Today I was planning on observing
for checking for understanding. I taught
the math lesson today, and the rest of the day was packed with a timed test,
class game day, and a number of other opportunities to practice being
flexible. I ended up with nothing
written on my sheet. Instead, I will
reflect on the lesson I taught in math.
The lesson
subject was learning about frequency charts and analyzing data sets with mean,
median, and mode. I followed the
Everyday Math plan almost exactly, which is not something I usually like
doing. We started with a warm up,
practicing finding the middle place in a list of 5, 15, and 16. This relates to finding the median. Next, I showed the students a list of their
head measurements (which we’d used for a previous lesson). The list was unorganized and random. Next, we made a frequency chart from the
data. After doing that on chart paper at
the front as they followed along in their journals, I asked them to find the
mean. They have done this before, but
were still very unsure about the concept.
I hadn’t anticipate this taking so long, but they were very lost. After reviewing mean, we thought of
strategies for finding it another way using the frequency chart. I had to lead them to the answer, hinting at
using multiplication. They’ve been doing
multiplication for a while now, but they don’t automatically use it as a
strategy. We all agreed that it was a
lot easier to find the mean using the chart.
Next we
worked on the median. I had written
their measurements on post-it notes, so each student brought up their post-it
and we ordered them. I had one student
come up to the board and took off one from each side until we got to the
middle. While she did that, I used the
frequency chart to cross off my tallies, seeing if we got to the same
answer. They are very confident with
median.
I then
introduced the mode as the number that occurs most frequently. I used this language carefully, however many
students became confused about using the biggest number versus the number with
the highest frequency. As I went around
during individual work time, I noticed a lot of students getting confused with
a list of numbers. When I referred to
the frequency chart, they always could understand that, but had trouble with
the list. I had anticipated the
opposite, that they would understand the list and have trouble with the
chart.
Finally, we
made a bar graph of our data. This was
mostly review and practice for them, but also linked to the frequency
chart. It turned into a long lesson, so
I didn’t push on this as hard in my discussion of it. I returned to mean median and mode in my
wrap-up. The students have a hard time
remembering which one is which, and struggle finding mean at all. I think that tomorrow’s lesson should focus
strongly on this, especially because these are things they will really need to
know for future classes and testing.
Tomorrow I would like to teach them my mean median mode song. I learned it in grade school and still
remember the whole thing.
Management
was, as always, somewhat of a struggle.
I really only had trouble with one resistant student (case study #2),
and a table of frequently off-task students.
During individual work time I checked on them, and all but one had the
concept down for the most part. I felt
better about being in front of the class.
Mrs. Lance runs a tight ship, and I’m jumping on board with it. I’m much sillier than her though, and not so
harsh about individual issues (broken pencil, dropping things on the
ground…some of the smaller stuff). I
think this is one of the reason I’m taken a little less seriously than her,
along with the fact that I’ve only known them a few weeks. One thing that was a definite strength of
mine came near the end of the lesson. I
could tell the students were fading and we were just starting our bar
graph. After each step, I had them show
me they were ready in sillier ways. The
first was putting their finger on their nose, next was striking a pose, then
rubbing their head, etc. There were only
a few students who started to get too silly with it, and once redirected were
not a problem. Overall, I think it was
an effective lesson.
Question of the Day: How does/has your relationship with
your principal affected your teaching?
Mrs. Lance had a bad experience with one of her principals
in Texas. This person was very
disrespectful to his staff. Jessica felt
unappreciated and disrespected on a daily basis. After putting up with it for years, she ended
up leaving her job. She said it created
a very negative work place.
Interestingly enough, she worked with his wife at another school. When they interacted outside of the work
space, she said he was a completely different person. Another situation was when Mrs. L’s son went
to the school she taught at. As a
parent, she felt that she didn’t get a lot of respect either, but as a teacher
had a great and productive relationship.
She said both personal/interaction AND policy/decision making are
important to the work environment.
I'm glad you decided to write about the lesson you taught because that's what I was most curious to know. It sounds like a lot went well with your teaching, including staying on pace with the lesson plan (even though you didn't love following it so closely), frequently checking for understanding, and managing behaviors. I know you're good at this already, but I was glad to see you looking deeper into students' misconceptions. For example, you noticed that a source of confusion bubbled up around the size of a number and the frequency with which it occurred. Once you pinpoint students' math "miscues", your teaching becomes a lot more efficient, right? Did you do any "in the moment" re-teaching to clarify? And if so, did you try a different approach?
ReplyDeleteI know it's too late for this advice, but in the next day's lesson, you might consider telling a little story about a student who is making the same mental mistake as some students did in your lesson. See if they can figure out what the student was doing "wrong". Stories are a very effective way to teach complex content. In general, I'll bet you can think of some stories from the real world of using mean/median/mode that would help students' understanding--a story that connects with them personally. Data about ice cream eaten in the summer, race times on Olympic Day, etc.
Teaching a song is a good idea as a mnemonic device--did you do that on Friday? I used to help my students remember median as the middle number in a list by having them think of themselves (ME-dian)at the center of attention--just where kids like to be :-)