"Dr. Barzilai, WE are the root of your problems!"
In-class comment on using correct 'mathematical grammar'

Quotes from weekly written cover-sheet assignment:

"After rereading my notes from last week, I felt like I was beginning to
make connections between things I have done as challenge problems in my
classes that I didn't even know were related"

"One of the main lessons I've learned this week is how to think about my
own thinking. The problems we solved in class made it possible to look at
the way we teach. The way we understand mathematical problems as teachers
helps us guide our students when they are faced with the same problems."

"I used the MSPP [Maryland State] standards to create my [concept] map
[of algebra] and was amazed that our curriculum really is a bit off
tracks according to these standards. Many of the outcomes that are listed
as 12th grade outcomes are addressed at length in my seventh grade
classroom."

 "Over the past few weeks, I have found myself paying more attention to
both how I write and speak mathematics. When talking to my students and
fellow teachers I find myself thinking should I use the term 'function'
or 'formula' or 'equation'" I am also a lot more aware of what I am
writing in my classroom...since our discussion I have been making an
effort to stop being so lazy and write the mathematics correctly. I have
been thinking [that] while the students and I understand what I'm doing
at the time, when they go home and review their notes, they are learning
mathematics incorrectly"

 "I saw firsthand, that it is more fun for students when they are
actively involved. As you noticed, half of us didn't even take a break
but continued working on the property problem. I also learned a bit about
functions . . . To be honest, I didn't realize just how much I don't know
about functions. It has only been in the past two years that we have even
begun to touch on functions in a way slightly more advanced than the
function machine concept that is often introduced in elementary grades

"When you were using picture proofs to prove Gauss' theorem and also to
prove the Distribute Property and the FOIL method, I would see light
bulbs going off in the minds of my students. I honestly cannot wait to
use these proofs in class just to see the understanding on their faces"

"[at my school] we used [an activity from the prototyp-ADEPT class] and
had a great discussion afterwards and the students then saw the need to
be aware of such things as the interval size and spacing as well as the
use of a jagged break when plotting data. It was a great way to increase
the motivation to learn or remember the information I wanted them to
gain.  Luckily, my principal was on his daily walk through each
classroom and he quickly picked one of the copies up and watched the kids
become absorbed in their discussions"

"It was also very helpful to work through the 'Connections' [CMP]
graphing activity and to hear how other teachers who use this activity
require students to support their answers with excepts from the
text. Although we know that this type of support is a requirement of
MSPAP, we do not have access to examples that are set up properly, as
this one is, to provide us with a model when instructing students in this
area. Thank you! I intend to use this with my students soon"

From end of semester self-assessment Narrative:

"...due to Math 506 [prototype-ADEPT Conceptual Algebra] I have
improved my mathematical grammar skills. I have always felt slightly
uncomfortable writing mathematical ideas out in full sentences, however
with the additional practice provided this semester, I feel much more
confident. I have also begun to expect a little more from my students
as well. It has become easier to grade their writing explanations, since
I have taken more time to develop my own expectations"

From Modified Lesson Plans Portfolio

"I think the real eye-opener for me was the realization that when using
my old lesson plans I really do not set high expectations of discovery
for my students. I compared my lists of objectives for my new and old
lesson plans and found that my students are not getting opportunity for
discussion, alternative representation, and conceptualization that they
are immersed in when using a different meta-cognitive approach to
learning math. I based my revised lesson plans on ideas from Math 506
[ADEPT Conceptual Algebra] and Dale Seymour Publications of Connected
Mathematics Series. After discussing with my principal the learning
benefits for the students of incorporating discovery and multiple
representation into our curriculum, he was very willing to look into
purchasing a math curriculum that was more suited to our needs.

"...my revised lesson plans and thoughts of a more conceptual approach to
teaching algebra will benefit my students for years to come. I want to
get away from the teaching of an algorithm and then practicing, to a
discovery of an algorithm through structured activities and group
discussion. the students will have a more in-depth understanding of a
concept, from why and how it functions, to where it
will be used again in their mathematical studies. Not only do I wish this
for my students, but also for myself"

"Prior to this class, I was very comfortable with the math content I
teach in my seventh grade pre-algebra classes. I was struggling, however,
with developing real life applications for my students. As a result of
this class, I am no longer so comfortable with the level of my math
knowledge and realize I need to "get out of my comfort zone" if I am to
grow as a teacher. I have been forced to struggle with math concepts that
I had forgotten, or had never studied, and even though they are not part
of my current curriculum, it is important for me to be familiar with them
if I am to be a more effective teacher.

"An added benefit to doing Dr. Barzilai's 'mental push-ups' has been the
struggle to understand new math concepts, something I had not done in
quite some time. I have always been sympathetic of the difficulties many
students face in pre-algebra, but that understanding has certainly
increased as a result of facing some of the same challenges
myself. Thinking about the methods I used as I struggled through some of
these problems has provided me with a new insight into the difficulties
of some of my students. Finally, as a result of writing Cover Sheets
[and] discussing my understanding and confusion on a particular topic, I
have had direct experience for the first time with two of the MSPAP
[Maryland State Standards] indicators, namely, "using mathematical
language and symbolism appropriately" and "presenting results in written
form."  After experiencing this myself, I am better prepared to instruct
and guide my students on the expectations of these indicators"