Segar Rogers

Secondary maths teacher. Old enough to remember chalk.

[Segar Rogers @SegarRogers]

ChatGPT.
Pinch.
Of.
Salt.

[Segar Rogers @SegarRogers]

@MathsImpact What sort of skills are you thinking of?

[Segar Rogers @SegarRogers]

@ProfSmudge @MathsImpact I see a lot of this. Pupils default to a procedure without looking at the situation. They’ve been drilled to react in only one way.

[Segar Rogers @SegarRogers]

Crazy thought-experiment. Take a class and teach them:

• quotative and partitive division concepts ... but teach them to write 12 ÷ 3 as 3 ÷ 12, mirroring the linguistic order of '3s into 12'.

Would quotative strategies dominate their thinking?

Crazy ;-)

[Segar Rogers @SegarRogers]

@jaytimotheus Nice article, thank you. (Think I've seen it before actually, and I thought the same then!). I agree, the language used can make or break it ... and with the right language pupils then don't really have any problems.

[Segar Rogers @SegarRogers]

Why are pupils so inclined to divide partitively rather than quotatively? The latter rarely crosses their mind … hence why 6 ÷ ¼ is deemed hard.

Is it linguistic? (‘6 divided BY 2’ vs ‘2 divided INTO 6’?) … and semiotically the ÷ symbol in 6 ÷ 2 attaches itself to the former?

[Segar Rogers @SegarRogers]

@SmartJacques Thanks for this. I like the idea of asking questions about division but without requiring any arithmetical calculation.

[Segar Rogers @SegarRogers]

@ProfSmudge That's interesting. I've read the abstract ... can't seem to find the whole paper. Wouldn't mind seeing the list of questions they asked.

[Segar Rogers @SegarRogers]

@techknowmath @s_carriker Lol ... I don't think you liked it ;-). Fair enough. I tend to be a why-before-what or a why-alongside-what person ... but I did like his indices lesson ... the point about cognitive load resonated with me ... so sometimes I now put the why second ... but I always give it.

[Segar Rogers @SegarRogers]

@ProfSmudge @SmartJacques Hahaha. I’ve not done it for a while but I have been known the put that on the board as the title for the class ;-)

[Segar Rogers @SegarRogers]

@RichardJMurphy But Richard, I like trigonometry :-)

[Segar Rogers @SegarRogers]

@benjamindickman Exactly :-)

1/tan(π/2) is undefined, yet:

cot(π/2)
= cotangent(π/2)
= tangent of the complement of π/2
= tangent of 0
= tan (0)
= 0

Not the same thing ;-)

[Segar Rogers @SegarRogers]

@Dave_Connell_11 I shall test this next week!!

[Segar Rogers @SegarRogers]

@Dave_Connell_11 I see what you mean. I agree that for most it’s about the method rather than the operation.

I’ve remembered a question I once asked a class in an effort to highlight what I see as partitive bias in pupils’ thinking:

38 million ÷ 2 million

They all said 19 million.

[Segar Rogers @SegarRogers]

@PardoeMary @ElgarDarren I agree. My point was that secondary age pupils often forget that this approach to division exists. They’re stuck with a partitive division model which, for your example, is less obvious.

[Segar Rogers @SegarRogers]

@ElgarDarren Yes … and I think it probably is … I’m thinking of Primary ‘grouping’ and ‘sharing’.

[Segar Rogers @SegarRogers]

@ProfSmudge Yes that’s true, good point.

[Segar Rogers @SegarRogers]

@thompo71 You’re sounding very Hackenberg, Norton & Wright ;-) … and a good point :-)

[Segar Rogers @SegarRogers]

@thompo71 @ChrisMcGrane84 @AndyBrown314 @onycoutts @aap03102 @nathanday314 @garyl82 @MathsWNBorders @mrwatkinsmaths Okay. I get it. The other 3 are:
10-24-26
24-45-51
24-143-145
Nice ... but a little obscure ;-)

[Segar Rogers @SegarRogers]

@thompo71 @ChrisMcGrane84 @AndyBrown314 @onycoutts @aap03102 @nathanday314 @garyl82 @MathsWNBorders @mrwatkinsmaths I don't understand this?! I see two 7-24-25s, an 18-24-30 and a 24-32-40 ... but how do I get the other three? They all have a 24cm blue side but we know nothing else about them??!! Feeling a little inadequate!