Advanced reasoning and communication in Maths

Kaur, B. (2012). Some “what” strategies that advance reasoning and communication in primary mathematics classrooms. In B. Kaur & T. L. Toh (Eds.), Reasoning, communication and connections in mathematics: Yearbook 2012, Association of Mathematics Educators(pp. 75-88). Singapore: World Scientific Publishing.

Background

Data has shown that mathematical tasks take up some 80% of maths lessons. At the same time, studies have shown that most gain is achieved in classrooms where students are consistently supported in their high-level thinking, reasoning and communication.

Aims

The author wishes to demonstrate how the development of ‘what’ strategies from textbook tasks could encourage students to talk about their thinking and reasoning.

Sample

The author selects a number of text book tasks to illustrate the creation of four different ‘what’ strategies.

Method

As well as illustrating the creation of four different ‘what’ strategies (‘What number makes sense?’, ‘What’s wrong?’, ‘What if?’ and ‘What’s the question if you know the answer?), the author gives an illustration of actual classroom use in Singapore. The students are put into groups and asked to solve the adapted textbook questions. Once they are satisfied that they have solved the questions, they must give their answers, justify them and say how they got them.

Here is an example problem and a possible adaptation using ‘What number makes sense?’:

Original:	Tickets to a concert cost $15 per adult and $8 per child. Mr Wang bought tickets for 4 adults and 5 children. How much did he spend altogether?
Adapted:	Tickets to a concert cost ____ per adult and ____ per child. Mr Wang paid ____ for ____ tickets. He bought tickets for ____ adults and ____ children. 4 5 9 $8 $15 $100

Findings

In the 60-minute lesson reviewed, the teacher used Think-Pair-Share for the tasks she had set up. The teacher monitored the students as they worked and made a note of common problems and misunderstandings. She also helped students to share their ideas. The students came up with a variety of approaches to the solution, some of which were very creative. The teacher found the approach a useful way of reviewing learnt material.

Implications

Getting students to vocalize their approach to solving problems helps them consolidate their learning and helps the teacher see where there might be problems that might call for corrective teaching.

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