Beliefs and Knowledge
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Keith
Feb 27, 2008, 3:54:05 PM2/27/08
to MthEd608Winter2008
What connections do you see between the beliefs discussed in Leatham
(2007) (Pre-service Secondary Mathematics Teachers' Beliefs about the
Nature of Technology in the Classroom) and the knowledge discussed in
Leatham (2008) (The Development of TPACK in 'Technology, Pedagogy and
Mathematics' Courses in the U.S.)?
(2007) (Pre-service Secondary Mathematics Teachers' Beliefs about the
Nature of Technology in the Classroom) and the knowledge discussed in
Leatham (2008) (The Development of TPACK in 'Technology, Pedagogy and
Mathematics' Courses in the U.S.)?
CJ
Mar 3, 2008, 11:52:32 PM3/3/08
to MthEd608Winter2008
One connection that I see between the summary of research on TPACK and
the beliefs of PSTs is the issue of ownership. (Isn't it funny when
you realize that a nickname for a certain kind of person, a PST,
applies to yourself?) Although I have thought about my own abilities
and confidence with using technology, I selfishly just assumed that I
was the only one who had this problem, and that everyone else just
knew what to do. These articles suggest otherwise. The TPACK article
talks about this meta-component of ownership as kind of a result of
all the other components. If you are proficient in the other
components, you are in a position to explore and increase your
knowledge of TPACK through practice. However, if you really don't know
much about teaching methods, affordances and constraints, student
learning, assessment, and curriculum in a TPACK way of knowing, then
you may too intimidated to introduce technology into your class. Or
you may think that using PowerPoint slides to present your lecture is
the epitome of technology in the classroom and never really make any
progress. If we have an idea about the potential of technology and
enough basic skills to explore mathematics on our own using
technology, when we use technology in the classroom we aren't limited
to simply presenting a pre-planned script or worksheet, but can
actually base our classroom activities in student thinking.
So, what does this have to do with the PSTs? I saw this ownership
issue come out most strongly in the Teacher Knowledge dimension of
their beliefs. For example, Jeremy didn't make any claims about using
technology in Algebra I or lower classes, because he didn't know the
curriculum. Therefore, he couldn't possess the curriculum element of
TPACK for Algebra I, and was smart enough to not just make something
up when asked if technology was necessary for that class. Ben had
confidence in his own ability to learn mathematics with technology,
but felt like he needed to learn more about certain technologies
before he could confidently ask his students to use them. Katie and
Lucy also expressed the idea that a teacher needed TPACK to be able to
use technology effectively. In this sense, Katie had confidence and
ownership while Lucy saw herself as lacking.
Although I have made this connection, I don't feel like Ben's concern
isn't easily remedied by an element of TPACK that is mentioned in the
research. Is knowing how to use certain technologies an important part
of TPACK? It seems to fit into the Teaching Methods category the best,
but Teaching Methods also seems to go way beyond that. Is it more
important that a teacher know all the functions of a graphing
calculator, or that they know how to use a limited number of functions
in ways that will help their students to learn? Or are both implied in
TPACK?
the beliefs of PSTs is the issue of ownership. (Isn't it funny when
you realize that a nickname for a certain kind of person, a PST,
applies to yourself?) Although I have thought about my own abilities
and confidence with using technology, I selfishly just assumed that I
was the only one who had this problem, and that everyone else just
knew what to do. These articles suggest otherwise. The TPACK article
talks about this meta-component of ownership as kind of a result of
all the other components. If you are proficient in the other
components, you are in a position to explore and increase your
knowledge of TPACK through practice. However, if you really don't know
much about teaching methods, affordances and constraints, student
learning, assessment, and curriculum in a TPACK way of knowing, then
you may too intimidated to introduce technology into your class. Or
you may think that using PowerPoint slides to present your lecture is
the epitome of technology in the classroom and never really make any
progress. If we have an idea about the potential of technology and
enough basic skills to explore mathematics on our own using
technology, when we use technology in the classroom we aren't limited
to simply presenting a pre-planned script or worksheet, but can
actually base our classroom activities in student thinking.
So, what does this have to do with the PSTs? I saw this ownership
issue come out most strongly in the Teacher Knowledge dimension of
their beliefs. For example, Jeremy didn't make any claims about using
technology in Algebra I or lower classes, because he didn't know the
curriculum. Therefore, he couldn't possess the curriculum element of
TPACK for Algebra I, and was smart enough to not just make something
up when asked if technology was necessary for that class. Ben had
confidence in his own ability to learn mathematics with technology,
but felt like he needed to learn more about certain technologies
before he could confidently ask his students to use them. Katie and
Lucy also expressed the idea that a teacher needed TPACK to be able to
use technology effectively. In this sense, Katie had confidence and
ownership while Lucy saw herself as lacking.
Although I have made this connection, I don't feel like Ben's concern
isn't easily remedied by an element of TPACK that is mentioned in the
research. Is knowing how to use certain technologies an important part
of TPACK? It seems to fit into the Teaching Methods category the best,
but Teaching Methods also seems to go way beyond that. Is it more
important that a teacher know all the functions of a graphing
calculator, or that they know how to use a limited number of functions
in ways that will help their students to learn? Or are both implied in
TPACK?
Janellie
Mar 4, 2008, 4:39:23 PM3/4/08
to MthEd608Winter2008
A primary component of TPCK in the literature and in the TPM courses
was "Teaching Methods." It is hard to tell from the article on
student beliefs whether or not pre-service teachers had a sufficient
knowledge of how to teach mathematics with technology. We did not see
an example of them teaching. However, from what the students
reported, it seemed like they were not confident in their ability to
teach with technology effectively. I too, do not believe I have an
adequate knowledge of how to do this. I'm sure that technology
classes are geared toward this goal, but many students tend to come
away feeling inadequate.
Another related relationship can be found in the component of
"Ownership." Some students had confidence in using technology and
helping their students do so, but Lucy, for example, did not have that
confidence or ability. This affected her beliefs about how students
should use technology in the classroom.
Many of the PSTs talked about their experiences with technology in
their own math classes. These experiences helped to shape their
beliefs about technology. One salient belief that was found amount
PSTs was that of alignment of classroom activities, lessons,
atmospheres, and assessments. Jeremy was disappointed in the way
MAPLE was used in his Linear Algebra class. He said that you
shouldn't let students use calculators on tests if they were not
allowed to use them in class and vise-versa. Alignment is related to
the component of assessment. If teachers are going to have a
technology-rich context during their lessons, they also should assess
using that technology-rich context.
Question: It seems like a lot of the beliefs held by PSTs came from
their experiences with using (or not using) technology in their
previous math classes (some good, some not so good). These beliefs may
be hard to overcome. What can teacher educators do to help overcome
potentially harmful beliefs that are deeply embedded within PSTs'
experiences?
was "Teaching Methods." It is hard to tell from the article on
student beliefs whether or not pre-service teachers had a sufficient
knowledge of how to teach mathematics with technology. We did not see
an example of them teaching. However, from what the students
reported, it seemed like they were not confident in their ability to
teach with technology effectively. I too, do not believe I have an
adequate knowledge of how to do this. I'm sure that technology
classes are geared toward this goal, but many students tend to come
away feeling inadequate.
Another related relationship can be found in the component of
"Ownership." Some students had confidence in using technology and
helping their students do so, but Lucy, for example, did not have that
confidence or ability. This affected her beliefs about how students
should use technology in the classroom.
Many of the PSTs talked about their experiences with technology in
their own math classes. These experiences helped to shape their
beliefs about technology. One salient belief that was found amount
PSTs was that of alignment of classroom activities, lessons,
atmospheres, and assessments. Jeremy was disappointed in the way
MAPLE was used in his Linear Algebra class. He said that you
shouldn't let students use calculators on tests if they were not
allowed to use them in class and vise-versa. Alignment is related to
the component of assessment. If teachers are going to have a
technology-rich context during their lessons, they also should assess
using that technology-rich context.
Question: It seems like a lot of the beliefs held by PSTs came from
their experiences with using (or not using) technology in their
previous math classes (some good, some not so good). These beliefs may
be hard to overcome. What can teacher educators do to help overcome
potentially harmful beliefs that are deeply embedded within PSTs'
experiences?
Shawn
Mar 5, 2008, 4:24:49 PM3/5/08
to MthEd608Winter2008
In Leatham (2007), Ben, Jeremy, Katie, and Lucy were PSTs that had
specific beliefs with regard to teaching and learning mathematics with
technology. Leatham (2008) describes a knowledge called TPACK and
specific objectives that help students develop their TPACK from TPM
courses across the nation. I think that the students mentioned in the
article have a certain level of TPACK already based on their own
learning of mathematics. Their beliefs about teaching and learning
mathematics with technology allow us access to their level of TPACK.
Ben felt that technology was good to use as long as it was done
correctly. He said that if you use technology in class, the students
should be able to use it on homework and on tests. He felt that this
consistency was important. This is an illustration of one of the
secondary TPACK components of TPM courses that teachers need knowledge
of how students learn content with technology. Jeremy wanted all of
his students involved with technology and felt that all students
needed a graphing calculator from Algebra I on up. It seems that
Jeremy understands one of the primary TPACK components, which is that
teachers should know how to teach content with technology. Katie
wanted to have technology available to her when she needed it. For
her it was like one of the options to use when solving a problem. One
could use an equation, a graph, or a calculator. The specific
knowledge of when to do this comes from one of the primary components
of TPACK which states that teachers should understand the
technological affordances and constraints and be able to take into
account their roles specific to the content. Finally, Lucy believed
that technology is a powerful learning tool. However, she felt that
no one should have access to the technology until after they know how
to do the mathematical topic by hand. This knowledge is from a
secondary component of TPACK which states that teachers need to know
the relationship between the curriculum and technology and know how to
manage that relationship.
specific beliefs with regard to teaching and learning mathematics with
technology. Leatham (2008) describes a knowledge called TPACK and
specific objectives that help students develop their TPACK from TPM
courses across the nation. I think that the students mentioned in the
article have a certain level of TPACK already based on their own
learning of mathematics. Their beliefs about teaching and learning
mathematics with technology allow us access to their level of TPACK.
Ben felt that technology was good to use as long as it was done
correctly. He said that if you use technology in class, the students
should be able to use it on homework and on tests. He felt that this
consistency was important. This is an illustration of one of the
secondary TPACK components of TPM courses that teachers need knowledge
of how students learn content with technology. Jeremy wanted all of
his students involved with technology and felt that all students
needed a graphing calculator from Algebra I on up. It seems that
Jeremy understands one of the primary TPACK components, which is that
teachers should know how to teach content with technology. Katie
wanted to have technology available to her when she needed it. For
her it was like one of the options to use when solving a problem. One
could use an equation, a graph, or a calculator. The specific
knowledge of when to do this comes from one of the primary components
of TPACK which states that teachers should understand the
technological affordances and constraints and be able to take into
account their roles specific to the content. Finally, Lucy believed
that technology is a powerful learning tool. However, she felt that
no one should have access to the technology until after they know how
to do the mathematical topic by hand. This knowledge is from a
secondary component of TPACK which states that teachers need to know
the relationship between the curriculum and technology and know how to
manage that relationship.
CJ
Mar 5, 2008, 6:14:52 PM3/5/08
to MthEd608Winter2008
Hey Shawn and everyone,
I liked how you characterized Katie's belief about having technology
available as an example of the affordances and constraints component
of TPACK. I would have initially seen this as an access issue, but I
think that you are correct to say that a teacher who understands the
affordances and constraints would see the importance of having
technology available when you want it, but not necessarily all the
time. This makes me wonder if the affordances and constraints could be
combined with access component of TPACK from the literature. On second
thought, I don't think that they should be combined. I think that
affordances and constraints is more of a content type knowledge where
we make decisions based on the mathematics we are teaching, while
access is more of a pedagogical/management type knowledge where we are
looking at our resources and other classroom goals to make decisions
about technology. Maybe?
Anyway, when Katie talked about having technology available when she
needed it, did you feel like she was referring to herself as
instructor, or was she saying that her students should always have
free access to calculators? It seemed like she was referring more to
herself having the option to include or not include technology in each
lesson.
I liked how you characterized Katie's belief about having technology
available as an example of the affordances and constraints component
of TPACK. I would have initially seen this as an access issue, but I
think that you are correct to say that a teacher who understands the
affordances and constraints would see the importance of having
technology available when you want it, but not necessarily all the
time. This makes me wonder if the affordances and constraints could be
combined with access component of TPACK from the literature. On second
thought, I don't think that they should be combined. I think that
affordances and constraints is more of a content type knowledge where
we make decisions based on the mathematics we are teaching, while
access is more of a pedagogical/management type knowledge where we are
looking at our resources and other classroom goals to make decisions
about technology. Maybe?
Anyway, when Katie talked about having technology available when she
needed it, did you feel like she was referring to herself as
instructor, or was she saying that her students should always have
free access to calculators? It seemed like she was referring more to
herself having the option to include or not include technology in each
lesson.
Tenille
Mar 5, 2008, 10:02:50 PM3/5/08
to MthEd608Winter2008
I think knowledge impacts our beliefs in two ways (that I can
articulate at the moment): knowledge informs our beliefs and knowledge
enables the enactment of our beliefs. I will use examples from both
articles to illustrate these two ideas.
Assuming that knowlege is defined as what we accept as true, knowledge
informs what we belief. Furthermore, gaining more knowledge can (and
should) either solidify or change our beliefs. This relates to the
sensible system conception put forth in the framework of Leatham
(2007). It is difficult to maintain a belief when we have knowledge
contrary to the belief (unless we don't believe that knowledge is
true). Many of the PST's beliefs were determined by their TPACK
(although I am inferring their TPACK from inferences Leatham made
about their beliefs). For example, Lucy's beliefs about the
availability of technology could change if Lucy had greater knowledge
regarding how students learn mathematics with technolgoy and
affordances and constraints of technology.
Knowledge also enables us to carry out our beliefs about teaching.
This was discussed somewhat in the teacher knowledge section. If Ben
and Jeremy want to use technology in a way that matches their beliefs,
they need to have a knowledge of teaching methods, curriculum, and
learning with technology.
articulate at the moment): knowledge informs our beliefs and knowledge
enables the enactment of our beliefs. I will use examples from both
articles to illustrate these two ideas.
Assuming that knowlege is defined as what we accept as true, knowledge
informs what we belief. Furthermore, gaining more knowledge can (and
should) either solidify or change our beliefs. This relates to the
sensible system conception put forth in the framework of Leatham
(2007). It is difficult to maintain a belief when we have knowledge
contrary to the belief (unless we don't believe that knowledge is
true). Many of the PST's beliefs were determined by their TPACK
(although I am inferring their TPACK from inferences Leatham made
about their beliefs). For example, Lucy's beliefs about the
availability of technology could change if Lucy had greater knowledge
regarding how students learn mathematics with technolgoy and
affordances and constraints of technology.
Knowledge also enables us to carry out our beliefs about teaching.
This was discussed somewhat in the teacher knowledge section. If Ben
and Jeremy want to use technology in a way that matches their beliefs,
they need to have a knowledge of teaching methods, curriculum, and
learning with technology.
Rachelle
Mar 5, 2008, 11:44:47 PM3/5/08
to MthEd608Winter2008
I saw many good connections between the PSTs' beliefs and the various
components of TPACK.
First, I felt that beliefs about alignment were strongly connected to
knowledge about access. I felt the connection was especially relevant
to the subcategory of alignment. The PSTs felt that they needed to
understand students' access to calculators at home if they were to use
calculators in class because they wanted all activities to be in
alignment. Also, their hopes for either constant or periodic
technology use would have to be negotiated with the realities of
access. I also think that the assessment component of TPACK is
connected to beliefs about alignment. If PSTs believe that the uses of
technology in classroom activities, homework, and tests all have to be
in alignment, then they must deal with the issue of how much they know
about assessing understanding that was developed with technology or
assessing understanding while technology is available.
I think that beliefs about purposeful use are linked to knowledge of
affordances and constraints. The PSTs did not want to use technology
just for the sake of it-- they wanted to have a purpose for using it.
Without a knowledge of the affordances and constraints of using
technology in the classroom, how could teachers deem a certain use of
technology as being more than just technology for the sake of
technology? Of course, these PSTs might not have a firm grasp on the
various affordances and constraints of technology, but whatever
understanding they possess will certainly interact with their beliefs
about purposeful use when they decide to actually use technology in
the classroom.
I felt that the belief about teacher knowledge connected strongly to
the teaching methods component of TPACK. I interpreted the teacher
knowledge belief to be that teachers need to know what to do with
technology in the classroom, which sounds an awful lot like teaching
methods. Also a part of teacher knowledge was knowing not only what to
do, but why it's good to use technology in that way. Pedagogy includes
knowing how and why you should do something in your classroom.
components of TPACK.
First, I felt that beliefs about alignment were strongly connected to
knowledge about access. I felt the connection was especially relevant
to the subcategory of alignment. The PSTs felt that they needed to
understand students' access to calculators at home if they were to use
calculators in class because they wanted all activities to be in
alignment. Also, their hopes for either constant or periodic
technology use would have to be negotiated with the realities of
access. I also think that the assessment component of TPACK is
connected to beliefs about alignment. If PSTs believe that the uses of
technology in classroom activities, homework, and tests all have to be
in alignment, then they must deal with the issue of how much they know
about assessing understanding that was developed with technology or
assessing understanding while technology is available.
I think that beliefs about purposeful use are linked to knowledge of
affordances and constraints. The PSTs did not want to use technology
just for the sake of it-- they wanted to have a purpose for using it.
Without a knowledge of the affordances and constraints of using
technology in the classroom, how could teachers deem a certain use of
technology as being more than just technology for the sake of
technology? Of course, these PSTs might not have a firm grasp on the
various affordances and constraints of technology, but whatever
understanding they possess will certainly interact with their beliefs
about purposeful use when they decide to actually use technology in
the classroom.
I felt that the belief about teacher knowledge connected strongly to
the teaching methods component of TPACK. I interpreted the teacher
knowledge belief to be that teachers need to know what to do with
technology in the classroom, which sounds an awful lot like teaching
methods. Also a part of teacher knowledge was knowing not only what to
do, but why it's good to use technology in that way. Pedagogy includes
knowing how and why you should do something in your classroom.
Shawn
Mar 6, 2008, 1:07:53 AM3/6/08
to MthEd608Winter2008
Janelle, I think that this is a good question. I agree with you about
how those beliefs with technology are created. I think that the way
to overcome potentially harmful beliefs is to replace them as much as
possible with positive experiences where learning with technology
works. With many such positive experiences, we can overcome harmful
beliefs and have the students learn why they had their bad experiences
and how to avoid others in the future.
how those beliefs with technology are created. I think that the way
to overcome potentially harmful beliefs is to replace them as much as
possible with positive experiences where learning with technology
works. With many such positive experiences, we can overcome harmful
beliefs and have the students learn why they had their bad experiences
and how to avoid others in the future.
erin...@byu.edu
Mar 6, 2008, 1:14:01 AM3/6/08
to MthEd608Winter2008
Two initial things: 1- it threw me off that Tenille and Rachelle were
not the first two to submit. i felt like I was at the wrong group.
2- Adam and Chance made it through the primaries! That's why I'm
posting so late. Yay! Vote again!
As far as the connections I see, first I'll list the knowledge/beliefs
discussed, and then I'll discuss the relationship/connections I see
between them.
Beliefs: specifically with each student, Ben's beliefs included: using
technology is the best pedagogical choice if used "correctly,"
technology could almost always be used but should actually only be
used when doing so is an advantageous pedagogical choice. Jeremy
believes that technology is a tool to teach math and should involve
ALL students; the "necessity" of technology comes from a strong desire
and commitment to use it, and is not a logical absolute. katie said
that technology should naturally be included in the classroom (by a-
providing constant access to the students, b- be used frequently
across the curriculum, and c- the teacher needs to know how to use
technology and have confidence in that knowledge. Katie believes that
technology should be a continuous and ongoing part of the learning
environment, and that teachers need to know both the math they're
teaching and the technology they're using. Lucy believed that
technology has the potential to be wonderful if it is used in the
correct setting/ the right way. More specifically, Lucy thinks
technology is an enhancement AFTER students have learned a concept.
Lucy and Katie believed technology was not the end-all, be-all to
teach with; in contrast Ben believed that "if you're going to use
technology, then you had better use it all of the time" and Jeremy
thought students should use technology in whatever ways were possible.
Knowledge: basically a summary of the paper: teachers need a knowledge
of how to teach content with technology, the affordances and
constraints of technology, how students learn content with technology,
how to assess student understanding in a technology-rich context, the
relationship between curriculum and technology, how the other
components of TPCK afford one's own abilities/confidence, how access
to technology affects teachers' ability to use it effectively, the
relationship between content areas and technology, how technology
allows one to represent core content concepts, and how the teaching/
learning of content can be influenced by local and national education
policy.
The relationships/ connections between these seem pretty direct (this
makes particular sense b/c these are written by the same author), and
that the beliefs stem from either a sure knowledge or a building of
the various components of the knowledge associated/needed for TPCK.
It seems like there is more knowledge than what the beliefs pair-up
with (does that make sense?), and I would attribute this to the fact
that these PST's are building their own beliefs and barely starting to
learn the various components of TPCK. As they gain experience, they
will certainly develop more/deeper beliefs that I think would
correlate more directly with all of the components of knowledge that
our great teacher discussed in his 2008 paper. Does anybody disagree?
not the first two to submit. i felt like I was at the wrong group.
2- Adam and Chance made it through the primaries! That's why I'm
posting so late. Yay! Vote again!
As far as the connections I see, first I'll list the knowledge/beliefs
discussed, and then I'll discuss the relationship/connections I see
between them.
Beliefs: specifically with each student, Ben's beliefs included: using
technology is the best pedagogical choice if used "correctly,"
technology could almost always be used but should actually only be
used when doing so is an advantageous pedagogical choice. Jeremy
believes that technology is a tool to teach math and should involve
ALL students; the "necessity" of technology comes from a strong desire
and commitment to use it, and is not a logical absolute. katie said
that technology should naturally be included in the classroom (by a-
providing constant access to the students, b- be used frequently
across the curriculum, and c- the teacher needs to know how to use
technology and have confidence in that knowledge. Katie believes that
technology should be a continuous and ongoing part of the learning
environment, and that teachers need to know both the math they're
teaching and the technology they're using. Lucy believed that
technology has the potential to be wonderful if it is used in the
correct setting/ the right way. More specifically, Lucy thinks
technology is an enhancement AFTER students have learned a concept.
Lucy and Katie believed technology was not the end-all, be-all to
teach with; in contrast Ben believed that "if you're going to use
technology, then you had better use it all of the time" and Jeremy
thought students should use technology in whatever ways were possible.
Knowledge: basically a summary of the paper: teachers need a knowledge
of how to teach content with technology, the affordances and
constraints of technology, how students learn content with technology,
how to assess student understanding in a technology-rich context, the
relationship between curriculum and technology, how the other
components of TPCK afford one's own abilities/confidence, how access
to technology affects teachers' ability to use it effectively, the
relationship between content areas and technology, how technology
allows one to represent core content concepts, and how the teaching/
learning of content can be influenced by local and national education
policy.
The relationships/ connections between these seem pretty direct (this
makes particular sense b/c these are written by the same author), and
that the beliefs stem from either a sure knowledge or a building of
the various components of the knowledge associated/needed for TPCK.
It seems like there is more knowledge than what the beliefs pair-up
with (does that make sense?), and I would attribute this to the fact
that these PST's are building their own beliefs and barely starting to
learn the various components of TPCK. As they gain experience, they
will certainly develop more/deeper beliefs that I think would
correlate more directly with all of the components of knowledge that
our great teacher discussed in his 2008 paper. Does anybody disagree?
Rachelle
Mar 6, 2008, 2:29:36 AM3/6/08
to MthEd608Winter2008
Erin,
I completely agree with you that there were more knowledge categories
than the beliefs matched up with. I thought the connections seemed
quite clear, but I there were many knowledge categories that didn't
seem to connect with any of the PSTs beliefs (for example
representations, research, communication, curriculum, etc). However, I
wonder if their beliefs would necessarily expand to contain all of
these different components of TPACK simply with experience. It seems
like most people don't realize how many different components are out
there. For instance, the TPM courses don't even cover all of the
components of TPACK, and so many experiences are not aiming to help
PSTs or practicing teachers develop every component of TPACK. I
believe that it would probably take some experience coupled with a
concious effort to learn about (and reflect on) all the components and
how they fit in with one's belief system.
Congratulations on the elections!
> > Mathematics' Courses in the U.S.)?- Hide quoted text -
>
> - Show quoted text -
I completely agree with you that there were more knowledge categories
than the beliefs matched up with. I thought the connections seemed
quite clear, but I there were many knowledge categories that didn't
seem to connect with any of the PSTs beliefs (for example
representations, research, communication, curriculum, etc). However, I
wonder if their beliefs would necessarily expand to contain all of
these different components of TPACK simply with experience. It seems
like most people don't realize how many different components are out
there. For instance, the TPM courses don't even cover all of the
components of TPACK, and so many experiences are not aiming to help
PSTs or practicing teachers develop every component of TPACK. I
believe that it would probably take some experience coupled with a
concious effort to learn about (and reflect on) all the components and
how they fit in with one's belief system.
Congratulations on the elections!
>
> - Show quoted text -
Tenille
Mar 6, 2008, 2:56:51 PM3/6/08
to MthEd608Winter2008
Erin,
I also agree with you. I thought that there were many components of
TPACK that I did not see represented in the PST's beliefs. I posited
that the PST's were missing those components of TPACK. I think that
if they had knowledge of representations, for example, then that
knowledge would have been reflected in their beliefs. As far as
whether or not they will gain additional knowledge through their
teaching experiences depends on whether or not they make those
experiences educative (Dewey, 1938). I also wonder whether we can
gain TPACK exclusively from our teaching experiences. Will teaching
provide all the opportunities for all the necessary educative
experiences or are there other necessary experiences that cannot be
gained from teaching?
Also, please don't read my initial blog post too closely. I wasn't
feeling well and posted it without proof-reading. Wow! I made lots
of errors, not just typos but other spelling errors that I would have
caught if I had taken a few minutes to read through it prior to
posting. How embarrassing!
I also agree with you. I thought that there were many components of
TPACK that I did not see represented in the PST's beliefs. I posited
that the PST's were missing those components of TPACK. I think that
if they had knowledge of representations, for example, then that
knowledge would have been reflected in their beliefs. As far as
whether or not they will gain additional knowledge through their
teaching experiences depends on whether or not they make those
experiences educative (Dewey, 1938). I also wonder whether we can
gain TPACK exclusively from our teaching experiences. Will teaching
provide all the opportunities for all the necessary educative
experiences or are there other necessary experiences that cannot be
gained from teaching?
Also, please don't read my initial blog post too closely. I wasn't
feeling well and posted it without proof-reading. Wow! I made lots
of errors, not just typos but other spelling errors that I would have
caught if I had taken a few minutes to read through it prior to
posting. How embarrassing!
Janellie
Mar 6, 2008, 3:05:39 PM3/6/08
to MthEd608Winter2008
First to Erin and Rachelle, it did seem like there was more categories
for knowledge than there were beliefs that matched up with it. Did we
know how Leatham (Keith) got students to say particular things? In
other words, what questions were they asked in order to figure out
their beliefs?
Second, I really like how Tenille connected knowledge, belief, and
action. She said, "Knowledge also enables us to carry out our beliefs
about teaching." I feel like knowledge, belief, and action are
related, but I often wonder why they aren't more closely linked. For
example, I have a lot of knowledge and beliefs, but my actions do not
necessarily always match up with that knowledge and those beliefs.
Perhaps I am thinking about knowledge and beliefs wrong. Maybe this
is why I'm doing my thesis on motivation. Why do students (people in
general) do what they do?
for knowledge than there were beliefs that matched up with it. Did we
know how Leatham (Keith) got students to say particular things? In
other words, what questions were they asked in order to figure out
their beliefs?
Second, I really like how Tenille connected knowledge, belief, and
action. She said, "Knowledge also enables us to carry out our beliefs
about teaching." I feel like knowledge, belief, and action are
related, but I often wonder why they aren't more closely linked. For
example, I have a lot of knowledge and beliefs, but my actions do not
necessarily always match up with that knowledge and those beliefs.
Perhaps I am thinking about knowledge and beliefs wrong. Maybe this
is why I'm doing my thesis on motivation. Why do students (people in
general) do what they do?
erin...@byu.edu
Mar 6, 2008, 5:00:13 PM3/6/08
to MthEd608Winter2008
Janelle - I think that most action is generated from some belief. I
think that these beliefs stem from the knowledge that we have... I'm
taken back to a discussion we had in seminar where we talked about how
just because somebody articulates something doesn't mean it adequately
or accurately represents their thoughts/beliefs/etc... I wonder if
that could be extended here? Just because somebody has knowledge of
something doesn't mean that the knowledge will form into a
corresponding belief. I find it probably that such a formation will
occur, but I wonder if we could actually say "will always" in such
definite terms? I definitely like how Tenille talked about action and
think this corresponds with the articulation discussed above. Why do
students do what they do? I think it's because they believe that
something that benefits them will happen as a result: good grades,
better grasp of a concept, more friends, not hungry anymore, etc...
There is some purpose to action, and thus they will act. The purpose
is, I think, what motivates us to action. Good luck though, that's
such a tough one!!!
A few of you have given me excellent replies and I am officially
revising my stance: I agree that experience along will not suffice in
building the knowledge requisite in TPCK, but I have utterly lost as
to what will? Obviously personal experience using technology, or
personal experience being taught by someone with or without TPCK... I
appreciated Tenille's reminder that experience is only helpful if it
is educative. How can we make our experiences more educative? I
think there's far more to it than just an easy fix, and am finding it
difficult to come up with any ideas...
think that these beliefs stem from the knowledge that we have... I'm
taken back to a discussion we had in seminar where we talked about how
just because somebody articulates something doesn't mean it adequately
or accurately represents their thoughts/beliefs/etc... I wonder if
that could be extended here? Just because somebody has knowledge of
something doesn't mean that the knowledge will form into a
corresponding belief. I find it probably that such a formation will
occur, but I wonder if we could actually say "will always" in such
definite terms? I definitely like how Tenille talked about action and
think this corresponds with the articulation discussed above. Why do
students do what they do? I think it's because they believe that
something that benefits them will happen as a result: good grades,
better grasp of a concept, more friends, not hungry anymore, etc...
There is some purpose to action, and thus they will act. The purpose
is, I think, what motivates us to action. Good luck though, that's
such a tough one!!!
A few of you have given me excellent replies and I am officially
revising my stance: I agree that experience along will not suffice in
building the knowledge requisite in TPCK, but I have utterly lost as
to what will? Obviously personal experience using technology, or
personal experience being taught by someone with or without TPCK... I
appreciated Tenille's reminder that experience is only helpful if it
is educative. How can we make our experiences more educative? I
think there's far more to it than just an easy fix, and am finding it
difficult to come up with any ideas...
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