Correcting student misconceptions in mathematics and science teaching
Habit pattern errors and misconceptions
When good teaching doesn't make perfect.

Correcting misconceptions—a fresh approach

science misconceptions          

This teaching program:

  • can greatly improve students' conceptual understanding
  • can quickly and permanently correct errors and misconceptions
  • can greatly improve transfer of learning and memory
  • increases student flexibility and adaptability to change
  • is being used by both large and small schools, home schools, colleges and universities
  • uses an innovative learning method officially endorsed by the South Australian Department of Education
  • is backed by published research, case studies and workplace trials
  • is readily adopted by teachers, tutors, home school tutors, trainers, instructors and coaches as part of their professional toolkit
  • can be learned through videos, self-paced courses and workshops ranging from $39 to $395 (some courses are still being developed).

Habit pattern errors

The problem is not learning the new; it's forgetting (unlearning) the old!

Old Way/New Way offers a new theory and a method for overcoming errors, misconceptions and entrenched old ways so teachers and learners can achieve continuous improvement.

Persistent errors and misconceptions, known as habit pattern errors, in the learning of science, mathematics, spelling and other school studies are notoriously resistant to correction by conventional teaching and learning methods. Old Way/New Way® offers a new theory and a user friendly method of correcting these errors, once and for all.

Transfer | learners just keep falling back to old ways | the transfer of learning problem

One of the most time consuming, frustrating and costly features of human learning is that, despite quality teaching, expert learning support and advice, caring friends, school counselors and the strongest self-determination to improve, students still improve only slowly and often keep falling back to old ways.

For example:

  • have you noticed that children keep misspelling the same words over and over, despite repeatedly being shown the right way and writing that out many times?
  • despite quality teaching, why do even capable children keep reversing letters and numerals?
  • why do students hang on to their wrong ideas and misconceptions in science and mathematics, despite being shown the error of their ways?
  • does improvement and change have to be so slow, difficult, frustrating and expensive?
  • did you know that with conventional change methods it can take up to 2,000 repetitions before a learner is competent and comfortable with the new way?

Because we are not a blank slate, self change is hard. Self-teaching attempts, observation, education, training and practice have given us prior knowledge and skills. Consequently, we all have our own way.

Knowledge and skills can become incorrect, incomplete or outdated over time, making us less effective as individuals, as employees, as partners, as parents, as professionals, as performers. We then face having to change ourselves.

But our "own way" of thinking and doing, developed and practiced over the years, has now become habitual and automated. Many of the routines we follow, from the time we get up in the morning to the time we go to bed, are automated and operate mostly beyond our conscious awareness. Many of these routines are not within our direct conscious control. In fact, much of our life is "automatic" and we run many things and respond to many situations as if we were on "automatic pilot."

This has clear advantages for us in our attempts to cope with life's demands. For example, when learning to drive we initially have to concentrate on each and every step while changing gears or executing a turn. With practice comes learning and what took so much concentrated effort and conscious control before now happens almost without thinking. Instead of concentrating on gear changing we can now leave that part to the "automatic pilot" and instead direct our energies to figuring out how to get to our destination.

Such automated skilled routines serve as well as long as nothing changes. Try changing to a car without a manual shift or one that has the windscreen wiper control lever on the "wrong" side and you will discover the interference generated by your prior learning.

Automatic, learned skill routines and ways of coping with the world that we have picked up over the years are not always the best ones. Sometimes, for one reason or another, we get it wrong. Our driving habits may not be the safest ones because we were not taught properly. Since you learn, i.e., automate, whatever it is that you practice, it is likely that when you practice inferior driving skills then that is what you will end up with as a driving habit.

If not corrected early, then, some of that faulty knowledge, those wrong ideas and inferior skills we have will have developed into learned errors, technique difficulties, misconceptions and ingrained bad habits.

Habits are automatic, reflex-like acts and behaviours that are not under conscious control - by the time you realise what you've done wrong, its too late to stop

Convinced that it's time to change, you seek help. An "expert" may point out your errors, show you a better way and you copy and practice it.

While this teacher, coach, trainer, therapist is alongside and giving you cues for the new, correct performance, you can do the right thing and appear to have improved.

You can do the right thing afterwards, too but you have to concentrate hard each time on exactly what to do. The new knowledge, action, technique or performance feels strange having done it the other way for so long.

Because the new technique differs from the old way there is a conflict or tension between them. Your brain detects this conflict and instantly activates a knowledge protection mechanism called proactive inhibition (PI for short).

PI is a well researched psychological phenomenon. PI protects all your learned knowledge and skills, right and wrong, and strongly resists and slows down any attempt to change or improve your prior knowledge and skills,

We all have this knowledge protection mechanism but it is stronger in some people. It is an unconscious mechanism and we have little or no control over it, as demonstrated here.

Demonstration of the brain mechanism that makes old habits die hard

This simple but intriguing activity is a demonstration of the powerful interference effect caused by prior learning.

Exactly what it means for you personally will become clearer after you have done the two short tasks and you interpret your scores.

Now, please proceed to the activity.

Interpretation of your scores

By doing the activity you experienced proactive habit interference, also known as the proactive inhibition (PI) effect and therefore better understand the powerful effects of prior learning on new learning.

From the point of view of the learner who is trying to correct his or her misconceptions, the explanation of how proactive habit interference blocks or slows down learning and adaptation is like this:

  • The new understanding, concept or mental map feels strange having thought it the other way for so long
  • Because the new understanding differs from the old familiar accustomed way there is a conflict or tension between them
  • The brain detects this conflict and instantly activates proactive inhibition (PI for short) or proactive habit interference, a well researched knowledge protection mechanism
  • PI protects all learned knowledge, right and wrong, and strongly resists and slows down any attempt to change or improve prior knowledge
  • We all have this knowledge protection mechanism but it is stronger in some people. It is an unconscious mechanism and we have little or no control over it
  • The level of PI a person has is not associated with their intellectual ability or "IQ"
  • PI is why old knowledge dies hard and why self-improvement is so difficult, slow and frustrating under conventional teaching and training methods
  • PI causes accelerated forgetting (within minutes or hours) of the new understanding and this is why you revert to your old incorrect ideas when you are placed under stress
  • You know what you're thinking wrong and what you should be thinking and you're highly motivated to improve but your brain (force of habit, i.e., PI) won't let you change
  • It is a sobering fact that with conventional teaching and learning methods it can take you up to 2,000 repetitions of the new knowledge or understanding before you are comfortable and competent with it and it eventually replaces your "old" way.

All this is known as the transfer of learning problem.

Now you know what the problem is and what it feels like, you are ready for the solution. Being aware of PI and it's effects, however, is not enough to overcome it. Simply re-teaching a skill, action or information, even when supported by specific videotaped feedback to improve awareness, is unlikely to work quickly, if at all. You need an alternative teaching method that bypasses habit interference altogether in order to accelerate learning and understanding. This teaching method is called Old Way/New Way®.

Old Way/New Way® learning

Personal Best Academy uses and teaches Old Way/New Way® to teachers, tutors, workplace trainers, instructors, sport coaches, players, athletes, physiotherapists, sport medicine practitioners, sport psychologists and other individuals seeking to improve human performance and adjustment.

Old Way/New Way® is not like behaviour modification, NLP, brainwashing or hypnosis, nor is it a kind of psychological conditioning.

It is readily incorporated into what educationalists normally do and is well accepted by learners—it is very user-friendly.

Based on a novel interpretation and synthesis of well researched and accepted learning principles, Old Way/New Way® is far superior to conventional approaches to correcting errors and misconceptions, improving understanding, correcting technique problems and developing new skills.

With Old Way/New Way® there is no need for special equipment, although the use of video feedback, stop-motion analysis and kinaesthetic feedback can be helpful with complicated performance skills.

Old Way/New Way® works with the brain, not against it, to accelerate the natural process of change.

Learning—a new model

  1. Old Way/New Way® is a unique example of successful collaboration between researchers and practitioners to design the most effective teaching and learning protocols.
  2. Old Way/New Way® is basically a Neo-Constructivist model - the learner is the one who is responsible for learning, understanding and changing.
  3. The teacher's ability to identify and diagnose the error or technique problem is critical, as is his or her ability to identify, explain and demonstrate to the learner the "correct" knowledge, skill or technique. This befits the teacher's role as the subject matter expert.
  4. The learner can be empowered through Old Way/New Way® to take on personal responsibility for improving.
  5. The learner's prior knowledge and skills (incorrect as well as correct) must be incorporated into any teaching strategy.
  6. If no conflict is likely between new and pre-existing knowledge and skills, then a conventional teaching strategy is OK and new knowledge and skills will consolidate and build on old.
  7. However, when prior knowledge and skills are likely to conflict with the new, the learner needs to follow prescribed Old Way/New Way® procedures and not just attempt to practice the new while ignoring pre-existing knowledge and skills.

Case studies

Many kinds of skills, technique difficulties, misconceptions, misunderstandings, actions and behaviours can be changed or corrected.

A complete list of case studies, published research and school and workplace trials can be found here.

Correcting misconceptions in science and maths

Roger Henderson, Principal of the all-new William Light R-12 School in Adelaide, South Australia, is in the middle of short listing an impressive list of applicants for senior positions but he still has time to talk to me about Old Way/New Way® and its derivative, the Conceptual Mediation Program (CMP).

"Its working very well here. We use it in Years 8, 9 and 10 to teach mathematics, chemistry and physics. In fact, I'm so convinced of its effectiveness that in this new school which is still being constructed all our Year 8 teachers will receive professional development in the CMP. Eventually we'll put it through the entire school," he explains enthusiastically.

He goes on, "Harry Lyndon was a great source of information and inspiration during the three years when we were introducing the CMP at Plympton High School. We learned a lot about the subtleties of effectively using such a powerful learning method."

"Why don't you go and see Old Way/New Way® and the CMP in action in one of our classrooms?" he offers. "David Wilkinson has a Year 9 mathematics class after the break and I'm sure he'd be happy to have you sit in and see how its done."

David meets me in the staff room and tells me how he's using Old Way/New Way® to help his son, a player for the Under 15 Redbacks cricket team, improve his batting and bowling. We walk together to his classroom and he introduces me to the students. Its 30 degrees Celsius, there's no breeze and everyone is feeling the heat.

While the class is settling down David shows me a list of six misconceptions revealed in a pre-test of students' understanding of the mathematical meaning of "area" that he will deal with in today's lesson.

Once David has got every student's attention, he starts the lesson by asking several students to read the mathematical definition of "area" that is written up on the blackboard. After pointing out the key features of this definition and discussing them, he then asks them to learn the definition using the "look, say, cover, write, check times five" procedure.

This involves students in writing down the definition, saying it out loud to themselves, covering it with their hand, writing it from memory and then checking to see if they were correct. This five-step sequence is then repeated another four times, making five repeats in all.

Some of the students complain about the heat and suggest that it would be good to have the rest of the day off, but they persevere with the task and eventually complete it. David explains to me that while students find 5LSCWC somewhat boring it is a very effective method for quickly committing new knowledge into memory.

While students are working David goes on to explain that even though his students have not received prior instruction in the concept of "area" this year, they nevertheless have formed their own ideas on what "area" is. Some of these ideas are in fact misconceptions and have to be corrected so that subsequent learning is based on a correct rather than an incorrect knowledge base.

The prevalence of basic misconceptions is widespread in many students despite careful teaching to try to ensure that they "get it right" the first time. Inattention, lapses of concentration, personal problems, lack of motivation and other preoccupations are just some of the reasons why initial learning does not always "take", leaving many students with a raft of misconceptions throughout their school years and even into tertiary studies.

Misconceptions are found among students of all ability levels. These misconceptions in their understanding of fundamental concepts interfere with their subsequent learning progress. Any attempt to teach a new correct idea over the top of a misconception results in the accelerated forgetting of the new idea.

David continues the lesson by uncovering a list on the blackboard that lists the six main misconceptions of the mathematical meaning of "area." He explains to the class that these are some of their own ideas on what "area" means. I note that he does not tell them that they are "wrong." "Lets look at this first definition," he says. "Patricia, you said that 'area' was 'the space inside something'. Some others also had that definition. Take a look at our original definition of "area" and read it to us, please?"

"Area is the amount of surface enclosed within certain boundaries," reads Patricia. "Its measured in square units - square centimetres, square metres, hectares." "How does that differ from your own definition of 'area', Patricia?" asks David. She hesitates a while. "Read your own definition again," suggests David. "Area is the space inside something," says Patricia. "And now read out the other definition," asks David. Patricia reads the definition. "Now, what's the difference between your definition and the other definition of area," asks David. "My definition is about space and the other is about surface,' she volunteers. "That's right! And what do you mean by 'space' inside something?" asks David. "Its got to do with the contents of something," explains Patricia. "Yes. And 'area' is not about content but about surfaces," offers David.

David continues, "Now, read your own definition of area again to us, Patricia." "Area is the space inside something," reads Patricia. "Now read the other definition again," asks David. "Area is the amount of surface area within certain boundaries. Its measured in square units - square centimetres, square metres, hectares," says Patricia. So, what's the difference between your old definition and this new definition of area? asks David again.

I think I'm starting to get the idea of how a whole-class Old Way/New Way® mathematics lesson goes. David continues by asking another student to read their own definition of 'area' which is, "the distance between an enclosed object." Like Patricia's incorrect notion of 'area', this new misconception is also shared by a number of other students and is handled in the same way. Other misunderstandings about 'area' include, "the inside of a square", "the amount of space inside a shape", "the amount of room in an enclosed shape", and "the amount of space around something." Eventually, each of these six shared misconceptions of 'area' is dealt with in turn by having students repeatedly compare their own definition with the correct mathematical definition.

In this way, students' misconceptions become their "old ways" and they are offered a "new way" of understanding the concept of "area." When the differences between their old and new way become clear they are asked to practice using their new definition of "area" and relate it to their other knowledge by writing six different sentences using their new meaning of "area." This completes the lesson.

I ask David what advantages this method has over conventional re-teaching to correct students' errors and misconceptions. "There are a number of important advantages over conventional re-teaching," he explains. "First, while we cover less content initially, because students understand the material better first time we subsequently have to spend less time going over old ground so we end up covering more content in the long run."

"Second, their level of conceptual understanding ends up being so much higher than with conventional teaching and re-teaching. In Year 9 we are handling concepts that are normally not introduced until Year 12 and the kids are coping well with it. On average they score around 80% to 90% on their summative tests." "What kind of testing do you do?" I ask, thinking that perhaps this involves less demanding testing like simpler recognition tests. "We test for understanding and application and not just for recognition and ability to recall information," he explains.

"The third advantage of Old Way/New Way® is that, because their understanding is so much better, their interest levels are maintained for much longer and we can develop a particular topic over an extended period. For example, after three months teaching about "forces" we were able to take them to a very advanced level of understanding; under conventional teaching students get confused which makes them easily distracted and disruptive after only two or three weeks on that topic."

He adds, "The fourth advantage is that students are less disruptive in class. Because they understand the material being taught, or at least have the means by which they can address their confusions, they are able to concentrate longer on their work and actually work harder. And because they achieve better grades they feel that the extra effort that this involves is justified. All students want to learn - that's why they are at school. Old Way/New Way® enables to them to do just that and do it better. A students' disruptiveness is very often simply an indication of their confusion and frustration in the learning process. They are protesting their lack of success and their inability to understand."

"What about parents - how do they feel about this program" I ask. "We have excellent parental support for the program. Parents see that their children are achieving consistently better so they are 100% behind the program," David explains.

My next question is, "What about the students themselves? What do they say about Old Way/New Way® and the CMP?" "We've collected student comments about the program and they all say that the effort required to use Old Way/New Way® is worth it because it helps them learn much better and they will therefore continue to use it. The point is that Old Way/New Way® requires them to think. Thinking is hard work. The difference with this method is that when students make the effort they can be sure to get good results, whereas with conventional re-teaching they still have to expend the effort but it will take them very much longer to get results and even then you can't be sure it will work."

My last question is, "What about you, David? Old Way/New Way® and the CMP are so radically different from conventional re-teaching styles. What did you have to do to change your own teaching style to something so different from how you used to teach? Don't they say that old habits die hard?" David explains, "Yes, I had to use Old Way/New Way® to change my own teaching style. Twenty-eight years of teaching tend to produce some fairly ingrained teaching skills and although I knew that I had to change and what I wanted to do, I always slipped back into my old teaching style every time I walked into a classroom. That is, until I mediated my old and new ways of teaching."

"Where do you go from here, David?" I asked. "Because Old Way/New Way® and the CMP are so successful we would like to become a Best Practice School or a Centre of Excellence school for the method. Plans are underway to prepare a school-based professional development course for other teachers interested in learning about Old Way/New Way® and the CMP. There's a long way still to go but we've certainly got a successful track record without equal anywhere and that's a good foundation to build on."

Update, August 1998. A Year 11 class of students who have studied science using Old Way/New Way® are now so far advanced in their level of understanding that they will be permitted to take the year 12 examinations this year.

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