journey to a school system employing empowered teachers who work with engaged parent volunteers in a relatively open and transparent system is a long, hard one. Occupy Math and his fellow travelers are prepared to help, but most of the impetus, the energy, the effort needs to come from engaged parents and dedicated teachers. The present sclerotic educational system will be very hard to change; as someone once observed “That would be too much like curtailing the powers of Parliament by an act of Parliament.” On the other hand, the internet creates enormous possibilities for getting together and making things better. Concerned parents and caring teachers can find one another more easily. People like Occupy Math can serve as experts and resources. Are you interested in educational reform? Do you have horror stories or uplifting anecdotes that might fit into a future post? Please comment or tweet!
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics