The lesson that I chose to observe was an Honors Geometry lesson on
complementary, supplementary, and congruent angles in one of the classes I intern
with Mr. Oddo at Dreher High School. This particular lesson came right after the
students had taken a test in the class before. It served as an introductory lesson into
the new section on angles. Therefore, the focus of the lesson was on introducing a
lot of new vocabulary terms to the students.
Mr. Oddo is generally one of the most high energy and engaging teachers I
have seen. However, in this lesson, the students were not very engaged. My instincts
tell me that this was due to the rote nature of the lesson. This class is also usually
the least engaged of the four classes I work with of Mr. Oddo’s. It is almost twice as
large as any of his other classes, so students generally tend to fade into the edge of
the room. During this lesson, 18 of the 27 students participated to any degree in the
lesson. However, only around 10 of those students were engaged throughout the
majority of the lesson. Five of the students were visibly not engaged at any point.
The overall access to opportunities to learn mathematics was reasonably visible. Mr.
Oddo does an excellent job of communicating the math terminology. He creates a
learning environment in his classroom that focuses on the proper precision of
Geometry. After a student described an angle vaguely, Mr. Oddo reminded the
students to “use the proper points to describe the angle” and then had students
practice describing other angles this way. He stressed repeatedly the importance of
using “the proper language” when describing the Geometry. Using the Kitchens
Rating Scale, I would rate Mr. Oddo’s lesson in the two range for access to
opportunities to learn mathematics. He had to prod the students to stay engaged
and even with this, there was a decent amount of off-task behavior.
As for mathematical analysis, there was very little analysis of the
mathematical content in the lesson. Again, I attribute this to the introductory nature
of the content. Mr. Oddo did tie in some interesting activities in the lesson to make
the students think. He used a dice graphic on the SmartBoard to model the
complements of an angle and how the two numbers must add up to the same
amount always. Though the content provided from this activity was not particularly
deep, it did break up the monotony and keep students somewhat interested. He and
I also provided the students with a simple proof of why linear pairs are
supplementary and vertical angles congruent. This also provided some added depth
to the lesson rather than just telling the students these facts. Again, I would rate this
lesson in the two level for mathematical analysis because the mathematical
activities were mostly diversionary, and though some collective understanding was
developed by the class, it was mostly teacher driven and not to a great depth.
Where this lesson excelled though, was in mathematical discourse and
communication. Throughout the lesson, Mr. Oddo kept the focus on developing the
understood terminology of the course. He made careful distinctions between similar
topics, such as “notice that I’m using the words congruent and equal
interchangeably here, though they do not mean exactly the same thing. Who can tell
me the difference?” and also, “do not get length and distance or lines and angles
confused. They have their own sets of vocabulary.” For any example problem done
in class, Mr. Oddo wanted a Geometric justification (the “why” behind the problem)
that allowed it to be solved in the manner used. This helped reinforce the
vocabulary that was being taught. For this lesson, and most of the lessons I have
observed him teach, I would give Mr. Oddo a 3 in mathematical discourse and
communication for the unrelenting focus he gives to the mathematical terminology.
Though this was one of Mr. Oddo’s weaker lessons, he still did a decent job of
catering to diverse learners through his lesson. The weakest part of the lesson was
probably the mathematical analysis as most of the information was base knowledge
level material that students needed to be introduced to, leaving little room for
analysis. However, he had a strong base in mathematical discourse and
communication, as per usual. Students are expected to know the terminology and
apply it correctly in practice. Talking to Mr. Oddo after the lesson, he knew that he
was not engaging all of the students in the lesson, and we discussed ways that we
thought would possibly get more engagement. Though not exemplified as well in
this lesson, this shows that Mr. Oddo is mindful of creating equal access to
opportunities to learn mathematics for his students and is seeking to engage all of
his students.
Diverse Lesson Assessment Rubric
Areas to Address
0
Access to
Opportunities to
Learn
Mathematics
(AOLM)
Paper does
not address
AOLM
Mathematical
Analysis (MA)
Paper does
not address
MA
Mathematical
Discourse (MD)
Summary
Total
Comments:
Paper does
not address
MD
Paper does
not
summarize
all three
above areas
(AOLM,
MA, MD)
and overall
impressions
of observed
lesson
1
2
Paper
mentions
AOLM
without
specific
examples
Paper
addresses
AOLM and
provides
adequate
examples
from
classroom
observation
Paper
mentions
MA without
specific
examples
Paper
addresses MA
and provides
adequate
examples
from
classroom
observation
Paper
mentions
MD without
specific
examples
Paper
addresses MD
and provides
adequate
examples
from
classroom
observation
Paper
summarizes
all three
above areas
(AOLM,
MA, MD)
and overall
impressions
of observed
lesson
3
Paper
addresses
AOLM and
provides
specific,
strong
examples
from
classroom
observation
Paper
addresses
MA and
provides
specific,
strong
examples
from
classroom
observation
Paper
addresses
MD and
provides
specific,
strong
examples
from
classroom
observation
Points
out
of
3
3
3
1
10