952 words - 4 pages

A Review of General Strategy Instruction and Schema Based Instruction in Solving Mathematical Base Word Problems.

Problem solving within mathematics is important as children need to apply and transfer their learning of how to solve calculations into everyday situations. Enabling children to deduce what algorithm is required in a given situation is important as the way in which a problem is approached (NCTM, 1989) is an essential skill, in addition to arriving at a correct answer. Furthermore the NCTM (1980) recognised that teaching problem solving to children develops their skills and knowledge that are used in everyday life whereby the inquiring mind, tenacity and receptiveness to problems ...view middle of the document...

xvi). Understanding the problem requires the learner to decide what calculation is required, what stages are involved in the problem and does the problem provide all of the relevant information required. Following on from understanding is devising a plan which requires the learner to draw on previous experiences and use these experiences to define a strategy to solve the problem. At this point students should also look at the problem to assess whether the problem can be redefined or expressed in other words. Similarly Rich (1960) describes this stage as the representational stage or as Garofalo and Lester (1985) described this stage as the orientation stage whereby the student needs to comprehend what processes or calculations are required to arrive at an answer.

The second stage requires the student to generalise and draw upon previous learning experiences whereby they need to assimilate previously learnt procedural knowledge to devise a plan of how they can solve the problem, devise a plan (Pólya, 1957), translation, (Rich, 1960) and organisation (Garofala and Lester, 1985).

However many students may misinterpret the information, select the wrong calculation or leave out a calculation that is required (Boaler, 2009; Marzocchi, Lucangeli, DeMeo, Fini and Cornoldi, 2003; Goldman, 1989; Nesher and Teubal, 1975). Boaler recognises many mistakes are made within the first two stages as the student is rushing into answering the problem without considering the problem properly. Marzocchi et al’s (2002) review of two studies shows that students over willingness to use irrelevant information leads to essential operations being omitted. In addition confusion may occur whereby key words are misinterpreted and the wrong calculation is selected which Nesher and Teubal’s (1975) study demonstrates. Furthermore Van de Welle (2007) supports Nesher and Teubal’s (1975) findings stating “…key words send a terribly wrong message about doing math.” (p.152)

The third...

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