After 20 years as a maths teacher and tutor, Dr Dion Khlentzos, has a clear view of what's necessary for building students' maths skills.
His top five keys to maths success include building on students' prior knowledge, relating maths to their everyday life and strengthening their motivation and belief in their own maths abilities.
He discussed the five keys in an interview on The Learning Capacity Podcast where he commented on STEM (Science, Technology, Engineering and Mathematics), and whether artificial intelligence will reduce the need for many people to understand maths.
Dr Khlentzos also commented on how technology like Zoom and Skype has enabled maths tutoring to be delivered to students who find it hard to attend face to face sessions with a tutor.
Listen to our discussion on the Learning Capacity Podcast
- How to help students succeed in maths
- Prerequisite maths knowledge
- Clarity of maths explanations by teachers
- How maths connects to real life
- How students can answer harder maths questions than they realise
- Motivating students about maths
If you would like to read the complete podcast transcript, here it is:
Episode 97 of The Learning Capacity Podcast
5 Keys for Building Maths Skills: Dr Dion Khlentzos
Peter Barnes: My guest on this episode of the podcast is Dr. Dion Khlentzos. Dr. Khlentzos is an educator, a registered psychologist, and an experienced mathematics teacher and tutor. He's been teaching and tutoring secondary school maths students for over 20 years. Today he's discussing the five keys to students' understanding of maths.
Welcome to the podcast Dion. Maths is a subject that can send a shiver up the spine of some students and have many parents confessing that even Year 7 Maths is a challenge for them, but it doesn't have to be that way does it?
Dion: No, it doesn't.
Peter: What have you learned from your experience over a couple of decades of teaching and tutoring maths? What are the keys to help students create a good foundation on which to build their maths understanding and skills?
1. Build on the Student's Previous Knowledge
Dion: I think firstly, one of the difficulties people find with maths is it builds on previous knowledge and students who may not have got some of the concepts that they had done previously then find that those concepts are being used again the next year and they can lose confidence at that point.
Therefore, when you teach maths to students you need to be very aware of the prerequisite knowledge that those students need to have. The teacher or tutor needs to be able to work with that, with the student and just to work out what knowledge they need to know before doing the topic that they're doing.
Peter: This is on every level. Are we talking about Year 1 in primary school, Year 2, Year 3, Year 4 then right up until high school, so prerequisite even at that young age and then prerequisite going into high school?
Dion: Yes, but not at the same level as each other. A child in Year 1 or 2 for example, doesn't have a lot of maths education. Of course, they have counting and other type of very basic skills but once they get to Year 7 and they've got all of primary school behind them then that's when students start to get a little bit more anxious about maths, I have found.
Peter: Okay. I've got some grandkids, one in Year 7, one in primary school and another one just started primary school, and I know that even in primary school there can be some anxiety about the maths.
Peter: Is that because there isn't a prerequisite knowledge of things like numbers, sizes and distances, is that part of it?
Dion: Yes. There are a few issues. One is primary school teachers sometimes say that maths is their least favorite subject.
Peter: Many people will probably say that.
Dion: Another issue is, students of course, as we all do, compare themselves with each other and even if they've actually got a reasonably good understanding of maths, if they see other children with what they consider to be a much better one in our competitive world, that can deflate them. By the nature of maths, sometimes those differences increase overtime, rather than decrease.
Peter: So if those differences increase, do you get students who are feeling like they are defeated, this is just too hard, they won't even try because they've proven to themselves that they can't do it. Do you see that?
Dion: Yes, definitely I see that. Usually the older they are, the more that's the case. Particularly if they find another subject or subjects they're more interested in, sometimes they throw their hands up in the air and give up, as do the parents sometimes.
Peter: So that's like not having a good mindset about maths, they believe they're no good at it, so what's the point of trying?
Dion: Yes, unfortunately some children fit into that category.
Peter: Their parents may or may not be enforcing that belief?
Dion: Often it is the case that the parents have had difficulties with maths as well. If at least one of the parents has done well, the child is more likely to have a positive concept about what they can achieve in the subject.
Peter: Those kids in your experience, can most kids become competent at maths, is there a percentage of kids who've got dyscalculia or whatever that condition is where they just can't do it? What's your fix on all of that?
Dion: Yes, there is a small percentage of students who find maths extremely difficult and I've taught students with a full range of abilities, from students who got one hundred percent in an HSC maths exam right down to those who struggle with every concept. But they are a pretty small minority, the students who are there. What I would say, even in those situations is nearly every child can answer questions that are more difficult than they thought they could answer.
Peter: That brings us back to their own belief in their ability and does it take us back to what you started with they need prerequisites for each level?
Dion: Yes. They need the prerequisite and they need help with explaining the concepts very clearly. Some students, a small percentage, are able to just read through the maths books and understand the work clearly and they don't need a lot of help.
But the majority of students really need clear explanations of how these concepts fit together and even intelligent students require the teacher or tutor to start at the basics. You can just go a little bit more quickly with them than with other students. I have found in my experience, that all students really like you to start with the basics.
Peter: So Dion:, I guess my understanding of this point is you've clearly said prerequisite knowledge is a key to building the foundation for maths success. Are there others? Other keys?
Peter: What are they?
Dion: The clarity of explanation by the teacher is very important. Relating the maths to real life examples and the students own experience is very important. The fact that students are actually able to answer questions harder than they thought they could answer, so not taking students’ lack of confidence at face value is important for the teachers, tutors and parents.
The students’ motivation is very important. For example, even the students who think they really wouldn't use maths at all, are still going to be doing some numerical work when they're working out the best value when they're shopping or how much time they've got to stop on a trip. All these sorts of things that involve time or cost or some sort of counting, it's very much their advantage to have some maths and that can increase their motivation as well.
Maths is also a prerequisite to a lot of other subjects. Particularly science subjects, economics and even psychology as I've done and some of the other human sciences, as well as the physical sciences.
Peter: Great. So you've given us five keys to building maths skills, the first one prerequisite knowledge, we've discussed to some extent. So now let's dig in with a little more depth into the other four. Now talk to me about Clarity of Explanation by the teacher.
2. Clarity of Explanation by the Teacher
Dion: So this is about, what does this topic mean that we're talking about? Not just starting with formulae and what they need to know, but what's this topic essentially about? How does it relate to work they've done previously in maths, and how does it relate to other subjects, maybe like science or geography? And just defining the concepts really clearly I find really helps students to start to get an understanding of what you're talking about as a teacher or tutor.
Peter: Do you find as a tutor and as a teacher you've got to spend quite a bit of time, or more time with some students on that aspect than others? Some just get it, but others you've got to put the explanation more concretely, is that how it works?
Dion: I find that having to give an explanation two or three or four or five times is more likely once we do the examples. Early on in a topic, if I'm just explaining what the topic is about, that doesn't necessarily require explaining it too many times, except in the sense of students with less ability I will certainly need to go more slowly than the students that are starting off more confident.
3. Relating maths to real life examples and the student's own experience
Peter: And the real-life example, the third key you mentioned, is that related to this clarity of explanation, or is that a slightly different aspect of building a foundation for maths?
Dion: That's to really connect with the student. Particularly for, I suppose, the disaffected or at least slightly unmotivated student who says what's the point of doing this? And I find that students will generally ask that question when they're finding the concept too difficult, so actually relating it to a clear example where it's something they would use in real life, I've found is very helpful.
Peter: Yeah I'm sure, because I'm sure you get students who say, look, this is just boring, or they're telling their parents, I don't know if they'd tell you. It's boring, I'm never going to use all that maths stuff that they're trying to teach me, so why should I bother with this? And I know there's lots of good reasons why they should bother. This whole emphasis on STEM in the last some years, the key idea of the STEM thing is that maths is going to be critical for future careers, getting jobs, and so forth. Some children will not develop sufficient maths to get those sort of jobs, so is that going to condemn them forever to a life of unhappiness?
Dion: I would certainly hope that it would not do that. It's true of course that some students are far more humanities-focused than sciences-focused, and indeed maths is not compulsory now in year 11 and 12 in the HSC in New South Wales, however it's still required to get into a large number of different courses, and even if it's not a prerequisite, the skills that students learn in maths, and there's several courses, from extension down to life skills courses in senior school that students can find useful and relevant to the work that they're going to do.
Peter: So the argument by some people, that don't worry about it, because artificial intelligence will handle all the maths you'll ever need, so you don't need to be bothered about it at school unless you're going to go and create artificial intelligence programs, so that's really not a valid point of view?
Dion: No. We're given lots of statistics on the news, in the online news, and the TV, and in advertising, and we need to be able to digest and understand those statistics to a certain extent, and to be able to interpret what they mean. Are they realistic? What does it mean for me? To actually create meaning from statistics is a lot more important than just being able to read them.
Peter: Yes, you can do all sorts of things from statistics, can't you? Okay, so that's really interesting. So real life examples, and the value of maths no matter what you're going to be doing in the future, no matter what's coming down the digital turnpike if you like, we're still going to need maths, and the need for maths teachers, for maths tutors, students getting competent at maths is going to be at least as important if not more important than it has been, correct?
Dion: Yes, I think the last thing we want in society is machines doing all our thinking for us.
4. Students are often able to answer harder questions that they think they can
Peter: Absolutely. Number four, you said the fourth key was understanding that students can answer harder questions than they think. Talk to us about that.
Dion: I've found with I suppose nearly all the students that I have taught or tutored, that as long as you start with the basics and they stay with you early on, you can start to increase the level of difficulty, for some only slightly, but still increase the level of difficulty of the types of problems that they do. And it will end up being at a level that is greater than what the students thought they could understand.
5 . Student Motivation
Peter: Well that leads to your fifth key, student motivation. So I imagine if the student succeeds in doing a maths problem or answering a maths question that they thought was difficult, that should motivate them, you would think.
Dion: That's right, yes.
Peter: And this motivation ties back into this whole business about their belief in their own ability and not getting defeated by, I'm not good at maths. And the answer's probably, I'm not good at maths yet, because I haven't been taught, or I haven't been tutored, or I haven't learned enough of it. Is that a fair statement of the motivation key?
Dion: Yes, I think I would summarize the motivation as being, what have I done and succeeded in, what can I do, and what do I want maths for what I'd like to do?
Maths Tutoring - Face to Face & with Zoom or Skype
Peter: Great. So you've been teaching and tutoring maths for a couple of decades, and I imagine when you started it was all face-to-face. For a large part of the time it's been face-to-face. So let's leave teaching for a second, but in tutoring, did you tutor one-to-one, or one to a group, a small group, or how does that work? And what's the best from your point of view?
Dion: Generally one-to-one, of course you can go the precise pace that the student wants and needs you to go. In terms of the student's resources or the parent's resources I suppose, it may well be appropriate to have small groups and I've taught and tutored and done maths coaching in small groups as well. And I think either are fine, but I think probably the most helpful to increase the student's ability as quickly as possible is one-on-one tutoring.
Peter: I have no doubt. I guess one to a small group or one to groups probably leverages your skills so you can help more kids, but you won't help them at the same rate as probably one-to-one. What about technology now, with Skype and Zoom, can they enable remote maths tutoring?
Dion: Yes, that is something that can be done with students.
Peter: That's a wonderful thing that technology's enabling.
Dion: Yes, that's right. Not all students are able to do face-to-face, so that's certainly something remote students can benefit from.
Peter: Great. So a couple of other questions. What should parents be doing to help their children to get a good start with maths? You've given five keys here in our discussion today, of those five, parents have got limited time, they've got varying levels of ability with maths, of those five, what would be the best thing for a parent to be doing with the child to help them be successful at maths?
Dion: I think if the parent can spend a little bit of time, at least a couple of times each week, just watching their child do maths, and see how they go with it, that can give them a good insight as to their ability and their interest in the subject. And then if they feel that they're not doing well enough, speak to the teacher or consider getting one-on-one help if that's something that they're able to do.
Peter: Now here's a gender question. In your experience as a maths tutor, what's the proportion of male compared to female students who come to you for tutoring?
Dion: Probably a little bit more male, maybe the ratio might be three to two, males to females. I think that's a traditional thing, that more males are wanting to go into fields that involve maths, but of course an increasing number of girls and women are doing that now as well.
Challenges & Successes
Peter: Now tell me about some of the biggest challenges you've had teaching and tutoring maths. What's been the hardest?
Dion: Well, there have been some students who just find the subject so difficult, and they come to tutoring really because their parents want them to come to tutoring, or perhaps because the parents are a little bit like their children, a bit exasperated that things don't seem to be improving.
And then with some students, because they lack so much confidence, it's difficult to get them to improve or to continually engage. But I've found that that's rare, though. I've found that the vast majority of students will stick at it if you can connect with them where they're at, at their ability, and start to help them there.
Peter: How about the opposite question. Of all the students you've coached in maths over the years, are there any that stand out as the greatest success you had?
Dion: Well yes. One student had actually not done maths in year 11 and 12 and came to see me at university because he needed to do maths as part of his course. I worked with him in doing the year 11 and 12 maths in a sort of accelerated format and he ended up getting university medal, that's the greatest success.
Peter: That must have been very satisfying. I get the sense that you enjoy maths, and you really enjoy helping kids with maths. Thank you Dion. It's been a great pleasure speaking to you.