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## Four Quadrant Sorts: How to Group Students for Instruction After Administering Universal Screening

Today in education, more than ever, teachers must know how to analyze data. Most teachers have mastered the art of administering assessments. There is no lack of evaluations. We use screenings, diagnostics, progress monitors and outcome assessments. And let’s not forget good old test preparation. Test preparation is probably the most widely used assessment of any other. One of the most useful ways of analyzing data and classifying children into groups that I have used is the “Four Quadrant Sort”. The purpose of this article is to explore different types of four quadrants in reading and mathematics.

__Classification no. 1 – Reading – Accuracy vs. fluency__

The first type I like to use is the reading fluency type. We use data from our universal AIMSweb RCBM (oral reading fluency) screening. Sorting is completed using fluency (words per minute) and accuracy (percentage correct) data. You can also use data from the DIBELS Oral Reading Fluency measure or any other assessment that gives you results in words per minute and percentages of accuracy. You can even take any reading passage you want to use and have all your students read it orally for one minute. Mark your mistakes. Use the total number of words, the number of errors, and the words read correctly to calculate your accuracy. Then you’ll only need a chart of suggested words per minute.

The first such quadrant is for students who are both accurate and fluent. Accurate means that the student has an accuracy rate of at least 95% correct (meaning that 95% of the words they read were correct). You can choose to use 98% as your accuracy cutoff score. Fluent means the student is above the 25th percentile in words per minute. This is according to the national standards table provided by AIMSweb. You may decide that your fluency cutoff is above the 50th percentile. These are your “enrichment” students. The second quadrant is for students who are accurate but not fluent. In other words, these students have accuracy rates of at least 95% (or 98%, if you choose). However, their fluency scores are not above the 25th percentile (or 50th percentile). These are probably your “goal” students. The third quadrant is for students who are neither accurate nor fluent. They have a percentage correct accuracy below 95% (or 98%). These students also have a fluency score in the 25th percentile or below (or in the 50th percentile or below) in words per minute. These are the real “intervention” kids. These are the children we choose to assess through a diagnosis. The fourth quadrant is for students who are fluent, but not precise. Usually, this is not a very large group of children. These students read enough words per minute to place them above the 25th percentile (or 50th percentile). However, their accuracy scores are not at the required 95% (or 98%). These students are more likely to be grouped with your “enrichment” or “reference” students, depending on how many words per minute they read. If there are enough students in that quadrant and you have the resources, they can be their own group.

__Ranking #2 – Reading – Fluency vs. understanding__

Another type of reading is that which focuses on fluency and comprehension. The comprehension measure we use for this type is the AIMSweb MAZE measure. It is an assessment of comprehension at the sentence level. This is basically a written version of a cloze test. Accuracy is not considered in this type. You may want to look at or add precision to this type if you have large groupings. For example, you might want to divide each quadrant into two parts: one part is 95% accurate or higher (or 98% or higher), the other part of the quadrant would be the ones below 95% (or 98%). . Essentially, you would take all four quadrants and turn them into 8 quadrants. This assumes, of course, that you have the staff to have eight groups of students.

The first quadrant is for those students who are adequate in both fluency and comprehension. So your words per minute are above the 25th percentile (or 50th percentile) and your comprehension score is above the 25th percentile (or 50th percentile). These are your “enrichment” students. [Remember, these students can be divided into two groups: One group would be those that are adequate in fluency, comprehension and accuracy. The other group will be those that are adequate in fluency and comprehension, but not accuracy]. The second quadrant is for those students who are adequate in fluency, but not in comprehension. Their fluency scores place them above the 25th percentile (or 50th percentile). Their comprehension scores are below the 25th (or 50th) percentile. [You can also split this quadrant into two groups: Those that are adequate in fluency, not adequate in comprehension, but adequate in accuracy. Those in the other group will be those that are adequate in fluency, not adequate in comprehension, and not adequate in accuracy]. The third quadrant is for those students who are not adequate in fluency or comprehension. They score below the 25th (or 50th) percentile on both the Oral Reading test and the MAZE test. [If dividing this group into two, one group would be those that are not adequate in fluency, comprehension or accuracy. The other group would be comprised of those that are not adequate in fluency or comprehension, but adequate in accuracy]. The fourth quadrant is for those students with adequate comprehension, but not fluency. So their scores on the MAZE comprehension tests put them above the 25th (or 50th) percentile. However, their score on the fluency measure places them below the 25th (or 50th) percentile. [A further division of this quadrant would mean that one group is adequate in comprehension, but not fluency and they are adequate in accuracy. The other group would be those that are adequate in comprehension, not adequate in fluency and not adequate in accuracy].

__Luck #3 – Math – Calculus vs. Concepts and application __

For this particular type, we use data from AIMSweb Mathematical Measures. DIBELS currently has a math test. I haven’t used it so I’m not sure if you can use it for this type. If there is a calculation score and a concepts and application score, you can use it for that type.

The first quadrant is for those students who are adequate in both calculus and concepts and application. That is, scores are above the 25th (or 50th) percentile in both calculus and concepts and application. The second quadrant is for those students who are adequate in calculus, but not adequate in concepts and applications. So they were able to score above the 25th (or 50th) percentile in calculus. However, they could not score above the 25th (or 50th) percentile on the concepts and application measure. The third quadrant is for those students who are not adequate in calculus or concepts and applications. Thus, these students scored in the 25th (or 50th) percentile or below in both Calculus and Concepts and Application. The fourth quadrant is for those students who are adequate in concepts and application, but not in calculus. This should be one of the smaller groups. These are students whose scores in concept and applications are above the 25th percentile (50). Their scores on the calculus portion are in the 25th (or 50th) percentile and below.

__Luck #4 – Phoneme Segmentation__

For those of you teaching kindergarten and first grade students, the type of phoneme segmentation will be important. It’s a little different from the types discussed above, but it’s still easy to use to determine student grouping. The two factors to consider are the fluency with which the student segments words into phonemes and whether or not they pass the assessment according to the criteria. Two of the most common assessments for this skill are AIMSweb and DIBELS.

The first quadrant is for those students who can segment all phonemes fluently (ie meet the criteria to pass the assessment) and have 95% or better accuracy. The second quadrant is for those students who segment phonemes with 95% or better accuracy. However, they do not pass the assessment of phoneme segmentation fluency. The third quadrant is for those students who segment phonemes, sounds, word parts, but their accuracy is less than 95%. They do not pass the phoneme segmentation fluency assessment. The fourth quadrant is for those students who are very fast, but not accurate. Its accuracy is less than 95%, but it dominates the assessment of phoneme segmentation fluency. They pass the evaluation, but their accuracy is low.

__Rank #5: Nonsense word fluency__

This type is especially useful for those of you who teach elementary school students. We will discuss two different types of NWF: one for word reading fluency and one for phonics. The first thing I will talk about is what the students are reading words.

The first quadrant is for those students who are reading whole words. They are not ringing. Some call this unification. The second quadrant is for those students who are reading words one sound at a time and then reading the whole word. The third quadrant is for those students who are doing some blending. Maybe they are reading them as a start and an end. The fourth quadrant is for those who are decoding words one sound at a time. The next type of nonsense word fluency is phonetic or alphabetic fluency. In this case, students are not yet reading whole words.

The first quadrant is for students who can read beginning and ending sounds. Maybe they will only read beginning sounds or ending sounds. The second quadrant is for students who have repeated consonant and vowel sound substitution errors. The third quadrant is for those students who have mid- or mid-vowel errors, usually deletions. The fourth quadrant is for students who cannot read the whole word or recode.

__where do you go from here__

My take on this four-quadrant instructional grouping strategy is very simple. You can take any two data you got through the assessment. Identify which of the skills you assessed is the more basic, prerequisite, and fundamental of the two. This is what should be suitable for Quadrant 1, suitable for Quadrant 2, not suitable for Quadrant 3, and suitable for Quadrant 4. The next thing to do is to take the next skill you assessed, the higher level skill, the one that based on the above, etc. This is the skill that is suitable for Quadrant 1, not suitable for Quadrant 2, not suitable for Quadrant 3 and suitable for Quadrant 4.

This may seem very simplified, but I came to this conclusion by comparing the type of accuracy and fluency in reading and the type of fluency and comprehension and also the type of calculation versus concepts and applications in mathematics. In all of these types, the ability listed first is the more prerequisite of the type’s two abilities. For example, accuracy precedes fluency. Fluency is essential to understanding. Being able to calculate is essential for those working in concepts and applications.

Let me give you an example of what I’m talking about here. I haven’t seen any for this particular set of skills: vocabulary and comprehension. Since vocabulary skill is widely believed to be a prerequisite for comprehension skill, I have chosen these two skills for this type. Take the results of the vocabulary and comprehension assessment. Determine what scores are appropriate in both skills. If you use a published assessment instead of one you’ve created, you don’t need to determine what an appropriate score is. This information will be provided to you.

The first quadrant would be those who are adequate in both vocabulary and comprehension. The second quadrant would be those students who are adequate in vocabulary, but not in comprehension. The third quadrant would be those students who are not adequate in vocabulary or comprehension. The fourth quadrant would be those students who are adequate in comprehension, but not in vocabulary.

I imagine that this particular type would be useful for those teachers who have children who are adequate in both accuracy and fluency. If there is a deficit in accuracy or fluency, chances are you won’t even bother doing this kind of vocabulary and comprehension. Remember, accuracy comes first. Four-quadrant ordering for accuracy and fluency

For more information on sorting, assessment, or quadrant intervention, check out my website at http://www.readingandmathintervention.weebly.com

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