The Reflective Educator

Education ∪ Math ∪ Technology

Tag: ETEC 533 (page 2 of 2)

February 4, 2009 / 0 Comments

List of resources for my ETEC 533 writing assignment

For my ETEC 533 class, I am planning on writing a short essay analyzing some current research on the effect of technology training for teachers on student achievement.  I’m interested in this because it combines two things I’m currently working on improving in my own professional practice, effective use of technology and leading professional development.

Here are some research links I’m planning on looking into in more detail:

Most of these links approach the idea from the perspective that if using technology shows no improvement on student scores, then teaching teachers how to use it will not have an effect either.  Assuming we can clarify that hurdle the next step is to show if there is a relationship between the amount of teacher training in a technology and its effectiveness in increasing student achievement.

 

 

February 3, 2009 / 0 Comments

Reflection of our course discussion about the use of technology in the classroom

Part of any useful activity is to make sure you reflect upon the outcome of that activity afterward.  This reflection helps you improve your practice and retain the connections you have developed through the course of the activity for a longer period of time.  Sustainable practice is only possible through careful reflection.

We just finished a week long exercise where we were to interview a person in our school or workplace and find out what their use of technology is, and what they think about the use of technology in a classroom.  After transcribing and analyzing the interview, we were supposed to post our observations to our class forum.  Once we finish our discussion, the last step is to write down what we got out of doing the activity.  My answers to the guiding questions are below.

How is your understanding of this issue changing? 

Well first I realized that there were some common threads between all of the interviews.  I had not thought that everyone had the same considerations about how to use technology, so it was encouraging to see some agreement between some very different people.  Pretty much everyone agreed that technology was most useful (or would lack use if this isn’t present) when it is carefully included as part of a repetoire of tools.  Technology should not be used for technology’s sake alone.

I was also surprised by how many people indicated an almost complete lack of support for training in their workplace for the use of technology.  In fact, I sent off a suggestion to my Alma Mater for a technology training course at my university and received a well reasoned out negative response.  It seems that even some teacher training programs are reluctant to take on the role of helping teachers come to grips with their technology woes.

What more would you like to learn or know?

I’d like to have more data.  Our anecdotal evidence was pretty convincing but there are definitely some sampling errors introduced by our biases when selecting interviewees.  It is unlikely that any Luddites would have consented to being interviewed for example, so most of us probably selected people who had some opinion about technology, one way or another.  A nationwide survey of teachers, where we find out what technology they use, where they want additional support, and what technology would they like to be able to use, would be a really useful tool. 

In what ways was your interview unique or similar to others?

Well my interview felt unique in the sense that the person being interviewed didn’t complain about the cost of the technology.  This is probably because we both currently work in a private school where the per student expenditures are higher than in a typical public school.  As well, our labour costs are incredibly cheap because of our location (Thailand) so the school has a much stronger budget for technology.

I’ve already mentioned a major similarity between my interview and other interviews, which was that technology as a tool  needs to be implemented carefully and not haphazardly.  Without this, it lacks purpose and can end up getting in the way of student understanding.

What does this say about the context/place or the issue?

It seems to me that, in terms of context, the use of technology is very similar in a wide variety of situations, but specific issues that arise can be quite location dependent.  In my school we have excellent physical resources, but lack strong internet connectivity.  Many of the videos and simulations we’d like to be able to use, for example, are much too bandwidth intensive to be useful in our part of the world.  However, unlike other schools we have all of the hardware that we need.  Instead of debating the cost of LCD projectors in classrooms, we have LCD projectors in every classroom in my school.  The context of the discussion that occurs is therefore very important as different observations can be made in different schools.  What seemed to be contextless however was the realization of all the participants in our discussion that technology, when used wisely, is a powerful educational tool.

Which issue do you want to explore further and why?

I’d like to have more of a  discussion about different types of technology.  I’d also like to be able to contact some of the people who were interviewed (which of course we cannot do because of privacy concerns) and get some more ideas from them.  Many of the teachers were mathematics teachers who had some very interesting ideas on how to use technology.

January 31, 2009 / 2 Comments

Introduction to Technology in the classroom course

We are having a discussion in one of our classes, ETEC 533 (Technology in the Mathematics and Science classes) where we are all talking about how little support we’ve received over the years in our use of technology.  We’ve all come from different education programs, but a common thread is that these programs usually have courses about how to use typical technologies, like Word or Powerpoint, etc… but no courses on the integration of technology into education.  All of us complained that we have almost no professional development time devoted to the use of technology in our classes.

So I took a look at the course schedule for my Alma Mater, UBC, and I discovered that there isn’t a single EDUC course which mentions the use of technology at all in their quick descriptions.  I did notice that the standardized time-tables seem to include 2 cohorts which talk about how to teach technology or computer related classes but there seem to be no elective technology courses at UBC.

I thought this is such a shame, because I know that technology is integrated into the teaching practice of so many professors on campus at UBC that the Education faculty should at least provide a survey course in the use of technology in education.  I’m sure such a course would be very popular.

Anyway I had some thoughts on how such a course should be run, and I thought that I might as well share them.  This is still a work in progress, so I’d appreciate any feedback or suggestions anyone has.

The course would run something like:

Title:
Use of Technology in Education

Course Description:
This course is intended to be an introduction to how technology is used in classes today.  It will help prepare students for the changing future where it is likely that technology will become a part of nearly every classroom.  Students will complete this course with a better understanding of how to use and implement technology within their own classrooms.

Course plan:
Unit 1 – Historical use of technology in a classroom (1 week)

Unit 2 – How is technology used at <insert university here>? (1 week)

Unit 3 – Arguments for and against technology use (2 weeks)

Unit 4 – Ways to use technology in your classroom (3 weeks)

Unit 5 – Keeping on top of new technology, habits for life (1 week)

January 24, 2009 / 0 Comments

Analysis of video interview of a fellow teacher describing their views toward technology

Again, as part of my ETEC 533 class, we are supposed to interview someone who teachers mathematics or science and find out from them what their opinion and perspective is on the use of technology in a mathematics or science classroom.  The table below includes a partial transcription on the left of an interview with a senior science teacher at my school.  It is clear from the interview that the teacher makes pretty extensive use of various types of technology as part of their teaching practice.

Transcribed from interview Analysis

Question:

How do you incorporate technology into your teaching?

Answer:

"… technology becomes another tool to use to help the students understand the objectives…"

"…if using a technology becomes a valuable way of doing this, then that’s what we do…"

"…students can investigate and learn without having to listen to me doing my ‘sage on the stage’."

This discussion seemed very familiar to me.  I realized pretty quickly that it was exactly the same discussion I had just had with my colleagues in my MET class.  Apparently, among people who use technology a lot in their teaching, it is just another tool.

My obvious question is, what would the response be among people who technology infrequently?  Is it clear that the reasons for the lack of technology use are things like "it’s too difficult", "it takes too much time", etc… However are there people who do not use technology simply because they haven’t found an effective way to use it?

I liked the the ‘sage on the stage’ mention in this person’s interview, especially since that is one of my primary uses of technology.  I like being able to direct the action, but I also like being able to have students make discoveries without my intervention.  Anything that leads to an ‘aha’ moment is what I want to be using.

Question:

Given unlimited resources, what other technologies would you consider introducing into your classroom?

Answer:

"… the thing we need to improve upon the most is quality simulations where the students are either given simulations to do, or are given the tools to create the simulations…"

"…could definitely use more of the higher order thinking type tools."

What was interesting to me about the interviewee’s answer to this question was that he wanted tools to help him with higher order thinking problems, just like every other teacher I know.  In other words, there is a great similarity between teachers, regardless of use of technology, we want to make our jobs of teaching abstract thought and reasoning easier.  Some of us just turn to technology to try and help with this difficult task.

As I expected, this teacher wanted access to more simulations.  I didn’t find out why specifically, that was probably part of my poor interview style, but it seems this teacher was making a link between using simulations and being able to develop higher order thinking skills.  I’d like to have seen his reasoning flushed out a bit more there.

Question:

How has technology, and your perception of technology, changed over the years?

Answer:

"… initially it was a fun thing to do and I was one of the few teachers at my school who got into doing the stuff …"

"It was a new way to explore learning on my part and the students’ part.  It then became clear to me, or clearer to me, that technology is a way to engage more than just the easiest of the senses."

"Technology is a way to engage the brain at the same time the hands and the mouth are moving.  I find that has been the best part of using technology."

"As technology has become all pervasive in our society it is pretty hard to amaze students anymore."

"Technology has done what it always wanted to do.  It has become the toaster.  It is now so pervasive everywhere that people just use it."

I was mostly curious about the answer to this question because of my own belief that although the technologies have changed over the years, our attitude toward them has not changed very much.  However this interviewee seems to refute this claim, and provided some excellent examples of why our view toward technology has changed.

At first it was a fun game, but as the technologies began to become more and more common, the ‘jee-whiz’ factor began to wear off.   Now students are less impressed with new technology, although I have personally noticed that when you use existing technology in unique ways, the students notice.

I’m not sure about the ‘technology becoming the toaster’ yet, as in my job I frequently have to give advice on using and trouble-shooting technology.  Every educator I know always has a back-up plan to a technology based lesson, not everyone I know has a back-up to their toaster.  Maybe we are getting there.
 

Question:

Would you say that technology increases student achievement, the use of technology I mean?

Answer:

"The use of technology increases student achievement in a round-about fashion.  It gets kids more engaged in the learning and since they are more engaged in [the learning] there’s actually some learning going on, so as a result scores or knowledge increase.  Whether or not technology is the sole arbitrator of that success is almost impossible to determine."

This is a really key question and answer in my opinion.  The use of technology is only appropriate if it serves the ultimate teacher need, that of instructing students and having them understand your course objectives.  If the technology helps the teacher meet this need, then it is worth using.  The interviewee agrees with me, and provides an explanation why, which I think I can expand upon.

First he says that technology helps with student engagement and that helps with learning because of the increased attention being paid during the lesson.  I also would argue that technology, if used in certain ways, helps a lot with student empowerment and with ownership of the material.  Students who through technology make their own discoveries and write down their own opinions are much more likely to remember what they have learned.

Question:

Would you say that including technology in your teaching makes more or less work for you?

Answer:

"..it’s just as another tool that I pick and choose to use."

"Sometimes technology is your friend, and then sometimes technology bites you. So on the days that it bites you, you definitely spend more time using it and trouble shooting it and trying to get things to work."

"…on balance using technology isn’t anymore time intensive than finding references in a textbook, or creating a worksheet, or giving kids something else to do."

As this teacher stated before, since technology is a tool, he chooses to use it when it is appropriate.  So this means that an approach where you use non-technological solutions mixed with technological approach is worth investigating.  It seems obvious to me, technology can’t solve every problem, and not every lesson has an easy way to incorporate technology.

He makes a good point about the ability of technology to be a chimera.  It is possible that everything runs smoothly with no difficulties, and it is possible that some key component of the technology you want to use fails at a critical moment, leaving you ‘high and dry’.  This is why any experienced users of technology always have a back-up plan for the mission critical situations, and why I argue, technology has not yet reached the status of the toaster.  More work needs to be put into the reliability of technology, and then a greater percentage of people will rely on it.

Question:

Can you describe an experience you had recently using technology which had an impact upon your teaching?

Answer:

"The best thing that I’ve done recently…is developed a website for students to access…putting everything on the website…has allowed me to then to simply say to the students here is the stuff now we are going to work together to get through it.  Then I become somewhat less of a paper pusher and more of a resource manager…"

What was interesting about this answer, is that I completely agree. This is also the best thing I’ve done recently, and it has had the most impact on my teaching.  I’ve gone beyond using a website (a manifestation of technology) as a source of information for the students however and am trying to empower them to contribute to the resource.

This I think is one of the ways we can help technophobic teachers the most, since it has the greatest level of reliability, and doesn’t require learning completely new skillsets in order to be able to master web technology.  The proliferation of ways to get involved and publish to the web also means the entry costs to using this technology are much lower. 

I foresee a time, in the not too distant future, where every teacher will have a website for use with their students.  Probably every student will have a webspace as well, although the social networking websites are trying their best to fulfill this driving need in our society to be as connected as possible.  Possibly our students’ generation will have less personal websites than our own generation.

In brief, I found that the answers the interviewee gave to the questions were very similar to my own and that there were great similarities in our approach to technology.  Given that my interviewee has much more experience using technology than I do, it leads me to believe that I am on the "right track" and that my time spent mastering technology is worth-while in my teaching practice.

Students also appreciate the effort that we put into trying to incorporate technology into their classes.  It makes their lives more interesting, and can brighten a sometimes dull experience of trudging between classes, where still somehow students are often spoon-fed material.

January 19, 2009 / 0 Comments

My analysis of two different video case studies on the use of technology in a classroom

These two case studies refer to videos I have watched as part of my Masters course, ETEC 533 and the copyright on the videos is unclear, so I am unable to show them here.

Learning Environment 6 with Teacher G (Post-secondary Applied Science)

This case study is about the use of a “clicker” or instant feedback device in a post-secondary applied science classroom.  The basic idea is, students have a remote clicker which they use to wirelessly transmit their answer on a multiple choice question presented at the front of the class.
The first thing I noticed about this video was that the instructor’s approach to teaching and what kind of information he was collecting seemed to be similar to what a secondary teacher might want to collect.  In other words, the position of the instructor in a post-secondary institution was less important than the fact he is an instructor.  This suggests to me that his experience with the “clickers” might be applicable to where I teach, in a secondary school.

The second thing I noticed is that what he likes about the clickers is the apparent engagement it creates among the students and how this could be useful.  However this has to be taken with a grain of salt, since as one of the students put it “Everyone else is just using PowerPoint or overhead projectors, so this is much more interesting”.  So the WOW! Factor might be critical here and we might be seeing a skew in our results.

The clicker technology though has the advantage of immediate feedback, not only for the students, but more importantly for the instructor.  Once you know whether or not everyone gets an idea, you can move on.  It seems to me that the clickers only allow for multiple choice responses, so this could be a bit of a disadvantage because it can be quite difficult to frame a multiple-choice question so that all types of learners are able to process the question and apply their knowledge to it.

There is another newer technology this reminds me of, where you create polls on a website, and students send in their responses via text message, and you can view all of the responses live on the website.  Very similar to the clicker technology, but might be more useful in a distributed learning environment.

The benefit of this technology is obviously the immediate feedback it gives the students.  A major drawback is the cost, both in terms of time setting up the multiple choice questions during the class to which the students respond and the cost of purchases enough remote clickers for every student.

Learning Environment 7 with Teacher E (Science, Elementary Preservice Teacher Education)

This case study is about using stop-motion animation to help teach physics concepts.  The basic idea here is, create an animation for the students to help them understand a concept in science.  An example would be, showing the animals in a food-chain actually eating each other in an animation, instead of using a simple picture with arrows pointing between the animals.

First reaction is that it must take an enormous amount of time to create the stop-motion animation.  This reaction was born out by the responses of the participants, nearly all of whom complained about how much time the animations took to create.

My second reaction was that I couldn’t hear the interviewer’s questions in most cases, so it was difficult to follow along the various videos for this case study.

One of the participants mentions that the stop-motion animation allows a teacher to present their instruction in a medium that the students of today, immersed as they are in digital media, can understand and appreciate more deeply.  By using the same digital media to present an idea, it is more likely to be understood.

Another participant used the students to help create the backdrop and pieces used in the stop-motion animation which he suggested help the students be even more engaged in the process, since it was their work they were seeing.  The same group suggested using a narrative as a way of helping students follow the process along more easily.

The instructor’s main point about the exercise was that the use of technology should be integrated into all of the courses a student takes, rather than as a stand-alone course.  He also mentions that if a textbook is “good enough” for learning a particular concept, then the use of technology to present the same concept should be carefully examined. 

A benefit of this technology is clearly the enhanced student engagement by the use of media.  A serious disadvantage is the amount of time taken to go through the process, whether it is classroom time with students or preparation time for the teacher outside of class.

Further questions

How much do these two different technologies cost to implement?

How much time does it take to learn how to use the technology?

How much time does it take to prepare the use of technology for the classroom?

Are there other cheaper alternatives that can be used within a classroom with similar effects?
 

January 13, 2009 / 2 Comments

An ideal classroom in which technology is used to facilitate real student understanding could exist, here’s how

Here is a quote from my class.  This guy has it right on.

  • all students would have laptops with integrated cameras, microphones, speakers
  • all students would work through configurable simulations of key concepts
  • all students would have full-time access to all the knowledge (and cruft) on the internet
  • students would track their own learning in a public learning log, possibly using blog or wiki software
  • anything that students say is within their core competency, they can be tested on
  • tests are given one person at a time, whenever the students are ready
  • teachers are there to teach concepts, lead labs, and ensure students are roughly on track with a learning schedule that will ensure they learn all needed concepts for state/provincial standards
  • frequently, students who have learned a concept would take a turn explaining it to the class. Who could do this and how often would be loosely coordinated schoolwide, so that as much as possible all students get opportunities to present in areas of their strengths
  • students would interact with others in learning communities all over the world via Skype. Sometimes a distance or foreign student might lead a discussion on a certain concept. (Note: I’m in conversation almost daily with members of my team in Italy, Norway, Ukraine, China, the United States, and the United Arab Emirates.) The school would seek out 5-6 learning institutions at similar levels and timetables so there’s a baseline of collaborators to start with, but students could talk to anyone if they’re on-topic.
  • teachers would frequently bring in social media output of practicing scientists/mathemeticians who are web2.0 producers when appropriate, helping to show relevance

– John Koetsier in ETEC 533.

This kind of classroom sounds fantastic to be in.  Instead of having to spoon feed a bunch of students who don’t really want to know what you are offering anyway, you as a teacher get to become a mentor and guide.  Students would be actively engaged and definitely interested in what they are doing.  Given that in our current system many students learn material which they never use again, and fail to learn even the most rudimentary of research skills, this kind of school would empower students to set their own goals and seek their own understandings of how things work.  The existance kind of school would be a sign that standardized testing would soon be getting a run for its money.

Obviously there are logistical things to work out.  How do we fund such a program, and how to we set graduation requirements so that a time-line for completing of high school still happens?

Questions like, "How do we make sure the students are being productive and not messing around all day?", "Can we make sure that some sort of basic curriculum gets covered in this scenario?", and "Will any students choose hard enough things to study that we will have people entering mathematics, physics and engineering at the university level?" are also a concern.

I think that the first two questions are legitimate, at least in our current paradigm.  I suspect that an open learning style like this would help save money that is spent on various classroom management initiatives (think study hall, detentions, jails…) and save society enough money to pay for these types of schools itself.  The second question is one where we can only answer it by realizing that suddenly, there is no need for a time-line to complete high school.  Students who are able to demonstrate competency in enough areas to attract interest in a university are free to go there.  Otherwise students will be trying to demonstrate their competencies to potential employers instead, and when they are ready, they can leave high school too.

Anyway, if anyone knows a place where education like this occurs at the high school level, or anything like it, let me know I’d love to visit.

January 10, 2009 / 2 Comments

What are the characteristics of properly used technology in a mathematics or science classroom?

Here is a question posed in my class this week.

What is a good use of technology in the math and science classroom? What would such a learning experience and environment look like? What would be some characteristics of what it is and what it isn’t?

Here are my thoughts in no particular order.

  • The technology is being used seamlessly in the lesson. Students do not need to spend 5 or more minutes learning the technology because they know how to use it already. This means that new technologies should be introduced separately from their use if possible, or be so easy to use that they require no special instructions
  • Technology should be used to provide simulations or examples which are either difficult to do in real life, or time-consuming. Its purpose should be to demonstrate an idea or help handle repetitive tasks as part of a bigger picture
  • If it is possible and easier to use a non-technological solution to presenting some information, this should be used as experiences grounded in what the children know are preferable (see constructivism).
  • Use of technology to facilitate communication that is above and beyond what is normally possible in the classroom is also an example of an acceptable use of technology. This can be used to extend instructional time outside of the classroom, by providing a classroom blog for instance for students to post questions, comments, and summaries of what they have learned.
  • The people implementing the technology (the teachers or instructional aides) need proper training first, no technology should be implemented by people who are not experts in the technology first. Otherwise, when problems occur, valuable instructional time will be lost when the teachers/aides cannot fix the problem quickly.
  • The technology needs to work without too many major bugs, it needs to be easy to use, and it should run quickly.

A good learning activity would have students using a web applet, for example, or a simple desktop application to run a simulation, and then analyze the data given by the simulation to come to some conclusions about what they have seen. Students would be engaged not by the technology, but by the simulation itself.

I guess that the use of technology should not be simple because it exists, but because it is much easier or less time-consuming than trying to make the same discovery using non-technological tools. I feel like under these circumstances, technology can actually be a useful replacement for a real-life experiment. It could also be useful if an experiment can be done under ideal circumstances in a simulation, and then confirmed in the less than ideal real world

One of my colleagues in the class, Tris says pretty much the same thing.  He gives some different examples though which are worth mentioning.  Specifically:

  • This could be by extending or enhancing a students understanding of an area of content (using a computer simulation or model)
  • speeding up a process (using a graphing calculator to graph functions rather than pen and paper)
  • improving a students grasp of basic concepts (using a computer game [to] memorize timestables)
  • increasing the number of learning styles or intelligences being addressed in the classroom, or reducing the cost of education (making content available online rather than purchasing textbooks – this being a hypothetical argument assuming no copyright issues)

– Tris (posted in the ETEC 533 discussion forums)

His ideas pretty much mirror mine, but I’m including his examples because it provides more ways of using technology in a thoughtful way. I particularly liked how refers implicitly to Howard Gartner’s multiple intelligences theory as a reason for using technology, which I think is excellent. Pretty much every teacher has noticed that students learn differently, and that providing multiple forms of representation of the material you are trying to cover is going to benefit your students. I’ve noticed that my use of daily classroom summaries seems to have helped reduce the gap in achievement between my ESL students and my other students. I should do some research to see if this actually the case, or if I am just imagining the gap closing.

Ian, another of my classmates agrees with me in one point, so I’m going to quote him here, since he says it better than me.

"Ironically, the use of technology in classroom teaching should endeavor to focus as little as possible on the technology as possible…" – Ian

A photocopier.This is a good observation to make since so often it seems technology is just used because it exists. If we think of older technologies, we can see that the ones that have been successful have followed this credo. I’m thinking of the overhead projector, a word processor running on a PC, the photocopier, etc… none of which people think of as "fancy technology" but which have made an enormous improvement on our profession. Can anyone imagine a school with no word processors, no photo-copiers and no overhead projectors?

 These old technologies are just seeing a resurgence in their development actually because of the green environmentalist wave that is sweeping across our society.  So maybe they aren’t so taken for granted as I think…

 What new technologies do we see in use today will become the norm for classrooms for the future?  Is every classroom going to have a smartboard?  Every student with a tablet PC?  Are wireless interfaces going to change the way we interact with technology?  I think the answer is that the same properties that made the older technologies (like a photocopier) so useful are going to be the properties which determine which technologies survive for the future.

January 10, 2009 / 0 Comments

Thinking about my first experience with technology

I am currently working on my Masters degree in Educational Technology and as part of my current course we are to create an e-folio for keeping track of our observation. 

Wang PC 240One of our first assignments was to reflect upon an early experience in our lives when we were exposed to or used technology, and discuss how and why we remember the experience.  Most people talked about early computer games or their earliest computers, I chose to talk about my first computer, a hand-me-down Wang.

My father gave me this computer when he bought his new computer, which if I recall correctly was an IBM portable computer.  The cool thing about it was that it came with a BASIC programming interface and an interpreter, so it was also the first computer that I did any programming on.  I had a reference book on BASIC my father had bought, and so I could look up functions and programming structures.  My dad was programming in BASIC at the time as well, so I’m sure I asked him for help once in a while.

What I loved about programming was the ability to make the computer do things (which is still what I love) like manipulating text, graphing graphics from text characters, etc…  I seem to remember constructing fun shapes using ASCII characters like Ascii 200 and Ascii 204.  You could create mazes, etc… and if I recall correctly there was very little space (or no space) between the characters so that the mazes looked seemless.

Over the years I worked on many mini-projects, my favourite being a computer game which I used as my science fair project in 10th grade (I got a C+, apparently you need to do a write-up even if what you’ve done is really cool).  I also remember programming a simplistic word processor, which included a simple word wrap algorithm and the ability to load and save files.  Think Notepad for DOS.

When I went to university, for some reason I set computers aside as a thing to be used as a tool, and used them more for recreation.  Had I paid more attention to them in school, I might have been able to start in this WWW craze much sooner.  Who knows what would have happened?

Anyway this early experience has definitely led me along a life-long path as an early adopter of technology and has helped me become an avid web design enthusiast.  My most recent project, creating desktop applications with Adobe AIR has been quite interesting, and I’m sure I’m not done now.

Newer posts »

Archived posts

Calendar

November 2024
M T W T F S S
 123
45678910
11121314151617
18192021222324
252627282930