Assessing the Mathematical Skills of Students with Disabilities

Fundamental Questions (1): What are the critical components of mathematics assessment that relate to instruction?

There are four key parts of math assessment that help educators to effectively assess student progress and guide instruction for students with disabilities. The four critical components of mathematics assessment are:

1. Aligning Assessment With Established Standards

2. Aligning Critical Standards With Meaningful Instruction

3. Combining Assessment Approaches

4. Integrating Appropriate Adaptations

Part-Whole-Connection Questions (1): What are the two types of assessment approaches?

Formal Assessments:

1. Standardized, norm-referenced tests

Standardized, norm-referenced tests are used to summatively assess student progress and performance. This type of assessment “[compares] one student’s scores to the scores of [other] students” (Hong, B., Ehrensberger, W, 2007, p. 42) to determine where a student’s learning is in comparison to their peers. This assessment can also use various samples of work from the student to determine individual student performance in comparison to past assessments. Furthermore, Standardized, norm-referenced tests only assess the “broad areas of basic concepts and operations” (Hong., et al, 2007, p. 43) rather than specific learning objectives. Educators can use the data from standardized, norm-referenced tests to gain insight on how to make instructional decisions based on how well students are doing overall, however, these results do not particularly assist educators in creating individualized instruction without the use of assessments that focus more on student mastery of specific learning objectives alongside.

2. Criterion-referenced tests

Unlike standardized, norm-referenced tests, criterion-referenced tests assess student performance based on “predetermined levels of mastery as specified in the curriculum or instructional goals” (Hong., et al, 2007, p. 43) pertaining to grade-level expectations. Criterion-referenced tests can provide educators with more insight through a “more in-depth look at the strengths and weaknesses of students” (Hong., et al, 2007, p. 43) in a targeted learning objective, thus ultimately enabling educators to obtain valuable feedback that is constructive when creating effective individualized instruction and assessments that better meets the individual needs of each student. This type of assessment “can be classified as either formal or informal, according to its administration” (Hong., et al, 2007, p. 43), therefore leaving room for educators to design and adapt a criterion-referenced test “based on content goals and objectives” (Hong., et al, 2007, p. 43) that positively impact student comprehension.

Informal Assessments:

1. Clinical or flexible interviewing

Clinical/ flexible interviewing is an informal “semistructured diagnostic interview designed to assist [educators] in making sense of students’ cognitive processes in mathematical reasoning” (Hong., et al, 2007, p. 43) by conducting informal one-on-one interviews. Educators can follow the Ten Guidelines for Conducting Clinical or Flexible Interviews to ensure they design and adapt assessments and instructions to be accessible and valuable for each student’s individual needs. Clinical/ flexible interviewing positively impacts instructional and assessment practices by “[encouraging] students to think more about the process of solving a problem than about simply arriving at an answer”, in result allowing educators to “analyze the root of the incorrect or misunderstood computational patterns” and “identify how students learn” (Hong., et al, 2007, p. 43) to effectively design and deliver instructions and assessments that promote each student’s learning.

2. Error pattern analysis

One key difference between clinical/ flexible interviewing and error pattern analysis is that clinical/ flexible interviewing focuses on having one-on-one conversations with students to gather data regarding student learning processes, whereas error pattern analysis focuses more on “[identifying] the mistakes students make on selected mathematics problems” and analyzing “how [students] arrived at the incorrect answers” (Hong., et al, 2007, p. 43) they provided. This assessment can be applied easily in the classroom as the educator and students can individually, or jointly, administer it. Regardless of who is performing the error pattern analysis, one must “score multiple samples of the student’s work, then analyze and identify possible error patterns” (Hong., et al, 2007, p. 43) the student is making. If educators involve students in assessments, students will become more involved in their learning processes, resulting in students effectively determining where their mistakes are happening and understanding strategies to prevent themselves from repeating the same mistakes.

Part-Whole-Connection Questions (2): What areas can educators make appropriate adaptations to better adhere to the individual needs of the students?

1. Presentation of the Testing Material

Educators can create adaptations to engage and deliver students with testing materials in ways that work best for their learning. Creating adaptations to present materials could include “pairing visual examples with text and allowing hands-on experiences that reflect real-life examples” (Hong., et al, 2007, p. 45), which leads to the material seeming less overwhelming and more intriguing for students. Making a simple adaptation to the appearance of testing material could include, leaving ample space between questions, enlarging the print, and highlighting instructions students need to know. Educators must make testing materials accessible and engaging because “the overall presentation of a test can affect how students approach” (Hong., et al, 2007, p. 45) the assessment. Adaptations of testing materials must be carefully considered and implemented “without compromising the validity and reliability of the test” (Hong., et al, 2007, p. 45) and tailored to the individual needs of each student to set students up for lifelong success.

2. Physical Environment

Physical environments can influence one’s ability to self-regulate and learn in various ways. Evidently, it is necessary to understand how to create an inclusive and adaptable environment for all students to be within. Making adaptations to student’s learning environments that can “[reflect] their learning preferences” and meet their individual needs will “maximize students’ performance” (Hong., et al, 2007, p. 45) and set them up for future success. Some examples of adaptations for physical environments include reducing loud noise levels, using appropriate lighting (fluorescent lights often cause headaches and are too bright), having different seating options available and displaying decorations that do not serve as a distraction.

Hypothesis Questions (1): If educators use various assessments and create more adaptations in the classroom, what would happen to the learning of students who do not have learning disabilities or difficulties?

Combining various assessments and adaptations will benefit all students learning rather than only those with learning disabilities or difficulties. Administering various ongoing assessments will enable educators “to obtain a more authentic picture of their students’ performance” (Hong., et al, 2007, p. 41), ultimately leading them to discover successful strategies to “meaningfully and accurately evaluate individual progress” (Hong., et al, 2007, p. 42) and design effective instruction and adaptations. Furthermore, using various assessment strategies and adaptations will enhance all student’s learning experiences by promoting engagement and ensuring that every student receives the support they need to succeed. One adaption I can think of that is beneficial for most students is having a visual schedule of the day plan for students to see.

Critical Questions (1): What should educators do if they want to create effective assessments and adaptations?

A step educators should take when wanting to create accessible assessments and adaptations for their students is to get to know the individual students. Information such as what prior understanding a student might have, student interests, likes and hobbies could play a large part in engaging students. To accomplish this, educators can have on-the-go conversations with students and become involved in each student’s learning by asking them questions. Furthermore, educators need to “have access to multiple sources of information about the student” (Hong., et al, 2007, p. 45) to create a more comprehensive and holistic picture of the student’s strengths, weaknesses and individual needs. It is vital that educators “listen carefully, communicate honestly, and provide constructive feedback” (Hong., et al, 2007, p. 45) for all parties involved with the students learning while working as a team to support the student.

Critical Questions (2): What is my opinion of this article?

I believe creating accessible assessments and adaptations can truly change how a student learns and how a student views learning. It is vital for educators to continuously try new strategies that are specific to the student’s individual needs. There is “no single assessment strategy [that] can yield a complete picture of a student’s performance” (Hong., et al, 2007, p. 42), therefore utilizing new strategies will provide educators with opportunities to collect more detailed data from the student, which ultimately influences the process of creating adaptations. Everyone can succeed if they are given the necessary tools and support. Administering various assessments and providing differing adaptions will ensure the individual needs of each student are being met. In addition, creating good relationships and working closely as a team with other individuals involved in the student’s learning will ensure everyone is on the same page regarding how they can support the student to succeed. Unfortunately, many students lack additional support when struggling, specifically in mathematics, because educators are “unaware of these practices, unable to implement assessment strategies appropriately, or unable to articulate how they assess students” in mathematics. This is problematic as students are not set up for lifelong success and will progressively fall further behind in their learning.

References:

Hong, B., & Ehrensberger, W. (2007). Assessing the mathematical skills of students with disabilities. Preventing School Failure, 52(1), 41-47.