Academic journal article Kuram ve Uygulamada Egitim Bilimleri

Effects of a Schema Approach for the Achievement of the Verbal Mathematics Problem-Solving Skills in Individuals with Autism Spectrum Disorders *

Academic journal article Kuram ve Uygulamada Egitim Bilimleri

Effects of a Schema Approach for the Achievement of the Verbal Mathematics Problem-Solving Skills in Individuals with Autism Spectrum Disorders *

Article excerpt

Individuals with development disorders experience inefficacies in cognitive processes, such as memory, generalization, metacognition, language, and academic skills (Friend, 2013, p. 8), and problems in retaining and generalizing newly acquired knowledge and skills (Heward, 2009, pp. 132-135). As a result, they lag behind their peers exhibiting typical development (Heward, 2009, pp. 132-135; Thomas, 1996, p. 135). Therefore, it is necessary for individuals with developmental disorders to acquire various information, skills, and behavior to prepare for social life, gain their independence, and lead their lives with minimum dependency on others around them (Çiftci-Tekinarslan, 2012, pp. 157-158; Ergenekon, 2012, p. 158). Individuals with developmental disorders need special assistance to acquire the skills that individuals with typical development learn through daily experiences (Sucuoğlu, 2009, p. 67).

In addition to communication, socialization, and behavioral disorders, individuals with Autism Spectrum Disorder (ASD), considered a development disorder, often have disabilities in cognitive skill areas such as reading, writing, language, and mathematics (Minshew, Goldstein, Tylor, & Siegel, 1994), which are also considered cognitive skills (Shapiro, 2011, p. 212).

Mathematical skills are important for the decisions made in daily life (Reyna & Brainerd, 2007). Individuals resort to mathematical skills every day without even recognizing it (Prater, 2007, p. 358). The use of mathematical skills increases an individual's independence and autonomous decision making at home and in professional and social lives (Browder & Snell, 2000, p. 497). Numbers, geometry, measurement, and data are the areas of learning in mathematics (Gürsel, 2013, pp. 448449). Within their context, process skills that students should acquire in mathematics classes include (a) problem solving, (b) reasoning, (c) communication, (d) association, and (e) projection skills (Gürsel, 2013, pp. 447-448; National Council of Teachers of Mathematics [NCTM], 2010). To be able to use the abovementioned skills effectively, individuals need to develop visual skills as well (Donaldson & Koffler, 2010).

The three learning levels in mathematical skills instruction are "concrete, semiconcrete, and abstract", and verbal mathematics problems are related to the semiconcrete skill level (Bender, 2009, p. 65). McCoy and Gehrke (2009, pp. 498-499) defined verbal mathematics problems as mathematical exercises that include real or imaginary situations expressed in words. Verbal mathematics problems can be in one of three types: "change," "grouping," or "comparison" (Jitendra, 2002; Marshall, 1991, p. 72). The following are some examples of these problem types:

a.Change-type problems: Fatma had 4 pencils. Her mother gave her 2 pencils. How many pencils does Fatma have now? Change-type verbal mathematics problems consist of a beginning (i.e., 4 pencils), change (i.e., 2 pencils), and ending set (unknown set).

b. Grouping-type problems: Caner has 15 red and clutch pencils. 5 of these pencils are red. How many clutch pencils does Caner have? Grouping-type verbal mathematics problems consist of two small sets (i.e., 5 red pencils and an unknown set) and a larger set (i.e., 15 red and clutch pencils).

c. Comparison-type problems: "Ali has 2 books. Mehmet has 3 more books than Ali. How many books does Mehmet have?" Comparison-type verbal mathematics problems consist of a compared set (i.e., 2 books), difference set (i.e., 3 more books), and referent set (unknown set) (Jitendra, 2002). The problem schemas of these problem types are shown in Figure 1.

According to Gooding (2009), difficulties encountered in solving verbal mathematics problems occur due to (a) individuals being unable to comprehend or analyze the words used in the problems when solving verbal mathematics problems or a lack of self-esteem when reading the problems, (b) individuals experiencing difficulties in transforming the words in verbal mathematics problems into numbers, (c) the context of the verbal mathematics problem and magnitude of the numbers on affecting individuals' calculation strategies related to the tendencies and individuals' choices of calculation strategies, or (d) errors that occur as a result of neglecting real-life variables when solving verbal mathematics problems. …

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