Teachers have a mountain of student data, but don’t always have time to connect that data to student outcomes. This is especially true of students with Specific Learning Disorders (SLDs). We have class data, RtI information, and annual performance test data. Let’s connect this data to our students with SLD’s. In this post, I’m going to focus on Criteria-Referenced Tests (CRTs) and Norm-Referenced Tests (NRTs).
CRTs (Criteria Referenced Tests)
Criteria-Referenced Tests (CRTs) score an individual student against a specific topic or standard. These CRTs include our classroom quizzes and tests, and they are based on the instruction we’ve delivered to a class. We give a quiz as a formative assessment, meaning we plan to use the data (the test scores) to drive future instruction: do we need to talk about adding fractions with same denominators again, or can we move on to adding fractions with different denominators? We expect (or hope!) that almost everyone will score above 80%. This shows that the class, as a group, has mastered the topic. Summative assessments, like chapter tests, are also CRTs. Individual student scores come from their performance against the criteria-- how many questions did they get right, divided by how many questions were given. We plan to end a topic after a summative assessment and move on to something new.
If you analyze your CRT data, you would expect to see distribution curve kind of like this:
This curve is pretty flat on the left, with most scores on the upper right end of the graph; this happens because most students should pass a quiz or test in class. I encourage you to take just one chapter of your textbook this year and graph the quiz and test scores from your class. What do you see? If you have students with the math learning disability dyscalculia, you will probably see higher quiz scores than test scores. This is because the SLD dyscalculia causes the brain to lose math knowledge over time. They learned it, but they forgot it (including basic math facts). That’s why using notes, reference sheets, worked examples, and having a calculator or times table sheet are the right accommodations for these students.
If you have a student whose scores increase between a quiz and a test, they have retained the math information they learned and built upon that prior knowledge. If a student continues this growth throughout the school year, we can assume they had a poor math foundation (low numeracy), not an SLD (dyscalculia). This helps explain why some students respond well to RtI programs and some don’t: RtI programs can increase numeracy, but they can’t rewire the parietal lobe of the brain, which is where dyscalculia resides.
NRTs (Norm-Referenced Tests)
A Norm-Referenced Test (NRT) compares students against a large group of other students around the state or around the country. These tests are aligned to a wide range of topics: state standards for a grade level, for example, or a standard of expected developmental abilities by age. NRTs are useful for measuring personal performance against typical performance, and have little to no relationship to our classroom instruction. They might be used to examine school or district performance, or they might be used to explore potential learning challenges an individual student might have.
An NRT could be reported as a scaled score or as a percentile rank; a scaled score shows whether one student performs better than one other student who took the same test (i.e., a scaled score of 3 is better than a scaled score of 4). A percentile rank shows how a student performed compared to all other students who took that same test (a 75th percentile rank means the student performed better than 75% of all people who took that same test, and is an above average rank). The results of an NRT look very different from CRT results:
The scores of an NRT have very different meanings than those of a CRT, but we can still connect this data to our classrooms. We should expect that most students will land in the 40th to 60th percentile-- pretty close to what most students their age would. Any high or low outliers should grab our attention. For example, a score at or below the 30th percentile qualifies a student for the math learning disability, dyscalculia. A scaled score of 1 out of 5 can also show a potential learning disability. For students with an SLD, the NRT scores show a discrepancy between what the student can do versus what we expect they should be able to do. Scan the reports for your class and look for individual discrepancies, too: a student who performs in the 90th percentile in reading, writing, and social studies, but the 50th percentile in math, shows a huge difference between what we expect and what they can do.
It’s important to remember that any test is only one piece of data, and is not a diagnostic tool on its own. However, assessments can give us a wealth of information about our students. NRTs can help us identify students who need extra support in a broad subject area, like math. CRTs help us identify whether or not students are retaining what they learn or building on what they learn. Together, they help us understand our students as learners and help us identify potential SLDs, areas of struggle, and potential accommodations.