Charles
Ungerleider, Professor Emeritus of Education, The University of British
Columbia
[permission
granted to reproduce if authorship acknowledged]
In last
week’s blog post, I tried to draw attention to other ways of calculating how
well a school’s student population is performing. This blog makes the case that
how we calculate performance reflects what we value. I argue that we should
place greater value on improving the performance of low-performing students
because doing so will produce better outcomes for them, for the communities in which
they live, and for society.
To save you the effort of clicking to the earlier
blog, let me explain that I contrasted two approaches. One approach was to create a “performance
index” by calculating the percentage of students in a school who had achieved or
exceeded a “provincial standard” in a jurisdiction. This adopts what I called a
levels approach. I explained that, in a levels approach,
the score or grade a student earns on some assessment indicates that: the
student has not begun learning or was excused from the assessment (level 0);
has begun learning but hasn’t made much progress (level 1); is progressing but
is not quite at grade level (level 2); is firmly performing at grade level
(level 3); or is exceeding the expected performance for students at the grade
level (level 4). The levels approach is the same as assigning grades (A, B, C,
D, F).
The problem with
this approach is that it ignores what is happening for students in levels 0 and
1. If, for example, school performance is measured by changes in the
performance index over time it is
reasonable to consider students who move from level 0 to level 1 and students
who move from level 1 to level 2. As a
way of including these students in the performance index I offered the idea of
a weighted mean. What I meant by a weighted mean is that I multiplied the
number of students at each level by the value of the level achieved (level 0,
level 1, level 2, level 3, or level 4), adding the products together, and dividing
the sum of those products by the sum of all the students assessed including the
students below level one and the students excused from the assessment.
I compared
calculating the percentage of students in a school meeting or exceeding the
provincial standard with the calculation of a weighted mean. I illustrated how
using weighted means provides more information about the performance of
students in a school than simply reporting the percentage at or above some level.
In my illustration, I created 8 fictional schools in which the proportion of
students at or above level 3 was 75% and varied the proportions of students performing
below level 3.
This approach showed
more clearly the mathematical differences among schools that had the same
proportion of students meeting the provincial standard. I argued that the
differences conveyed a more subtle and complete picture of student performance.
Let’s go one step
further. In the weighted mean I calculated, the weights were the percentage of
students in each level. Instead of the weights I assigned in my illustration,
imagine that I have assigned greater weight to bringing students from
level 0 to level 1, from level 1 to level 2, and from level 2 to level 3. (The
weights still must add to 1.) I assign those weights because, I place a
greater value on teaching a student who does not know how to read, for example,
to read at a rudimentary level or teaching a rudimentary reader to read competently
than I do on teaching a competent reader to excel. If one wants to improve the
overall performance of an educational system, focusing
on the low-performing students is the effective and the most equitable pathway.
I make this
argument knowing that, on average, low-performing students come from less
affluent backgrounds, have fewer family and community supports, and, if they
remain low-performing, are more likely to drop out of school. If low performing
students complete school, they are less likely to go on to further education,
will have more precarious employment, earn less, pay less tax, and be more
likely to have children who suffered from the same disadvantages as they did.
Breaking this
cycle by focusing on improving their performance is a benefit to them, to the
communities in which they reside, and to society.
Happy holidays . . . see you in 2020, Charles