Differential Learning in Mathematics

¶ … conveyed in an effective manner to meet the needs of students. It is an important aspect of differentiating instruction. Students with diagnosed learning disabilities will receive an IEP designed to address their specific learning issues and deficits. Presentation, response, timing (scheduling) and setting can all be addressed in differentiation. Memory; auditory, visual, and even motor processing; attention deficits; abstract reasoning issues; and organizational problems can all cause issues for students that can be improved with differentiated instruction (Ginsberg & Dolan, 2003, p. 87).

In-class assessment can take place in both in traditional formative and performance-based ways. Formative assessment is used during the learning process so the teacher can check in to see what the student has retained. This can be observational or in the form of quizzes or other graded formats. But while performance-based assessment can take the form of conventional tests there are other methods besides exams, including flexible interviews which ask students to demonstrate what they have learned, such as how to solve a problem.

Students can be asked to do so either publically in a class or in a private interview. This allows the teacher to determine if the student understands why he or she is performing certain actions, versus simply performing such actions by rote. Of course, the traditional method of assessment is requires both formal and informal tests.

While standardized tests have been much criticized, provided they are not the only way of monitoring student progress, they can provide a valuable method of ensuring that the instructional format is truly meeting student needs (Ginsberg & Dolan, 2003, p. 98). Tests also ensure that assessment is fair and balanced and not influenced by teachers' biases. Achievement tests assess student performance in specific mathematics content areas while cognitive tests assess students' ability to understand specific concept areas (Ginsberg & Dolan, 2003, p. 98).

Chapter 5: Number and Operations One of the principles of current mathematics education is that students should understand numbers, not merely how to manipulate them. Students who are computationally fluent are not simply efficient and accurate in their methodology but also flexible (Rathmell & Gabriele, 2013, p. 109). This means that students have more than the basic skill set to cope with the challenges of mathematical worksheets; they must also be able to know what skills to use to cope with a new computational challenge.

New standards-based tests demand that students show how they achieved their answer to assess comprehension. Students should understand there are many different ways to find an answer. Flexibility is fostered by instructional strategies that show different representations of the same idea: not simply showing subtraction on paper, for example, but also physically representing it before the child. Innovative methods of representation generate new thinking strategies (Rathmell & Gabriele, 2013, p. 109).

Both a sense of what numbers truly mean and procedural skills in manipulating numbers are required for the child to flourish academically. When teaching flexible approaches to computation, however, it is important that the instructor keep certain developmental factors in mind. Young children may not be able to cope with concepts such as the fact that regardless of the order something is counted in, the number remains the same, because of their need to meet developmental milestones (Rathmell & Gabriele, 2013, p. 112).

Children with learning deficiencies may face additional challenges, such as memory problems in retrieving numbers (Rathmell & Gabriele, 2013, p. 113). Flexibility can also be useful in educating students with special needs, given that although the student may not understand the abstract conception of the mathematical principle, through concrete manipulation they may begin to grasp the strategy. All students can benefit from multiple approaches and forms of interpretation. Teaching students more effective computational approaches in a step-by-step fashion can often notably improve their learning (Rathmell & Gabriele, 2013, p. 122).

Chapter 6: Algebra Algebra is often taught relatively early in a student's middle school or high school career but many students, particularly students with learning disabilities, struggle to grasp its basic concepts (Lannin & Van Garderen, 2013, p.141). Weak abstract reasoning skills, combined with computational and memory deficits as well as low self-esteem all conspire to make learning algebra especially difficult for LD students.

The most basic concepts of algebra can be fostered as early as grade school, when children learn the intrinsic properties of numbers such as even and odd and zero.