Students learning and understanding will therefore be more broad and in depth about the subject. Bringing thoughts back to the basics of mathematics to embolden the students understanding and make the subject less daunting. This simply means that the teacher should encourage children to explore the points relating to problems. Together with allowing students to inspect these multiple aspects so that they have a flexible understanding of the topic.īasic Ideas – “Teachers with PUFM display mathematical attitudes and are particularly aware of the “Simple but powerful basic concepts and principles of mathematics” (e.g. This means the teacher should respect the multiple aspects of problems and solutions, moving away from there only being one answer. Multiple Perspectives – “Those who have achieved PUFM appreciate different facets of an idea and various approaches to a solution, as well as their advantages and disadvantages In addition, they are able to provide mathematical explanations of these various facets and approaches…” (Ma, 2010, pp. In the students learning this would mean that their knowledge learnt would not be fragmented but rather connected. Also the importance of highlighting this to students when teaching so that they can discover and see these links. This means being able to make links and see connections between mathematical concepts in a wide range of things in society. To achieve the expected knowledge that Ma thought a teacher should have, she came up with 4 principles that would enable a teacher to have a profound understanding of fundamental mathematics:Ĭonnectedness – “A teacher with PUFM has a general intention to make connections among mathematical concepts and procedures…” (Ma, 2010, pp. Although the term ‘profound’ is often considered to mean intellectual depth, it’s three connotations, deep, vast, and thorough, are interconnected.” (Ma, 2010, pp. “By profound understanding I mean an understanding of the terrain of fundamental mathematics that is deep, broad and thorough. She figured that during a teachers training they should be made aware and become habitual with basic (fundamental) mathematics as this is what the teachers in China have knowledge on from the start (Ma, 2010). Ma (2010) concluded that the reason the U.S.A were so behind was because teachers didn’t obtain an extensive understanding of elementary mathematics. Ma wanted to understand why the U.S.A were in a much lower rank for test results than China was. Once I came across Liping Ma’s book and read up about her theory then I was able to understand it better and see the links in all my future lectures. At first I just brushed it over as I said to myself I can research into it later on in the module as I didn’t understand it and quite frankly found it confusing. Our first ever lecture in this module introduced us to PUFM (profound understanding of fundamental mathematics). I have mentioned in a serious blog how i didn’t like maths in high school but ‘Discovering Mathematics’ has made me appreciate it again as i now have a deeper and broader understanding of fundamental mathematics and how this links with wider contexts. It’s nothing to do with complex equations or any horrible higher maths recaps. I get misty-eyed when I think about this model nearly being over as I have enjoyed it so much and learned things I would never have known about otherwise. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.įollow our Number Sense blog for more math activities, or find a Mathnasium tutor near you for additional help and information.As I write this blog, semester 1 of 2nd year is almost at its end. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. DNA moleculesĮven the microscopic realm is not immune to Fibonacci. When a hawk approaches its prey, its sharpest view is at an angle to their direction of flight - an angle that's the same as the spiral's pitch. And as noted, bee physiology also follows along the Golden Curve rather nicely. Following the same pattern, females have 2, 3, 5, 8, 13, and so on. Thus, when it comes to the family tree, males have 2, 3, 5, and 8 grandparents, great-grandparents, gr-gr-grandparents, and gr-gr-gr-grandparents respectively. Males have one parent (a female), whereas females have two (a female and male). In addition, the family tree of honey bees also follows the familiar pattern. The answer is typically something very close to 1.618. The most profound example is by dividing the number of females in a colony by the number of males (females always outnumber males). Speaking of honey bees, they follow Fibonacci in other interesting ways.
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