Educating the heart with maths and statistics

What has love got to do with maths?

This morning at the Twitter chat for teachers, (#bfc630nz) the discussion question was, How and what will you teach your students about life this year? As I lurked I was impressed at the ideas and ideals expressed by a mixed bunch of teachers from throughout New Zealand. I tweeted:  “I wonder how often maths teachers think about educating the heart. Yet maths affects how people feel so much.”

My teaching philosophy is summed up as “head, heart and hands”. I find the philosophy of constructivism appealing, that people create their own understanding and knowledge through experiences and reflection. I believe that learning is a social activity, and I am discovering that mathematics is a social endeavour. But underpinning it all I am convinced that people need to feel safe. That is where the heart comes in. “People do not care how much you know until they know how much you care.” Relationships are vital. I wrote previously about the nature of teaching statistics and mathematics.

Teachers are people

In the culture of NZ Maori, when someone begins to address a group of people, they give a mihi, which is an introductory speech following a given structure. The mihi has the role of placing the person with respect to their mountain, their river, their ancestors. It enables the listeners to know who the person is before they begin to speak about anything else. I am not fluent in te reo, so do not give a mihi in Maori (yet), but I do introduce myself so that listeners know who I am. Learners need to know why I am teaching, and how I feel about the subject and about them. It can feel self-indulgent, thinking surely it is about the subject, not about me. But for many learners the teacher is the subject. Just look at subject choices in high school students and that becomes apparent.

Recently I began studying art at an evening class. I am never a passive learner (and for that reason do feel sympathy for anyone teaching me). Anytime I have the privilege of being a learner, I find myself stepping back and evaluating my responses and thinking of what the teacher has done to evoke these responses. Last week, in the first lesson, the teacher gave no introduction other than her name, and I felt the loss. Art, like maths, is emotionally embedded, and I would have liked to have developed more of a relationship with my teacher, before exposing my vulnerability in my drawing attempts. She did a fine job of reassuring us that all of our attempts were beautiful, but I still would like to know who she is.

Don’t sweeten the broccoli

I suspect that some people believe that maths is a dry, sterile subject, where things are right or wrong. Many worksheets give that impression, with columns of similar problems in black and white, with similarly black and white answers. Some attempt to sweeten the broccoli by adding cartoon characters and using bright colours, but the task remains devoid of adventure and creativity. Now, as a child, I actually liked worksheets, but that is probably because they were easy for me, and I always got them right. I liked the column of little red ticks, and the 100% at the end. They did not challenge me intellectually, but I did not know any better. For many students such worksheets are offputting at best. Worksheets also give a limited view of the nature of mathematics.

I am currently discovering how narrow my perception of mathematics was. We are currently developing mathematical activities for young learners, and I have been reading books about mathematical discoveries. Mathematics is full of creativity and fun and adventure, opinion, multiple approaches, discussion and joy. The mathematics I loved was a poor two-dimensional faded version of the mathematics I am currently discovering.I fear most primary school teachers (and possibly many secondary school maths teachers) have little idea of the full potential of mathematics.

Some high school maths teachers struggle with the New Zealand school statistics curriculum. It is embedded in real-life data and investigations. It is not about calculating a mean or standard deviation, or some horrible algebraic manipulation of formulae. Statistics is about observing and wondering, about asking questions, collecting data, using graphs and summary statistics to make meaning out of the data and reflecting the results back to the original question before heading off on another question. Communication and critical thinking are vital. There are moral, ethical and political aspects to statistics.

Teaching mathematics and statistics is an act of social justice

I cannot express strongly enough that the teaching of mathematics and statistics is a political act. It is a question of social justice. In my PhD thesis work, I found that social deprivation correlated with opportunities to learn mathematics. My thoughts are that there are families where people struggle with literacy, but mostly parents from all walks of life can help their children with reading. However, there are many parents who have negative experiences around mathematics, who feel unable to engage their children in mathematical discussions, let alone help them with mathematics homework. And sadly they often entrench mathematical fatalism. “I was no good at maths, so it isn’t surprising that you are no good at maths.”

Our students need to know that we love them. When you have a class of 800 first year university students it is clearly not possible to build a personal relationship with each student in 24 contact hours. However the key to the ninety and nine is the one. If we show love and respect in our dealings with individuals in the class, if we treat each person as valued, if we take the time to listen and answer questions, the other students will see who we are. They will know that they can ask and be treated well, and they will know that we care. When we put time into working out good ways to explain things, when we experiment with different ways of teaching and assessing, when we smile and look happy to be there – all these things help students to know who we are, and that we care.

As teachers of mathematics and statistics we have daunting influence over the futures of our students. We need to make sure we are empowering out students, and having them feel safe is a good start.

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Anxiety, fear and antipathy for maths, stats and OR

I love mathematical subjects. I love statistics and teaching statistics, and I love Operations Research and teaching Operations Research. But I do not represent the majority of people in the world and I definitely do not represent the majority of my students who come into my courses.

Many people don't really like mathematics.

People take my courses because they are required to. They don’t really want to do statistics and quantitative methods. However, by the end of the course, many have discovered, to their joy, that they CAN do maths, and actually enjoy it. It is empowering for them and wonderful for me. Emotional students have told me how the course has changed the way they see themselves and mathematical subjects. One young woman had previously failed two traditional statistics courses. However after passing our course, she went on to further stats courses, and eventually had a marketing internship involving data analysis, worked as a tutor on our course and completed a postgraduate degree. This is the letter she sent me after passing the course:

“I just thought I would let you know that I have really enjoyed this course, considering I hated maths this is not to be taken lightly! I was told it would be a good course for me to take but was slightly sceptical. However, I think being able to continuously see your progress and results gave me a lot of motivation and a great sense of achievement.

People enjoy succeeding.

“The tutorials were also fantastic, the tutors were always friendly and very helpful and a lot of credit must go to them. Obviously without these tutorials I would not have passed the course.

“Thank you for offering a course that has enabled me to understand and even at times enjoy stats!”

Ideas for helping students overcome antipathy towards mathematical things.

Perserverance

One difference I have noticed between people who succeed at maths and those who don’t, is what they do when they get something wrong. When I do a problem and get a wrong answer, I do not see it as a personal failure, but try again. However people who are less secure in their ability to do maths get upset at each wrong answer, and give up easily so that they can avoid further failure.They seem to take mistakes personally.

We do two things in our course to help with this. We have a large bank of problems for students to try over and over again, and tell them explicitly that we expect them to do the practice test at least seven times before they are ready for the supervised test. This way they see the failure as part of the process, rather than as a reflection of their own inadequacy. Secondly we begin our course with quite easy material and build up to more difficult. This way they start to experience success, and learn that the key to passing is putting in more time.

Relevance

Another issue is that people who dislike mathematics, often do so because it feels irrelevant and a waste of time. Sometimes this is an excuse, but, tied in with the first reason, it is easy to see that people will not spend a lot of time dong something that makes them feel like a failure, and for which they cannot see the purpose. So another thing we do in our course is make sure that every single example is there because it is useful for them, and has a real world application to which they can relate, or at least which they can see is important. For example, our questions on Binomial distribution are based on marketing, human resources, and retailing examples. Our analysis is done on data collected from the students themselves. In our Operations Research course we get them to work out a MCDM scenario related to what they will do at the end of the course. Statistics and Operations Research are inherently interesting and practical, so it should not be difficult to keep them that way.

Borrowed self-efficacy

Self-efficacy is the belief a person has in how well they can accomplish a task. Studies into effective learning have found that the level of self-efficacy a person has regarding a certain subject or learning in general is a good predictor of how well they will do. You could say that it may be quite realistic – that they believe they can do it because they can. But studies have controlled for that and the effect is still there. Now we can’t inject people with self-efficacy, but we can lend it to them. Self-efficacy can be borrowed from the instructor or the course. We tell them that this is a course for people who have previously found maths difficult. We tell them how successful other people like them have been in the course. We tell them how well it is designed and how much we are willing to help them to succeed in learning the material. Students feel this encouragement and take heart from it.

Love

People don’t care how much you know until they know how much you care. I believe you need to love the students. I’m talking here about genuine, respectful love for other human beings. We need to care about them as people, not just students in our classes. We need to love our subject and believe intrinsically in it. This shines through, even when we don’t give face-to-face lectures. One student told me he knew I was a good teacher because I was so thorough. I am thorough because I love the students and want them to succeed.

Love is not a word used often in secular higher-education. However I have been privileged to see many great teachers, whose whole approach was centered in love for the students.

These are my ways to help students who are anxious, fearful or less than keen to be taking my course.  I teach them to see failure as a step to success, build the material up in small steps, make it real, help them develop self-efficacy, and let them feel how much I care. The rewards are so worth the effort!