A practical example from Secondary Mathematics by Martin Richards Maths teacher, coach and author 1
I am a Maths Teacher, and Certified Coach. I live in Gothenburg, Sweden. Although I retired from teaching some years ago, I still feel the need to talk with students about their learning, especially in Mathematics, so I am grateful that, once a week, I can go to the local Library where a mix of volunteers: University students, parents and pensioners, are ready to help schoolchildren with their homework. 2
The following story of working with one of the teenagers illustrates how an educator chooses between two skill sets, sometimes supporting the student, sometimes explaining the subject. Coaching supporting the student Teaching explaining the subject The act of choosing is a dynamic one, reflected in the changing relationships between the teacher, the student and the subject. Progress is measured in how well the student performs in solving problems on their own. I worked for many years as a Math teacher. I blended student-encouragement techniques from the world of coaching, with problem-solving techniques from the world of Mathematics. I found that combining the two sets of techniques was a delightful balancing act which has resulted in powerful learning for every student that I have worked with. 3
certain that choosing and balancing applies to other subjects too. 4
She was about 13. Let’s call her Lisa. She was here with her mother, who had put Lisa’s name on the list of students waiting for help. Her mother came up to me and showed me the list asking me, by flapping the sheet of paper with gentle insistence, to help her daughter as soon as possible. By this time I think they had been working for half an hour, maybe forty minutes, with the Maths problems in the homework. I recognised Lisa and her mother. They were often here, and they were always struggling with Mathematics. I like working with Lisa because she is teachable. She listens, she tries. She doesn’t let mistakes prevent her from trying again and again; and in the end, she gets it. Always. Lisa’s mother did not speak very good Swedish, at least not with me. She made herself understood by energetically smiling, waving her hands and pointing. I think she did the same when helping her daughter with her homework. Helping her daughter was done with love that shone through every nod and smile, and every gentle nudge of her hand on her daughter’s arm, urging her with these simple gestures to have another go, read it again, think again and never give 5
hope that her daughter will have a better chance of a good life in this country. It’s strange isn’t it, but a good life often boils down to being good at Maths, and English, (and in this country Swedish as well). I felt like the richest man in the World. I’d always been good at Mathematics, my native language is English and I had learned, after a couple of years of struggle, to speak Swedish. 6
and the mathematical problem When it came to Lisa’s turn, her mother pulled up a chair beside her daughter and invited me to sit down as though this was her living room, and invited me to help her Lisa with the Maths homework that was displayed on a computer screen. It’s not just Algebra A quick glance told me everything I needed to know. It was algebra. Equations. For some people, algebra was like a foreign language and equations feel like earthquakes in their bellies. Equations spark fear in all those who have not yet mastered them because they know equations are the grammar of Mathematics and that without equations they will never master it, and that increases the risk of them not having a good life. 7
On the screen the teacher’s reasoning - the way the equations were to be solved - was colour-coded. The equation was written in black ink, and the thoughts of the invisible mathematics teacher were written in red ink. To the initiated, this coding was blindingly obvious, and I took in the meaning of the entire page in a single blink. Lisa was not one of the initiated, and for her, the page was covered in illegible scribbles, coded beyond her understanding. 8
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