國小數學學習困難學童之心理數線表徵發展及其數線估計能力之研究

Mental Number Line Representation and Number Line Estimation by Elementary Students with Mathematical Learning Difficulties

連文宏(Wen-Hung Lien) ； 洪儷瑜(Li-Yu Hung)

《特殊教育研究學刊》 43卷1期 (2018/03) Pp. 29-51

https://doi.org/10.6172/BSE.201803_43(1).0002

摘要

本研究目的在於探討國小數學學習困難學童之心理數線表徵發展及其數線估計能力表現，研究指出，「數字在數線位置估計作業」所探討的心理數線表徵發展與數線估計能力（以估計誤差量作為指標）是研究學童數感能力的方式之一，然本研究以電腦化方式進行施測，得以進一步分析數線估計速度表現，並以三種方式進行分析，團體、個別、嘗試次。所有國小二年級與四年級的受試者都經過兩次數學與閱讀測驗，結果均低於百分等級35以下所篩選為數學學習困難合併閱讀困難、單純數學學習困難、單純閱讀困難、以及正常發展等四組學童。研究結果指出，有數學學習困難之學童在國小二年級時，其心理數線表徵仍依賴模糊表徵（介於對數和線性表徵之間），然無數學學習困難之學童已依賴線性表徵；到了國小四年級，四組學童均已依賴線性表徵，顯示國小二年級數學學習困難學童之心理數線表徵有發展遲緩現象，但是到了國小四年級則能跟上同儕的發展。至於估計誤差量與估計速度之數線估計能力，在國小二年級與四年級有數學學習困難學童之表現均顯著低於無數學學習困難學童，顯示隨著年級發展，有數學學習困難學童之數線估計能力仍顯著低落，此能力似乎為其核心缺陷。據此，本研究針對數學學習困難學生的數感能力研究、診斷與教學提出具體的建議。

關鍵字

心理數線表徵 ； 數字在數線位置估計作業 ； 數線估計能力 ； 數學學習困難 ； 閱讀困難

並列摘要

Purpose: Mental representation of numbers is considered to possess not only quantitative but also spatial properties; therefore, researchers have designed various tasks to estimate it. Mental number line representation, derived from the Spatial- Numerical Association of Response Codes effect, compresses large numbers as logarithmic functions, according to Dehaene (1993). The linear function becomes dominant as children grow. Therefore, this study investigated the development of mental number line representation and number line estimation in elementary school students who have mathematical learning difficulties (MLD). These types of representation and estimation assessed with the “number-to-position” task have been recommended as indicators of number sense in the literature. Methods: A computerized number-toposition task was designed using the Visual Basic program, and performance and speed were recorded when participants indicated the positions of numbers in lines shown on the screen. Four groups of students in the second and fourth grades were screened. Standardized mathematical and reading tests were administered. A cut-off score of ＜35th percentile for 2 consecutive years was used as the screening criterion for classifying the students into one of the following four groups: MLD with reading difficulties (RD) (MLD-RD), only MLD (MLD-only), only RD (RD-only), and normal achievement (NA). All students were tested using the computerized number-to-position task, and the data were examined through group, individual, and trial-by-trial analyses.Results/Findings: According to performance in the group and individual analyses, the mental number line representation of second-grade students with MLD (with/without RD) depended on ambiguous representation (falling between the logarithm and linear representation), and that of the students without MLD depended on the linear representation. However, in all groups of fourth-grade students, the mental number line tended to depend on the linear representation. This result indicated the developmental delay in terms of mental number line representation in second-grade students with MLD. As they progressed to higher grades, the students with MLD caught up with their typically developing peers in terms of their development of mental number line representation, as proven by the results of the fourth-grade students with MLD. In terms of estimation error and speed, there were significant differences between the students with MLD (including the MLD-RD and MLD-only groups) and those without MLD (including RD-only and NA groups) in both grades. This result indicated that number line estimation ability is the core deficit in students with MLD. Conclusions/Implications: The mental number line representation deficit decreases with progression to higher grades. Students with MLD catch up with their peers without MLD by the fourth grade. However, they still differ in terms of errors and speed. Accordingly, the metal number line presentation is defined as students’ number sense and is recommended for the assessment of the development of number sense or for evaluating the effectiveness of intervention.

並列關鍵字

number-to-position task ； mental number line representation ； number line estimation ability ； mathematical learning difficulties ； reading difficulties

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