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"Ollerton, Mike"
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Mathematics for human flourishing: Chapter 13 Love
After toiling for two years to try to solve a particular research problem, I discovered a fundamental error in a paper that I had based my ideas on. Love is the greatest human desire - for exploration, meaning, play, beauty, performance, truth, struggle, power, justice, freedom, community - and live is served by them. Speaking personally, I love teaching mathematics with a passion.
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Same starting point, different outcomes
Other solutions are to divide themselves into one group of six or into six 'groups' of one. [...]with 6-1 = 6 I am always interested in listening to their descriptions as to whether groups of one are actually 'groups'? Earlier in the year I had used the same task of dividing amounts into equal sized groups. [...]I decided to bid them farewell, with a morning's work on sequences, where one particular sequence began with the number 3 and continued by successively adding 2; thus 3 + 2 + 2 + 2 + 2 + 2 ... producing many prime numbers, including 3, 5, 7, 11, 13, as well as some non-prime numbers; the first few of these are 9, 15, 21. The difference was how much more confident the Year 6 children were, especially with regard to knowing that each prime number had exactly two factors and how, by using this knowledge, they knew that number 1 was not prime.
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Mathematics for human flourishing: Chapter 10 Justice
For my part I suggest traditional school mathematics assessments, via high stakes national examinations, are deeply inequitable and fail to give students opportunities to demonstrate their mathematical thinking skills; their capabilities to discuss, explore, pattern spot, conjecture, generalise and, ultimately, prove. Arguments about what content should be included in high school mathematics fail to acknowledge the elephant in the room: we haven't yet figured out how to teach the concepts of algebra well to most students. In a recent piece in MT279, he shares his rationale for the formation of teaching mathematics for social justice and discusses the importance of developing the agency of learning mathematics.
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Mathematics for human flourishing: Chapter 8 Struggle
(Donaldson, p.115) A key issue in my practice is to try to create a classroom culture where I offer tasks that are both accessible and challenging; to encourage students to experience struggle in positive ways. What follows is an extract from a blog that appears on the Grayrigg CE School website https:// www.grayrigg.cumbria.sch.uk I have no idea what the children in my school will be when they are older, I don't know which bit of their curriculum learning will be most important to their personal success, but I am confident that the ability to push themselves, be resilient when they wobble, endure when something doesn't quite go as planned and to learn from mistakes will be important, not only in their future careers, but for the type of person they become and their personal well-being, because the most important thing children need to know is that it's OK to not be perfect. Fortunately, here at Grayrigg they have an excellent role model of imperfection in their head teacher - I am proud to be imperfect, I get so many things wrong, but fortunately I love to wobble! (Kirsty Cooper, Grayrigg Headteacher) I see a strong connection here between Kirsty's wobbling and:
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Mathematics for human flourishing: Chapter 7 Truth
The lesson involved practical equipment; the visit, however, clashed with the farewell assembly for Y11 students and, because I was a form tutor, I anticipated the assembly would over-run into the first lesson of the day. Because the lesson was a continuation of the previous lesson, I made sure they knew what they would be doing, where the equipment was and that some visitors would be arriving to ask them about the work they were doing. All was calm, indeed the noise level increased slightly upon my appearance and the lesson came and went. Are there any patterns for non-prime numbers that end in 1,7 or 9?); * Using Dienes apparatus, explore what different totals can be made with just four pieces of ones and tens.
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What might a humane mathematics education look like?
What would you do? (Postman and Weingarter, 1969 p65) Whilst the above quote refers to school education per se, I suggest there is much to be considered here, with regard to school mathematics and how testing, across compulsory education, has negative impacts upon children's mathematics education. How might you assess and report on students' communication skills in mathematics? I suggest journal writing, where students go beyond 'doing' mathematics and communicate, through writing about how they have solved mathematical problems and how they have developed these tasks. [...]how can students' engagement, with 3D geometry, be assessed through an examination question? The aim should be to show 'mathematics as a process, as a creative activity' in which pupils can be fully involved, and not as an imposed body of knowledge immune to any change or development.
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Mathematics for human flourishing: Chapter 6 Permanence
[...]a task that might involve summing sequences of unit fractions, or the reciprocals of powers of two, or powers of three, or cube numbers or Fibonacci numbers, which would lead to 'such discoveries. (Page 97) What the permanence of mathematics offers is trust that mathematical reasoning is solid ground that will not move. A beautiful quotation in a letter from Chris Jackson, a prisoner with whom Francis communicates throughout the book, puts the importance of learning mathematics into a different stratosphere:
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Adding fractions and some fascinating questions from Lila
(See Figure 1) Whilst this is my interpretation of giving learners direct instruction, I do so in order to teach children how to add fractions without telling them how to add fractions. Attending to their folded pieces of paper the equivalences between ... and ... and between ... and ... is intended to provide a sense of a common denominator. Returning to Lila's lesson and just after determining the result ... her first question was: ... but my teacher won't let me fold up pieces of paper, so how does this help? I wondered if there may be some pedagogical dissonance between me and her teacher, especially as Lila and her family live in America, all of whom were visiting their grandparents, for several weeks, because of Covid restrictions for travelling to the USA.
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