Scenario: Christiana teaching average

Country: Cyprus

Grade (student age): Year 6 (age 11-12)

Contributed by: Marilena Petrou

Context – national, curricular, professional, other

Christiana was a final year university student in a teacher praparation programme , Teacher training in Cyprus involves taking part in a 4 year university degree in elementary education. Teachers are trained to teach all subjects of the school curriculum and during their last year the take part in a school based placement where they teach a series of lessons in all subjects throughout the year. With the completion of the programme the teachers are qualified to teach. The lesson took place in a school-based placement towards the end of her four-year teacher preparation.

Scenario

Christiana, was teaching mean with a Year 6 (pupils age 11-12) class. In the episode below the students were given a table that showed the goals that a team scored in each of its games. They were then asked to calculate the average in a total of seven games. One student proposed to add the number of goals in each game and multiply by 7. Another student disagreed and said ‘we need to divide by 7’ instead. Christiana did not comment on the correctness of the solutions and said:

Christiana:        Let’s try both ways and see.

(The students tried both, the one resulted in an average of 3.14 goals and the other in an average of 144)

Christiana:       So, what do you think?

Phani:              It is 3.14

Christiana:       But why?

Phani:              Because you need to divide.

Christiana:      Why not to multiply. Why not 144?

Marinos:         It can’t be 144 because it is bigger than 22. The total number of goals was  22.The   average can’t be bigger than that.

Christiana:       Well done! The average is an indication of the goals scored in each game. It was not possible for the team to score 144 goals in one game since it scored 22 in a total of seven games.

 

Knowledge Quartet Coding Commentary

Contributed by: Marilena Petrou

Knowledge Quartet Dimension: Contingency

Knowledge Quartet Code: Responding to students’ ideas (RCI)

Scenario: Christiana teaching average

The dialogue above helped the students realise why 144 was not a reasonable answer. Later in the lesson a student noticed that:

‘since the average is an indication of the number of goals scored in each game, this explains why there was a need to divide the total number of goals by the number of games’.

Christiana developed a discussion based on children’s mathematical thinking and their responses to her question, in which students were encouraged to explain their point of view. She took both suggestions and aked students to try and evaluate. She challenged them to deal with opposing views. According to Ryan and Williams (2007) clarifying another’s thinking, in order to understand your own, may be important in developing mathematical thinking.

References

Ryan, J. and Williams, J. (2007) Children’s mathematics: Learning from errors and misconceptions, (Berkshire, Open University Press).