National Council of Teachers of Mathematics

Mathematics Instruction for Students With Disabilities, Grades 7-12

Fennell & National Council of Teachers of Mathematics, (2011, p. 164), quote Freudenthal that 'geometry with respect to children's education plays a role in how children grasp the space in which they operate'. It provides useful and practical knowledge that enables children to not only know and conquer this space, but also conquer and make it better to live in. More importantly, there is enhanced revelation and development of unsuspected strengths, such as drawing and manipulating forms in children with special needs when they learn geometric and special tasks (Fennell & National Council of Teachers of Mathematics, 2011, p. 164). It thus offers alternatives in which learners capitalize on, especially those with language and communication difficulties (Fennell & National Council of Teachers of Mathematics, 2011, p. 178).

With respect to geometry, the pre-k-12 instructional programs enable learners to achieve various tasks.

They should learn the analysis of two- and three-dimensional geometric shapes and the arguments about their relationships.

The learners should use representational systems including coordinate geometry to describe spatial instructions and specify locations.

The learners should do mathematical situations analysis using transformations and symmetry. They can use flips, turns and slides to learn the geometric transformations properties and effects. They can also use tracing, paper folding and mirrors to explore symmetry.

The learners should 'use visualization, spatial reasoning and geometrical modeling to solve problems' (Fennell & National Council of Teachers of Mathematics, 2011, p. 164).

However, teachers teach what is appropriate for the cognitive development of the learners, such that learners in the lower grades learn the most basics of geometry, while those in the higher grades, the most complex. For instance, grade 1 students simply learn to compose and decompose geometric shapes, while grade 7 students learn to decompose three-dimensional objects to understand the respective formulas of how to find the surface areas and volumes.

Teachers of students with special needs should apply specific instructional guidelines to achieve the desired results. For instance, they should utilize the most effective methods to teach geometry, such as the direct instruction and the cognitive strategy instruction approaches (Fennell & National Council of Teachers of Mathematics, 2011, p. 179). Additionally, special needs teachers should utilize instructional materials that benefit the students with special needs.

Chapter 8

With respect to measurements, learners should:

understand the objects' measurable properties as well as the measurements systems, units and processes (Fennell & National Council of Teachers of Mathematics, 2011, p. 197).

determine measurements using the appropriate formulas, tools and techniques (Fennell & National Council of Teachers of Mathematics, 2011, p. 198).

Learning measurement is important in people's daily lives, such as determining the shortest distances for particular purposes. Learners apply measurements across all disciplines, including geography to measure geographical features and history for events (Fennell & National Council of Teachers of Mathematics, 2011, p. 200). Early acquisition and development of measurement knowledge and skills makes children live a better life.

However, students with learning disabilities may find it hard to acquire these knowledge and skills in measurement. Teachers should use instructions that are inclusive since measurement learning has a high level of engagement of the cognitive, visual and physical skills. Students with disabilities, sometimes require alternative objectives or specialized instructions to develop competency in measurement knowledge and skills (Fennell & National Council of Teachers of Mathematics, 2011, p. 201). Additionally, teachers can use adaptive materials for learners with special needs.

Teachers can consider using circular adaptations for students with special needs. This approach can be useful in ensuring that the teacher meets the temporal needs of the learners because it considers integrating topics in learning activities (Fennell & National Council of Teachers of Mathematics, 2011, p. 204). For instance, students with perceptual difficulties have difficulties structuring arrays and they need additional time and experience making them (Fennell & National Council of Teachers of Mathematics, 2011, p. 210). Circular adaptation also considers incorporating both skill development and reasoning in teaching (Fennell & National Council of Teachers of Mathematics, 2011, p. 204). Therefore, the approach provides solutions for such difficulties that students face as using formulas with area and volume measurements. Since the difficulties are due to their lack of knowledge about arrays, when teaching these areas of measurements, teachers should ensure that students not only learn mere formulas, but also their meanings (Fennell & National Council of Teachers of Mathematics, 2011, p. 209).

Chapter 9

Pre-k-12 instructional programs concerned with data analysis and probability standards ensure that learners:

Formulate questions addressable with data and collect, organize and present relevant data for their answers;

appropriately select and use statistical methods for the data analysis;

based on the data, develop and evaluate inferences and predictions; and Understand and apply probability's basic concepts (Fennell & National Council of Teachers of Mathematics, 2011, p. 219).

Learners from the 6th grade onwards are usually cognitively ready for statistics and probability. By learning these mathematics branches, learners make meaningful connection to not only other mathematics branches, but also with other disciplines. In the long run, statistical and probabilistic reasoning influence their productivity and participation in the society (Fennell & National Council of Teachers of Mathematics, 2011, p. 220). However, there are some learners in grades 6-12 who face challenges with cognitive development that affects problem-solving skills. Teachers of such students make sure that they accommodate them using the approaches that help the students to achieve the expectations mentioned above.