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.
Tuesday, March 25, 2008
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
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