How To Improve Children's Success With Arithmetical Word Problems Through The Use Of A Range Of Scaffolding Strategies Targeted At The Language Domain

Reville, Kathleen (2002). How To Improve Children's Success With Arithmetical Word Problems Through The Use Of A Range Of Scaffolding Strategies Targeted At The Language Domain. EdD thesis The Open University.



Written arithmetical word problems provide a fascinating link and spiral of dependency between the mathematical and language domains. The correct solution to these problems relies upon an ability to interpret the text correctly, coupled with the ability to find the correct arithmetical equation and sufficient computational skills to solve it (Hegarty et al 1995, Reusser and Stabler 1997 and d’Ailly 1997). The written arithmetical word problems that are being discussed are those that present a problem in word form and require the solver to extract information from the text to form an arithmetical equation and thus find the answer to the question. These problems frequently require knowledge of multiplication and division for their solution, but all the children in the studies discussed in this thesis were given addition and subtraction sums of the combine, compare and change type because the younger children were unsure of multiplication and division processes. This eliminated any possibility of different processes affecting the outcome of the research which may have occurred if older children had been given multiplication and division and the younger ones had been given addition and subtraction problems. Although the semantic structure of the text can affect the type and degree of difficulty of the problems - and this will be discussed in detail in Chapter Two of the thesis - the following are examples of the underlying structures of arithmetical word problems used in this research:

Greg and Tara were collecting shells on the beach. Tara had 18 shells.
Greg had 9 shells more than Tara. How many shells did Greg have?

Andrew has 17 shells and Greg has 27 shells. How many shells do they have altogether?

Tara had 18 shells. Greg gave her 27 more shells. How many shells does Tara have now?

There is considerable evidence that children find these written arithmetical word problems difficult (e.g. Stem 1993, Hegarty et al 1995, d'Ailley 1997, Greer 1997, Gravemeijer 1997, Reusser and Stabler 1997, Yoshida et al 1997, Wyndham and Saljo 1997) because their complexity demands that the solver uses knowledge and skills from both mathematical and language domains, and many children either fail to appreciate this or do not use their knowledge judiciously. A child who is good at computational arithmetic may fail to formulate the correct arithmetical equation because of a lack of understanding of the text and will not reach a correct solution. A child who understands the meaning of the text of these problems but fails to recognize the appropriate arithmetical equations will not be able to answer them accurately. A child who understands the text and has knowledge of the required arithmetical process and uses the correct arithmetical equation, but is inaccurate in arithmetic, will also produce a wrong answer. For many children, arithmetical word problems are fraught with difficulties that result in failure. Children can easily misconstrue this lack of success as their deficiency in mathematics; therefore, it is imperative that the source of the children’s difficulties should be identified and that solutions should be sought.

The interdependency of the language and mathematical domains in these problems accentuates both the differences and similarities between the domains in aspects of learning and teaching styles. It also emphasizes the resistance of most pupils to transferring learning from one domain to another. Although they unite domains, in schools written arithmetical word problems are traditionally situated in the mathematical domain where their mastery is seen as a test of mathematical ability, demonstrating that the pupil can apply mechanical processes to real world situations (Hegarty et al 1995, Greer 1997, Gravemeijer 1997, Yoshida et al 1997, Wyndhamn and Saljo 1997). Written arithmetical word problems are considered to indicate that the learner has sufficient understanding of arithmetical processes to move beyond the rote learning of arithmetical number facts and apply these facts to solving problems.
'Problem solving is seen as a decisive test of genuine skill and understanding.’ (Wÿndham and Saljo 1997)

Arithmetical word problems are still a fixture within the school curriculum although some express doubt about the relevance of the type of problems usually given in schools (Gerofsky 1996). It may be easier to persuade adults to change and adapt the text and focus of word problems than to remove them from the curriculum. These problems are potentially important to the curriculum because they hold the possibility of encouraging cross domain learning, an accurate interpretation of written texts and making mathematics learning relevant to life outside the school environment.

My initial concern was to find a solution to children’s difficulties with these problems within the mathematical domain because the problems are presented to children within this domain in school. I decided to explore the possibility of scaffolding children in the mathematical domain as an attempt to address this issue. However, the Initial Study indicated that it was necessary to approach the issue by helping children to interpret text within the language domain by using scaffolding techniques, and then transfer that ability to interpret text to the mathematical domain and this is the main focus of this thesis.

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