As the semester comes to a close, there is a lot of information (theories, tools, ideas) that can significantly impact the American educational system. In my mind, the key to being productive with this information is being able to sort through it and pick out which pieces can be implemented and provide a positive impact on the learning processes of today's classroom.
While legislators are pushing for more and more standardized testing, research has shown that increasing pencil and paper exams may be a step backwards. With the technology that is available, we are able to provide students with exceptional learning environments that differ greatly from the standard methods that have been in place for quite some time. Require students to construct projects as assessment not only alleviates the monotany of traditional testing, it requires students to learn skills outside the spectrum of the one particular subject area. Likewise, constructivism provides assessments that match the types of skilled labor that may be required of them in the workplace.
One key software category that has grown by leaps and bounds is that of online collaboration. I expect that we will continue to see growth with some focus aimed towards the educational market. Online collaboration provides a great deal of flexibility and authentic interaction to distance education. Students are now able to collaborate in real time with one another whereas several years ago bulletin board posting and text chat rooms were about the only options available. As video becomes more mainstream and software more robust, the interactivity will continue to increase, allowing distance education to become a viable option for an increasing number of subject areas.
Although we speak of a day when the instructor can be "replaced," it is important to realize that as a goal, it is distant. While self-sufficient learning has its advantages (the student sets the pace, instantaneous feedback, etc), we are not ready to do away with the traditional instructor. With this in mind, it is important to focus on instructional tools and how they can bring more to a presentation. We have mentioned streaming video in class and there are various other instructional tools, as well as alternative assessment means, that can transform the traditional classroom into a media rich learning center. When exploring options for classroom teaching, it is important to make certain that the piece of technology being used actually serves a purpose, as opposed to simply present for the sake of using technology.
One example I have run into is a Smartboard. If I simply show a Powerpoint file on a Smartboard and write handwritten notes on the slides, is this an improvement over using an overhead projector? No. However, if I supplement the powerpoint with streaming video and interactive applets, I have used a piece of technology in a way that enriches the students' learning. By coupling this with a constructivist form of assessment or a self-paced interactive practice program, I am increasing attentiveness, participation and retention.
As the semester closes, it is important to be willing to buck the trend of increasing pencil and paper testing and using the theories to increase actual learning in the classroom. Although it requires extended effort to decide on a theory, create the materials needed and grade the assessments that the students have created, the benefit of student-led learning and increased attentiveness will easily outweigh the one-time costs.
Monday, April 28, 2008
Monday, April 14, 2008
Fitzgerald and Teacher Education using Hypermedia
Fitzgerald's article brings up the idea of how technology can improve teacher education and preparation programs. The key issue is how to take the future teacher's learned knowledge of educational theory and relate it to their experience in the classroom. Although the article speaks of using laserdisc players, a technology that has come and passed, there is still a gaping hole that laserdisc (or anything else) has failed to fill. As a recent graduate of a teacher education program (2006), there is still a lack of transitioning tools from the role of student to that of teacher.
From what I have experienced, teacher education programs do a fair job of teaching theories and educational ideals but do poorly at showing how to adapt them into the role of educator, partly because the jobs of a teacher has changed so much in the past twenty years. The only way that successful teachers are bred is with time in the classroom (and passive observation does little).
Technology holds promise for bridging the gap between sitting in an educational methods course and being in front of a classroom teaching. Case Based Reasoning can prove very valuable. There are quite a few common scenarios that young teachers wind up in and commonly mishandle when under the pressure of having to make a split second decision (I still kick myself in the rear on a regular basis when I realize I mishandled a situation 30 minutes after it has happened). With case based reasoning and video, future teachers can see the situation unfold as the teacher does, but instead of having to make a decision with immediate consequences they can study what is happening and discuss what the proper response should be.
We did a little bit of this in my math methods course at UNC Pembroke and although it was brief, it has proved very effective. For example, we used case based reasoning to learn that something as simple as having two trashcans in a room can make the life of a teacher easier. We also talked about how to calm down students who are upset and may become violent. To be able to use video and multimedia for this would help tenfold.
Video capability for teacher education also makes it easier for future teachers to learn how to truly teach and to manage well. With video, it is easy to pause, rewind, select clips nonlinearly, and compare clips, allowing students to see good teaching methods verses average and poor teaching methods. When students observe active teachers in person, there is no guarantee of what will be seen or what will be retained. With video, students get much of the benefit of an observation with a much greater level of control. Most importantly, it can help show the difference between telling, showing, and teaching, which is a tough skill for new teachers to develop.
References: Fitzgerald, G. E., Wilson, B., & Semrau, L. P. (1997). An interactive multimedia program to enhance teacher problem-solving skills based on cognitive flexibility theory: Design and outcomes. Journal of Educational Multimedia and Hypermedia, 6(1), 47-76.
From what I have experienced, teacher education programs do a fair job of teaching theories and educational ideals but do poorly at showing how to adapt them into the role of educator, partly because the jobs of a teacher has changed so much in the past twenty years. The only way that successful teachers are bred is with time in the classroom (and passive observation does little).
Technology holds promise for bridging the gap between sitting in an educational methods course and being in front of a classroom teaching. Case Based Reasoning can prove very valuable. There are quite a few common scenarios that young teachers wind up in and commonly mishandle when under the pressure of having to make a split second decision (I still kick myself in the rear on a regular basis when I realize I mishandled a situation 30 minutes after it has happened). With case based reasoning and video, future teachers can see the situation unfold as the teacher does, but instead of having to make a decision with immediate consequences they can study what is happening and discuss what the proper response should be.
We did a little bit of this in my math methods course at UNC Pembroke and although it was brief, it has proved very effective. For example, we used case based reasoning to learn that something as simple as having two trashcans in a room can make the life of a teacher easier. We also talked about how to calm down students who are upset and may become violent. To be able to use video and multimedia for this would help tenfold.
Video capability for teacher education also makes it easier for future teachers to learn how to truly teach and to manage well. With video, it is easy to pause, rewind, select clips nonlinearly, and compare clips, allowing students to see good teaching methods verses average and poor teaching methods. When students observe active teachers in person, there is no guarantee of what will be seen or what will be retained. With video, students get much of the benefit of an observation with a much greater level of control. Most importantly, it can help show the difference between telling, showing, and teaching, which is a tough skill for new teachers to develop.
References: Fitzgerald, G. E., Wilson, B., & Semrau, L. P. (1997). An interactive multimedia program to enhance teacher problem-solving skills based on cognitive flexibility theory: Design and outcomes. Journal of Educational Multimedia and Hypermedia, 6(1), 47-76.
Tuesday, April 8, 2008
Jonassen and Case Based Reasoning
When Jonassen explains how telling stories can help novice learners gain "experience," what instantly comes to mind is football. My favorite course in college was a coaching football class and case based reasoning was oftentimes used to explain which offensive and defensive sets will prove most effective against a particular opponent's setup.
While CBR has limited use in my math classroom, I am looking forward to using it when I'm done with graduate school and begin coaching. There is quite a bit of time spent in both baseball and football (my two sports of choice) practice going over scenarios, seeing how they play out, and what to do when the situation arises. Baseball in particular uses CBR many times a day during practice. Quite a bit of time is spent in a baseball practice presenting a scenario, looking for the best way to solve it, and then mentally indexing it with other scenarios that are practiced.
What separates good coaches from poor coaches is how they approach CBR cases on the practice field. I was always taught growing up that "you practice like you play and you play like you practice," meaning that in order to play effective baseball you have to practice each scenario at full speed and full effort. Even with this in mind, effective presentation of the case at hand is important, as practices can't replicate the pressure and stress of games.
What is important when teaching these scenarios is to explore the possibilities, how different reactions cause other reactions to occur. This is where the story-telling part comes into play. The scenarios carry a greater relevance when a situation can be pinpointed back to a previous game. From here, the coach can talk about what went right, what went wrong, and can replay the situation and explore what happens if the ball is thrown to a different base, if players are in different spots, etc.
Because stories are easier to recall than basic knowledge, they present a great way of teaching baseball and football strategy. If a game and play is attached to a lesson, it's easier for players to pick the best option presented to them, both during film sessions and on the field in the heat of battle.
References: Jonassen, D. H., & Hernandez-Serrano, J. (2002). Case-based reasoning and instructional design: Using stories to support problem solving. Educational Technology Research and Development, 50(2), 65-77.
While CBR has limited use in my math classroom, I am looking forward to using it when I'm done with graduate school and begin coaching. There is quite a bit of time spent in both baseball and football (my two sports of choice) practice going over scenarios, seeing how they play out, and what to do when the situation arises. Baseball in particular uses CBR many times a day during practice. Quite a bit of time is spent in a baseball practice presenting a scenario, looking for the best way to solve it, and then mentally indexing it with other scenarios that are practiced.
What separates good coaches from poor coaches is how they approach CBR cases on the practice field. I was always taught growing up that "you practice like you play and you play like you practice," meaning that in order to play effective baseball you have to practice each scenario at full speed and full effort. Even with this in mind, effective presentation of the case at hand is important, as practices can't replicate the pressure and stress of games.
What is important when teaching these scenarios is to explore the possibilities, how different reactions cause other reactions to occur. This is where the story-telling part comes into play. The scenarios carry a greater relevance when a situation can be pinpointed back to a previous game. From here, the coach can talk about what went right, what went wrong, and can replay the situation and explore what happens if the ball is thrown to a different base, if players are in different spots, etc.
Because stories are easier to recall than basic knowledge, they present a great way of teaching baseball and football strategy. If a game and play is attached to a lesson, it's easier for players to pick the best option presented to them, both during film sessions and on the field in the heat of battle.
References: Jonassen, D. H., & Hernandez-Serrano, J. (2002). Case-based reasoning and instructional design: Using stories to support problem solving. Educational Technology Research and Development, 50(2), 65-77.
Tuesday, March 25, 2008
Bransford and MOST
I've found MOST environments to be quite intriguing, even though they have only limited use for my subject area. I find the idea of teaching literacy by such a non-traditional method to be not only useful, but ultimately necessary for struggling readers.
Although I've always had above average literacy skills in English, I can remember taking French courses and really struggling in them. This was in the mid to late 1990's and I can remember my teacher being one of the top educators at the school. She was very up to date on technology and tried to immerse us in the language as much as possible. Unfortunately, resources were limited, multimedia was just taking off, and the dominant technique for learning french was rope memorization.
Reading up on the MOST environment and how Bransford discussed its merits with struggling learners, I couldn't help but envision how this can directly affect foreign language classrooms (whether we are teaching Spanish to American youth or teaching ESL students English). I can remember watching a movie in French 3 and being able to follow what was happening, even though I would never be able to translate the dialogue if it was written out on paper.
The downside to the MOST environment is the preparation and materials that it requires. It is not as simple as showing movies. From what I've experienced in my math classroom, integrating video productively into the standard course of study is often hard, as the flow and pacing of the video very rarely matches up to the pacing of your classroom. Plus, you generally have a range in mind of student ability that you aim for when you are teaching and often times a video misses that range.
Although the implementation of MOST takes more time (haha, pun intended) than preparing a simple instruct-recall lesson, it does a world of good, particularly for the students you are trying to reach. The idea of being immersed in a foreign language, recreating the story line, analyzing what has happened, it makes the idea of taking a foreign language class sound much more pleasant.
References: BRANSFORD, J. D., SHARP, D. M., VYE, N. J., GOLDMAN, S. R., HASSELBRING, T. S., GOIN, L., O'BANION, K., LIVERNOIS, J., SAUL, E., & THE COGNITION AND TECHNOLOGY GROUP AT VANDERBILT (1996). MOST ENVIRONMENTS FOR ACCELERATING LITERACY DEVELOPMENT. IN S. VOSNIADOU, E. DECORTE, R. GLASER, & H. MANDL (EDS.), INTERNATIONAL PERSPECTIVES ON THE DESIGN OF TECHNOLOGY-SUPPORTED LEARNING ENVIRONMENTS (PP. 223-255). MAHWAH, NJ: ERLBAUM.
Although I've always had above average literacy skills in English, I can remember taking French courses and really struggling in them. This was in the mid to late 1990's and I can remember my teacher being one of the top educators at the school. She was very up to date on technology and tried to immerse us in the language as much as possible. Unfortunately, resources were limited, multimedia was just taking off, and the dominant technique for learning french was rope memorization.
Reading up on the MOST environment and how Bransford discussed its merits with struggling learners, I couldn't help but envision how this can directly affect foreign language classrooms (whether we are teaching Spanish to American youth or teaching ESL students English). I can remember watching a movie in French 3 and being able to follow what was happening, even though I would never be able to translate the dialogue if it was written out on paper.
The downside to the MOST environment is the preparation and materials that it requires. It is not as simple as showing movies. From what I've experienced in my math classroom, integrating video productively into the standard course of study is often hard, as the flow and pacing of the video very rarely matches up to the pacing of your classroom. Plus, you generally have a range in mind of student ability that you aim for when you are teaching and often times a video misses that range.
Although the implementation of MOST takes more time (haha, pun intended) than preparing a simple instruct-recall lesson, it does a world of good, particularly for the students you are trying to reach. The idea of being immersed in a foreign language, recreating the story line, analyzing what has happened, it makes the idea of taking a foreign language class sound much more pleasant.
References: BRANSFORD, J. D., SHARP, D. M., VYE, N. J., GOLDMAN, S. R., HASSELBRING, T. S., GOIN, L., O'BANION, K., LIVERNOIS, J., SAUL, E., & THE COGNITION AND TECHNOLOGY GROUP AT VANDERBILT (1996). MOST ENVIRONMENTS FOR ACCELERATING LITERACY DEVELOPMENT. IN S. VOSNIADOU, E. DECORTE, R. GLASER, & H. MANDL (EDS.), INTERNATIONAL PERSPECTIVES ON THE DESIGN OF TECHNOLOGY-SUPPORTED LEARNING ENVIRONMENTS (PP. 223-255). MAHWAH, NJ: ERLBAUM.
Monday, March 17, 2008
Vanderbilt's Tech Group and Logarithms
In the second article by the Vanderbilt Cognitive and Technology Group, the authors mention logarithms and how they become easier to understand when students understand how they can be used as a tool for multiplication instead of some arbitrary exercise.
Even as a math teacher, I've always struggled with logarithms and had no idea exactly what they are used for. However, after reading this article and overview of anchored instruction, it pleasantly surprised me that I use this quite a bit. The idea of math as a tool for solving problems is pretty natural. Even average math teachers look for ways to relate what is being covered into real world scenarios.
The article mentions a laser disc movie that presents the problem of a boat and its owner being home before sunset and not running out of gas. This reminds me of my favorite video we show: Donald Duck in Mathmagicland. While not completely part of an anchored instruction lesson, it borrows some of its features. What I've found works very well with this video is a series of questions that students answer briefly. The video has several problems that Donald runs into and the narrater uses math to show him how to solve. Not only is the video entertaining, it does a good job of explaining what the golden ratio is and how it is found throughout nature. The video also talks about music and how to make a string play an octave higher, you simply need to capo it halfway up.
Unfortunately, it appears we are losing a little bit of the background to base mathematics on, or it is at least changing. Many of the topics we cover can be tied into some sort of construction or structure. As fewer and fewer kids are forced to be handy around the house, constructing simple structures becomes less and less a relevant skill. I find that I am increasing focusing my math tie-ins on cooking, electronics, and such.
References:
Even as a math teacher, I've always struggled with logarithms and had no idea exactly what they are used for. However, after reading this article and overview of anchored instruction, it pleasantly surprised me that I use this quite a bit. The idea of math as a tool for solving problems is pretty natural. Even average math teachers look for ways to relate what is being covered into real world scenarios.
The article mentions a laser disc movie that presents the problem of a boat and its owner being home before sunset and not running out of gas. This reminds me of my favorite video we show: Donald Duck in Mathmagicland. While not completely part of an anchored instruction lesson, it borrows some of its features. What I've found works very well with this video is a series of questions that students answer briefly. The video has several problems that Donald runs into and the narrater uses math to show him how to solve. Not only is the video entertaining, it does a good job of explaining what the golden ratio is and how it is found throughout nature. The video also talks about music and how to make a string play an octave higher, you simply need to capo it halfway up.
Unfortunately, it appears we are losing a little bit of the background to base mathematics on, or it is at least changing. Many of the topics we cover can be tied into some sort of construction or structure. As fewer and fewer kids are forced to be handy around the house, constructing simple structures becomes less and less a relevant skill. I find that I am increasing focusing my math tie-ins on cooking, electronics, and such.
References:
Cognition and Technology Group at Vanderbilt (1992). Anchored instruction in science and mathematics: Theoretical basis, developmental projects, and initial research findings. In R. A. Duschl, & R. J. Hamilton (Eds.), Philosophy of science, cognitive psychology, and educational theory and practice (pp. 244-273). Albany, NY: SUNY Press.
Sunday, March 9, 2008
Schank and Goal Based Scenarios
Goal based scenarios, and Schank in his article, touch on one of the most problematic issues that educators face: motivation. As Schank points out, "Lessons are taught in a way in which use of the knowledge or skills is divorced from how they would be used in real life (p166)." I see this frequently in the math courses I teach and to be honest, when they ask "When will I use this?" or "Why do we have to learn this" I do not always have a good response. Sadly, much of our material is covered for only two reasons, 1) to promote algebraic thinking and reasoning and 2) because more material will build on it in the future. What urks me is that not only do I realize the pointlessness of much of what I teach, I want to teach poignant information just as much (probably more so) than they want to learn it.
Of all of the math courses I have ever taken, the one of most use was not even advertised as a math course and was an elective, Personal Finance. I've heard quite a few people mention the same feeling, that Personal Finance was one of the most useful and important courses they have ever taken. I've run into many more that could have used it and don't realize it. Case in point:
About 2 months ago I was back in Stanly County, a very rural area of NC where I grew up. A friend of my younger brother was talking about buying a Harley Davidson, and how he had been financed for about $12,000 and was looking forward to buying the $10,000 or so bike he was wanting (a Sportster) and could afford $2000 in accessories since they would finance those two. He also mentioned how if he could get his mom to cosign for him, he would get a better interest rate and higher amount to finance and could get a little bit more stuff for his bike. I talked to him a little bit about insurance, how first bikes usually get dropped or laid down, how there are a lot of hidden costs, and how its best not to get roped into more than can be comfortable afforded. I was worried about the kid, because he was about to get himself in a bad financial situation and pay a lot of money for a motorcycle he was going to drop and scratch.
I was back home a couple weeks ago and the guy's girlfriend mentioned that he had gotten a bike. I asked if he had bought the $12k bike and she said that no, he hadn't, that he had found a 4 year old Sportster that had the accessories he wanted for about $6k and he had gotten a loan from the credit union.
I don't know if I had anything to do with him changing his mind, but I realized at that point that Algebra 2 and whatever math class this kid had as a senior have served him absolutely no purpose in life (he is a diesel mechanic). What kids need as a senior is a math class that incorporates goal based scenarios and focuses less on parabolas and more on personal finance. It would be very easy to also incorporate a few basic applied mathematical skills that used to be taught in vocational courses.
This can be done, but it is up to the teacher. Senior math course offerings range from "discreet math" to pre-calculus. A pre-calculus course doesn't have the flexibility to deviate from the textbook curriculum, but nearly all of those students will be attending 4 year universities where the aforementioned applied math skills can be learned in a personal finance course. On the other hand, fewer of the kids taking discreet math will move on to a university and the discreet math course, while having a set curriculum from the state, leaves much of the pacing and curriculum choices up to the instructor.
I'm leaning on my department chair to let me teach a section of discreet math next year. I have a lot of ideas on possible units, including scenarios where students model purchasing a car, constructing a building, and more. Math can be exciting, but only when it's relevant. Goal based scenarios help make that happen.
References: SCHANK, R. C., BERMAN, T. R., & MACPHERSON, K. A. (1999). LEARNING BY DOING. IN C. M. REIGELUTH (ED.), INSTRUCTIONAL DESIGN THEORIES AND MODELS (2ND ED., PP. 161-182). MAHWAH, NJ: ERLBAUM.
Of all of the math courses I have ever taken, the one of most use was not even advertised as a math course and was an elective, Personal Finance. I've heard quite a few people mention the same feeling, that Personal Finance was one of the most useful and important courses they have ever taken. I've run into many more that could have used it and don't realize it. Case in point:
About 2 months ago I was back in Stanly County, a very rural area of NC where I grew up. A friend of my younger brother was talking about buying a Harley Davidson, and how he had been financed for about $12,000 and was looking forward to buying the $10,000 or so bike he was wanting (a Sportster) and could afford $2000 in accessories since they would finance those two. He also mentioned how if he could get his mom to cosign for him, he would get a better interest rate and higher amount to finance and could get a little bit more stuff for his bike. I talked to him a little bit about insurance, how first bikes usually get dropped or laid down, how there are a lot of hidden costs, and how its best not to get roped into more than can be comfortable afforded. I was worried about the kid, because he was about to get himself in a bad financial situation and pay a lot of money for a motorcycle he was going to drop and scratch.
I was back home a couple weeks ago and the guy's girlfriend mentioned that he had gotten a bike. I asked if he had bought the $12k bike and she said that no, he hadn't, that he had found a 4 year old Sportster that had the accessories he wanted for about $6k and he had gotten a loan from the credit union.
I don't know if I had anything to do with him changing his mind, but I realized at that point that Algebra 2 and whatever math class this kid had as a senior have served him absolutely no purpose in life (he is a diesel mechanic). What kids need as a senior is a math class that incorporates goal based scenarios and focuses less on parabolas and more on personal finance. It would be very easy to also incorporate a few basic applied mathematical skills that used to be taught in vocational courses.
This can be done, but it is up to the teacher. Senior math course offerings range from "discreet math" to pre-calculus. A pre-calculus course doesn't have the flexibility to deviate from the textbook curriculum, but nearly all of those students will be attending 4 year universities where the aforementioned applied math skills can be learned in a personal finance course. On the other hand, fewer of the kids taking discreet math will move on to a university and the discreet math course, while having a set curriculum from the state, leaves much of the pacing and curriculum choices up to the instructor.
I'm leaning on my department chair to let me teach a section of discreet math next year. I have a lot of ideas on possible units, including scenarios where students model purchasing a car, constructing a building, and more. Math can be exciting, but only when it's relevant. Goal based scenarios help make that happen.
References: SCHANK, R. C., BERMAN, T. R., & MACPHERSON, K. A. (1999). LEARNING BY DOING. IN C. M. REIGELUTH (ED.), INSTRUCTIONAL DESIGN THEORIES AND MODELS (2ND ED., PP. 161-182). MAHWAH, NJ: ERLBAUM.
Monday, March 3, 2008
Thoughts on Collins
In the article, Collins begins by discussing how schools have transitioned into unattached learning, where concepts are taught as opposed to skills. With the exception of some vocational education courses at high schools and community colleges, Collins is correct. I have a standard course of study I have to teach in my Algebra 1 class. Although kids need to be able to set up equations and multiply binomials to set up optimization problems, we practice this with X's and Y's, whereas before public schooling, young adults learned to optimize materials by apprenticing an experienced craftsman. There were no X's and Y's, but they learned through practice how to build an object and minimize waste. Although seemingly different, the two methods teach the same type of reasoning.
Most people would agree that it is important to implement some type of real-world connection in the public school classroom, whether for science, math, social studies, english or any subject. The cognitive apprenticeship gives teachers a way to not only relate their material to life situations, but to also keep students involved. Particularly for a reading assignment, having students create their own deep questions forces them to improve their comprehension capability and focus on what is being said, verses simply skimming the article and answering basic recall questions.
I have several projects and activities that implement the apprenticeship or something similar in my classroom. For Algebra 1, on Tuesday we are doing an activity where students are given a sheet of paper and their goal is to build a box with the largest possible volume. I'm then going to ask them about the algebra involved and we are going to come up with equations we can use for optimization. We also have an activity in Geometry where we go outside and investigate symmetry in automotive symbols and logos. With this, students work in groups and what often takes places is a higher-level student takes a car logo and explains symmetry to a lower-level student using that logo.
One key difference between the reciprocal teaching method and what I use is that reciprocal teaching requires the teacher to precisely model the activity beforehand. For a high school classroom, I think it's more important to push the students to accurately follow the directions given and synthesize what is being asked. For what I'm doing, the role of coach is more appropriate to the goal of these activities.
References:
Most people would agree that it is important to implement some type of real-world connection in the public school classroom, whether for science, math, social studies, english or any subject. The cognitive apprenticeship gives teachers a way to not only relate their material to life situations, but to also keep students involved. Particularly for a reading assignment, having students create their own deep questions forces them to improve their comprehension capability and focus on what is being said, verses simply skimming the article and answering basic recall questions.
I have several projects and activities that implement the apprenticeship or something similar in my classroom. For Algebra 1, on Tuesday we are doing an activity where students are given a sheet of paper and their goal is to build a box with the largest possible volume. I'm then going to ask them about the algebra involved and we are going to come up with equations we can use for optimization. We also have an activity in Geometry where we go outside and investigate symmetry in automotive symbols and logos. With this, students work in groups and what often takes places is a higher-level student takes a car logo and explains symmetry to a lower-level student using that logo.
One key difference between the reciprocal teaching method and what I use is that reciprocal teaching requires the teacher to precisely model the activity beforehand. For a high school classroom, I think it's more important to push the students to accurately follow the directions given and synthesize what is being asked. For what I'm doing, the role of coach is more appropriate to the goal of these activities.
References:
Collins, A., Brown, J. S., & Newman, S. E. (1990). Cognitive apprenticeship: Teaching the crafts of
Sunday, February 24, 2008
Ryan and Problem Based Learning
Having used Problem Based Learning in my classroom, I found Ryan's article interesting if a bit outdated. Although it requires more time than traditional teaching methods, problem based learning is an excellent way to introduce mathematical concepts, particularly in Geometry, where so much of what we do can be represented physically.
Although Ryan's use of e-Talk and Hypercard is dated, the ideas and goals presented are still valid and achievable using current technology. To illustrate this point, I'll use the "Tower Wars" project I do for Geometry and include a few plans I have to update the project for the 21st century.
The idea behind the project is for students to build the tallest tower (that remains structurally sound) given 50 popsicle sticks and certain restrictions (types of adhesives, other materials, etc). The first time I assigned the project, I simply gave the students the rules, let them put themselves in groups, and gave a due date. The second time around, sensing a need for more structure and the opportunity to teach additional skills, I implemented two more "stages" to the project.
The first stage required each group to submit a blueprint of the tower they were designing, with three different angles of views and notes on the design specifics. The second stage required students to build a digital proposal similar to the blueprint using an online Ajax-based application and submit their proposal to me in PDF format. I found that requiring these two extra pieces served two benefits: 1) it required students to build a 21st century skill set by forcing them to learn and use a software program that they were not familiar with and 2) it forced them to spend more time planning and designing their towers.
My ideas for the future fall in line with what Ryan was suggesting in the article. My main goal is to improve collaboration. Currently this is the greatest roadblock that the students encounter. Because this project falls during our surface area and volume units, there is not a great deal of time for work to be done in class, therefore most work is done independently after school. Most of the students in my Geometry class are sophomores and do not have driving licenses. Face to face collaboration is hard for the groups to achieve and most often, one group member does the majority of the work. My plan is to set up some sort of online collaboration solution where students can synchronously or asynchronously work on the design of the project. Although Ryan's hypercard solution is outdated and limited, there are several solutions that I am looking into integrating into this project.
References: RYAN, C., & KOSCHMANN, T. (1994). THE COLLABORATIVE LEARNING LABORATORY: A TECHNOLOGY-ENRICHED ENVIRONMENT TO SUPPORT PROBLEM-BASED LEARNING. IN RECREATING THE REVOLUTION: PROCEEDINGS OF THE 15TH ANNUAL NATIONAL EDUCATIONAL COMPUTING CONFERENCE (NECC) (PP. 160-167). BOSTON, MA.
Although Ryan's use of e-Talk and Hypercard is dated, the ideas and goals presented are still valid and achievable using current technology. To illustrate this point, I'll use the "Tower Wars" project I do for Geometry and include a few plans I have to update the project for the 21st century.
The idea behind the project is for students to build the tallest tower (that remains structurally sound) given 50 popsicle sticks and certain restrictions (types of adhesives, other materials, etc). The first time I assigned the project, I simply gave the students the rules, let them put themselves in groups, and gave a due date. The second time around, sensing a need for more structure and the opportunity to teach additional skills, I implemented two more "stages" to the project.
The first stage required each group to submit a blueprint of the tower they were designing, with three different angles of views and notes on the design specifics. The second stage required students to build a digital proposal similar to the blueprint using an online Ajax-based application and submit their proposal to me in PDF format. I found that requiring these two extra pieces served two benefits: 1) it required students to build a 21st century skill set by forcing them to learn and use a software program that they were not familiar with and 2) it forced them to spend more time planning and designing their towers.
My ideas for the future fall in line with what Ryan was suggesting in the article. My main goal is to improve collaboration. Currently this is the greatest roadblock that the students encounter. Because this project falls during our surface area and volume units, there is not a great deal of time for work to be done in class, therefore most work is done independently after school. Most of the students in my Geometry class are sophomores and do not have driving licenses. Face to face collaboration is hard for the groups to achieve and most often, one group member does the majority of the work. My plan is to set up some sort of online collaboration solution where students can synchronously or asynchronously work on the design of the project. Although Ryan's hypercard solution is outdated and limited, there are several solutions that I am looking into integrating into this project.
References: RYAN, C., & KOSCHMANN, T. (1994). THE COLLABORATIVE LEARNING LABORATORY: A TECHNOLOGY-ENRICHED ENVIRONMENT TO SUPPORT PROBLEM-BASED LEARNING. IN RECREATING THE REVOLUTION: PROCEEDINGS OF THE 15TH ANNUAL NATIONAL EDUCATIONAL COMPUTING CONFERENCE (NECC) (PP. 160-167). BOSTON, MA.
Monday, February 18, 2008
Haller and Cooperative Learning
This article caught my attention for two reasons. First, it was done at NC State, which doesn't mean a whole lot but it does add a nice touch. Second, Haller describes how the same scenario resulted in two different methods of cooperative learning problem solving.
I found the results somewhat troubling, as I would expect college students to be able to manage better in a group environment. At the same time, I understand how the interactional difficulties can occur. In fact, I believe some type of difficulties can be expected out of groups of any age or sex demographic. Most importantly, I now have a much clearer idea of what to look for when I assign my students activities to work on in groups.
As a teacher, I have seen both the Transfer of Knowledge and Cooperative Sequence scenarios take place. Although Haller is quick to point out that the sample sizes are not large enough to pinpoint any statistical conclusions, the Cooperative Sequence was most popular among female groups. My observations in my classroom have also pointed to this. Within a mixed group or a group of males, the Transfer of Knowledge method usually wins out, with one dominant participant taking the role of "teacher." It is usually in the groups of girls that true group collaboration takes place. However, it is important to note that each method has its strengths.
Haller's tips for minimizing problems with cooperative learning are very useful. Although this article speaks towards engineering education, the guidelines that Haller presents are useful in the high school setting as well.
As educators, we are taught from the beginning that group environments and cooperative learning are very beneficial in ensuring that a maximum number of students become proficient in the course of study. However, creating a successful cooperative learning environment is not easy and it does require planning, effort and responsiveness on the part of the instructor. Failure to do so can result in an unpleasant experience and minimal gains in student achievement. As Haller lists methods for improving collaborative learning, she is also quick to point out how interactional problems can detract from the learning that should be taking place.
References: Haller, C. R., Gallagher, V. J., Weldon, T. L., & Felder, R. M. (2000). Dynamics of peer education in cooperative learning workgroups. Journal of Engineering Education 89(3), 285-293.
I found the results somewhat troubling, as I would expect college students to be able to manage better in a group environment. At the same time, I understand how the interactional difficulties can occur. In fact, I believe some type of difficulties can be expected out of groups of any age or sex demographic. Most importantly, I now have a much clearer idea of what to look for when I assign my students activities to work on in groups.
As a teacher, I have seen both the Transfer of Knowledge and Cooperative Sequence scenarios take place. Although Haller is quick to point out that the sample sizes are not large enough to pinpoint any statistical conclusions, the Cooperative Sequence was most popular among female groups. My observations in my classroom have also pointed to this. Within a mixed group or a group of males, the Transfer of Knowledge method usually wins out, with one dominant participant taking the role of "teacher." It is usually in the groups of girls that true group collaboration takes place. However, it is important to note that each method has its strengths.
Haller's tips for minimizing problems with cooperative learning are very useful. Although this article speaks towards engineering education, the guidelines that Haller presents are useful in the high school setting as well.
As educators, we are taught from the beginning that group environments and cooperative learning are very beneficial in ensuring that a maximum number of students become proficient in the course of study. However, creating a successful cooperative learning environment is not easy and it does require planning, effort and responsiveness on the part of the instructor. Failure to do so can result in an unpleasant experience and minimal gains in student achievement. As Haller lists methods for improving collaborative learning, she is also quick to point out how interactional problems can detract from the learning that should be taking place.
References: Haller, C. R., Gallagher, V. J., Weldon, T. L., & Felder, R. M. (2000). Dynamics of peer education in cooperative learning workgroups. Journal of Engineering Education 89(3), 285-293.
Saturday, February 9, 2008
Comments on Wilson
In his research paper, Wilson describes his experiment with guided design and serial decision making and the outcomes he noticed. To basically sum up his experiment, he presented a large class with a ship-wreck scenario in which they must rate the usefulness of several items recovered from the shipwreck. Each individual creates and list and then small groups are formed, where each group comes up with a list. Then, the "accuracy" of each list is checked against a list created by an expert.
What struck my interest from this article is that this is the same basic method that Green Hope's (the school where I teach) administration uses at faculty meetings for including the faculty in problem solving. Anytime there is an issue they wish to tackle, we break into smaller groups. Each group then presents its solution and we discuss the results as one large group again.
I can echo many of Wilson's observations pertaining to the experiment. Wilson (2004) mentions "Six of the sixty-two teams experienced the “monster” of team learning. One three-
person team failed to reach a solution in the time provided, experiencing complete
collaborative breakdown in their deliberations (p. 8). I have seen this in our faculty meetings. Teachers can be particularly ornery, especially when presented with a task that they do not want to participate in. I have seen groups not come up with any result at all, or only have a couple of answers thrown together for the sake of having something.
However, as Wilson also observed, most often the outcome is positive. Individuals have opinions on topics that are often a little extreme, or based on incorrect assumptions. The group atmosphere is good at pulling in common sense without ignoring innovative ideas. Also, the logistics of sharing information is much more efficient using this method. It is very difficult for good ideas to be heard when dealing with a larger group. Many people are afraid to speak their mind and others are all too willing.
One variable that Wilson takes into account is the existence of an "expert" within groups. He was able to recognize these individuals by their score being higher than that of the group (with regards to accuracy). This also exists in the faculty meetings that we have. Often times we deal with issues that I know nothing about. Many times there is a large number of people in the group who are ignorant to the issue at hand. As Wilson noted, the experts typically understand that they are the expert of the group and help guide the decision-making process in the right direction.
References: Wilson, P. N. (2004). Mutual gains from team learning: A guided design classroom exercise. Cardon Research Papers in Agricultural and Resource Economics (No. 2004-07). Tucson, AZ: University of Arizona.
What struck my interest from this article is that this is the same basic method that Green Hope's (the school where I teach) administration uses at faculty meetings for including the faculty in problem solving. Anytime there is an issue they wish to tackle, we break into smaller groups. Each group then presents its solution and we discuss the results as one large group again.
I can echo many of Wilson's observations pertaining to the experiment. Wilson (2004) mentions "Six of the sixty-two teams experienced the “monster” of team learning. One three-
person team failed to reach a solution in the time provided, experiencing complete
collaborative breakdown in their deliberations (p. 8). I have seen this in our faculty meetings. Teachers can be particularly ornery, especially when presented with a task that they do not want to participate in. I have seen groups not come up with any result at all, or only have a couple of answers thrown together for the sake of having something.
However, as Wilson also observed, most often the outcome is positive. Individuals have opinions on topics that are often a little extreme, or based on incorrect assumptions. The group atmosphere is good at pulling in common sense without ignoring innovative ideas. Also, the logistics of sharing information is much more efficient using this method. It is very difficult for good ideas to be heard when dealing with a larger group. Many people are afraid to speak their mind and others are all too willing.
One variable that Wilson takes into account is the existence of an "expert" within groups. He was able to recognize these individuals by their score being higher than that of the group (with regards to accuracy). This also exists in the faculty meetings that we have. Often times we deal with issues that I know nothing about. Many times there is a large number of people in the group who are ignorant to the issue at hand. As Wilson noted, the experts typically understand that they are the expert of the group and help guide the decision-making process in the right direction.
References: Wilson, P. N. (2004). Mutual gains from team learning: A guided design classroom exercise. Cardon Research Papers in Agricultural and Resource Economics (No. 2004-07). Tucson, AZ: University of Arizona.
Monday, February 4, 2008
Reflection on Kulik
Although the audio-tutorial method has its place among certain subjects, the thought of math classes being taught in this method makes me cringe. Having participated in an online math course during my undergrad at UNC Pembroke, I have reservations about math being taught in almost any distance method that does not allow an instructor to:
a) show how a problem is solved
b) get immediate feedback on how a student is doing
c) view the facial expressions of a student
d) assess not just the final answer but also the processes taking place in a student's work
That being said, the audio-tutorial method offers quite a bit as a supplementary method of instruction, particularly with the current multimedia capabilities that are present. For the subjects I am teaching, I envision a tutorial with visuals, audio and motion that allow students to take individual concepts and review them as deemed necessary.
Where the audio-tutorial method offers a great deal of promise is in the sciences and social studies subjects. In science, it allows students the benefit of being able to progress as they comprehend the material. Multimedia elements are able to help teach concepts and keep the material from being too dry. While there is no substitute for a hands-on lab, interactive applets do provide some level of experimentation with laws and theorems. For social studies, there are already vast resources available that cover our world and its' history in great depth. All that is needed is an organizational layout and the instructor can almost be replaced in many cases. When all that a history teacher does is lecture, he lends himself to replacement pretty easily.
As technology has evolved over the past fifteen years, the audio-tutorial method has become an increasingly rational method for inclusion in public education. While an audio-taped lesson would be very dry, the inclusion of photos, video and non-linear interactivity allows such a lesson to be spiced up to where it is bearable for the student. It still requires more effort and self discipline on the part of the student, but in return offers the learner a chance to break free of the structure enforced by the traditional learning environment.
References: KULIK, J. A., KULIK, C. C., & COHEN, P. A. (1979). RESEARCH ON AUDIO-TUTORIAL INSTRUCTION: A META-ANALYSIS OF COMPARATIVE STUDIES. RESEARCH IN HIGHER EDUCATION, 11(4), 321-341.
a) show how a problem is solved
b) get immediate feedback on how a student is doing
c) view the facial expressions of a student
d) assess not just the final answer but also the processes taking place in a student's work
That being said, the audio-tutorial method offers quite a bit as a supplementary method of instruction, particularly with the current multimedia capabilities that are present. For the subjects I am teaching, I envision a tutorial with visuals, audio and motion that allow students to take individual concepts and review them as deemed necessary.
Where the audio-tutorial method offers a great deal of promise is in the sciences and social studies subjects. In science, it allows students the benefit of being able to progress as they comprehend the material. Multimedia elements are able to help teach concepts and keep the material from being too dry. While there is no substitute for a hands-on lab, interactive applets do provide some level of experimentation with laws and theorems. For social studies, there are already vast resources available that cover our world and its' history in great depth. All that is needed is an organizational layout and the instructor can almost be replaced in many cases. When all that a history teacher does is lecture, he lends himself to replacement pretty easily.
As technology has evolved over the past fifteen years, the audio-tutorial method has become an increasingly rational method for inclusion in public education. While an audio-taped lesson would be very dry, the inclusion of photos, video and non-linear interactivity allows such a lesson to be spiced up to where it is bearable for the student. It still requires more effort and self discipline on the part of the student, but in return offers the learner a chance to break free of the structure enforced by the traditional learning environment.
References: KULIK, J. A., KULIK, C. C., & COHEN, P. A. (1979). RESEARCH ON AUDIO-TUTORIAL INSTRUCTION: A META-ANALYSIS OF COMPARATIVE STUDIES. RESEARCH IN HIGHER EDUCATION, 11(4), 321-341.
Thoughts on Davis
The Keller Plan sparked my interest because it offers a means to implementing differentiated instruction. Educators have always struggled with how to allow students to move at their own pace, typically giving up and teaching to the middle third of the class. The Keller Plan allows students to receive a study guide and learn individually. Also of important, it allows for asynchronous learning, offering the flexibility for distance education.
21st century technology now makes the Keller Plan (or atleast many elements) feasible in classroom environments across multiple ages and disciplines. I have a Blackboard site set up for my Geometry and Algebra 1 classes which hosts a variety of notesheets, interactive educational tools, links and textbook resources. Although very few of students ever log on (ahh the bane of teaching academic non-honors courses), it is available should they ever develop a wild spark of interest.
Davis (p2) points out the disadvantages of the Keller Plan, particularly in its most traditional sense. It is tough to provide the personal attention needed for the Keller Plan to operate when teaching in the traditional classroom setting. Also, distance courses require much more self-discipline on the part of the student (ironic, given this post is a week late).
In the high school setting, one possible workaround for these drawbacks is an ICR (inclusion) classroom, where a special education teacher is assisting a traditional classroom teacher in a core class, often with a high number of special needs students present. I am teaching an ICR Algebra 1 part 2 and an ICR geometry and am planning on implementing many of the Keller characteristics in the class. I've been looking for a way to allow my brighter students to work at their own pace and this shows quite a bit of promise.
References: DAVIS, R. L., & RAGSDALE, K. M. (N.D.). DESIGN OF AN EFFECTIVE, WEB-BASED, GLOBAL LEARNING ENVIRONMENT USING THE KELLER PLAN.
21st century technology now makes the Keller Plan (or atleast many elements) feasible in classroom environments across multiple ages and disciplines. I have a Blackboard site set up for my Geometry and Algebra 1 classes which hosts a variety of notesheets, interactive educational tools, links and textbook resources. Although very few of students ever log on (ahh the bane of teaching academic non-honors courses), it is available should they ever develop a wild spark of interest.
Davis (p2) points out the disadvantages of the Keller Plan, particularly in its most traditional sense. It is tough to provide the personal attention needed for the Keller Plan to operate when teaching in the traditional classroom setting. Also, distance courses require much more self-discipline on the part of the student (ironic, given this post is a week late).
In the high school setting, one possible workaround for these drawbacks is an ICR (inclusion) classroom, where a special education teacher is assisting a traditional classroom teacher in a core class, often with a high number of special needs students present. I am teaching an ICR Algebra 1 part 2 and an ICR geometry and am planning on implementing many of the Keller characteristics in the class. I've been looking for a way to allow my brighter students to work at their own pace and this shows quite a bit of promise.
References: DAVIS, R. L., & RAGSDALE, K. M. (N.D.). DESIGN OF AN EFFECTIVE, WEB-BASED, GLOBAL LEARNING ENVIRONMENT USING THE KELLER PLAN.
Monday, January 21, 2008
Reflection on Novak
Topic: Concept Maps
Having used concept mapping as both the student and the instructor, I understand the benefits and frustrations behind concept mapping. From experience, I have found that concept mapping helps summarize material at the end of a unit by pulling together sections that may originally appear unrelated and highlighting the similarities between theorems, solutions, and processes. There is no doubt that it promotes a deeper understanding of the material.
Novak (2006) pointed out that "One of the powerful uses of concept maps is not only as a learning tool but also as an evaluation tool..." (p. 6). Because successful concept mapping requires students to possess an understanding of the material, it acts as a better evaluation tool than old standbys such as essays, which only require students to regurgitate material into well crafted language.
Common frustrations exist for both sides when using concept mapping. Because students are unfamiliar with how to set up concept maps, I present them with a blank map and places to merely fill in the blanks. Doing this feels as though I am spoon-feeding too much, but if I merely asked them for a map without presenting them with an outline, most of the students would not be able to organize and process the material well enough to show me what they know. From the vantage point of the student, I find organizing my thoughts into a concept map very difficult. The process of organizing my thoughts into a map is time consuming and challenging.
References:
Novak, J. D. & Cañas, A. J. (2006). The theory underlying concept maps and how to construct them. Technical Report IHMC CmapTools 2006-01. Pensacola, FL: Florida Institute for Human and Machine Cognition. Retrieved November 4, 2007, from http://cmap.ihmc.us/Publications/ResearchPapers/TheoryUnderlyingConceptMaps.pdf
Having used concept mapping as both the student and the instructor, I understand the benefits and frustrations behind concept mapping. From experience, I have found that concept mapping helps summarize material at the end of a unit by pulling together sections that may originally appear unrelated and highlighting the similarities between theorems, solutions, and processes. There is no doubt that it promotes a deeper understanding of the material.
Novak (2006) pointed out that "One of the powerful uses of concept maps is not only as a learning tool but also as an evaluation tool..." (p. 6). Because successful concept mapping requires students to possess an understanding of the material, it acts as a better evaluation tool than old standbys such as essays, which only require students to regurgitate material into well crafted language.
Common frustrations exist for both sides when using concept mapping. Because students are unfamiliar with how to set up concept maps, I present them with a blank map and places to merely fill in the blanks. Doing this feels as though I am spoon-feeding too much, but if I merely asked them for a map without presenting them with an outline, most of the students would not be able to organize and process the material well enough to show me what they know. From the vantage point of the student, I find organizing my thoughts into a concept map very difficult. The process of organizing my thoughts into a map is time consuming and challenging.
References:
Novak, J. D. & Cañas, A. J. (2006). The theory underlying concept maps and how to construct them. Technical Report IHMC CmapTools 2006-01. Pensacola, FL: Florida Institute for Human and Machine Cognition. Retrieved November 4, 2007, from http://cmap.ihmc.us/Publications/ResearchPapers/TheoryUnderlyingConceptMaps.pdf
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