Roles of language in forming mathematical knowledge Piet Human - - PowerPoint PPT Presentation

Roles of language in forming mathematical knowledge

Piet Human

Ukuqonda Institute

I talked to myself and I thought: Eight slices is more than two slices

I talked to myself and I thought: Eight slices is more than two slices But then I thought: It can be the same!

2 fifths is something different than 8 twentieths But 2 fifths is equivalent to 8 twentieths “equivalent to” ??????????

2 fifths is something different than 8 twentieths But 2 fifths is equivalent to 8 twentieths 2

5 = 8 20

Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. Who eats more bread? They eat the same . . . . . . . . . . . . . . . . .

Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. Who eats more bread? They eat the same amount of bread.

Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. Who eats more bread? They eat the same amount of bread.

The clause “amount of” is a very different kind of language, a different genre of text, than the

• ther text in the above.

Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. They eat the same amount of bread. Ben eats two fifths of a loaf, and Tembi eats eight twentieths of a loaf. They eat the same amount of bread. Two fifths is equivalent to eight twentieths. Two fifths and eight twentieths are two different ways of representing/describing the same quantity. Two fifths and eight twentieths are two different ways of representing/describing the same number.

Description of actors, material objects and material actions: Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. They eat the same amount of bread. Condensed description of actors, material objects and material actions: Ben eats two fifths of a loaf, and Tembi eats eight twentieths of a loaf. They eat the same amount of bread. Description of a relationship between conceptual objects (quantities, numbers): Two fifths is equivalent to eight twentieths. Descriptions of a relationship between forms of representation: Two fifths and eight twentieths are two different ways of representing/describing the same quantity. Two fifths and eight twentieths are two different ways of representing/describing the same number.

Description of actors, material objects and material actions: Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. They eat the same amount of bread. Condensed description of actors, material objects and material actions: Ben eats two fifths of a loaf, and Tembi eats eight twentieths of a loaf. They eat the same amount of bread. Description of a relationship between conceptual objects (quantities, numbers): Two fifths is equivalent to eight twentieths. Descriptions of a relationship between forms of representation: Two fifths and eight twentieths are two different ways of representing/describing the same quantity. Two fifths and eight twentieths are two different ways of representing/describing the same number.

Cape Town and Mangaung are cities. Is Polokwane also a city?

2 5 and 8 20 are equivalent fractions.

Is 5

8 also an equivalent fraction?

We may claim, and I do, that to progress in mathematical learning, learners need to learn to use different genres of text. It can possibly be helpful if mathematics teachers are aware of this, and of the different text genres that are relevant, and take responsibilty for introducing learners effectively to these genres.

Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. How much bread do Ben and Tembi together eat?

The LoLT options

• English as LoLT monolingual
• Home language as LoLT monolingual
• English and Home language by code-switching,

translanguaging or parallel

• Multilingual

All four options are currently in use.

My view: Leave the choice of LoLT at to the discretion of teachers/schools, as is the case currently, hence give them space to do what they are most comfortable with in their particular contexts. Rather use our debating and innovative energies and capacities to address the real challenge: Promotion of progressive development of mathematical (STEM) language, irrespective of LoLT choice.

Demanding of teachers that they change their LoLT practices and policing implementation will not necessarily promote progressive development of mathematical (STEM) language, in fact it may inhibit it. In any case: to change the LoLT policy and implement it will require strong political will and educational management capacity, neither of which are currently at the country’s disposal.

Let us rather do what is possibly possible:

Support mathematics (STEM) teachers to actively promote progressive development

• f mathematical (STEM) language in their

classrooms. The NGO’s, teacher training institutions and research institutions can start doing this today.

But, it will require a lot of work: Linguistic analysis of mathematical texts, in all the languages including isipetori In-service training of teachers

2 5 + 8 20 = 10 25

2 5 + 8 20 = 10 25 = 2 5

Complete mathematical rubbish! Why do so many learners produce this?

2 5 + 8 20 = 2+8 5+20 = 10 25

Flawed classroom language is a major contributor to this kind of rubbish.

2

5 + 8 20 = 10 25 “2 over 5” + “8 over 10” instead of “2 fifths” + “8 twentieths”

The semiotic quadrangle

Language (Discourse) Representations (“squiggles”) Things Thoughts

“2 over 5” + “8 over 10 2 5 + 8 20 empty

2 5 + 8 20 = 2+8 5+20 = 10 25

2 fifths + 8 twentieths 2 5 + 8 20 2 fifths is equivalent to 8 twentieths 8 20 + 8 20 = 16 20

What can the classroom discourse be about?

Representations Language (“Squiggles”) “2 over 5” and 8 over 20

Squiggle discourse

Things Rubbish thoughts

Representations Language (“Squiggles”) “2 fifths” + “8 twentieths” “equivalence”

Meaningmaking discourse

Things Mathematical thoughts

Description of actors, material objects and material actions: Ben cuts a loaf of bread into 5 equal slices, and he eats 2 of the slices. Tembi cuts a loaf of bread into 20 equal slices, and she eats 8 of the slices. They eat the same amount of bread. Condensed description of actors, material objects and material actions: Ben eats two fifths of a loaf, and Tembi eats eight twentieths of a loaf. They eat the same amount of bread. Description of a relationship between conceptual objects (quantities, numbers): Two fifths is equivalent to eight twentieths. Descriptions of a relationship between forms of representation: Two fifths and eight twentieths are two different ways of representing/describing the same quantity. Two fifths and eight twentieths are two different ways of representing/describing the same number.

Representations Language (“Squiggles”) “2 fifths” + “8 twentieths” “equivalence” Things Mathematical thoughts

(“Squiggles”) “2 fifths” + “8 twentieths” “equivalence”

Discourse about language and representation: linguistic discourse

Things Mathematical thoughts

DBE Curriculum Advisors

Role of language in forming mathematical knowledge Apart from its obvious role as a medium of communication, language is a tool for organising and forming mathematical knowledge.