Academic journal article
By Paterson, Anne
Australian Primary Mathematics Classroom , Vol. 11, No. 3
In education, the term "metacognition" describes thinking about thinking. Within mathematics, the term "metacomputation" describes thinking about computational methods and tools (Shumway, 1994). This article shows how the Six Thinking Hats can be used to demonstrate metacognition and metacomputation in the primary classroom. Following are suggested teaching and learning sequences for developing these concepts, using Dr de Bono's hats as graphic organisers.
A Melbourne primary school recently adopted Edward de Bono's Six Thinking Hats across all grade levels as an adjunct to their meta-cognitive curriculum. First, each hat and its thinking style was introduced individually progressing to the introduction of hat sequences. Figure 1 illustrates all Six Thinking Hats by colour and type of thinking identified as relevant to the mathematics curriculum in no particular order.
[FIGURE 1 OMITTED]
While the Thinking Hats can be organised into different sequences of any number and in any order, certain sequences work better than others do. It is recommended that Yellow Hat be presented first in order to "set the stage for innovation", while presenting Red Hat after Green Hat is recommended for "prioritising key areas" and "discarding others" (McQuaig, 2005).
A source reference currently used by this primary school is Teaching Thinking Skills in the Primary Years: A Whole School Approach, by Michael Pohl. The evaluation sequence known as "the sequence for usable alternatives" can be used to consider problems such as the benefits and aspects that are more challenging found in "Would you rather ...?"-situations. Pohl uses the example of, "Would you rather spend all of your pocket money or save some?". This sequence can also be used for choosing between whether to use a calculator, pencil and paper method or a mental computation strategy. A class brainstorm may uncover several reasons to choose particular methods that individual students may not have arrived at on their own. Once each option has been assessed for benefits and difficulties, Pohl's suggested sequence for making choices is Yellow Hat, Black Hat, and Red Hat. Pohl further suggests a design sequence of Blue Hat, Green Hat, and Red Hat for children exploring and inventing. This could be specifically used for computational strategies, for both written and mental methods. The primary school was also developing a "numeracy block" using whole/ part/whole teaching. It was decided that spending more time applying Blue Hat and Green Hat thinking would cater for students needing extension, as this requires higher order thinking.
Figure 2 illustrates a traditional teaching learning sequence that seeks a definitive response to a number fact such as, 6 x 7. As this question has a single answer it can be regarded as factual or informative and therefore in the realm of White Hat. The emotional response that this question can evoke from students can be positive or not: confidence if the answer is known or anxiety if not and speed of response was required for success. The student would usually either refer to existing knowledge to solve such examples, either by reciting tables or an instrumental procedure such as removing zeros (McIntosh, De Nardi, Swan, 1994) in the example of 60 x 70. If the student already knows the answer, this is White Hat thinking as no learning has taken place. If however, students are asked to explain their mental computation methods as in a study by Paterson (2004), first they reflect on their answers using Blue Hat thinking. Students are also more likely to use Green Hat to check using a different method and then both Yellow and Black Hats to evaluate which is the best method if the two answers do not match. Increasing student opportunities for using their own invented methods and mental computation are more likely to develop conceptual rather than instrumental learning through the use of Green Hat thinking.
[FIGURE 2 OMITTED]
Figure 3 demonstrates a metacognitive teaching and learning sequence in an attempt to show how current mathematical teaching pedagogies being implemented in schools today can fit into a Six Thinking Hats teaching sequence. …