COUNTING WORDS

LEARN  MATHEMATICS  -  CREATE NARRATIVES

Writing numbers

Rogério Lourenço

1997 - Ciências Sociais - UFRJ

2000 - Comunicação, Imagem e Informação - UFF  

2001- 2008 - Empresa Municipal de Multimeios - MULTIRIO

2010  - Gramática Gerativa e Estudos de Cognição Museu Nacional -UFRJ

2010 - Rede Nacional de Pesquisa

2015  - Doutorado em Linguística - UFRJ

2017  - Laboratório de Estudo do discurso Imagem e Som - Museu Nacional - UFRJ

 

The image of mathematics

 is a cultural practice

Mathematics

Language & Mathematics

CAGLIARI, L. C. Alfabetização e Linguística, 2000.  Editora Scipione.

AN DISCOURSE ANALYSIS OF BRAZILIAN PUBLIC SCHOOL MATHEMATICS OLYMPIAD (OBMEP)

METAIMAGEM

The test

Osvaldo bought a cheese with a equilateral triangle shape.

 

He wants to equally divide the cheese among his four cousins and himself. 

 

Make a draw indicating how he can make the division.

A triangular cheese

( OBEMP 2011 / questão 97)

The answer

To divide a cheese in 5 equal parts is sufficient to divide it in 5k equal parts and give  k parts to each one. 

 

One way to do this partition is shown on the figure, where the cheeses was partitioned on 25 = 5 × 5 triangles.

The project

  1. open platform
  2. to learn mathematics
  3. to learn how to narrate

website || app

Portuguese          Mathematics

  •     1    Triangle 
  •     ÷  Division   
  •     4   Cousins + 1
  • Cheese ( equilateral divisor )
  • To divide  ( verb ) 
  • Cousins ( N dividend ) & Oswaldo

languages

grammar                                              notation

Steps

  • resources (similar initiatives)
  • technologies (available)  
  • MVP (prototype)

resources

 grammar, MathML, Parsing, Regex...

HTML, CSS3, Canvas, D3 , Javascript, SVG...

technologies

prototype

MVP:

basic operations

 ( + )   ( - )   ( × )   ( ÷ )

Pedro plays with boards

Pedro plays with a square checked board 4 x 6  and with pieces from types A, B andC.

 

Explain why it is not possible to cover the board with type B pieces.

discourse & mathematics

Pedro plays with a square checked board 4 x 6  and with pieces from types A, B andC.

 

The answer counts the squares on the pieces and cover the board with the c type piece as shown in the picture.

discourse & mathematics

Manipulate

the

DOM

<text>

options

 circular menu 

the number line

4.1.1 AN DODECAGON. (N2Q3_2010)

The picture shows an regular dodecagon decomposed into six equilateral triangles, six squares and one regular hexagon, all with same size sides.

a) If each triangle has the same 1 cm   area, which is the hexagon´s area ?

2 


“All regular hexagons can be divided into 6  equilateral triangles (6-2) - 180=720 / 6=120 ✗ 120/2=60.

 

So if the equilateral triangles above are equals to the sid hexagon´s side, the equilateral triangles from hexagon, have the same side of the equilateral triangles from the hexagon, have the same side from equilateral triangles from the pictures, and consequently, the same area.

 

Therefore  the hexagon has the area: 6 x 1cm   = 6 cm  

 

ANSWER 1

2 

2 

ANSWER 2


6 cm. As the hexagon is regular, it can be divided into equilateral triangles  in the following way.

Each triangle has área 1 cm , since they are congruent to the other (all sides from all figures have the same size, and the triangles sides from the hexagon  have the  same side from the hexagon, having also the same side).

For 6 triangles, the área is 6 x 1 cm   = 6 cm  ”

2 

2 

2 

2 

ANSWER 3


“We know one regular hexagon can be divided into 6 equilateral triangules with same side of the side of the hexagon, as drawn in the figure.

As the triangles that form the hexagon have the same side from others making the dodecagon, ( equalling the hexagon) then all  will have the same area: 1 cm.

As each hexagon is formed by 6 triangles, it will be igual to 6.1= 6 cm  . ”

2 

2 

ANSWER 4


“The regular hexagon can be divided into 6 equilateal triangles. As each triangle has área of 1 cm  , the hexagon has 6 cm  .”

2 

2 

ANSWER 5


” If all have the same side measures , it is enough to divide  the hexagon into six triangles.

 

If the area of the triangle is 1 cm  , multiply  by 6 (number of triangles from the hexagon) and we will have área of 6 cm   pertaining  to the hexágono. “

2 

2 

ANSWER 6


“If we connect a edge to opposite side, we will see the line will be the  bisector of two angles, then each angle will have 60°,

if we do that to all edges we will have 6 congruent equilateral triangles.

 

As the área of the others is 1 cm  , the hexago area will be 6.1= 6 cm  

2 

2 

(1) To infer the square having the same side of each side of the equilateral triangle 

 

(2) verify the picutre is composed by one of sides of the square .

The conclusion , in this case,  is  (6 x 1 cm = 6 cm  ).

To observe the picutre... the answers use the graphical resource.

2 

2 

interface

The picture  shows a regular dodecagon decomposed into six equilateral triangles, six squares  and one regular hexagon , all with same sides mesures.

?

javascript

http://www.mdpi.com/2227-9709/4/3/28/htm

motivation

Thank you.

metaimagem@gmail.com

counting words

By Rogério Lourenco

counting words

The project aims to build an open web platform for learning math through the construction of narratives. The central challenge is to realize that mathematics is a cultural practice done with and by language. The current stage of the project is to create an online platform so that it is possible to try learning models that unify the teaching of Portuguese and mathematics from a practice of narrative construction. There are still many points to be researched, among them, the code to implement the platform. People can collaborate with code. An initial idea is to use graphic libraries (SVG, D3) to produce a version that includes transformations of the problems in accordance with the desired narrative. In an ideal scenario, the project provides a place where you can enter numeric operations and construct narratives to understand how to solve the problem. Or vice versa, you have a problem and can decompose the statement into parts to perform the numerical operations. The major vision of the project is to contribute to Brazilian education, but more ambitiously for the way one looks at words and numbers in general.

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