Dean S. Conis
SEC 590
Formative and Summative Assessment
The sequence of the units I taught in my Algebra 1 classes was dictated by the
Math Department and a software package called Agile Mind. I started instructing
during the unit on Systems of Equations, but was independent by the time we were
studying Quadratic Equations. There I begin.
Surveying Agile Minds Algebra unit 19 and the units that followed, I got the idea
of what we were to cover. We were going to study the quadratic equation centered on
the y-axis. This is a small subset of quadratic equations, and two parameters were to be
emphasized. Zeros and roots where not includes in the sequence as of yet. The
sequence seemed strange to me but it was the guiding framework to follow, and the
information to backwardly design from.
I anticipated the sorts of conceptual issues that students might have going into
this material based on the sorts of issues I’d seen tutoring related material. I had not
been with these students when they covered the precursory material months before. So
I assumed very little skill in this area. The initial issues of concern were: use of
functions, domain and range, signed numbers and their treatment in the various forms
a quadratic equation can take on. Also unknown was the understanding the rate of
change and the shape produced by a continuous domain. I needed to understand what
they knew as a group and as subgroups.
The formative assessment took the form of bell ringers. Signed integers and
simple signed rational numbers were provided in a table as the domain with space for
the function values. It gave the students a chance to recall what they had learned
previously and I was able to see the types of responses the students produced. I
collected the bell ringer but emphasized that it was not homework or graded. I looked
at the responses as I collected them, but proceeded to the first lesson of the unit mainly
terminology and the general shape of the parabola.
The formative assessment beginning the second lesson of this unit challenged the
student’s ability to distinguish between negative coefficients and the squaring of
negative numbers. After assessing the replies of the students we immediately
addressed the possible confusions that arise before we started the next lesson. The
parameters of the equation were introduced and we elaborated on these ideas and
practiced examples for the next two days. No formative assessment on the third day.
Then came spring break.
Even though the students were given a worksheet to be completed over spring
break, the expectation was that they would have forgotten everything previously
covered. We started class with a challenging bell ringer with a table and graph. The
problem areas were noted and emphasized during our lessons the rest of the week.
The rest of the formative assessment was based on student questions and
homework evaluated. We built up our concepts with more particular cases of our
limited subset of functions but also reemphasized those areas we were having most
trouble with. We also introduced some new material that we would cover later as
contrast. Some of the new material caused too much confusion and was delayed for
future a unit.
As we reviewed for the upcoming test we targeted these problem areas, and the
repetition may have been a bit boring to some of the students. Variations on the
themes, animations from the Agile Mind package and graphing calculator use where
included to make the lessons more interesting and to appeal to different types of
learning styles.
The summative assessment occurred as the quiz April 29th. For the two days
before the quiz there was no class due to PSAE testing. The students were given work
to keep the contents learned active. The quiz was comprised of two parts. There was a
multiple choice section and a constructive response section. All of the questions were
drawn from Agile Mind.
I assumed that with all the reviewing we had done as a class that the test scores
would reflect familiarity with the material. I was wrong. The low achievement I had
witnessed was still in place. Please see the spread sheet Alg 1 4-29-11 Quiz Results.
As I graded the quizzes I awarded partial credit for anything that resembled a
thoughtful attempt to solve a problem. Modeling a problem or setting up a problem
were indicators of at least a partial understanding. Faulty execution was pointed out
and introductions of error were indicated and the correct solution was shown, so that a
student who wished to solve the problems in the future could learn from their errors.
What I found as I was grading was a large portion of problems not even
attempted. More than half of the quizzes were at least half blank. A few quizzes were
handed back with only a name. I volunteered to stay after school to give anyone who
wanted more time to complete the quiz the opportunity to do so, and had only a few
LEP students show up. These LEP students were the best performers. The language
issues they had were outweighed by their willingness to put more effort into their
work.
I entertained the idea that perhaps I was not teaching the students very well and
I asked my supervising teacher(s) about it. I was told that, except for some particular
communication issues that I was still working on, this was not the case. This low level
performance has been chronic.