Assessment Result Calcuations

Assessment Results Calculations

An assessment result has limited value if the administrator can not see a trend over time in how the student is performing.  Therefore, the difference in academic performance between a previous assessment result must be calculated, but the difference in time must also be calculated in order to obtain a trend. The following terminology is used when making these calculations.

When there are multiple assessment result records associated with the one assessment code, the student is being tested multiple times on the subject area.  The set of assessment results records creates a picture of how the student performs over time.

Each of theses assessment result records can "look back in timetime" and calculate improvement since the last assessment result record associateassociated to that same assessment code.

Level Equivalent Assessments Calculations

The level equivalent assessment measures the academic performance in terms of grade levels.

For example, a student's  assessment result record is linked to the assessment code record names "IXL basic arithmetic".  At the beginning of the term, September 4, 2023, the student scores 720.  This score means 7tth grade second month. An assessment result record is made with date and score, linked to the assessment code, "IXL basic arithmetic" Four months later on January 5, 2024, the student scores a 840.  AnotherThis assessmentscore resultmeans record8th isgrade made,4th bothmonth.  linked to the same assessment code record.

• 4-SEP-2023    720    IXL Arithmetic
• 5-JAN-2024    840    IXL Arithmetic
• The difference in scores is: 840-720 = 120 in improvement = 1.2 grade years of progress
• The difference in time is 5-Jan 2024 - 4-SEP 2023 = about 19 weeks  = 1 term or half a school year.
  
• The studentstudent's improvesimprovement byrate 120is over1.2/0.5 19= weeks.3.4 grade levels per year (or 3.4 times the expected rate)

Generally this data may be plotted on a chart to show the student's progress over time. However, PEMS looks back and calculated improvement at each point in time that an assessment was taken.  The assessment result record contains a complete snapshot of academic performance at that time.   To do this, the academic performance fields are in every single assessment result record.  When a new assessment result record is entered, PEMS finds any other records related to the same assessment code. If a record is found, PEMS calculates a series of differences so that every single assessment record shows the rate of advancement, at that point in time.

 

Naming Convention

• AP stands for Academic Performance, in the example above, AP is 720 and 840.
• The letter "D" stands for difference, just like delta or the 'd' in calculus.
  
• DT stands for the Difference in Time frame.  Time is measured in terms, grade spans, and grade levels. In the example above, the difference in time is 19 weeks, but the difference in time frame is 10.5 termacademic years.

 

Examples

AP = Academic Performance, D stand for Difference, therefore:

• DAP = different in Academic Performance values between two assessment result records that are associated to the same assessment code record.  In the example above, DAP = 840 - 720 = 120.

DT = the difference in time,time as measured in academic years,  therefore: 

• DTterm = the difference inover timea frameterm is one term.
• DTGrade = the difference in time frame isover the gradeyear level, from the beginning of 7th grade, to the end of 7th grade.
• DTSpan = the difference in time frame isover the grade span, from the beginning of 6tha grade tospan the end of 8th grade.

 

Rate Calculations

DAPDTerm  is the difference in academic performance divided by the corresponding difference in terms.time.  This is the near term outlook, looking at how the student is progressing term by term.

DAPDTGrade is the difference in academic performance divided by the corresponding difference in gradetime. level. This value looks at how the student performed in a giver academic year.

DAPDTSpan is the difference in academic performance divided by the corresponding difference in grade span.time.  This value takes the widest look at progress over a longer horizon.

 

Fractional Time framesis always measured in portion of academic years

At any one point in time the student may not have completed a whole term, a whole grade level, or a whole grade span.  ThereforeTime is  between assessment results is always measured in units of academic years.  The DT or "delta time" is derived from the time frame must be calculated as a fraction of the actual progress in time.   If the student has a start date after the term, the datedifference of the assessment minus the start date yields the number of days, which will yield the portion of term so far completed.

The differenceresult in term,days DTterm,divided  if a full term is not complete,  is the portion  the term that has been completed, like 0.5 if two of four months were completed at the time of the assessment result.

The difference in grade level, DTGrade, if a full grade year was not completed, is that portion of a standard grade year that transpired between the assessment result records. We knowby the number of days in an average academic year, we know the days between the assessment result dates.

The difference in grade span, DTSpan, depends on the assigned span. If a student is in at three-year span, then we calculate the portion of the three-year span transpired between the assessment results.year.

 

Selecting the correct DAP - which assessments results oto use

A student may take an assessment at anytime in the academic school year.  When calculating  time frame differences, PEMS selects the most relevant historical assessment record.  

• For the term time frame, PEMS finds the oldest assessment within the current term.
• For the Grade time frame, PEMS find the oldest assessment result at the students current grade level.
• For the Grade Span time frame, PEMS find the oldest assessment result within the grade span.

For a new student that has only two similar assessments, the all values above are the same.  The values are only different as more assessments are taken. In the second term the DAPDTGrade uses the very first record, while the DADTerm uses a more recent record to make the calculation.

Calculations Workflow

When ever a new assessment result record is entered, each result is associated to an assessment code.

 PEMS searches for prior assessment result records, and calculates the difference in academic performance  between assessment result records and the difference in time frames.  Then PEMS calculates all the various parameter explained herein.

There is no need for this algorithm to be triggered on the event, the algorithm can run nightly to update all assessment result records.

 Once entered, these values are never recalculated.