Completely agree with Alf. I remember trying to teach angles to a low ability class in a secondary school and they really struggled. A week or so later I taught bearings (not my favourite topic) even though it was not on their curriculum, and suddenly they all understood angles as it was a skill they wanted to use and could see a use for. I think we do kids a disservice by working solely with whole numbers, then we say oh by the way here are these things called fractions, or decimals, or negatives. Mathematics should be exciting and inspiring - and my experience is that this approach results in much better exam results!
Great talk! In my opinion, there is no one "right" way to teach math; rather, there is a variety of approaches that can be used depending on the nature of a class or student. However, students should be exposed to challenging problems to encourage their minds to observe and explore.
Nice stuff. I'm fond of the idea of a network which suggests that mathematical ideas can keep developing, they are not either mastered or not-mastered. The notion of 'purpose' also resonates, which you can't access in small steps as small steps don't reveal where you're going. And for me, 'complexity' can be introduced through challenging tasks which might lead students to stumble, but in doing so give them a sense of what they need to learn. DEK
Thanks Alf! Great video, but I might disagree? I think this messiness is great if you want kids to enjoy lessons and maths, but if we're trying to get them to pass GCESs then mastery is the better method. You've got to work on those basics before you can answer any exam questions. Sure you can have fun with maths but it's not practical in the UK education system.
I think you missed the whole point here. Alf is not suggesting that students "have fun". He is suggesting that students learn mathematics. By focusing on GCSEs solely the mathematics might get lost completely - because the focus would often then be on practicing for solving GCSE types of task , which often leads to emphasis on solving procedural tasks with little or no focus on noticing, wondering, conversation, or understanding. What is more important in your opinion: To pass GCSEs or to enjoy mathematics? What is the role of schools: To make students pass GCSEs or to introduce them to and enhance their interest in mathematics?
First example ("Grid of numbers") would be MUCH easier to grasp concept of positive vs negative if it was 19 units x 19 units with 0 at the very centre. Positives show number line "wrapped" by decades ascending toward upper right from 0 and negatives likewise descending toward lower left... Why is double digit 10 shown on same row as 9 other single digit values? Why does the row of "teens" suddenly end with 20? Why is triple digit 100 even there? If you want to introduce new learners to periodicity, then use materials that make the regularity obvious... Not really impressed...
ATTENTION, fastinating mathematics for your grand- children. POMEGRANATE AND NATURAL NUMBERS. Despite my respectable age, i,m still a big fan of delicious pomegranate. At a peaceful moment of the day, in the middle of the night, i was watching TV, and for my curiosity, i started to squesse a pomegranate and... count the number of seeds in it. Since it turnd out to be an interesting three-digit number, i soon noticed, that it was the product of three prime numbers. ATTENTION! Qestion num- ber 1: How much? was the number of seeds in a pomegranate, if is is also equal to the pro- duct of the ages of Max,s three minor grandchildren, who i know well, wich show the second, foutth and sixth primes / numbers/ , respec- tively. ATTENTION , question number 2: Tell the ages of Max,s grand- children. Thank You for the mathematics lessons.
Completely agree with Alf. I remember trying to teach angles to a low ability class in a secondary school and they really struggled. A week or so later I taught bearings (not my favourite topic) even though it was not on their curriculum, and suddenly they all understood angles as it was a skill they wanted to use and could see a use for. I think we do kids a disservice by working solely with whole numbers, then we say oh by the way here are these things called fractions, or decimals, or negatives. Mathematics should be exciting and inspiring - and my experience is that this approach results in much better exam results!
Great talk! In my opinion, there is no one "right" way to teach math; rather, there is a variety of approaches that can be used depending on the nature of a class or student. However, students should be exposed to challenging problems to encourage their minds to observe and explore.
Finally after like 5 videos of "Experts" describing this I found someone that has a legitimate understanding of it
Nice stuff. I'm fond of the idea of a network which suggests that mathematical ideas can keep developing, they are not either mastered or not-mastered. The notion of 'purpose' also resonates, which you can't access in small steps as small steps don't reveal where you're going. And for me, 'complexity' can be introduced through challenging tasks which might lead students to stumble, but in doing so give them a sense of what they need to learn. DEK
I love you Sir!
Thanks Alf! Great video, but I might disagree? I think this messiness is great if you want kids to enjoy lessons and maths, but if we're trying to get them to pass GCESs then mastery is the better method. You've got to work on those basics before you can answer any exam questions. Sure you can have fun with maths but it's not practical in the UK education system.
I think you missed the whole point here. Alf is not suggesting that students "have fun". He is suggesting that students learn mathematics. By focusing on GCSEs solely the mathematics might get lost completely - because the focus would often then be on practicing for solving GCSE types of task , which often leads to emphasis on solving procedural tasks with little or no focus on noticing, wondering, conversation, or understanding. What is more important in your opinion: To pass GCSEs or to enjoy mathematics? What is the role of schools: To make students pass GCSEs or to introduce them to and enhance their interest in mathematics?
First example ("Grid of numbers") would be MUCH easier to grasp concept of positive vs negative if it was 19 units x 19 units with 0 at the very centre. Positives show number line "wrapped" by decades ascending toward upper right from 0 and negatives likewise descending toward lower left...
Why is double digit 10 shown on same row as 9 other single digit values?
Why does the row of "teens" suddenly end with 20?
Why is triple digit 100 even there?
If you want to introduce new learners to periodicity, then use materials that make the regularity obvious...
Not really impressed...
ATTENTION, fastinating mathematics for your grand-
children.
POMEGRANATE AND NATURAL NUMBERS.
Despite my respectable age,
i,m still a big fan of delicious
pomegranate.
At a peaceful moment of the day, in the middle of the night,
i was watching TV, and for my curiosity, i started to
squesse a pomegranate and... count the number of
seeds in it.
Since it turnd out to be an
interesting three-digit number,
i soon noticed, that it was the product of three prime
numbers.
ATTENTION! Qestion num-
ber 1:
How much? was the number
of seeds in a pomegranate, if
is is also equal to the pro-
duct of the ages of Max,s
three minor grandchildren, who i know well, wich show
the second, foutth and sixth
primes / numbers/ , respec-
tively.
ATTENTION , question
number 2:
Tell the ages of Max,s grand-
children.
Thank You for the mathematics lessons.
His examples are unclear