Visual Representation in Mathematics: Special Education Teachers’ Knowledge and Emphasis for Instruction

Abstract

The use of visual representations (VRs) in mathematics is a strongly recommended practice in special education. Although recommended, little is known about special educators’ knowledge of and instructional emphasis about VRs. Therefore, in this study, the authors examined special educators’ own knowledge of and their instructional emphasis with VRs in mathematics for students with disabilities (SWDs) in Grades K-12. A total of 146 teachers (pre- and in-service) responded to an online survey. A mixed methods triangulation research design was utilized. Findings include the following: (a) teachers hold conceptions about VRs and the roles they serve in problem solving; their ideas, however, lack depth and are narrow in perspective; (b) what teachers emphasize about VRs to SWDs tends to match their own conceptions, but the explanations they provide for SWDs need expanding and refinement; and (c) given their narrow conceptions, VRs may be limited to a peripheral role in special educators’ instruction.

The Utilization of Project Based Learning and Guided Discovery Learning: Effective Methods to Improve Students’ Mathematics Ability

“…The representation ability is highly recommended in mathematics learning (Garderen, Scheuermann, Poch, & Murray, 2016). This ability is one of the priorities that must be developed in learning mathematics to build an understanding of concepts and mathematical proficiency that cannot be separated in mathematics learning (Oktaviyanthi & Supriani, 2017;Syafri, 2017) The mathematical representation ability is still considered a problem because many learners who have difficulties in visualizing (Fatmaryanti & Sarwanto, 2015;Garderen et al, 2016;Krawec, 2014) Lack of student representation development (Hutagol, 2013) students cannot represent the mathematical problems into mathematical expressions or images so that learners cannot solve the problem (Yusnita, Masykur, & Suherman, 2016) Nowadays, there are many learning models that can be used for maximizing the learning, some of them are Project Based Learning (PBL) and Guided Discovery Learning (GDL) models. The PBL model is a model that requires the students to be active throughout the process and teachers lead the process, provide feedback to the students and assess performance.…”

Kemampuan Representasi Piktorial Operasi Hitung Pecahan pada Mahasiswa Pendidikan Guru Sekolah Dasar

“…Representasi dari ide matematika tersebut menjadi dasar bagaimana seseorang memahami dan menggunakan ide matematika. Garderen, Scheuermann, Poch, & Murray (2018) menyatakan representasi membantu siswa dalam memahami masalah matematika dan memudahkan dalam menyelesaikanya. Dalam pelaksanaan pembelajaran, diharapkan dapat memfasilitasi siswa dalam mengembangkan standar representasi menurut NCTM (2000) yaitu: (1) membuat dan menggunakan representasi untuk mengkomunikasikan ide matematika, (2) memilih dan melakukan translasi pada berbagai representasi untuk memecahkan masalah, (3) menggunakan representasi untuk memodelkan, menafsirkan permasalahan matematika.…”

Demonstrating Conceptual Understanding of Fraction Arithmetic: An Analysis of Pre-Service Special and General Educators’ Visual Representations

“…Results of a survey study (Gagnon & Maccini, 2007) indicated that ~70% of general educators and ~40% of special educators reported feeling prepared to demonstrate concepts using two-dimensional graphics or pictures (i.e., VRs); and overall, teachers reported using VRs and concrete manipulatives only 1 to 4 times per month. Results of a more recent survey study of special educators’ knowledge of and instructional emphasis on VRs indicated that special educators held “narrow conceptions” (p. 7) about the role VRs can play in problem-solving, and authors suggested that teachers’ use of VRs in mathematics instruction needs expansion (van Garderen, Scheuermann, Poch, & Murray, 2018).…”