What I Found Compelling and Not-So-Compelling about These Two Research Articles

[Keith]

As you read through these two articles, what aspects of the reports of
this research did you find compelling?
Were there aspects that were not-so-compelling?
In essence, the question is this, "Did you buy the arguments put forth
in these papers? Why or why not?"

[Tenille]

Much of what I read fell into the not-so-compelling category. In
reading the Suh & Moyer paper, I agreed that the students' ability to
solve algebra problems improved from the pre- to post-test. However,
the study's lack of a control group (a group of students who used
neither physical nor virtual manipulatives) leaves me to wonder
whether the students' improvements were a result of the manipulatives
or if they would have shown the same improvement if manipulatives were
not used in the instruction. Furthermore, while I agree that there
were some qualitative differences between the physical and virtual
manipulatives used in this study, I wonder how generalizable those
differences are to all physical and virtual manipulatives. For
example, all virtual manipulatives don't have the symbolic algebra
incorporated into the applet and thus the claim that virtual
manipulatives have an explicit link between pictorial and symbolic
representations would not hold in this situation. Additionally, the
claim that students using the physical manipulatives were given more
opportunity to use invented strategies is dependent on how the
physical manipulatives were implemented in the classroom. If the
teacher used the physical manipulatives to teach the traditional
algorithm, then the students would likely not develop their own
strategies for solving equations. As a final criticism of this paper,
I would like to consider the discrepancy between the example story
problem given on page 8 and the test story problem on page 17. I do
not see the need to use algebra to solve the former problem and I
don't think that third graders would naturally solve the problem using
algebra. In contrast, I would likely use algebra to solve the problem
given on the test. I felt that this was a weakness in the writing of
the report, but I am not sure how it would affect the results of the
study.

In the Recker, Dorward, and Nelson paper, I found their results to be
agreeable given the type of teachers they studied: experienced teacher
who were comfortable with technology. In the article they
acknowledged that the experience of the teacher may impact the
granularity of internet information they incorporated into their
classroom; however, I don't think that they considered how the
teachers' technology experience would impact different aspects of the
study or whether their technology experience could even be considered
average for the typical teacher. I also found the juxtaposition of
motivators and barriers to teachers' use of technology in the
classroom a weakness of the study. Time was a prominent factor in
both questions (with the teachers claiming that saving time was a big
motivator and that it took too much time to sift through everything
was a barrier) and I felt that the researchers should have explored
this apparent contradiction.

[Rachelle]

I was not-so-compelled by many of the arguments made in the Suh and
Moyer paper. Particularly, the most un-compelling thing was their
emphasis on "immediate feedback and self-checking system" as a
strength of virtual manipulatives. Given my experience in TAing Math
110, many students use immediate feedback to senselessly search for
patterns, which they are often unable to generalize to any other
problems. I guess it could be different with younger children if they
haven't had enough experience to learn how to beat the system, but I
really don't remember that much about being a third grader. Another
less-than-compelling aspect of the paper was the authors' assumption
that if students could include words like "subtracted from both
sides," then they understood equality. For years in junior high, I
knew the right words for solving equations but I didn't have a solid
understanding of how those words related to equality. On a more
positive note, I found it very compelling that there were third
graders doing algebra. Their work on page 171 particularly impressed
me.

On the Recker, Doward, and Nelson paper, I found it un-compelling that
they discussed one of the biggest motivations for using technology is
the speed of obtaining information and then in the next section
discussed one of the biggest barriers being how time consuming it
could be. I thought it odd that they gave no discussion on that
seeming contradiction.

On Jan 9, 3:30 pm, Keith <LethaLeat...@gmail.com> wrote:

[Rachelle]

I'm glad that Tenille pointed out the lack of the control group in the
Suh & Moyer paper. Originally I thought they were testing the
differences between virtual manipulatives and physical manipulatives
since those were the only two groups in the study. Thanks for pointing
that out because I was left a little mystified, wondering if I had
missed the point.

I also appreciate Tenille's bringing up the issue of teachers'
experiences with technology, which was not discussed in the Recker,
Dorward, & Nelson paper. It would seem important to look at teachers
with a wide range of teaching experience as well as technology
experience to get a good understanding of how those two factors affect
technology use.

> > in these papers? Why or why not?"- Hide quoted text -
>
> - Show quoted text -

[Tenille]

(This first paragraph is actually a reply to Rachelle's reply of my
initial blog. But don't worry, I will address Rachelle's initial blog
in the second paragraph.) First, I would like to revise my thinking.
I agree with Rachelle that Suh & Moyer's intent was to determine the
differences in student learning, if any, between the use of physical
and virtual manipulatives. I feel that the issue of whether or not
manipulatives in general affect student learning must be established
first. I think that Suh & Moyer were attempting to address this claim
in their literature review, but I was not convinced that they treated
the issue adequately. I think that I was confused by the results
given on page 12. The authors showed gains in the students'
understanding in both groups, implying that those gains were related
to the use of virtual or physical manipulatives, which I don't think
is the case.

Now, in reply to Rachelle's initial post. I would like to thank
Rachelle for reminding me of my experiences with technology and Math
110. I also found that students in my sections tried to use the
immediate feedback to find a (false) pattern in the solutions. It
reminds me of Erlwanger's Benny who made sense of the mathematics he
was learning in a completely nonsensical way. How many of my students
constructed "Benny-like" rules to help them make sense of the feedback
they received from the technology they were using. I think that
Rachelle's response finally helped me realize and articulate what was
really bothering me about the Suh & Moyer paper: Technology in and of
itself is not the answer. I think that so often in education,
technology is viewed as the golden answer. In fact, "the teacher uses
technology in the classroom" was on my principal's teacher evaluation
checklist, without any consideration for how the technology was used.
Technology, when misapplied in classroom instruction, does not help,
and in most cases hinders, student learning. (My goal in that
sentence was to see how many commas I could use. :)) As stated on the
NCTM web page, the technological tool, whether the calculator or
computer, cannot replace the teacher. While Suh & Moyer allude to
this idea when they cite Kaput, I do not feel that it was given the
attention it is due.

[CJ]

Recker, Dorward & Nelson
The truth is, I didn't find the Instructional Architect very
compelling. I even tried to go to the site to figure out what it was,
and all I got was an error message saying "Problem loading page." I
went to the site because I didn't really understand the description in
the article, and then there didn't seem to be any data or findings
specific enough to the Instructional Architect to help me understand
what it was. And so, I don't know why they even talked about it in the
paper except maybe to get people to go and see what it is . . .
publicity? I think that their conclusion that keyword searches are
limited agrees with my own experience, and it would be nice to be able
to browse indexed materials. Also, I fit into the "frills and extras"
user category, but I was surprised to find that there are other people
like me. I guess I don't consider myself really big on internet
resources, but if I need pictures of football players intercepting
passes to introduce the concept of y-intercept to my 7th graders, the
internet is my man. I do believe that most people don't look for
entire lesson plans, because most teachers seem to already have an
idea of what they want to teach and how to go about it, and it's kind
of encouraging to think that maybe they are using their experience and
their students' needs to guide their instruction rather than looking
for a pre-packaged script to perform. I guess my question is, "How do
people go about deciding that they have something that is worth
posting on the internet in the first place?" Now that might be an
interesting study. Also, could someone please help me to understand
the final paragraph of the paper. That might be a good way to reply to
my blog.

Suh & Moyer
Well, the thing that bugged me about this article is that the authors
concluded that the manipulatives helped overall, but there was no
control group to compare the numbers to. I don't know what the control
group kids would do, maybe just use symbols or pictures or something,
and if you could really call them a control group, but I don't think
that there is enough data to claim that these students learned more or
better between the pre-test and the post-test than students who
studied equations without manipulatives. Personally, I would choose to
use manipulatives in my teaching, but not because this article
convinced me to do so. It might be more useful to think about
equations that model situations in real life, and then reason through
those situations rather than manipulate meaningless quantities. Who
knows? I for sure don't, because the people that I tried to teach how
to solve equations, well, they weren't very good at it in the end. I
did like how the authors described the differences between the two
types of manipulatives. I checked out the virtual version online, and
it really does do a lot to help kids avoid common mistakes. Also, it
writes the equations for them. However, I don't know if this is
preferable or not and the results didn't seem varied enough to suggest
one way or another. Maybe it would be good for students to experience
both types of manipulatives . . . hmm. But I do like how the authors
recognized the differences between the two varieties.

On Jan 9, 3:30 pm, Keith <LethaLeat...@gmail.com> wrote:

[sdbr...@mathed.byu.edu]

In the article about online resources, I didn't find the quotes very
compelling. The focus group frequently quoted about the good points
about their Instructional Architect program. There were few
criticisms. I'm not sure if all the teachers were really that
complementative and not critical, but, knowing teachers, I don't
believe the authors told the whole story. I do believe the comments
and main purposes for the teachers using something like the
Instructional Architect to find extra activites to supplement the main
text for the course. This I would find valuable. In sum, I'm sure
that this is a fine program, but there is nothing spectacular about it
that would have me switch to it.

In the article about the manipulatives, I found it compelling that
students were able to make a good foundation in their algebra skills
with the use of maniuplatives, virtual or non. However, there were
more things that were not-so-compelling about the article. In the
first full paragraph on p. 158, the advocated the use of a Cognitive
Information Processing Theory approach to learning math and not a
constructivist or social constructivist approach. I'm still not too
sure on the implications that has, but it must have a big impact.
Also, on p. 166 with their table of results, I wasn't convinced that
virtual manipulatives made that much difference. I'm not really good
with statistics, but the mean posttest scores between the two groups
only differed by about 3% (80.55%-83.33%). It may be statistically
significant, but the scores are really close. In addition, the jump
from pretest to posttest was higher with the group using physical
manipulatives than the virtual ones (from 30-83, a difference of 53,
and 21.66-80.55, a difference of 58.89, respectively). This higher
gain means more to me than a difference of 3% on a test.

On Jan 9, 3:30 pm, Keith <LethaLeat...@gmail.com> wrote:

[CJ]

This is a reply to Tenille's reply to Rachelle's reply to her article.
Even if there was no control group, I still feel like in the end they
tried to make the case that the manipulatives had helped. Page 171:
"These results show that different manipulative models, both in the
physical and virtual environments, may have unique features that
encourage relational thinking and promote algebraic reasoning." I
think that "may" is in the wrong place, and that they could say that
". . . manipulative models, both in the physical and virtual
environments, have unique features that may encourage relational
thinking and promote algebraic reasoning." Yes, I can see that
manipulative have unique features, but I still can't see how you can
make a very strong case for relational thinking and algebraic
reasoning, especially when it is compared to . . . nothing.
Additionally, I would like to thank Tenille for exhibiting courage and
modesty in revising her thinking and, as someone put it, "writing a
book" for her response. You are forever raising the bar for me. Now,
if one of you other people would get blogging, I may feel compelled to
respond to you as well.

[Shawn]

I would agree with "CJ" on these articles. She would go to the
Internet for the extras. I'm not sure that I would go only for
pictures, but maybe a math activity here and there, too. So, as I
said before, if the Instructional Architect had something really
outstanding that it did which differed from all the others out there,
I wouldn't use it.

As Chris states along with others about the manipulatives article,
there is a problem with not having a control group. Even though the
students used manipulatives to help them understand algebra concepts,
would a control group do better with direct instruction? My guess is
that they could do as well if not better. They might have more
trouble drawing pictures, but do better working symbolically. Not
sure, but it would be interesting if someone researched that.

[Janellie]

What I find not-so-compelling about technology is that you may think
you have posted a reply, but in fact, you've probably pushed the
"discard" button instead.

I did not find these articles compelling in the sense that they did
not inspire me to change my teaching practices or views on teaching
with technology. If anything, they only strengthened my conviction
that technology is not always a profitable resource in a mathematics
classroom. Specifically, from the Suh and Moyer article, I did not
think that the digital manipulatives promoted relational understanding
for the children. This can specifically be seen toward the end of the
article (p. 171) where examples of student work were shown for algebra
word problems. Although students were able to show a picture and
translate it into a number sentence, the explanation and solution were
purely procedural. They did not have to show why they did certain
procedures or how their solutions connected to the problem situation.
Furthermore, I do not necessarily believe that an advantage of digital
manipulatives is how they keep "students from practicing erroneous
solutions" (p 166). Students will often use this feature to just
guess and check. In this situation, it did not seem to help students
explore as much as I would like.

I was convinced that the teachers interviewed in the Recker, Dorward,
and Nelson were honest and the researchers presented accurate
information. The findings were not particularly striking. One thing
I like about the article that would relate to me is the advantages and
disadvantages of using digital resources. Teachers said that they use
such resources because it saves them time. On the next page, teachers
said they got frustrated at using searches because they spent a lot of
time on "fruitless searches". I often determine whether or not I will
use online resources by weighing how much time it will take to find it
with how much time it would save me (because I would not have to look
for other sources). If a teacher could truly have "easy access to
large numbers of high-quality learning resources" (p 97) then this
would be WONDERFUL and well worth the time. I think creating such an
access would be more difficult than the authors made it sound.

On Jan 9, 3:30 pm, Keith <LethaLeat...@gmail.com> wrote:

[Janellie]

Chris brought up a GREAT question. "How do people go about deciding

that they have something that is worth posting on the internet in the

first place?" I fear that far too often people post ideas that they
liked themselves. However, that does not mean they are necessarily
good ideas. I think that it would be really good if the sources on
the internet would have to meet certain requirements or reviews before
being posted. However, then the question becomes, who would review
all these materials? What would the standards for submission be?
Perhaps this can be done with some web searches (in a manner similar
to Wikipedia). I know for me the most frustrating thing about
searching the web is running into a lot of worthless material,
especially when searching for activities, tasks, and lessons for the
classroom.

On Jan 16, 7:27 pm, CJ <christine.johnson....@gmail.com> wrote:

[Janellie]

I think Chris asked a WONDERFUL question when she said: "How do people

go about deciding that they have something that is worth posting on

the internet in the first place?" Every time I try to search for
something on the internet, I end up discovering a lot of worthless
information and websites. I wonder if it would be possible to set
certain requirements for online submissions or have people review
information for quality. The question then becomes, what would the
requirements be and who would regulate what gets added? Perhaps there
can be certain search engines or databases that could do this (in a
manner similar to Wikipedia). I do not necessarily think this will
happen, so I should probably just become more educated on HOW to
locate quality resources.

On Jan 16, 7:27 pm, CJ <christine.johnson....@gmail.com> wrote:

[ohsow...@comcast.net]

The two papers were polar opposites in credibility and quality. The
"discovery and use online" article was well-written. The background
research established a point of need in the research. The manner in
which the study was carried out lent itself to be credible because of
the duration, duplicatability of the non-computer user science and
math teachers (especially some of the older ones) and the realistic
approach to the studies limitations. This paper is believable. I
find my interest in the focus of the study waning as the ability to
duplicate the subjects will soon be obsolete. I am not so sure
focusing your efforts fostering technological buy-in to the non-
computer using math or science teacher would be worth the trouble. I
am however interested in the virtual manipulative database created at
USU.

The paper "developing students' rep" left me wondering why it was
written. Did the data show anything significant? Was the study's
duration sufficient to show any effect other than the novelty effect?
I concluded, why invest in technology when physical manipulative out
perform or run neck-in-neck with virtual manipulatives according to
the study data. I like some of the background research, but the study
did not strike me to measure much. What did the paper add to existing
research?

On Jan 9, 3:30 pm, Keith <LethaLeat...@gmail.com> wrote:

[erin...@byu.edu]

I decided that instead of writing stuff on paper as I read, i ought to
just type as I read... why not? Also, it was quite tempting to just
go ahead and read everybody else's papers and respond to them before
actually giving my initial gut reaction. That would take away some of
my joy, however, as I'm sure that others said the same things I hope
to say. My goal for next week is not to be the last person to post
and to get it done before returning to my apartment where my roommates
provide such a wonderful distraction.

The Suh and Moyer paper, in the first few pages, does nothing to
impress me. I begin to wonder why we are reading it, but then I
realize that technology is a new-age way to provide additionaly
representation that can enable learning about the different "types" of
learners. As I read about the study they did with the two groups of
students, I wonder why there was no group who did not use
manipulatives - essentially this study cannot claim that manipulatives
increase deeper understanding if there is no base with which to
compare students'understanding. As Suh and Moyer were discussing
examples of student work and the results, I feel like they did not
demonstrate the understanding inplicit in student work thoroughly
enough, and have thus provided no evidence for the claim(s) they made
in their opening statement. In general, I feel that this paper was
something that one of our graduate students would write for seminar.
I wanted more of a discussion of the results, more connections and
irrefutable proof that what they were claiming had to be true. The
one part that was somewhat compelling was the concept that certain
representations/ methods have unique factors that would help
particular students grow in depth and breadth of understanding - this
was always something in the back of my head that I agree with, but I
had yet to articulate this. So props to Suh and Moyer for stating the
thoughts in my head - maybe they're gypsy mind readers!

After the first page of the Recker, Dorward, Nelson article, I am
hooked! Maybe it is because we just made our own digital research
page, providing data about data, or perhaps it is because I use such
sites as Google, yahoo, and wikipedia on a frequent basis when I am
looking for particular information. Regardless, I am loving this
article right now and am eager to see how their study develops and
what conclusions the authors are able to make. A few more pages into
the paper, I am still enjoying it greatly - the organization and
thoroughness helps the paper to flow better (succint and easy to
follow). And finally, at the end of the paper, I can certainly say I
enjoyed that paper. Maybe it is because it was so written with a
style and vocabulary that are easy for me to understand, but I feel
like that paper almost read like a novel. What I found compelling was
the concept that teachers are most interested with sites/ suggestions
made by fellow teachers. In my discipline class, our instructor told
us that great teachers do not have to come up with everything on their
own - they can learn to rely on others and borrow superior ideas.
Online learning resources certainly help facilitate this in a very
simple way!

In summary, I feel that the Suh and Moyer paper did not present a
strong enough argument to cause me to take time and give thought to
its subject; the Recker, Dorward, and Nelson paper was, however, very
resourceful and supported what convictions I had about appropriate use
of the Internet as a learning resource.

On Jan 9, 3:30 pm, Keith <LethaLeat...@gmail.com> wrote:

[CJ]

Here is a reply to Amy's comments. If I understand you correctly, you
are saying that soon there will be very few teachers who are not
completely comfortable conducting an internet search for teaching
resources. I think that you do have a point, because each generation
seems to be more and more comfortable with technology. However, if I
can consider myself a computer-using individual, I still appreciate
how the paper does bring to light some of the difficulties/annoyances
of performing an internet search. There really is a lot of non-useful,
unreliable stuff out there, and I anticipate that it will just get
worse. (Especially if anyone can publish a webpage on google groups.)
Does everyone get how Boolean operators (or whatever they're called)
work but me? Maybe I do need to take a class about the internet. Maybe
I am an old person and just don't want to admit it.

[erin...@byu.edu]

Two thoughts:
1- referring to what a few people said regarding teachers' level of
experience in the classroom compared to their level of experience with
technology, I think that it would have been much more beneficial had
Recker, Dorward, and Nelson examined both factors more in depth.
Instead of only using experienced teachers (experience being time in
the classroom) who were "comfortable" with technology (I feel unsure
of how they decided whether a teacher was qualified to be
"comfortable" - did I miss that or was it never mentioned?), I think
their argument would have been greatly strengthened if they had used a
variety of teachers (first year, second, almost-retired) with a
variety of technological capabilities/ comfortability. For example,
during my student teaching, there was a "new" teacher (in his second
year) who could do amazing things with technology and the internet and
as such was able to help his students develop a greater level of
understanding. There was also a very experienced teacher who was able
to use a little bit of technology/ the internet and would even call
himself "comfortable" with the internet, but he rarely used it to help
students build understanding at all (in fact, he would only use it for
non-math things that would entertain the students and boost their
opinion of him as a "cool teacher").
2- I really loved Janelle's response to Chris' question about how one
decides that something is worth posting on the internet. I believe
this takes us into the realm of subjectivity and opinion. Janelle
(who has a great nickname) hits the nail on the head when she says
that people post ideas that they like themselves - this gives that
information an element of worth and value, and are thus "good ideas."
How could one person say "you have a great idea" and "yours is stupid"
to every single thing that goes on the internet? It must be of some
worth or value to some person somewhere, or it would never get posted
in the first place. I certainly agree that some information is more
useful than others at given times, namely when I am looking for very
particular information or need to use it for something specific like
writing a paper, getting a source, finding local chinese restaurants,
etc... Part of the appeal of the World Wide Web is that it is
universally accessible, which includes the ability to contribute to
it. Perhaps, if we're looking for more specific information, we ought
to search specialized databases, journals, encyclopedias, and the
like. Such collections of information would certainly require
somebody to review the information to ensure its validity and
usefulness before including it, and then you would need to answer the
questions such as "who reviews it" and "what standards are the works
held to". As far as the world wide web, I think it would be
impossible and even a really bad idea to require every thing that was
ever posted to be reviewed and accepted/ rejected - what about the
right/ freedom to express oneself? (Of course, there are certain
expressions that are socially inapproriate such as nudity, vulgarity,
swear words, etc... Typically such things are kept off of easily
accessible, public domains where you would be surfing at home, school,
work, etc..., and there are available applications/ police type things
that help with this). Anyways, i think that the internet has to be
accessible and that we need to always be able to find useless things
that interfere with our scholarly/ academic/ otherwise searches for
information, how else would we be able to find distraction and
procrastine?

[Janellie]

You're right Erin. Without all those useless internet websites, how
would I have an excuse for procrastinating? :-) I really did
apprectiate what you said about freedom of expression. I can imagine
that restricting the internet too much could become a DISASTER.
Perhaps it wouldn't hurt if there were some sort of moral standards on
there...but then there would be the question of whose moral
standards.

[ohsow...@comcast.net]

I anticipate that as Chris mentioned, technology would be an add-on to
my lesson if it helped drive home some point in a way that the
students could not duplicate, or easily (within the allotted school
time frame).

"Worth" is in the eye of the exhibitor! (Unless he's selling
something...)

The final paragraph says the government gave them money to write about
technology and science...but the prior paragraph says: To understand
the value of technology in the classroom requires more studies focused
on in class technology use where the use is not imposed, but a natural
part of learning where appropriate tools/resources are sought out by
the user (students) and not artificially introduced by the research
staff or teacher.

On Jan 16, 7:27 pm, CJ <christine.johnson....@gmail.com> wrote: