Polygon Properties
Teaching Children Mathematics
By Rebecca R. Robichaux and Paulettte R. Rodrigues
http://www.nctm.org/eresources/view_media.asp?article_id=9290
Summary
Can third grade students do geometry? Why, in fact they can do very sophisticated geometry with the right teaching and activities. Students in Mts. Robichaux dove into the properties of geometric shapes in a sorting and classifying activity. According to the van Htele theory of geometric thinking there are three levels of geometric thinking. At the first level, level 0 students think about thing on a visual level, at this point appearance and familiarity with shapes dominates the reasoning about geometric objects. As students progress into the second level, level 1, they develop description; they are about to sort and develop language that allows them to distinguish one property from another. At the third level, level 2, the informal deduction level the students can distinguish properties and even make arguments about why shapes are similar or not similar based on the properties that they do or do not possess.
It is expected that as they enter high school geometry classes that the students have passed through level 0 and level 1 of the van Htelen scale. The students must be comfortable and functioning at level 2. The NCTM standards also require that students are actively using all of the process standards and that each content standard is frequently being revisited and redefined.
In this article the students went through two activities that, through inquiry and exploration, allowed them to define the properties of polygons, distinguish and classify the shapes based on predetermined characteristics and develop questions and riddles based on their understanding of polygons and their properties. In the first activity the students were given shape and sort bags that contained many different polygons, these examples covered every thing imaginable, there were concave and convex polygons, a variety of vertices, edges, angle sizes and varying complexities. The students sorted the shapes as many different ways possible. Each time the students sorted their shapes they identified the qualities that they were looking for and recorded their answers on a response sheet. This process required the students to develop a representation of how each sort was completed. As the students worked through this process they developed more language and terminology which helped them in their discussion. Next, the students worked with geo-boards and attempted to create shapes based on predetermined “riddles.” At this point in their activities the students explored the idea of impossible polygons and determined through trial and error which characteristics could not exist in the same shape. The students then created their own riddle as an assessment, allowing the students to “show off what they know” rather than berating students who still needed additional work with the material. At that point in the activities all of the students could create a riddle; however, some were considerably more sophisticated than others.
Application
This is certainly applicable in the classroom. Activities like these present teachers with a way of teaching material in a way that is real and alive. Polygons are interactive and changing in this activity. They have properties and they can fall into nonexistence when certain properties are combined. They students are working in a hands-on, minds-on activity that allows them the opportunity to make mistakes and discuss their mathematical ideas in a non-threatening and encouraging environment. I hope that I will have the opportunity to use this activity in the classroom one day.
Robichaux, R. & Rodrigues, P. (2010). Polygon Properties. Teaching Children Mathematics. 16(9) 524.
Saturday, May 1, 2010
Tuesday, April 27, 2010
Manipulatives
1. How do you hold every student accountable?
Initially I think it is important to allow every student to play and handle the manipulatives. It is natural to want to play with new things. College students have trouble with this sort of thing. Thus, I strongly feel that it is unreasonable of teachers to put manipulatives in front of students and expect them to overcome the urge to play. Furthermore, I feel that it sends the wrong message to tell students to play. Lifelong learning comes from a desire to explore and understand. Yet, teachers are insistent on stomping these behaviors out of children.
After the students have been allowed a period of exploration and play I feel that the teacher should take some time to model and introduce the materials. This is an important step as it will start to show students they ways that the materials can be applied to the mathematics content. This is the point when the teacher can ask guiding questions and get students vocalizing their thoughts and ideas. Students will build their vocabulary and ability to talk about the manipulatives only through hearing the teacher speak about the manipulatives. I feel that it is unreasonable to expect the students to use communication effectively if the teacher has not first modeled this step.
I don’t know that I know all the ways that teachers can make students accountable and find an observable way to measure the students learning using manipulatives. However, these are some of the ideas I have. Hands-on activities and group work activities lend themselves very well to observation and checklists. Watching students work through a problem when they are required to use communication and teamwork is a perfect opportunity for the teacher to take an observation role. In the older grades it might even be appropriate for the teacher to “interview” each student and ask them to explain their reasoning in a formal manner.
Another technique that a teacher might consider would be to have the students produce some kind of product. The students might journal on their experiences. Older students might consider blogging about their problem solving and thought processes. Students could draw a picture, type their work into a word processing software, capture a screen shot of their work, or even produce a project, poster or brochure.
I also think that a series of steps, guiding questions or a guided handout might be useful for keeping students on-task and engaged with the material. I saw a very interesting program that had students experimenting with pattern blocks. The teacher had created a series of questions that corresponded with a power point. Each question was multiple choice and as the students used the pattern blocks to determine the answer they answered with automatic clickers. The clicker software immediately polled the class and showed the data as a bar graph. Then the teacher asked the students with the correct answer to explain how they reached their conclusion. I felt that this was one great example of how to make mathematics education everything it can be. The students were using the manipulatives in a systematic and directed fashion; they were using technology in a meaningful way. Students were accountable for their work and they were talking about their problem solving and reasoning.
2. I have already addressed “hands-on” and “hands-on, minds-on” in the previous question. When the students are playing and becoming oriented with the materials they are “hands-on.” However, at that stage there knowledge is undirected. It takes purpose and guidance for students to progress to the level when they are “hands-on, minds-on.” Again, it is the difference between good teaching and poor teaching. Manipulatives are not enough and without strong instruction they are all useless as worksheets. I would even go as far to say that a teacher’s classroom management makes a big difference with their ability to successfully employ manipulatives in the classroom. I can easily see a lesson going wrong simply because the teacher doesn’t have assertive discipline and clearly defined boundaries in the classroom. Finally, when working with manipulatives a teacher is going need to be especially sensitive to the special needs in the classroom as well as the gifted students.
3. Process Standards
Problem Solving- I feel that it is fairly evident how students are using problem solving as they work with math manipulatives. Manipulatives allows students to easily and quickly engage in guess and check. It is especially important in this day and age that students get feedback as they work. Students who play video games and use technology frequently are accustomed to offering input every ten to fifteen seconds and accustomed to some level of feedback every twenty to thirty seconds. Manipulatives offer this level of engagement and can easily supplement activities that would otherwise leave students unengaged and disinterested.
Reasoning & Proof- Reasoning and proof doesn’t just happen as students work with manipulatives. Rather, they emerge in the way that the teachers couple the manipulatives with other work. When students must defend their work and document their proof this process standard becomes a natural part of the activity.
Communication- Communication is another process standard that flows naturally with the activity. However, the danger is that the students don’t use the correct terms and vocabulary. Thus, it runs the risk that the students are able to work through the activity but cannot explain what they did, how they did it or why they did it. It takes the teachers active modeling for students to learn the correct habits. Teachers should not assume that students will learn this on their own. As a result, communication becomes one of the valuable indicators of whether or not the instruction is effective or not.
Connections- Students have a remarkable ability to make connections between mathematics and other experiences in their lives. However, I feel that the teacher must be the facilitator in helping the students to realize the connections within mathematics.
Representation- Representation and math manipulatives go hand in hand. However, I feel that students abilities to utilize representation is sometimes far more capable than my own. Student’s creativity and cleverness is a constant surprise to me. The ways that they think about mathematics and problem solving should be nurtured and encouraged through the careful and deliberate use of math manipulatives.
Initially I think it is important to allow every student to play and handle the manipulatives. It is natural to want to play with new things. College students have trouble with this sort of thing. Thus, I strongly feel that it is unreasonable of teachers to put manipulatives in front of students and expect them to overcome the urge to play. Furthermore, I feel that it sends the wrong message to tell students to play. Lifelong learning comes from a desire to explore and understand. Yet, teachers are insistent on stomping these behaviors out of children.
After the students have been allowed a period of exploration and play I feel that the teacher should take some time to model and introduce the materials. This is an important step as it will start to show students they ways that the materials can be applied to the mathematics content. This is the point when the teacher can ask guiding questions and get students vocalizing their thoughts and ideas. Students will build their vocabulary and ability to talk about the manipulatives only through hearing the teacher speak about the manipulatives. I feel that it is unreasonable to expect the students to use communication effectively if the teacher has not first modeled this step.
I don’t know that I know all the ways that teachers can make students accountable and find an observable way to measure the students learning using manipulatives. However, these are some of the ideas I have. Hands-on activities and group work activities lend themselves very well to observation and checklists. Watching students work through a problem when they are required to use communication and teamwork is a perfect opportunity for the teacher to take an observation role. In the older grades it might even be appropriate for the teacher to “interview” each student and ask them to explain their reasoning in a formal manner.
Another technique that a teacher might consider would be to have the students produce some kind of product. The students might journal on their experiences. Older students might consider blogging about their problem solving and thought processes. Students could draw a picture, type their work into a word processing software, capture a screen shot of their work, or even produce a project, poster or brochure.
I also think that a series of steps, guiding questions or a guided handout might be useful for keeping students on-task and engaged with the material. I saw a very interesting program that had students experimenting with pattern blocks. The teacher had created a series of questions that corresponded with a power point. Each question was multiple choice and as the students used the pattern blocks to determine the answer they answered with automatic clickers. The clicker software immediately polled the class and showed the data as a bar graph. Then the teacher asked the students with the correct answer to explain how they reached their conclusion. I felt that this was one great example of how to make mathematics education everything it can be. The students were using the manipulatives in a systematic and directed fashion; they were using technology in a meaningful way. Students were accountable for their work and they were talking about their problem solving and reasoning.
2. I have already addressed “hands-on” and “hands-on, minds-on” in the previous question. When the students are playing and becoming oriented with the materials they are “hands-on.” However, at that stage there knowledge is undirected. It takes purpose and guidance for students to progress to the level when they are “hands-on, minds-on.” Again, it is the difference between good teaching and poor teaching. Manipulatives are not enough and without strong instruction they are all useless as worksheets. I would even go as far to say that a teacher’s classroom management makes a big difference with their ability to successfully employ manipulatives in the classroom. I can easily see a lesson going wrong simply because the teacher doesn’t have assertive discipline and clearly defined boundaries in the classroom. Finally, when working with manipulatives a teacher is going need to be especially sensitive to the special needs in the classroom as well as the gifted students.
3. Process Standards
Problem Solving- I feel that it is fairly evident how students are using problem solving as they work with math manipulatives. Manipulatives allows students to easily and quickly engage in guess and check. It is especially important in this day and age that students get feedback as they work. Students who play video games and use technology frequently are accustomed to offering input every ten to fifteen seconds and accustomed to some level of feedback every twenty to thirty seconds. Manipulatives offer this level of engagement and can easily supplement activities that would otherwise leave students unengaged and disinterested.
Reasoning & Proof- Reasoning and proof doesn’t just happen as students work with manipulatives. Rather, they emerge in the way that the teachers couple the manipulatives with other work. When students must defend their work and document their proof this process standard becomes a natural part of the activity.
Communication- Communication is another process standard that flows naturally with the activity. However, the danger is that the students don’t use the correct terms and vocabulary. Thus, it runs the risk that the students are able to work through the activity but cannot explain what they did, how they did it or why they did it. It takes the teachers active modeling for students to learn the correct habits. Teachers should not assume that students will learn this on their own. As a result, communication becomes one of the valuable indicators of whether or not the instruction is effective or not.
Connections- Students have a remarkable ability to make connections between mathematics and other experiences in their lives. However, I feel that the teacher must be the facilitator in helping the students to realize the connections within mathematics.
Representation- Representation and math manipulatives go hand in hand. However, I feel that students abilities to utilize representation is sometimes far more capable than my own. Student’s creativity and cleverness is a constant surprise to me. The ways that they think about mathematics and problem solving should be nurtured and encouraged through the careful and deliberate use of math manipulatives.
Tuesday, April 20, 2010
Technology
In an ever changing technological world there is a lot to be said about the technological tools that can be used in mathematics. The past generation was stuck in a very dangerous place, the students knew far more about the technology than the adults who were teaching them. This created a very strong technological push in education. Now, master teachers, like my Novice teacher, are much more comfortable with technology. However, the newest generation of teachers, entering the field, has the biggest advantage.
One of the most important aspects of working with technology is the comfort level. Personally, I am very comfortable with technology. I enjoy playing with programs and learning what they can do and how they can be used in the classroom. I can directly compare this will my parents generation, they are almost afraid of technology; afraid to break it, afraid to make mistakes, afraid to play. But because I was virtually raised with all the technology that I use now, I have a very different view of the tools.
Two of the most valuable technological tools that I have learned about in class are the smart board and the geometers sketchpad. Both are tools that are going to be very commonplace, especially in the upcoming years. I was very impressed with the wide ranging applications that both tools are equipped to handle. Its amazing how much the programs have improved in the last few years. Furthermore, it is exciting to think that these programs will continue to be improved and how much more they will be able to do in the future. The most important thing that I have taken away from exposure to these programs is that as a teacher I have to take the initiative to make myself comfortable with the programs. These technologies are not a gimmick. In the same way that math manipulatives cannot save mathematics, neither can technology. There is still the pressing need for good teachers and strong instruction. However, technology can be used in congruence with the existing curriculum to augment and supplement learning.
There have also been some wonderful programs that I have been exposed to outside of class. Just recently I attended a webinar on mathematics visualization using internet software. There are a number of programs such as moodles and thatquiz that can be used in the teaching and assessing mathematical concepts. I also feel that some of the illumination applets are extremely useful. However, as with all things these programs must be coupled with instruction, guidance and hands-on exploration.
There are times when the natural constraints of technology are a benefit. There are also times when the nature of technology programs and software limit students understanding and ability to explore the material. Therefore, it is the teacher’s know how that makes or breaks a classroom.
One of the most important aspects of working with technology is the comfort level. Personally, I am very comfortable with technology. I enjoy playing with programs and learning what they can do and how they can be used in the classroom. I can directly compare this will my parents generation, they are almost afraid of technology; afraid to break it, afraid to make mistakes, afraid to play. But because I was virtually raised with all the technology that I use now, I have a very different view of the tools.
Two of the most valuable technological tools that I have learned about in class are the smart board and the geometers sketchpad. Both are tools that are going to be very commonplace, especially in the upcoming years. I was very impressed with the wide ranging applications that both tools are equipped to handle. Its amazing how much the programs have improved in the last few years. Furthermore, it is exciting to think that these programs will continue to be improved and how much more they will be able to do in the future. The most important thing that I have taken away from exposure to these programs is that as a teacher I have to take the initiative to make myself comfortable with the programs. These technologies are not a gimmick. In the same way that math manipulatives cannot save mathematics, neither can technology. There is still the pressing need for good teachers and strong instruction. However, technology can be used in congruence with the existing curriculum to augment and supplement learning.
There have also been some wonderful programs that I have been exposed to outside of class. Just recently I attended a webinar on mathematics visualization using internet software. There are a number of programs such as moodles and thatquiz that can be used in the teaching and assessing mathematical concepts. I also feel that some of the illumination applets are extremely useful. However, as with all things these programs must be coupled with instruction, guidance and hands-on exploration.
There are times when the natural constraints of technology are a benefit. There are also times when the nature of technology programs and software limit students understanding and ability to explore the material. Therefore, it is the teacher’s know how that makes or breaks a classroom.
Saturday, April 17, 2010
Errors
Working with student errors has been one of the more interesting, frustrating and enlightening components of the Math Methods classroom. Its it amazing to see how logical student mistakes are.
Literally two days after we finished the Errors in class I experienced a real life example that cemented my understanding of how important it is to understand student errors. When you understand the error it becomes infinitely easier to correct the problem. I was grading papers before class with a student, this student is very bright and often comes in early to socialize with people who are at his level, teachers, and he was looking at the paper I was grading and commented that it appeared that the student seemed to think that the fraction with the largest denominator was the largest fraction. I studied the paper for a moment. He was right. I called that student up for a few minutes at the beginning of the class and allowed her to make correction on her paper. The second time around she only made a few computational errors. I pulled the young man aside and complimented him that he realized something that they teach in college courses, something that I still struggle with, he was very proud of himself, deservingly so.
This experience made me appreciate how much frustration, both for the teacher and the student, can be avoided when the teacher is knowledgeable about the types of mistakes that students make. Students generally make mistakes that are very logical, they confuse a rule or even make up their own, but generally their misunderstandings can be correctly if they are understood. One of the greatest dangers is when teachers include “short cuts.” Instead of simplifying the problem teachers add a new layer of rules and procedures. It actually becomes more confusing to the student. Sadly, teachers think that shortcuts are useful because they assign worksheets that ask the students to perform the same computations over and over again, creating a need for a quick solution. If teachers assigned work that focused on quality over content this wouldn’t be such an issue.
All in all I feel that I’ve learned a lot from seeing the wrong way to approach mathematics.
Literally two days after we finished the Errors in class I experienced a real life example that cemented my understanding of how important it is to understand student errors. When you understand the error it becomes infinitely easier to correct the problem. I was grading papers before class with a student, this student is very bright and often comes in early to socialize with people who are at his level, teachers, and he was looking at the paper I was grading and commented that it appeared that the student seemed to think that the fraction with the largest denominator was the largest fraction. I studied the paper for a moment. He was right. I called that student up for a few minutes at the beginning of the class and allowed her to make correction on her paper. The second time around she only made a few computational errors. I pulled the young man aside and complimented him that he realized something that they teach in college courses, something that I still struggle with, he was very proud of himself, deservingly so.
This experience made me appreciate how much frustration, both for the teacher and the student, can be avoided when the teacher is knowledgeable about the types of mistakes that students make. Students generally make mistakes that are very logical, they confuse a rule or even make up their own, but generally their misunderstandings can be correctly if they are understood. One of the greatest dangers is when teachers include “short cuts.” Instead of simplifying the problem teachers add a new layer of rules and procedures. It actually becomes more confusing to the student. Sadly, teachers think that shortcuts are useful because they assign worksheets that ask the students to perform the same computations over and over again, creating a need for a quick solution. If teachers assigned work that focused on quality over content this wouldn’t be such an issue.
All in all I feel that I’ve learned a lot from seeing the wrong way to approach mathematics.
Tuesday, April 6, 2010
A smorgasbord of assessment options
Summary- April
This article fits perfectly with the assessment assignment that the class recently finished. The author of this article, Kathy Bacon, reminds teachers that there are a plethora of assessment options and that student and teacher must remember that choosing the correct type of assessment is as critical as the information being taught. Bacon takes a moment to remind her audience what a student centered classroom should look like: it should be a place where the instruction is guided from the data gathered during assessment. This simply means that instruction and assessment must match the students thinking and way of communicating.
What is the best way to understand how to pair assignment and assessment; through the strategic use of excellent classroom examples. The students in Bacon’s classroom use every type of assessment. There is an example of a performance based assessment where a student created a three-dimensional duck and demonstrated her ability to identify shapes. Another student started to explore the properties of different solid shapes in a rudimentary proof. Students in the class keep learning logs and take pen and pencil exams as well. The author even provides an example of a test she gave to her students which contains true/false, short answer, multiple choice and essay questions. The key to success is that the teacher frequently uses formative and summative assessments. Both the teacher and the students are aware of the purpose of the assessments and are cognizant of the way that the data generated will be used.
Application
It is clear from the article that Kathy Bacon is an exemplary mathematics teacher. Her fifth grade students are producing very complex, sophisticated and thoughtful work. Their understanding of reasoning and proof is quite remarkable. I am currently novicing in a fourth grade classroom and based on my understanding of the students ability levels I feel certain that this work would be far too difficult for them in fifth grade. However, it seems evident that Kathy Bacon has been able to bring her students to a high achievement level. I am certain that this is due in part to her ability to assess and mold her lessons to the students needs. She stresses the fact that she often chooses assessment on the most effective way to get the information she needs with the smallest investment of time. She is fortunate that her school has a block schedule and that she has a ninety-minute block of time in which her students can be engaged in inquiry based activities.
I feel that as a teacher the most important thing is to take the time to do things well. Initially, Bacon probably spent a great deal of time designing her units and matching the assessment to the content being taught. But with repetition the process gets easier and less time consuming. It is an investment initially; however, the results in the long run are undeniable. Her students are high achieving and their knowledge is more than skin deep, they have an enduring understanding of the material due to the nature in which is has been taught.
Teaching Children Mathematics
Kathy A. Bacon
http://www.nctm.org/eresources/view_media.asp?article_id=9232
Bacon, K. (2010). A smorgasbord of assessment options. Teaching Children Mathematics. 16(8) 458.
This article fits perfectly with the assessment assignment that the class recently finished. The author of this article, Kathy Bacon, reminds teachers that there are a plethora of assessment options and that student and teacher must remember that choosing the correct type of assessment is as critical as the information being taught. Bacon takes a moment to remind her audience what a student centered classroom should look like: it should be a place where the instruction is guided from the data gathered during assessment. This simply means that instruction and assessment must match the students thinking and way of communicating.
What is the best way to understand how to pair assignment and assessment; through the strategic use of excellent classroom examples. The students in Bacon’s classroom use every type of assessment. There is an example of a performance based assessment where a student created a three-dimensional duck and demonstrated her ability to identify shapes. Another student started to explore the properties of different solid shapes in a rudimentary proof. Students in the class keep learning logs and take pen and pencil exams as well. The author even provides an example of a test she gave to her students which contains true/false, short answer, multiple choice and essay questions. The key to success is that the teacher frequently uses formative and summative assessments. Both the teacher and the students are aware of the purpose of the assessments and are cognizant of the way that the data generated will be used.
Application
It is clear from the article that Kathy Bacon is an exemplary mathematics teacher. Her fifth grade students are producing very complex, sophisticated and thoughtful work. Their understanding of reasoning and proof is quite remarkable. I am currently novicing in a fourth grade classroom and based on my understanding of the students ability levels I feel certain that this work would be far too difficult for them in fifth grade. However, it seems evident that Kathy Bacon has been able to bring her students to a high achievement level. I am certain that this is due in part to her ability to assess and mold her lessons to the students needs. She stresses the fact that she often chooses assessment on the most effective way to get the information she needs with the smallest investment of time. She is fortunate that her school has a block schedule and that she has a ninety-minute block of time in which her students can be engaged in inquiry based activities.
I feel that as a teacher the most important thing is to take the time to do things well. Initially, Bacon probably spent a great deal of time designing her units and matching the assessment to the content being taught. But with repetition the process gets easier and less time consuming. It is an investment initially; however, the results in the long run are undeniable. Her students are high achieving and their knowledge is more than skin deep, they have an enduring understanding of the material due to the nature in which is has been taught.
Teaching Children Mathematics
Kathy A. Bacon
http://www.nctm.org/eresources/view_media.asp?article_id=9232
Bacon, K. (2010). A smorgasbord of assessment options. Teaching Children Mathematics. 16(8) 458.
Tech-Knowledgy and Diverse Learners
Summary
This article goes hand in hand with the topics that have been covered recently in class as well as what was talked about at the last BSEA meeting. Technology is the topic and its application in the classroom continues to baffle many and excite others. The response to technology ranges from extreme dislike to extreme enthusiasm. Jennifer Suh, the author of Tech Knowledgy & Diverse Learners, stresses the most important components of technology, the knowledge and skills that the teacher must possess when working with technology, the limitations of technology and the instances when she feels that technology is actually more appropriate than math manipulatives. Her article focuses on the application that technology has when working with diverse learners; however, I would argue that the same is true for all students.
Jennifer Suh begins the article by discussing the specific problems that ELL and special needs students struggle with. The practice is that when these students struggle that teachers use math manipulatives to make the abstract concepts more concrete; however, this can introduce a new problem. This can result in information overload. Suh proposes that the “built-in constraints” actually work to the students benefit. One of the points that I most agree with is that the computer software generally offers immediate feedback; thus, maximizing on the time spent engaged with the material. These programs are also generally very good at forcing the students to use the mathematical vocabulary, which may not be something they naturally do when working with the math manipulatives.
The article contains three specific examples of computer programs that fit all of the qualifications that Suh identifies as essential components of exceptional technology based tools. I was most impressed by the interactive line graph on the Healthy Forest site. The application shows not only the diagram and the simulation but also incorporates tiered lessons and math vocabulary. I feel that the more abstract examples are still relevant. However, they are not as interactive and user friendly.
The article finished with Suh final thoughts on the subject. Truly the technology is only as effectives as the teachers ability to recognize effective programs and software. The teacher must also be able to marry the technology with appropriate forms of assessment. Finally, the work must be combined with other forms of experimentation and opportunities for the students to use the information in other contexts.
Application
I feel that this article offers three specific and excellent uses of technology; however, I have a growing concern regarding teachers ability to assess this type of work. While discovery and exploration are necessary components of the learning process I don’t see an effective way to assess students as they work with and learn from these technology programs. Unless the teacher decides to award participation points or checklists, which I do not feel are an adequate assessment of this math content, it is virtually impossible to generate a grade or truly measure the student’s understanding. This just reaffirms the fact that technology, like manipulatives, cannot be the only method of instruction used in the classroom.
Mathematics Teaching in the Middle School
Jennifer M. Suh
http://my.nctm.org/eresources/view_media.asp?article_id=9197
Suh, J. (2010). Tech-knowledgy and diverse learners. Mathematics Teaching in the Middle School. 15(8) 440.
This article goes hand in hand with the topics that have been covered recently in class as well as what was talked about at the last BSEA meeting. Technology is the topic and its application in the classroom continues to baffle many and excite others. The response to technology ranges from extreme dislike to extreme enthusiasm. Jennifer Suh, the author of Tech Knowledgy & Diverse Learners, stresses the most important components of technology, the knowledge and skills that the teacher must possess when working with technology, the limitations of technology and the instances when she feels that technology is actually more appropriate than math manipulatives. Her article focuses on the application that technology has when working with diverse learners; however, I would argue that the same is true for all students.
Jennifer Suh begins the article by discussing the specific problems that ELL and special needs students struggle with. The practice is that when these students struggle that teachers use math manipulatives to make the abstract concepts more concrete; however, this can introduce a new problem. This can result in information overload. Suh proposes that the “built-in constraints” actually work to the students benefit. One of the points that I most agree with is that the computer software generally offers immediate feedback; thus, maximizing on the time spent engaged with the material. These programs are also generally very good at forcing the students to use the mathematical vocabulary, which may not be something they naturally do when working with the math manipulatives.
The article contains three specific examples of computer programs that fit all of the qualifications that Suh identifies as essential components of exceptional technology based tools. I was most impressed by the interactive line graph on the Healthy Forest site. The application shows not only the diagram and the simulation but also incorporates tiered lessons and math vocabulary. I feel that the more abstract examples are still relevant. However, they are not as interactive and user friendly.
The article finished with Suh final thoughts on the subject. Truly the technology is only as effectives as the teachers ability to recognize effective programs and software. The teacher must also be able to marry the technology with appropriate forms of assessment. Finally, the work must be combined with other forms of experimentation and opportunities for the students to use the information in other contexts.
Application
I feel that this article offers three specific and excellent uses of technology; however, I have a growing concern regarding teachers ability to assess this type of work. While discovery and exploration are necessary components of the learning process I don’t see an effective way to assess students as they work with and learn from these technology programs. Unless the teacher decides to award participation points or checklists, which I do not feel are an adequate assessment of this math content, it is virtually impossible to generate a grade or truly measure the student’s understanding. This just reaffirms the fact that technology, like manipulatives, cannot be the only method of instruction used in the classroom.
Mathematics Teaching in the Middle School
Jennifer M. Suh
http://my.nctm.org/eresources/view_media.asp?article_id=9197
Suh, J. (2010). Tech-knowledgy and diverse learners. Mathematics Teaching in the Middle School. 15(8) 440.
Wednesday, March 24, 2010
Walking Around: Getting More from Informal Assessment
Cole, K.A. (1999). Walking around: getting more from informal assessment. Mathematics Teaching in the Middle School 4(4), 224-227.
In this article, Walking Around: Getting More From Informal Assessment, the author, Karen A. Cole, addresses walking around the classroom and using frequent informal observation as a component of her teaching approach. Her research was funded by the National Science Foundations in corporation with the Middle School Math through Applications Project. This program was targeted toward middle school mathematics classes and was a comprehensive curriculum that was project-based and student centered. The teacher described the two most important aspects of the process; observation and conference. Observation is fairly straightforward; the teacher must listen to the student’s conversation and stay attuned to potential misconceptions, clarifications and opportunities to ask more in depth and higher order thinking questions.
A possible weakness or problem with this strategy is that it can be very difficult to observe all students equally. Thus, the teacher must be very deliberate when it comes to this type of assessment. The teacher must allow every student the opportunity to talk, provide the students with regular excellent examples of proper discussion and explanation. Furthermore, the teacher can use one-on-one conferences as a time to catch up with students and offer them individualized instruction and attention. I feel that this article might have benefited from some specific suggestions that the author of Informal Assessment: A Story from the Classroom, used. I feel that this technique is more effective if the teacher selects specific students to observe and specific traits to observe.
In this article, Walking Around: Getting More From Informal Assessment, the author, Karen A. Cole, addresses walking around the classroom and using frequent informal observation as a component of her teaching approach. Her research was funded by the National Science Foundations in corporation with the Middle School Math through Applications Project. This program was targeted toward middle school mathematics classes and was a comprehensive curriculum that was project-based and student centered. The teacher described the two most important aspects of the process; observation and conference. Observation is fairly straightforward; the teacher must listen to the student’s conversation and stay attuned to potential misconceptions, clarifications and opportunities to ask more in depth and higher order thinking questions.
A possible weakness or problem with this strategy is that it can be very difficult to observe all students equally. Thus, the teacher must be very deliberate when it comes to this type of assessment. The teacher must allow every student the opportunity to talk, provide the students with regular excellent examples of proper discussion and explanation. Furthermore, the teacher can use one-on-one conferences as a time to catch up with students and offer them individualized instruction and attention. I feel that this article might have benefited from some specific suggestions that the author of Informal Assessment: A Story from the Classroom, used. I feel that this technique is more effective if the teacher selects specific students to observe and specific traits to observe.
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