My aims are simply put ...
They are to teach students how to properly learn maths and how to realise their full potential, whatever that may be. If at the same time they catch themselves actually enjoying what they are doing, then that is a bonus for us all! To set us off on the right track it’s important to address some core fundamentals.
It’s impossible to address all potential students at one time, so I choose to connect to those who maybe have the most to learn and possibly feel they have most at stake emotionally. That said a number of my students are talented youngsters who are on a mission to set the world on fire! I like the variation. It keeps me alive. Many parents reading what follows will likely not find anything new. It probably will resonate well with them though, and sheds light on my viewpoint. It gives insight as to exactly how I would be working with their children.
Acknowledging the Value of Maths
Above all, students need to keep an open mind regarding the possible long-term role of maths in their lives. This can only be long-lasting if they feel confident in the subject, and that, in turn, requires they master the content. There’s no room for indifference. It’s particularly relevant to students planning to take science-related subjects or architecture for example. But, even social science students require mathematical insight. An open mind means they are less likely to block themselves from giving it their best shot.
Assuming they are motivated, it can still be hard to get students to appreciate the level of attainment that is required in order to demonstrate proficiency. Also, they rely on the teacher in school totally to set the pace. Sometimes it happens that the pace is too slow and that they do not finish the syllabus in time. Often students and parents are blissfully unaware until it is too late. That is why I, personally, work students according to my timetable, regardless of what is happening in school.
Allowing whole classes to fall behind, as alluded to above is even affecting the way maths and science-related subjects are being taught in universities nowadays. The phenomenon is known as The Mathematics Problem. Lecturers are finding that students who have already been selected for their chosen courses are not sufficiently prepared for the mathematical content. It’s not their fault, but it has to be fixed. Many universities have been working hard on supporting their students and getting them through. Even students enrolled on maths (-only) degree courses are suffering too, and feel ill-equipped and in need of support. Their training at school did not adequately equip them with solid knowledge.
Key Focal Drivers
I have all my students throw themselves whole-heartedly into mental maths and mastery of basic skills right off the bat. Many panic a bit initially, when they twig that we are spending a lot of time (in their eyes) reworking year 6 maths. Their mind is on the trigonometry or ‘subject of formula’ that brought them to me in the first place. They want to fast-forward to their holy grail and don’t see it happening any time soon if we can’t get off mental maths.
But, the ability to ‘fast-forwarding’ is actually our goal. One that can only be attained after we plug the holes in their basic knowledge. We want to achieve a permanent fix, not a temporary patch-up. Once students see for themselves that they have not just learnt some maths, but have actually learnt how to think mathematically, they begin to relax. Sometimes they are even known to enjoy their new-found skills. Perversely, once the initial crash course in the basics is over, their rate of progress escalates and all is well again.
Fractions, Fractions, Fractions
The permanent fix we are aiming for ensures that students can handle basic questions at any time of the school year. For example, take fractions. Every year, from at least year 5, students spend a few weeks on fractions. Afterwards, the teacher moves on and (some) students promptly forget all they learnt, only recapturing the knowledge when they revise at the end of the year. Then they forget it again. Generally, students are not concerned by this and see it as normal.
For sustained progress, however, they must retain these skills year round. You see, if you allow yourself to forget what you know about fractions, how are you going to recognise the connection between fractions and other parts of the syllabus? Fractions will remain an isolated topic and the benefits of joining the dots between related topics will be completely lost.
We have already seen how very important mental maths is. Students who struggle with this are always distracted during the introduction of new topics. At this time, it’s natural for the teacher to ask students to carry out simple calculations along the way, just to hold their attention. If they struggle with these, then instead of listening to what the teacher is saying, they are knocked-out by the calculations. Ears are firmly closed and eyes are not looking forward. Effectively it’s a block-out!
It’s also common for students to give upon their times tables after year 6. They take their cue from the teacher in class, noticing that they are not giving lessons dedicated wholly to tables anymore. Wrongly, they assume it can’t be that important after all, and that they got away with it. The calculator is king.
Of course, the calculator can tell you what six times seven is. Nowadays it can even get you equivalent fractions and convert from improper fractions to mixed numbers. What it cannot do though, is help you understand the rules for algebra. This issue can be resolved as long as the tutor doesn’t let up on flagging opportunities for practice during the lessons.
Before we move on:
It’s worth emphasising that improving mental maths requires a change in behavior patterns and that can only be done on the spot. You can set homework relating to this, but it is only academic, it doesn’t highlight the cases where mental maths could have provided a faster and easier solution. In fact, it is only with practice that mental maths can ever become faster and easier! Parents can help enormously by showing their children in real time exactly when they are using mental maths themsleves. For example, in the restaurant or on public transport, or in the kitchen or at the garage.
Everything that is allowed to happen in algebra with letters only works because it mirrors the rules for arithmetic exactly. If you don’t have good arithmetical skills for reference, how can anyone teach you algebra? In that case, algebra becomes a set of different rules and regulations to be applied in certain recognisable situations. Trouble is, every ‘situation’ starts to look decidedly unlike any other you ever met before.
Assume you accept that you can’t understand algebra and still are not ready to ask for help. You will get away with it; but only until fractions pop up in geometry or graphs or statistics. When you first learn about perimeter and areas the teacher keeps it simple and only uses whole numbers. Then, the next time it comes around, a year later, the side lengths are allowed to include fractions, say. E.g. A rectangle whose length is four and a half centimetres and width is three and three quarter centimetres. If you can’t add and multiply fractions you will neither calculate the perimeter nor the area. You will fail.
You may not realise you failed because you can’t do fractions. Because you keep getting the wrong answers you will probably think you cant ‘do’ perimeters and areas. The idea of a perimeter is a simple one, but it becomes confusing if you think you got that, but somehow the answers are all wrong. In that situation a student may not be able to properly diagnose their shortcomings. This is where the rot sets in as confusion and disappointment reign. Rapid action is required, before things become too serious.
Online Resources – Friend or Foe
Modern technology provides a vehicle for today’s students to firmly grasp mathematical ideas, even relatively abstract ones, that were so inaccessible in the past. Some schools have jumped in with both feet and are already way ahead. Their students have easy access to incredible resources and their results reflect this. Bear in mind, it’s the quality and not quantity of supporting material that makes the difference.
Fortunately, well-recognised and respected teachers like Craig Barton and Dr. Jamie Frost and John Tranter are generously carrying the rest of us along with them. They are sharing their outstanding creations and compilations – often free of charge.
I admit, that until fairly recently I was very skeptical about online educational resources. That was mainly because I witnessed so many students missing the point. Even if they mastered the game they generally missed the message. That need no longer be the case. It has become possible for students to learn the lesson as long as educators pick and choose material wisely!
I recommend that anyone trying to support maths students with online content sticks to authors and websites that have already gained recognition. Examples are the ones I mentioned above. Don’t stray too far off the beaten track. Every man and his dog thinks they can create resources and much of it has limited value. So many of my Google searches never quite hit the mark and have caused me to waste massive amounts of time. Finding potentially good material is not the end either. Often the instructions are found to be lacking and yet more time has to be invested to discover the full power the tools. Finally, after all that, it can happen that the resource is just not good enough and that you cannot make use of it. Back to square one.
Are You a Social or a Solitary Learner?
Trend for self-study
Increasingly, the trend towards self-study is causing problems for a number of students. By self-study I mean that sections of a course, or even the whole course is presented in the form of a text that students read at their own pace. Generally, they only have input from a teacher if they get stuck. It is fine for undergraduates, and has been an accepted mode of learning for them for years. Younger, maybe shyer children, who lack confidence however, can find it very stressful. If a student is struggling and their mathematical vocabulary is not up to par they will not be able to make any headway and may choose to suffer in silence. That’s even more frustrating for them.
Another point is that many authors online are simply rewriting material that already exists and are not adding anything of value themselves. It means that looking up the same material in five or six places only results in lost time. Whatever the student was not grasping in the first text is probably not going to be well-explained either in most of the other places. I saw this when I was showing young children how to use the internet to support their school-work. Despite being given the usual obvious pointers, it was noticeably often overwhelming for them.
I can relate to them getting bogged down with self-study and not knowing how to get themselves out of it, resisting asking for human help. I recently bit the bullet and installed WordPress in order to make my own website. All seems crystal clear when you have been sold on the idea of simply choosing a ready made website and replacing their content with yours. Easy peasy! To boot, I’d done it years before and thought this time around should be a piece of cake. That time I did it completely single-handed and had no hiccups.
Creating a website out of the box is not a ‘plug and play’ scenario, whatever anyone tells you! FAQs cover anything that could possibly go wrong and there are blog posts to guide even the least experienced newbies. Somehow, though, you just can’t quite get to the bottom of your little problem – even with all the written support. You don’t want to give-in either because you can see others in similar positions getting on with it – even having intelligent conversations with each other. Website building is slightly different to self-study in that it has a learning curve, which will be overcome given a lot of time and effort. The lesson is that the pain and suffering can be minimised by reaching out asteep nd asking for human help.
Many students I meet are in a similar fix. They need help from a ‘human’ buddy, whether that be a teacher or friend or tutor. Electronic assistance just doesn’t cut it. They can waste literally tens to hundreds of hours over the course of the year. At times they may feel they are making good progress, only to find later on that they are back at square one. What they thought they had learned can disappear in a puff of smoke.
When you try to go it alone and the topic seems inaccessible, the only recourse is to try to fill in the gaps with educated guesses. I have experience of this too. In fact, anyone who has been involved with maths research will know this situation all too well. For students able to string together logical arguments this kind of reverse-engineering is all well and good.
For others, though, it’s a disastrous way to work and can really do more harm than good.
Did you know it’s not always true that ‘Practice makes perfect’. In the maths teaching circles they say ‘Practice makes permanent’. Left to your own devices for too long it can be very difficult for anyone to undo your wrong-thinking. It requires a re-wire and in my lessons I tackle this head on. We beat it by making new connections between old topics and presenting them in an entirely different way.
Home-schooling has really taken off over recent years and I assume that many of those parents face similar challenges to private tutors. They are not writing the courses bu they are aware which parts of it have not been understood and need supplementing. I am continuously reviewing the quality of my work and consequently looking for new techniques and facilities. That naturally feeds into a discussion I have with myself about how best to contribute to the home-schooling arena.
There are already plenty of home-schooling courses for families to follow. True, these provide an overall framework that keep you on the straight and narrow. However, the course writers walk a tight-rope between detail and direction. Even as a mathematician, it can be hard to follow some lesson plans to the extent they are given. It can happen they have you jumping between four textbooks and that they detail the writing on the whiteboard line-by-line and all in one lesson.
I have a friend who always says that delivering a lesson according to a lesson plan is like being an actor on stage, except that the audience is allowed to heckle!
Imagine that if your audience is only one and that one is your son or daughter who doesn’t want to play the game today! As such times a tutor can come in very handy! My role is to provide support as the person who delivers the maths content. I am also looking at the bigger picture for the future. Parents need to have access to the same resources as school teachers and tutors. Actually, it’s not the access to the material that is the problem, it is the lack of trusted opinions. To that end I’m steering this website in that direction. I’m happy to meet new students, of course, but I want the website to be much more than a landing page. I want parents to actually find it supportive and informative.
Let me Know
If you are a parent or even a maths tutor and have any ideas or issues you would like addressing feel free to drop me a line and let me know.I hate to sound like a party political broadcast, but “Together we are better!”