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.
Sunday, March 9, 2008
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.
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