Friesen comments:
Friesen comments:
Several thoughts:
1. When students are working on their warmup
(and other) problems and you select several students to present solutions,
think “5 Practices for Orchestrating Productive Mathematics Discussions.” When there are multiple solutions AND you see
them as you peruse the student’s solutions, this strategy can be quite
effective.
Anticipate solutions
Monitor student work
Select student work
Sequence the student
solutions
Make connections
Often you may be
looking for one solution, but you can also use their solutions as a takeoff
point for related things you know need to be addressed. (Of course there are time constraints.) Or you can present a follow-up alternate
solution when appropriate as well.
2. Is there a time available for the iPad that
can run in background to accomplish your “timing” needs?
3. Getting to better know your students by
standing outside the classroom as they enter for the day is very
important. Take that opportunity to
communicate with several students each day.
Calling them by name is important.
For instance, today you might set this as goal, “when Tom and Maria come
in to class, I will address them by name”
Force yourself to do things like this.
It helps you learn their names, builds a more personal rapport with the
students, and they see you as someone who know them and cares about them.
Friesen
comments:
It was very fortunate for you to have
visited the Diff. PreCalculus class this semester. You noted quite different environments,
varying levels of motivation to learn mathematics, and important teacher
behaviors appropriate for the very different settings.
On the one hand, you have more
“classroom management / motivation” issues to address in the Algebra
class. On the flip side, you have more
“content preparation” challenges to address in the Diff. PreCalc class. Ben characterized these differences as “cool
and laid back” versus “sort of an enforcer.”
What strategies and practices (in Alg. &/or Diff. PreCalc) can a
teacher use to “keep the students motivated, on task, and interested in
learning mathematics?”
Friesen
Comments
If there were the 10
Commandments / Principles / Absolute Musts for Mathematics Teaching, surely they
would be include:
“You must take every
opportunity afforded you to remind / review / restate
a)
where
to decimal place goes
b)
slope
is “diff of y’s over diff of x’s”
c)
2nd
quadrant has negative x-value and positive y-value
d)
(0,0)
is called the origin
e)
neg
x neg = pos and neg + neg = neg
f)
|x|
> 5 use OR ; |x|
< 5 use AND
g)
derivative
is increasing over an interval then graph is concave up
h)
2nd
degree equation has 2 solutions
These things never go
away. A teacher must formally and
informally weave these ideas into their work.
Short phrases like these, throughout the school year, can address
student misconceptions, provide a gentle reminder, and reinforce their
understanding of mathematics.
As
I commonly say, “it doesn’t matter what you taught and they learned in October,
but rather what matters is what they know in May.”
Oct 3 Friesen Response:
This was a very important activity for
you.
A.
You learned to know a student at a much
more personal level than you otherwise would have.
B.
Your first impressions of that student
changed as a result of his interview responses.
So, without formal interviews, how do
you get to know all the other students in your classes? This is a real challenge for teachers with 5
or more classes with 25 or more students in each class.
One suggestion I might have is for you
to “pick a student” prior to class. When
the students come the classroom in at the beginning of class, take the
opportunity to strike up a conversion with student. What do you say? Perhaps:
A.
“How is it going today?”
B.
“Do you have a game (or music or
theater or ??) today?”
C.
“Do you have a lot of homework today?”
D.
On a Friday, perhaps, “Are you doing
anything interesting this weekend, besides homework?”
E.
“Any questions on the homework?”
Or you might stand
outside the classroom door and “bump into” the student who you might be seeking
out today. Tomorrow you might especially
wish to engage another student. Over time,
you would be building a more personal relationship with each of these students
and they would see you as someone who is not always “very serious and stern.”
Friesen comments
As Travis (see his comment) and you
have noted, teaching (and learning) “conditional statements” is not easy. Students may need a thorough introduction to
forming the initial conditional. Often
NOT ENOUGH time is devoted to that concept, textbooks do a poor job and generally do not give proper exercises. In short form here are some exercises that
might help students (similar to what you say in your 2nd paragraph
above):
A.
sidewalk is wet, rains
B.
Is it “if the sidewalk is wet, then it
rained.” Or “If it rained, then the sidewalk is wet.” Of course, there are parameters like the
sidewalk is “not covered, etc.”
C.
Sun shines, see my
shadow (you are not outside,etc.)
D.
Is it “If the sun
shines, then I see my shadow.” Or “if I see my shadow, then the sun is
shining.” (lamp light inside the house
after dark, for instance.)
E.
Ran to the store,
took less time to get there.
F.
Is it: “if I ran to the store, it took less time to
get there.” Or “If it took less time to get to the store, then I ran to the
store.” (no could have ridden in a car.)
Once the initial conditional is
properly formed, then let all the work begin‼!
One of the best ways to accomplish
the “basics of logic” is to refer back to it, apply it, and model it THROUGHOUT
THE GEOMETRY COURSE (and other courses also) at every opportunity. Examples:
1.
A.
if the slope is
positive, then the graph increases from left to right.”
B.
“If the graph does
not increase from left to right, then the slope is not positive.” What does “not increase”
mean? Flat or decrease
What
does “not positive” mean? 0 or neg
slope
2.
A.
If the absolute value of a number is > 5, then the graph of the point
on a number line is more than five units from 0. (|x|>5)
B.
If graph of a point on the number line is NOT more than 5 units from 0,
then it’s absolute value is NOT > 5.
(|x|≤5)
I would encourage you to experiment with the placement of the document camera in the classroom. Try it in the present location (I think you already have) and your alternate choice. How do you feel when moving it? Ask a few students if they noticed a difference? Sometimes they are the best judge of what really works and what doesn't work as well.
Also experiment with the use of whiteboards. And even try to have students put their work on the board from time to time. This works especially well when you know a student's work can be used to demonstrate or model a solution.
In your Block Algebra class, are the students randomly assigned to the 7-8 tables in the room? Or is there a "leader" or "bright student" or "teacher-student" at each of the tables? Are there any "tables" that do not work as well as a team? If so, why do you think that is the case?