A Safe, Supportive Math Classroom
by Dr. Margaret Taplin
Institute of Sathya Sai Education, Hong Kong
|Recently I had a conversation with some
colleagues who teach in a university. They were very worried about something they had
noticed about their undergraduate students - a fear of making mistakes. They had noticed
that these students were very reluctant to hand in assignments in case they were 'wrong'
and were often spending time very unproductively in checking and re-checking their
answers. While it is, of course, important to encourage students to be careful about
checking their work, and to help them to develop a repertoire of checking strategies, this
conversation does seem to reflect a growing problem, that more and more students are
becoming afraid to try new things in case they fail, and/or become depressed and question
their own self-worth if they do make mistakes. Mathematics, with its emphasis on 'right'
or 'wrong' answers can potentially reinforce these fears. On the other hand, however, the
mathematics classroom can also be the perfect environment for sensitive teachers to help
their pupils to face up to and overcome these fears - and, of course, the earlier in the
child's school life that this support begins, the better.
|The purpose of this article is to illustrate some
ways in which mathematics teachers can help to create a secure, supportive classroom
environment in which the pupils learn to not fear failure and to value making mistakes as
an opportunity to learn and grow. Each section begins with a quotation from the Sathya Sai
Education in Human Values programme, a world-wide, secular programme designed to support
the integration of values education across the curriculum. The sources of these quotations
have not specifically been acknowledge because they appear in similar form in many
different places, but the quotations have been printed in italics. More details about
these ideas are discussed in my book 'Education in Human Values Through Mathematics,
Mathematics Through Education in Human Values'. For further information about how to order
this book, please contact email@example.com
True education should make a person
compassionate and humane.
|It is likely that unwillingness to participate in
the mathematics classroom arises from lack of understanding and compassion,
which can often be unconscious, by teachers and other pupils. Consequently, we need to ask
the question: how can we encourage more effective participation by any students not
- Do not be angry if a child cannot understand something or makes a mistake, because this
can lead to fear of failure.
- Show him/her how to recover from the mistake and try again.
- Tell them about famous people who were not afraid to make mistakes (see stories below),
or about some of the mistakes you have made - but also encourage accuracy and patiently
ask them to correct their careless errors. A useful source of ideas is a book called
"Mistakes That Worked" by Charlotte Foltz Jones.
|Students should not allow success or
failure to ruffle their minds unduly. Courage and self-confidence must be instilled in the
- Use positive visual and body-language cues (nodding, smiling) and prompts (ah ha, hmm)
to encourage them to arrive at appropriate answers.
- Be careful not to frown if a child makes a mistake, and don't allow other children to
frown if a classmate makes a mistake either.
|There is over emphasis on quick and
easy gains rather than patience, fortitude and hard work.
|Peter was a very clever eleven-year-old. In the
final year of his primary schooling, there was only one test on which he scored less than
100%, and then he only lost half a mark. His classwork was always done quickly and
correctly. When he knew that he could succeed, he was confident and willing to work hard.
To challenge his thinking, Peter's teacher would give him some difficult problems. If
Peter could not immediately see a way to solve a problem, he became a different child. He
would sit, drawing on his notepad, or wander around the room. He would even ask his
teacher if he could spend the time tidying the storeroom. Peter, who was normally so
successful and confident, was afraid to tackle a difficult task because he was afraid that
he might fail. So his solution was to quit, to make the fears go away. Fortunately, the
story had a happy ending, because Peter and his teacher worked together to help him to
develop more courage to tackle difficult problems rather than taking the easiest path of
|Many writers have written about students such as
Peter, who expect solutions to come to them quickly and easily and will give up rather
than face negative emotions associated with trying the task. Another concern is that they
often are not aware of when it is worthwhile to keep on exploring an idea and when it is
appropriate to abandon it because it is leading in a wrong direction. They need to know
when it is appropriate to use a particular approach to the task, and how to recover from
making a wrong choice.
|Clare, aged ten, was given the following problem
|By changing six figures into zeros you can make this
sum equal 1111.
|Clare selected the strategy of changing numbers in
all three columns simultaneously. She worked at the task with patience and fortitude
for two hours. As she worked, she said to herself, "I know that this is going to work.
All I need is time, to find the right combination." After she repeated the strategy 21
times, her teacher interrupted and suggested that it might be time to look for another way to
solve the problem.
|In Peter's case, it was not enough for his
teacher to tell him that frustration, for example, is a normal part of problem solving,
and to encourage him to spend more time working on the task. Clare, on the other hand, was
"overpersevering", locked into persistently pursuing one approach when it may be
more appropriate when stuck to use other strategies, even such as help-seeking. One of the
responsibilities of a mathematics teacher is to help pupils to learn how to persevere when
the problem-solving process becomes difficult. They also need to know how to make
decisions about avoiding time being wasted on "overperseverance".
|STRATEGIES FOR ENHANCING PERSEVERANCE
- Equip learners with a range of strategies/techniques for solving different types of
- Encourage them to experience the full range of positive and negative emotions
associated with problem solving.
- Promote the desire to persevere.
- Help them to make "managerial" decisions about whether to persevere with a
possible solution path (when to keep trying, and when to stop).
- Encourage them to find more than one way to approach the problem.
One sequence of strategies which
is used frequently by successful, persevering problem solvers is the following:
- Try an approach.
- Try it 2-3 times in case using different numbers or correcting errors might work.
- Try something different. (You might decide to come back to your old way later.)
|One student used this
sequence to persevere successfully with a problem.
|When you are teaching the appropriate topic, take
a minute to tell your pupils an anecdote about one of the famous mathematicians who
contributed to this particular field of mathematics. It is important for pupils to be
aware of the 'human' side of these famous people. "Using biographies of
mathematicians can successfully bring the human story into the
mathematics class. What
struggles have these people undergone to be able to study mathematics?..." (Voolich,
About Famous Mathematicians
|Education should impart to students
the capacity or grit to face the challenges of daily life.
- For students who have tried but are still having
difficulties, McDonough (1984) advised that the teacher:
- ask the pupils to restate the problem in their own words and if this
indicates that they have mis-read or mis-interpreted the card, ask them to read the
- to help with the understanding of the written instructions question the
pupils carefully to find out if they know the meanings of particular words and phrases (i.e.
- have the pupils show the teacher what they have done, compare this to
what is asked in the instructions, and question the pupils to see if they could think of
another method, for example, "Could you have done this another way?" or, "Have
you ever done a task like this before?"
- if necessary, give the children a small hint but only after
questioning them carefully to find out what stage they have reached.
- If the teacher follows procedures such as those described above, the pupils will be
encouraged to be more thoughtful and self-reliant.
- If pupils are panicking or unable to think what to do, introduce them to the valuable
technique of silent sitting - that is, sitting for a few minutes in a state of complete
outer and inner silence. You can tell them about famous mathematicians who have
solved problems by using this technique. For example, Sir
|By example and precept, in the
classroom and the playground, the excellence of intelligent co-operation, of sacrifice for
the team, of sympathy for the less gifted, of help...has to be emphasised.
|Some teachers' comments:
|I was concerned about two things. One was
the way I could use praise to develop self esteem. The other thing was the way in which I
was involved in my pupils' activities. I chose these issues because I had got into the
habit of teaching from the front of the room and responding to the students' answers with
comments such as "Okay", "Good", "Sensible". I was also
concerned that the girls were outnumbered by boys in the class and there was an underlying
assumption that the boys were better than the girls, made particularly evident by a vocal
group of boys. I consciously placed myself with different pupils in the classroom and
moved to groups when asking or answering questions. I deliberately targeted the quieter
children to encourage them to participate in group/class discussions. I developed a
repertoire of responses to students' answers, including, "Good thinking
strategy," or "Can you clarify that response?" I allowed more response
time, focused on permitting girls to respond following incorrect answers and followed
their answers immediately by further questions. Although I only had two weeks in which to
implement these initiatives, I felt sufficiently positive about the change in quality of
the students' responses to warrant continuing this approach. (Primary School Teacher)
|four components of language skills:
speaking, listening, reading and writing. Interactions are indeed the heartbeat of the
mathematics classroom. Mathematics is learned best when students are actively
participating in that learning. One method of active participation is to interact with the
teacher and peers about mathematics. (Primary School Teacher)
|I chose to work with a group of children
about whom I felt I knew very little. I realised that these children could have ability
which was not being shown, so I decided to make a more concentrated effort to provide a
variety of experiences and activities, to allow some 'non-performing' children to
demonstrate their skills. I also recognised the need to discourage a group of 'noisy' boys
from putting down the girls and their contributions. A colleague undertook a similar
exercise with an older class. She was surprised that she knew the boys better as being
more confident and responsive. She intends to investigate this further by asking a
colleague to observe her teach to find out whether her suspicions are true that she is
responding more to the boys than to the girls. (Secondary School Teacher)
|Education must award self-confidence,
the courage to depend on one's own strength.
- Some of us may believe that it is acceptable to be untruthful if it is to avoid hurting
somebody else's feelings. On the other hand, some people can also be cruelly truthful and
blunt if they do not like something about another person. We need to realise that neither
of these behaviours is really appropriate.
- If we are patient and consistent in our approach and give criticism with compassion, we
will have a more significant influence on the child's subconscious levels of thinking than
- This does not mean that you have to be blunt or to hurt somebody else's feelings by
telling them something unkind. For example, when correcting students you could say,
"I don't like the way you answered that question. I like it better when you give me a
sensible answer and I know that you have put thought into it." Or you could say,
"I don't really like the way you have done this piece of work. I prefer it when you
do it more slowly and make fewer mistakes". This means that you are making it very
clear to the other person why you are not happy and how you would prefer her to behave.
|The teachers who wrote the comments above were
asked to recommend ideas which they could try in their classrooms to encourage more
understanding of those students who may not feel safe to participate as fully as they
should or could be. Recommendations included:
- give continuous encouragement, mainly verbally. Value everybody's responses and have
firm rules about interruptions and 'put downs',
- encourage a balance between co-operative and competitive teaching and learning styles,
- demonstrate an 'expectation' for students to participate,
- encourage group work and peer tutoring, particularly on activity-based and
- allow students sufficient time to complete their work,
- encourage different strategies for approaching and solving problems,
- talk to the non-participators about their reasons for lack of participation - perhaps
our perceptions are invalid.
|Bell, E.T.(1937). Men of Mathematics
(Touchstone Edition, 1986). New York: Simon & Schuster. ISBN 0-671-62818-6 PBK
|Lovitt, C. & Clarke, D. (1992). The
Mathematics Curriculum and Teaching Program, Professional Development Package, Activity
Bank Volume 2. Victoria, Australia: Curriculum Corporation. ISBN 0 642 53279 6.
|McDonough, A. (1984). 'Fun maths in boxes', in
A.Maurer (Ed.). Conflict in Mathematics Education, (pp.60-70). Melbourne,
Australia: Mathematical Association of Victoria.
|Perl, T. (1993) Women and Numbers. San
Carlos, California: Wide World Publishing/Tetra. ISBN: 0-933174-87-X
|Voolich, E. (1993). 'Using biographies to
'humanize' the mathematics class'. Arithmetic Teacher, 41(1),16-19.