Four Quadrant Sorts: How to Group Students for Instruction After Administering Universal Screening Assessments in Math and Reading

Today in education, more than ever before, teachers have to know how to analyze data.  For the most part teachers have mastered the art of administering assessments.  There is no shortage of assessments.  We use screeners, diagnostics, progress monitors, and outcome assessments.  And let’s not forget the good old test prep.  Test prep is probably the most-used assessment of any other.  One of the more useful ways to analyze data and sort kids into groups that I have used is the “Four Quadrant Sort”.  The purpose of this article is to explore several different reading and math four quadrant sorts. 

Sort #1 – Reading  -  Accuracy vs. Fluency

                The first sort I like to use is the sort for reading fluency.  We use the data from our universal screener AIMSweb RCBM (oral reading fluency).  The sort is completed using both fluency (words per minute) and accuracy (percent correct) data.  You could also use data from the DIBELS Oral Reading Fluency measure, or any other assessment that gives you results in words per minute and accuracy percentages.  You could even take whatever reading passage you want to use, have all your students read it orally for one minute.  Mark their errors.  Use the total number of words, number of errors and words read correctly to calculate their accuracy.  All you would need then is a chart of suggested words per minute, like the one by Hasbrouck & Tindal. 

                The first quadrant of the sort is for students that are both accurate and fluent.  Accurate means the student has an accuracy percentage correct of at least 95% (meaning that 95% of the words they read were correct).  You may choose to use 98% as your accuracy cutoff score.  Fluent means the student is above the 25^th percentile in words per minute.  This is according to the national norms table provided by AIMSweb.  You may decide to make your fluency cutoff be above the 50^th percentile.  These are your “enrichment” students.  The second quadrant is for the students that are accurate, but not fluent.  In other words, these students have accuracy percentages of at least 95% (or 98%, if you choose).  However, their fluency scores are not above the 25^th percentile (or 50^th percentile).  These are most likely your “benchmark” students.  The third quadrant is for the students that are not accurate or fluent.  They have an accuracy percentage correct below 95% (or 98%).  These students also have a fluency score at the 25^th percentile or below (or 50^th percentile or below) in words per minute.  These are the real “intervention” kids.  These are the kids we choose assess using a diagnostic.  The fourth quadrant is for the students that are fluent, but not accurate.  This is normally not a very big group of kids.  These students read enough words per minute to place them above the 25^th percentile (or 50^th percentile).  Their accuracy scores however, are not at the required 95% (or 98%).  These students are most likely to be grouped with your “enrichment” or “benchmark” students, depending on the number of words per minute they read.  If there are enough students in this quadrant and you have the resources, they can be their own group.   

Sort #2 – Reading  -  Fluency vs. Comprehension

                Another sort for reading is one that focuses on fluency and comprehension.  The comprehension measure we use for this sort is the AIMSweb MAZE measure.  It is a sentence-level comprehension assessment.  It is essentially a written version of a cloze test.  Accuracy is not considered in this sort.  You may want to look at or add accuracy into this sort if you have large groupings.  For example, you may want to split each quadrant into two parts:  one part is accurate at 95% and above (or 98% and above), the other part of the quadrant would be those that are below 95% (or 98%).  Essentially you would be taking the four quadrants and turning them into 8 quadrants.  This is assuming, of course, that you have the personnel to have eight groups of students.

                The first quadrant is for those students that are adequate in both fluency and comprehension.  Thus, their words per minute are above the 25^th percentile (or 50^th percentile), and their comprehension score is above the 25^th percentile (or 50^th 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 that are adequate in fluency, but not in comprehension.  Their scores in fluency place them above the 25^th (or 50^th percentile).  Their scores in comprehension are below the 25^th (or 50^th) 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 that are not adequate in fluency or comprehension.  They score below the 25^th (or 50^th) 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 that are adequate in comprehension, but not fluency.  So their scores on the MAZE comprehension tests place them above the 25^th (or 50^th) percentile.  However, their score on the fluency measure place them below the 25^th (or 50^th) 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].

Sort #3 – Math  -  Computation vs. Concepts & Application

For this particular sort, we use the data from the AIMSweb mathematical measures.  DIBELS currently has a math test.  I have not used it, so I am not sure if you can use it for this sort.  If there is a computation score and a concepts & application score, you can use it for this sort.

The first quadrant is for those students that are adequate in both computation and concepts & application.  That is, the scores are above the 25^th percentile (or 50^th) in both computation and concepts & application.  The second quadrant is for those students that are adequate in computation, but not adequate in concepts & applications.  So they were able to score above the 25^th percentile (or 50^th) in computation.  They were not able, however, to score above the 25^th (or 50^th) percentile on the concepts & application measure.  The third quadrant is for those students that are not adequate in computation or concepts & applications.  So these students scored at the 25^th (or 50^th) percentile or below on both computation and concepts & application.  The fourth quadrant is for those students that are adequate in concepts & application, but not computation.  This should be one of the smaller groups.  These are students whose scores on the concept & applications are above the 25^th  (50^th) percentile.  Their scores on the computation portion are at the 25^th (or 50^th) percentile and below.

Sort #4 – Phoneme Segmentation

For those of you who teach kindergarten and first grade students the sort for phoneme segmentation will be an important one.  It’s a little different from the previously discussed sorts, but is still easy to use to determine grouping of students.  The two factors to consider are the fluency with which the student segments the 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 (meaning they meet the criteria for passing the assessment) and they are accurate at 95% or higher.   The second quadrant is for those students that segment phonemes with 95% or higher accuracy.  However, they do not pass the phoneme segmentation fluency assessment.  The third quadrant is for those students that 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 that are very quick, but not accurate.  Their accuracy is below 95%, but they are fluent in the phoneme segmentation fluency assessment.   They pass the assessment, but their accuracy is low.

Sort #5 – Nonsense Word Fluency

This sort is especially useful for those of you who teach primary level students.  We will discuss two different NWF sorts: one for word reading fluency and one for phonics.  The first one I will discuss is the one where the students are reading words.

                The first quadrant is for those students that are reading whole words.  They are not sounding them out.  Some call this unitization.  The second quadrant is for those students that are reading words a sound at a time, then reading the whole word.  The third quadrant is for those students that are doing some blending.  Perhaps they are reading them as onset and rime.  The fourth quadrant is for those who are decoding the words a sound at a time.

The next Nonsense Word Fluency sort is the one for phonics or alphabetic principle.  In this case the students are not yet reading whole words.

                The first quadrant is for the students that can read the initial and final sounds.  Maybe they will only read initial sounds or final sounds.  The second quadrant is for the students that have repeated substitution errors for consonant and vowel sounds.  The third quadrant is for those students who have errors on the middle or medial vowels, usually deletions.  The fourth quadrant is for students who are unable to read the whole word or recode.

Where do you go from here?

                My take on this whole four quadrant sort for instructional groupings strategy is very simple.  You could take any two pieces of data that you have obtained through assessment.  Identify which one of the skills you assessed is the more basic, prerequisite, fundamental of the two.  This is the one that needs to be adequate in quadrant 1, adequate in quadrant 2, not adequate in quadrant 3 and adequate in quadrant 4.  The next thing to do is to take the next skill you assessed, the higher level one, the one that builds upon the previous one, etc.  This is the skill that is adequate in quadrant 1, not adequate in quadrant 2, not adequate in quadrant 3 and adequate in quadrant 4.

                This may seem oversimplified, but I came to this conclusion through comparing the sort for accuracy vs. fluency in reading and the sort for fluency vs. comprehension and also the sort for computation vs. concepts & applications in math.  In all of these sorts, the skill listed first is the more prerequisite of the two skills in the sort.  For example, accuracy comes before fluency.  Fluency is essential in order to be able to comprehend.  Being able to compute is essential for those working on concepts & application.

                Let me give you an example of what I’m talking about here.  I have not seen a sort for this particular set of skills:  vocabulary and comprehension.  Since it is widely believed that vocabulary skill is a prerequisite to comprehension skill , I have chosen these two skills for this sort. Take your vocabulary and comprehension assessment results.  Determine what adequate scores are on both of these skills.  If you use a published assessment, rather than one that you created, you won’t have to determine what an adequate score is.  That information will be provided for 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 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 vocabulary.

                I imagine this particular sort would be useful for those teachers who have kids that are adequate in both accuracy and fluency.  If there is an accuracy or fluency deficit, you most likely won’t even bother doing this vocabulary and comprehension sort.  Remember, accuracy comes first.