Communication jarmilas presentation

Communication in the classroom

Jarmila Novotná

Charles University in Prague

Faculty of Education

e-mail: [email protected]

Programme

Language and communication

Posing questions

Didactical situation of formulation

Games focusing on communication and terminology

Other activities

Communication and language used in the classroom

In the past: main focus of the teacher’s language

Nowadays: • More focus on the communication between

the teacher and students and also among students

• Attention shifts from the language of texts to the language of discourse

Important elements of a constructvist form of teaching: discussion with the teacher and discussion among students

Posing questions

„Good“ question

• Requires more than mere referring to known facts.

• Students may learn something when they answer it and the teacher can learn something about his/her students from their answers.

• There exist several answers that could be accepted.

Creation of “good” questions

Starting from the end

• a) Define the topic

• b) Create a closed question and find the answer to it

• c) Transform the formulation and create a “good” question


Phase a) Phase b) Phase c)

Rounding 12 seconds My coach told me that I covered 100 m approximately in 12 seconds. What time could his stop-watch show?




Area 6 cm2 How many triangles with the area 6 cm2 could you draw?





Fractions 3½

The product of two numbers equals 3½. Which numbers might it be?





Fractions 3½


Money 35 EUR The customer paid 35 EUR in the shop. What did he buy and what was the price of the products?





Fractions 3½


Money 35 EUR The customer paid 35 EUR in the shop. What did he buy and what was the price of the products?

Diagram x x x x x x x x x x x x x x x x x 1 2 3 4 5

What might this diagram represent?


Adapt a commonly used question

• a) Define the topic

• b) Choose a common question

• c) Convert it into a “good” question



Geometry What is a square?

What do you know about a square?





Subtraction 731 – 256 = Replace the digits so that the difference of the two numbers is between 100 and 200.





Subtraction 731 – 256 = Replace the digits so that the difference of the two numbers is between 100 and 200.

Example of “good” questions from outside mathematics

Biology: How do crayfish walk?

Misconception: Backwards!

Method: careful observation of crayfish in a pellucid aquarium

Crayfish walk backwards when in danger, when they fear something; but when at ease and when they look for food, they walk forwards. And because crayfish when observed by people in nature feels endangered, the myth that crayfish walk (only) backwards was born.

Careful observation of crayfish in a pellucid aquarium can uproot this misconception passed on in literature and folk tales.


Interdisciplinary situation

A “good” question in interdisciplinary situations is such a question which combines both the above mentioned approaches: mathematical modelling as well as observation of real situation typical for natural sciences. The following example illustrates this approach.


Interdisciplinary situation

Closed question: A driver wanted to cover 200 km on a motorway. Most of the way he was driving at the allowed speed limit 130 km/h. However, he spent half an hour in a tailback driving only 80 km/h. What was his average speed? (The answer is: 115,5 km/h.)

“Good” question: You have an important meeting in a town which is 200 km away. You can use a motorway where the speed limit is 130 km/h. The meeting starts at 10 o’clock. What time should you leave home to be at the meeting in time?

Use of “good” questions in the classroom

1. Posing a “good” question

• Not only posing the question, but also verification that everybody understands.

• Students should have the opportunity to ask the teacher e.g. what it means to answer the question.

• Students’ task: to find the answer; the teacher does not do it for them.


1. Posing a “good” question - example

Two fifth (2/5) of students of the school visit daily the school library. How many students can be in the school and how many from them visit daily the library?

Recording on the table/distributing sheets with the assignment …

Collective reading of the problem

Explanation of one or more students’ question (in their language)

The teacher’s help does not contain any hint for the solving process.


2. Students are finding answers to the posed question

• Recommended form: group work

• Too many students do not know how to start

interrupt the work and discuss together

• If it does not help pose a simplified question

• The teacher observes what students do but does not intervene in their work

• It is not necessary to wait till all groups find the answer


2. Students are finding answers to the posed question – example

Two fifth (2/5) of students of the school visit daily the school library. How many students can be in the school and how many from them visit daily the library?

Simplification, e.g. other fractions (½, ¼, …)

Help, e.g. the use of buttons, a picture, …

Question for fast solvers, e.g. What happens when 3/5 instead of 2/5 of pupils visit the library?


3. Whole class discussion

Groups present their solutions and explain why they choose their solving procedure.

Each group summarizes the procedure, the teacher records all answers of all groups on the blackboard

Recommendation: pose further questions similar to the original one so that they can see that their procedure is/is not applicable more generally


3. Whole class discussion – example Two fifth (2/5) of students of the school visit daily the school library. How many students can be in the school and how many from them visit daily the library?

Examples of answers:

• In the school, any number of students can be.

• In the school, there are 100 students, 40 of them visit the library.

• The number of students in the school is a multiple of 5, e.g. 5, 10, 15, 20, … . 2, 4, 6, 8, … are visiting the library

Difference in the level of generality of proposed solutions, in its level of real life perspective, …


4. Summary

• If everything works as it should, some students should be able to do the summary without the teacher.

• The fact that a group presents the correct answer does not mean that they understand everything. Therefore it is useful to summarize important places and explain them.

• Also here it is useful to assign students further questions similar to the original one in order to show them that their procedure is applicable more generally.


4. Summary – example Two fifth (2/5) of students of the school visit daily the school library. How many students can be in the school and how many from them visit daily the library?

Similar question might be e.g. :

• In a survey it was found that ¾ of population like Beatles. How many people answered the question and how many of them like Beatles?



Different course of the lesson

Other expectations of the teacher

Fast reaction to students’ proposals and recognizing of correct answers

Managing the classroom discussion that allows finding doubtful, incomplete etc. answers

Role of the teacher

• When starting the activity – instructions, motivation

• During the activity, the teacher does not offer hints, students work on their own as much as possible

• Final discussions: The teacher should be a moderator of the debate; assures that the debate rests in the objective, factual domain

• He/she does not decide about the correctness but helps students learning to explain, use and accept legitimate arguments and to defend their statements

Role of the teacher

• Final discussions, the teacher should be a moderator of the debate; assures that the debate rests in the objective, factual domain

• He/she does not decide about the correctness but helps students learning to explain, use and accept legitimate arguments and to defend their statements

The teacher may delegate these activities to a student or a group of students

Examples of activities

• General, adaptable to any content

• Focusing on concrete thematic units

Is it true?

It is not possible to construct a triangle with the lengths of sides 4, 5 and 9.

YES NO Do not know

Diagonals in each trapezium divides in two. YES NO Do not know

A right-angled triangle cannot be equilateral. YES NO Do not know

The area of a triangle depends only on its height. YES NO Do not know

All face of a cuboid are always rectangular. YES NO Do not know

The number 675 is divisible by 3. YES NO Do not know

7 is a divisor of 504. YES NO Do not know

The smallest prime is 1. YES NO Do not know

Sprint

Every At least one No

square rectangle trapezium parallelogram kite

has does not have

just three sides of the same length. just one right angle. perpendicular diagonals. just two parallel sides. at least two sides of the same length. perimeter inversely proportional to its area.

Graph

Classroom activities (motivation)

What does this graph represent?

What do the axes represent? Which units may be used?

Graph – Possible follow-up activities

The house where Peter lives has the altitude exactly 300 m. In

the morning, Peter set out for a short excursion .

What does the axis x represent?

What do the data on the axis y represent? In which units?

Examples of games focusing on communication and terminology

They may be used in any part of the lesson.

They may serve as a tool for motivation, practicing, revision etc. but also for “discovering”.

They can be easily adopted to the age, level and learning styles of individual students.

All types of communication can be applied.

They can comply with various learning styles of students and teachers.


How many things can you think of that...?

In groups, students try to think of and note down as many things as they can that fit a given definition. After two or three minutes, pool all the ideas on the board, or have a competition to see which group can think of the most items. The definitions might be:

... are rectangular,

... are round? ... you can divide into seven pieces? ... are smaller than zero?


Blackboard Bingo

Write on the board 10 to 15 Maths items (e.g. numbers, a simple equation, a triangle, ... ). Tell the students to choose any five of them and write them down. Then read out the items, one by one in any order, but in a different way than they are written on the board (e.g. instead of 4, you might say 16/4, instead of 2x + 1 = 0, you might say -1/2, and so on). If the students have got the items you call out, they cross them off. By shouting „Bingo“, they will tell you they have crossed off all their five items.


What’s the explanation? This activity practices the properties of mathematical

objects. Describe to the students or show them on a picture a property of a mathematical object. They ask Yes/No questions in order to find out what is the true explanation for the presented property.

Here are some examples of the situations:

It holds for any positive numbers a, b, c, d: ½(a + b) (ab).

9 999 999 999 is not a square of a natural number.

In the triangle ABC with the angles α, β, γ it holds:

cotg α cotg β + cotg β cotg γ + cotg γ cotg α = 1.

It holds for the area S of a rhombus ABCD with the angle α at the vertex A: S = a2 sin α.


Noughts and Crosses This game is played as the typical Noughts and Crosses game, i.e.

two teams, one has got noughts, the other crosses. The winner is the team who first get the full line of their symbol (i.e. a line of crosses or noughts).

The teacher prepares a square number of tasks/questions (e.g. 9, the topic depends on what he/she wants to practise) and draws a grid on the blackboard as the following one:

Each number corresponds to one task/question.

The teams take turns in picking up the numbers

of tasks/questions. If they answer the question

right, the teacher makes a cross/nought instead

of the number of the question/task. In this example,

the winner must get three noughts/crosses in the

line or on the diagonal.

1 2 3

4 5 6

7 8 9


Noughts and Crosses This game is played as the typical Noughts and Crosses game, i.e.

two teams, one has got noughts, the other crosses. The winner is the team who first get the full line of their symbol (i.e. a line of crosses or noughts).

The teacher prepares a square number of tasks/questions (e.g. 9, the topic depends on what he/she wants to practise) and draws a grid on the blackboard as the following one:

Each number corresponds to one task/question.

The teams take turns in picking up the numbers

of tasks/questions. If they answer the question

right, the teacher makes a cross/nought instead

of the number of the question/task. In this example,

the winner must get three noughts/crosses in the

line or on the diagonal.

1 2 3

4 5 6

7 8 9

1 2 3

4

5 6 7

8 16 24

17

9 10

18 19

11

12 20

21

13

22 23

15 14


Unusual view This activity could be designed as a lead-in when

starting the chapter of a 3D space. Draw familiar objects from an unusual point of view. Ask the students to identify it. Encourage different opinions. The objects might be:


Correcting mistakes This activity could be used to identify and correct

mistakes and to encourage monitoring by students of their own mistakes.

Write up a few problems on the blackboard that have deliberate mistakes in them. If you wish, tell the students in advance how many mistakes there are in each sentence. With their help, correct them.

Some examples of possible problems:

67.98 - (63.7 - 9.72) x (-2) - 1 = 67.98 - (63.7 + 9.72) - 1 =

= 67.98 + 63.7 - 9.72 - 1 = 131.68 - 9.72 - 1 = 122.96 - 1= 121.96

Mark the invisible lines of this prism:

-42/25 - 5/25 : 1/12 - 6/12 = - 47/25 : (-5)/12 = -564/300


Jumbled numbers Choose a few numbers and write them up on the

blackboard.

E.g. 2 0 1 8

Then ask students to: (an example)

Use the four digits to make a number which is more than ... .

Use the four digits to make a number which is less than ... .

Use the four digits to make a different number which is less than ... .


Brainstorm round a concept

Take a concept the class has recently learnt (e.g. fractions), and ask the students to suggest all the words and ideas they associate with it. Write each suggestion on the blackboard with a line joining it to the original word (you create something like a mind map). This activity can be done as individual or pair work. It can be used, for example, as an introduction to the next topic, or for comparison, or it can just help the teacher to realise how the students perceive and understand the concept.

In the proposed activity the learners are asked to work in pairs, one of them providing the other with a sequence of instructions for the drawing of a geometrical figure. Both learners are then asked to describe the figure and to define it.

The activity seems to correspond with a good way of dealing with mathematical notions, introducing them through a nice mixture of theoretical and practical activities.

Geometrical puzzles

The basic rules are:

Learners work in twos.

A member of each pair is given a piece of paper with the name of a (plane or solid) geometrical figure that must be kept secret from the partner until the end of the activity.

The first learner provides the other with a sequence of instructions how to draw the figure.

Only unitary instructions that correspond with a single graphical activity of the partner are allowed. For example, the instruction “Draw a segment” is allowed, the instruction “Draw the axis of the segment AB” is not allowed, because it requires the determination of the middle point M of the segment AB first, and the perpendicular in M to AB after.

Each instruction given/received is written on a sheet of paper by both learners.

Geometrical puzzles

The basic rules are:

If necessary, an instruction can be repeated, but neither modified nor explained.

For the drawing pupils make use of a sheet of squared paper and a pen (no pencil, ruler, compasses, etc.). No deletions are allowed.

The in-progress drawing cannot be shown.

When the sequence of instructions has come to an end, the final drawing is shown and compared with the name of the given geometrical figure.

Both learners are asked to give the name, the description and finally the definition of the geometrical figure.

Discussion in the whole class, rooted in the final drawings and the given directions, concludes the activity.

Geometrical puzzles

General

The development of awareness and critical attitudes towards the use of language and its interpretation.

The awareness of how important it is to use specific and unambiguous language.

The increase of the learners’ capacity to understand and to elaborate oral instructions.

The stimulation of “critical” listening to instructions.

The improvement of the ability of reading, understanding, respecting and applying the rules of the didactical activity.

The acquisition of the notion of simple instructions.

The ability to respect the pace of the classmates.

The capacity to state the reason for the choices made and used during the activity.

Geometrical puzzles - aims

Mathematical

The improved usage of mathematical language.

The reinforcement of the knowledge of geometrical language.

The improvement of drawing skills.

The consolidation of geometrical knowledge.

The ability to visualize three-dimensional objects from their two-dimensional representations and to represent solid figures on the plane.

The capacity of describing basic plane and solid geometrical figures by pointing out the properties necessary and sufficient to define them.

The development of the ability to find a proper balance between the description and the definition of a plane or solid geometrical figure.

The awareness of the relevance of the definition in geometry.

The capacity to compare and evaluate different kinds of input from the debate in the context of the correct construction of the concept of geometrical figures.

Geometrical puzzles - aims

Material

Sheet of paper, pencil/pen, form for recording instructions

Assignments and questions for students

Hints for students

Instructors

Drawers

Geometrical puzzles

Geometrical puzzles – Instruction sheet

Geometrical puzzles – Examples

Geometrical puzzles – Examples

Geometrical puzzles

Didactical situations

Didactical situation= an actor (e.g. the teacher) organizes a plan of action with the intention of modifying or causing the creation of some knowledge in another actor (a student)

A-didactical situation: partially liberated from direct teacher’s interventions, enabling students to develop their knowledge individually

Didactical situation

A-didactical situation

Devolution Situation of action of formulation of validation

Institutionalisation

Group work

Important to choose

• instructions

• possibilities for using the activity

• organizational forms

…so that communication is developed