There are a few questions you should consider:

• Have you exhausted all suitable approaches with this student?

• Is there perhaps a difference in your personalities that is preventing the kind of positive response you are accustomed to? Why is this problem happening?

• Are you sure you have adequately attempted this challenge?

• Is it a suitable time in the year and in the student’s best interests for you to pass this student onto another tutor?

Some students are just difficult to work with and are likely to challenge any tutor; at least until they “see the light”. You want to make sure if you stop tutoring this student it is because you specifically are not suited to them NOT because you cannot handle the challenge. Otherwise the next tutor is likely to have the same trouble as you but the student will needlessly have to acclimatize to a new tutor.

If you don’t feel that you are adding value then talk to the parents. It probably shouldn’t be in the form of “I’m not suited to work with your son” though. Rather it should be a consultation to answer the following two questions:

• Why is he not responding and what can be done about it?

• Is it perhaps best if another tutor takes over, are you the problem?

Discuss:

• What they think can be done about the concentration issue and lack of effort?

• Can part of the problem be resolved by the parents – for example by enforcing homework habits?

• What do they hope you will accomplish? Do you think you can do that?

• What feedback has the student given about you?

• You don’t feel like you are helping him enough and maybe somebody else would be better suited? What do they think about that? How do they think the tuition is going? Etc

Although the situation is not a positive one, parents will typically appreciate the honesty and professionalism in such a situation. At the end of such a conversation there should be a clear decision, based on what is best for the student, either:

• You will continue with the student for now BUT specific new approaches will be used to improve the situation.

• You will pass the student onto another tutor, with sufficient feedback that the tutor can prepare and tackle the situation adequately.

Stern or Friendly is up to you. However, it isn’t advisable to take either of the approaches mentioned. Neither a stern teacher nor a friend is the role of the tutor. The important question is which way would serve your student better?

As a friend you will ultimately lose credibility and the expert status you are bestowed as a tutor. The student will not take you seriously enough to do what you say. On the other hand, as a stern teacher the student may do more of what you ask but will inevitably develop a resentment or dislike toward you. Parents would not tolerate this for long; they tend to place a high value on the student enjoying the learning process or at least having positive feedback for their tutor.

A one-on-one tutoring situation is very different to traditional teaching roles. You WILL NOT succeed in tutoring a student unless it is as a team. You must enlist their support, both of you must be playing for the same team otherwise your efforts will be counterproductive. The way you achieve this is by establishing yourself as their mentor/tutor. A mentor is a “trusted counsellor or guide”, what you can do is counsel the student about mathematics. Be friendly and nice enough that they “trust” you but be stern and professional enough that they view you as a “maths counsellor”.

This means being nice and friendly but still exercising your authority to an extent – only do it in a consultative fashion rather than “stern”. If you need to be stern because the student isn’t implementing your suggestions try to involve the student in your cause. Explain what is wrong and why. Ask if student agrees with you? Have a conversation about the problem as a mentor (not stern, not friendly – just sincere and nice). You can literally say “Sam, this isn’t working as well as it should. I think it’s because of X, Y and Z which I’m not sure you agree with. Tutoring is a process and the quality of tutorials will depend on me knowing how best to work with you, so we should probably talk about this. What are your thoughts?”

Then, TOGETHER with the student decide on a course of action. Ask what he thinks is a suitable solution? Including the student in decision making will increase his commitment to the decision!

Obviously such a direct approach will work better with high school students but a softer version of this is still useful for primary math students.

It is hard to answer your question because of the lack of specificity. What specifically is wrong with his problem solving skills? Is it that he simply doesn’t get what to do a lot of the time and gets stuck? Or does it seem to you that he has the right knowledge and could have answered most of the problem questions but for some reason he left them to go through with you?

Problem solving ability can for our purposes be looked at as two general pillars:

• The skill part

• The psychological part

THE SKILL of problem solving is really all about globalising a problem and then breaking it down. Go through this process again and again when you get stuck in the problem until you arrive at a solution. A student must learn to:

1.    Decipher the meaning of the question and understand what the problem wants (chunk up)
2.    Break it down and decide on at least the next step by putting pen to paper and doing some working out (chunk down)
3.    Realign with the meaning of the question to understand where they are up to in the process and then continue once again (chunk up then chunk down)

This is the general gist of the problem solving process. Strong problem solvers do this naturally. Consciously or not, problem solvers go through their own version of the Self Questioning process:

1.    What does the question want?
2.    What am I given?
3.    What do I know about this?
4.    What haven’t I used yet?
5.    What else do I need to do? Anything? Let me at least back-check first…. etc

While your student may be reluctant to consciously go through this process because it is “lame” or whatever, he must already do this to some extent with the questions that he gets correct. You should explain this process to him and see if you can find some common ground. Try to find how he naturally does this and point it out when you see it – hopefully this will connect some dots. At the very least – when he gets stuck with problems probe him with these questions rather than giving him the answer.

THE PSYCHOLOGICAL PART: Has your student ever left a question for you to help him with but upon looking at it you knew that the question was not even close to beyond his skill? This is a really common experience, especially with students who are accustomed to being “bad at math”. As a student improves in maths they must break through or at least stretch various psychological barriers if they are to improve further. One such barrier is learning when to give up and when not to give up.

The nature of problem solving (real problem solving – not easy questions in the guise of challenge) is that a student is not supposed to know how to do it straight away. They are supposed to figure it out by “playing” with the maths. It is this very “playing” that stretches problem solving capacity.

Not only must students feel that It’s OK To Be Wrong, but that it’s ok to be wrong again and again until you figure it out. This is where lots of developing students fall short. They don’t really appreciate this truth and come to believe that a question is beyond them when it is not.

If this happens with your student, start to break the pattern. Sometimes, you may even blatantly refuse to answer a question – especially if it was a really easy one. Instead probe him through it using self questioning techniques to demonstrate to him that he was capable of answering it on his own. Over time the goal is to stretch his expectations of himself and condition him to “play” with the math when he gets stuck.

Ezy Math Tutoring

There are a few issues in what you have described above. Probably the most important thing to focus on immediately is demonstrating that rule dependency does not work for maths, so let’s focus on that.

Unfortunately you can’t tell a student this simple truth and expect them believe it – sometimes they will but most of the time a conversation alone will not be enough to change their behaviour. Fortunately your student is in year 11 maths and mature enough that you can speak directly. Regular conversations must take place within tutorials to push the concept of Seeking Understanding. This should not be done as preaching or a speech on your part but rather a consultative conversation. Always get his feedback:

• What do you think?

• Do you agree? Why? Why not? How do you know?

An effective approach is to demonstrate the truth of what you are suggesting in practical terms rather than just preaching:

• “The definition of insanity is trying the same thing over and over again but expecting different results” – Einstein said these wise words; explore this with your student. He has been working hard at his maths but yet, real success seems to elude him, why does he think this is happening? Obviously he is doing something wrong in his approach? Many students have gone from failure to extreme success in maths – many of them probably did not work much harder than your student? How can this happen? It’s all in the approach. Either way, if he is not getting results using the current approach it makes sense to try something else? Point this out.

• Here is a useful proverb for your student: “Give a man a fish and you feed him for a day, teach him to fish and you feed him for a lifetime”. Maths is the same, once he understands a concept in depth he will always know it. Otherwise revision will be necessary in extreme quantities. Certainly there must be some concepts that he really does comprehend? Take questions from those topics and ask him to do a few; then contrast this by asking him to try questions from a previous topic where he just memorized the rules. Point out how much easier it is when he understood the content.

• Find out why he thinks you can only succeed in math by being a genius? Why does he believe that his only choice is to memorize rules? Where did these ideas come from? Probably from some friends of his who must also struggle with maths if they give such advice. Ask him if he would go to a dentist to fix his car? He would probably go to a mechanic, not a teeth expert. Same goes for maths. Explain that to fix his maths he must listen to those who succeed in maths (such as a maths tutor).

The goal is to get him to question his faith in rule dependency. With enough of these demonstrations, gradually, he will inevitably be forced to confront his own false beliefs about rule dependency. Then it should be easier to get him on-side.

The ultimate purpose here is to change the student’s focus such they when they look at a question or your explanation their internal dialogue is saying:

• “What does this mean? How can I figure this out? What is this about? How does this make sense? What haven’t I tried yet? Which concept is this related to?”

Their internal dialogue should NOT be saying:

• “What was the rule for this? This was done in class – what was written on the board again? What’s the answer? How can I remember this rule/process?”.

This is a really common problem for maths students. Answers tend to be either right or wrong and nobody likes to be absolutely wrong. These sorts of confidence issues are usually tied to a student’s beliefs about themselves and what it means to be right/wrong in maths. While you should talk about this regularly to instil confidence and improve her beliefs, this is a long term process. In the shorter term some concepts to consider:

• You need to create a tutoring environment where she feels “safe” to be wrong.

• Regularly discuss the fact that it is impossible to learn maths without being wrong many many times first. Maths thinking is a skill, not knowledge and only through the risky practice of thinking and trying can it be learned (not the practice of trying questions safely and mindlessly).

• One effective technique is to make mistakes yourself or at least play up the extent to which you are challenged by her questions. Sometimes act unsure of yourself to demonstrate that you are not perfect in maths either and are willing to make mistakes – even though you did really well in school, show that you still can struggle.

• When doing this point out to her that “I’m not 100% sure, let me try this” … “actually I think this is how you do it” … “yep figured it out”… When a student sees the process by which mistakes are made confidently it serves to make the “mistake making process” more relatable – especially if they have a good and trusting relationship with you.

• When she does make a mistake praise her for it, if you could see that it took effort for her to try. Give her another similar question and when she succeeds or gets further than last time, point out how her previous risk taking made it possible for her to improve.

• The goal in trying a question isn’t necessarily to get it right, in tutorials it’s just for practice. The goal is to learn, not to get it right. Getting it right is just a bonus. When failing at a question students experience the pain immediately but don’t reap the benefits of their failure until later. This creates an experience skewed toward the present rather than the future which is a version of the student who is successful in math. Shift her focus to the learnings and improvements rather than wrongs and rights. Lace your tutorials with this kind of talk and eventually it will rub off, hopefully.

Most importantly the students must understand why these strategies are important and that ALL successful maths students do this, although many do it without realising. Remember, you want to enforce the use of these strategies but without being forceful. If the student is to ever be independent of their tutor, they must learn to use these techniques. As a maths tutor, this is part of your responsibility.

Internally the students must have some sort of mental objection to some of these strategies otherwise they would listen to you. It is probably best to start by figuring out what these are. Speak with them openly and point out how you notice they are not making much effort with the strategies – ask them why? Consult with them about your experiences and understanding of the strategies – help them to understand why the strategies work and try to relate it to their own experience. Don’t instil these concepts as dogma, rather just as an effective approach. Typically it will take numerous discussions to bring a student around to realising that these strategies work!

What else really helps is to allow students to make maths mistakes and then get them to do the same question but use a strategy. They will either get it correct OR at least have a stronger rapport with the question. Point this out to them.

For example, if they don’t put pen to paper and make a bunch of mistakes or get stuck tell them, ok, now let’s try it with Pen To Paper. Get them to write down the question and probe them to put down extra bits of information in an orderly and structured fashion. Slowly, they should start connecting the dots (if not then probe them a little more). At the end they should definitely have experienced the benefit of putting pen to paper – make sure they are aware of it. Make them aware how when all the maths was out of their head and on paper, it was easier to think. Make them aware how seeing all the information simultaneously helped them tie it together. Make them aware how making a small mistake somewhere was a lot easier to overcome because they had already written down lots of useful ideas. Etc.

Give them the experience of how the strategies are effective – then they will not need more convincing.

Generally speaking, to maintain memory of topics throughout the year they must:

• Do the tutoring consistently and regularly

• Do revision throughout the year

Each lesson you should devote some time to covering gaps in knowledge and revision. Or if time is scarce just set revision for homework and make sure to cover any problems next tutorial.

It is really a question of planning and structuring the tuition over the course of months, with a long term global view rather than a short-term perspective which focuses only on current content and getting by the next test.

You should never start/stop doing revision – it is just a part of our tutoring process – always. Every lesson some time is spent on gaps/revision. If a student is reluctant then you should at least plan what revision needs to be done as soon as you know a test is coming. Preparation for tests needs to be structured as shown in CEP10.

To answer your question in a sentence: avoid the situation where the student is faced with a test and they have not seen or practiced those topics for a long time. With adequate planning and structuring this should be easy. The thing is that you know what topics they have covered since the last test. You know what other topics are related to those topics. You know how long it has been since the last test. You know which topics were specifically challenging for your student. You know which topics your student is likely to have trouble with (not remember well) if they were faced with a surprise test next week. Why wait for a test? Using the knowledge above you should be able to tell when weaknesses are present and when various topics are likely to be remembered weakly. Always be asking yourself “What should they revise now? What revision would also help with current work? What topic would they struggle with if a test was given in 2 days?” Based on this set revision homework.

Without a regular process like above how can a student be expected to remember everything all at once?

Furthermore, this sort of approach really helps with end of year exams. At the end of the year the exam covers a year’s worth of content not just 1-3 topics. Often it is impossible to cover all those topics for revision in the time available. However, if revision was attended to throughout the year the student will remember much more to start and ultimately perform much better in their exam.

 
Interesting situation. It is great that you have a strong enough relationship with the student that she wants to chat with you. While having a chat every now and again is part of the job, you are certainly not there to chat.
Here’s one approach and a  few general points:

• Obviously you don’t want to become a strict authority figure or damage the positive light in which the student looks at you. Whatever you do, be mindful of this.

• When re-focussing on the maths content it is important not to do it in a rude way or squash the student’s enthusiasm.  Probably don’t tell her “stop talking”. This is a little aggressive and may create negative sentiment.

• Rather than telling her what NOT to do, you can focus on telling her what needs to be done but only once she is paying attention to you:

• Gesture at the workbook. “Mary.” Wait for the student to stop talking and give you attention. Look serious but not mean or aggressive. If she doesn’t stop talking, say again a bit more sternly and with expectation look at her. “Mary”. Be serious when you are interrupting her so that she knows you mean business.

• Once her attention is on you, smile. This will show that while you are being serious, you are still friends. Then, seriously but with a smile tell her  either:

• “Mary, we really need to do this work, you can tell me about it when we finish.” ; “Mary, this is really important” etc… then just move on with the tutorial.

• Inevitably she will still interrupt with stories about friends etc. Tackle this the same way each time, eventually she will develop what is called an “anchor” to your facial expression when you are being serious. She will start to recognise that when you look at her that particular way, she needs to focus on the math.

• Another way to let her know that this is an issue without hurting her feelings is to bring it up in front of the student while talking to the parents. You may say something like “Well, she is really doing well, Mary loves to have a chat and tell me about her friends, but she is focussed most of the lesson and we are getting a lot done”. This way she will become aware that you consider chatting too much during tutoring to be a problem.

• Always balance this with being friendly and having some fun – the student is in year 6 and we can’t expect them to be serious 100% of the time. If she is being enthusiastic talking about math stories with her friends then at least she is being enthusiastic about a topic which for many students is dull – not necessarily a bad thing.

If the problem persists another approach will have to be adopted. Possibly discussing it with the student would be the next step.

Homework is quite a specific matter. While some students are open to it others are not, the same goes for their parents. It is important to establish a mutual understanding between yourself, the student and the client regarding homework expectations. When this discussion takes place you should ascertain more carefully the students goals and based on this advise what you think is a necessary amount of homework. Support your conclusions with examples of the student forgetting a lot of content. It is important that there is agreement on this so that a regular pattern of homework can be established as you suggested.

Most certainly, at least some homework is recommended, otherwise progress will be challenging and retention will be diminished. Also, consider these two ideas for increasing retention – they are both simple and require very minimal effort.

• Get the student to make notes in a notes book after each tutoring session. Perhaps they will only do it 4 days later or just rush through it without thinking much. Either way, retention will still be increased considerable. The process of explicitly expressing the concepts on paper with colours and examples goes a long way to create stronger associations in one’s mind. This makes the concepts more concrete and less abstract and hence the ideas are easier to recall. You can even set note-taking as a homework task.

• At the end of a lesson take five minutes to do a review of the tutorial. Everything that was covered that tutoring session should be very quickly revised. Ideally the student should just talk you through everything that was done in that tutorial, explaining the basics to you along the way. This will have an effect of tying together some of the concepts and put them in a wider context with several of the ideas being related to each other. This in turn will create greater comprehension and retention.

Usually when you first start with a student the initial lessons are used to help them catch up. This is quite normal. Typically we help them with their immediate school work first so that they don’t fall further behind. Then start to work on topics which they have gaps in but are relevant to the current course of study. Ultimately we want to be spending some time one gaps, current content, future content – all in one lesson.

Regarding the notes, this is unfortunately a common scenario – many teachers do not provide notes. Consider why you want to give students notes in the first place? Notes serve a reference point when students get stuck, also notes are great materials when revising or preparing for a maths test.

Notes, are most effective when a student writes them on their own. Notes with a student’s own comments, remarks, working out, practice questions etc are by far the most useful. Otherwise the student can just look at their textbook for notes, formulas, tips etc. However, when a student creates their own notes it really goes a long way to develop their understanding and greatly improves retention. DO NOT waste your own time writing notes for them – at most you can make a few basic notes but that’s all – students should create their own notes, it is a useful skill and facilitates comprehension. If she doesn’t know how to create notes, teach her – it’s all part of the tutoring role.

Perhaps a good approach here is to have the student create her own notes either after each lesson or every fortnight. There should be a separate book for notes which will eventually become like a mini-textbook of maths examples and illustrations – written by the student, for the student. As you move through new concepts and gap topics, get the student to write a few pages of notes for home work.