Subject-specific training in mathematics teaching for students with intellectual disabilities (IDs) has been little studied in the academic field and is uncommon in the practice of teacher education. Given that teachers face significant challenges in regard to teaching mathematics to ID students, it is necessary to know whether there is a need for subject-specific training. If yes, what kind of subject-specific training do teachers need? What kind of subject-specific knowledge should be covered? How can this kind of training contribute to improving mathematics teaching for ID students?To answer the above questions, this study focuses on one particular teacher professional development programme (BE MATHS programme) for mathematics teachers who teach ID students in special schools in Hong Kong. Programme effects and the contributing factors of the effects are examined to explore whether and how subjectspecific support can contribute to the profession of teaching mathematics to ID students.The study is conducted via a mixed-methods approach. First, it uses quantitative measures to examine teachers’ changes in mathematics teaching efficacy and students’ changes in their academic engaged time in mathematics classes. Second, a qualitative approach is used to explore the contributing factors of the changes.Quantitative results show that the programme has a significant positive effect on teachers’ mathematics teaching outcome expectancy and a conditional positive effect on teachers’ personal mathematics teaching efficacy. It is also found that the programme can improve teachers’ mathematics teaching by engaging more students in mathematics learning.The qualitative findings in this study show that the design of teaching and learning trajectories with subject experts is a substantial learning activity for teachers. During the design process, teachers and subject experts identified knowledge gaps within the mathematical content to be delivered to ID students and successfully inserted

This study aims to report on the psychometric properties of SCALE, a newly developed assessment instrument, that is based on the central curriculum for students with intellectual disabilities, using Rasch Analysis. Results indicated that the SCALE could classify students into at least 13 levels of abilities, and that the range of item difficulty was capable of stratifying students’ abilities into 8 to 11 attainment levels. The Rasch statistics demonstrated that the assessment results using SCALE had a high degree of validity and reliability. Its uni-dimensionality as an instrument to measure the attainment levels of the four Key Learning Areas in the central curriculum was also supported. Results from the Rasch Analysis showed that the SCALE measure is a well-validated instrument in identifying the differential levels of attainment. Based on the SCALE data, teachers can design learning materials and activities to match the performance levels of individual students. In addition, the use of the SCALE attainment descriptors to differentiate students’ attainment levels would enable teachers in schools to document progress of their students within an academic year. Subsequently, this enables them to reflect on their teaching effectiveness and make adjustments for the following year. 本研究旨在報告「融通學習成效量表」(SCALE)的心理測量數據特性。「融通學習成效量表」(SCALE)是為連接特殊學校與主流學校課程而研發出來的一項嶄新的評估工具。研究採用等級量尺模式分析法 (Rasch Analysis)‧結果顯示SCALE能把學生的學習能力表現至少可分13個不同程度;且其項目難度也能將學生能力分為8至11個學習能力表現水平級別。從統計數據顯示出SCALE擁有極高信效度。單一構念向度方面的數據亦顯示出SCALE能辨別出有特殊教育需要的學生於四個主要學習領域的學習能力表現之差異。故此,老師能使用SCALE的評估結果,去設計適合個別學生能力的教材及活動。此外,SCALE中的學生學習能力表現指標,亦能讓老師根據SCALE評估結果所提供的實證來衡量學生於每一學年間的學習進度,從而反思自己的教學效能,並在下一個學年為學生的教學作相應的調整。
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Background: Since 2005, professionals in nine special schools collectively had developed an assessment tool called SCALES for all students regardless they are in special or mainstream schools in Hong Kong. Based on the concept of “one common curriculum for all”, SCALES is classified into the four Key Learning Area (KLA) strands of learning as in the mainstream curriculum framework, namely, Chinese, Science, Personal, Social and Humanities Education (PSHE) and Mathematics. This means that for the first time all of the students are being measured by exactly the same criteria irrespective of the ability or disability. Aims: In this study, we aim to apply Rasch measurement approach to analyzing a this innovative evaluation tool for children with special needs due to intellectual disabilities. Since Rasch measurement can convert ordinal measures into interval measures, the latter of which is fundamental for objective measurement in human sciences (Bond and Fox 2007). Methods: By using Winsteps, statistics such as infit and outfit mean square, person separation index, reliability, and dimensionality of the measurement scales are supported empirically. Results: The uni-dimensionality of the four major subject areas is supported with good psychometric properties such as high reliability and person separations that help differentiation of subjects. Selective applications of some items of these scales could be used by practitioners for quick screening and better intervention for care of children with special leaning needs. Conclusion: The scales are supported with both subject experts’ observation and quantitative evidence from sophisticated psychometric tests. Successful establishment of the instrument by subject experts is evident and quality-assured administration of the Rasch-based items in the future is recommended as the SCALES has proved to be a valid and reliable assessment measure for diverse learners.