The article entitled "Polygon Properties: What is Possible?" found in the Teaching Children Mathematics May, 2010 issue, is written by Paulette R. Rodrigue and Rebecca R. Robichaux. The article discusses the relatively simple idea of sorting shapes and solving riddles in the classroom with young children. The authors promotes that these specific activities can be used to help promote the advancement of geometric thinking in younger children. The authors also do an excellent job of connecting these activities and the overall process to nctm standards such as mathematical communication and cooperative learning.
I found this article particularly interesting because it related directly to an issue discussed in our reflections and evaluations of the curriculum plan presentations. On the evaluation sheets we were asked which content areas we see getting the least attention, and I specifically mentioned Geometry. I said then, and will say now, that I believe this is due in large part to the fact that many educators see the concepts in Geometry as something that cannot be taught any earlier than the middle school level. That is simply not the case, they just need to be taught in a different way. By providing activities such as those listed in this journal article (solving riddles and sorting simple shapes and patterns) we can provide young students with the basis for Geometry, while peaking their interest in a content area that would otherwise not be addressed.
Sunday, May 2, 2010
Wednesday, April 28, 2010
Manipulative Blog
Upon completion of our in class blog work, I was immediately struck with a few lasting thoughts and ideas. First off, I understood completely why we were asked to complete this rather basic investigation so late in the semester. Because, manipulatives and their use are such an important part of creating a successful math learning environment. They can help make math both fun and easier to understand for students, therefore, it is very important that we as future educators understand how to truly utilize them in a classroom. This is why we have waited until the end of the semester, as we are now much more knowledgeable on the content and process standards, etc.
To discuss the actual manipulatives, as I mentioned in class, the two that I were most struck with, were the unifix cubes and the pattern blocks. As Dr. Grant has mentioned before and mentioned multiple times on Tuesday, pattern blocks are essentially the universal manipulative. Meaning, they can be used to teach multiple concepts and grade levels. They are a very basic and effective teaching tool, and I would be sure that I had them in my classroom.
The other manipulative that I was particularly impressed with was the unifix cubes. I can relate back and remember using them in middle school classrooms in my own early education, and they seemed to make a difference. They allow students to explore a wide array of concepts (not quite as wide as the pattern blocks), such as percentages, surface area, ratios, etc. They are simple and soft (meaning students cannot get hurt/hurt other using them) and students can have fun using them.
To discuss the actual manipulatives, as I mentioned in class, the two that I were most struck with, were the unifix cubes and the pattern blocks. As Dr. Grant has mentioned before and mentioned multiple times on Tuesday, pattern blocks are essentially the universal manipulative. Meaning, they can be used to teach multiple concepts and grade levels. They are a very basic and effective teaching tool, and I would be sure that I had them in my classroom.
The other manipulative that I was particularly impressed with was the unifix cubes. I can relate back and remember using them in middle school classrooms in my own early education, and they seemed to make a difference. They allow students to explore a wide array of concepts (not quite as wide as the pattern blocks), such as percentages, surface area, ratios, etc. They are simple and soft (meaning students cannot get hurt/hurt other using them) and students can have fun using them.
Tuesday, April 27, 2010
Technology Blog
As we all are well aware, technology was a very integral and continuous aspect of this course and the work involved. From day one, we were asked to complete simply technology tasks such as signing in on the smart board (the only time I have ever done that in a class), and setting up and maintaining an online blog (much like a personal journal of reflections from the semester). Throughout this blog I will address a few pieces of technology that really stood out to me within this course.
To begin, the smart board. While I had seen smart boards, and even written on them once or twice, before coming to class, I had absolutely no idea of their actual capabilities. We used them to do everything from take and discuss notes as a class, to creating our own interactive manipulatives for student use. We were required to sign in on the smart board each and every day, using new ways to do so, forcing us to explore some of the most basic functions and options the smart board provides. I am very grateful for the opportunity to work with this piece of technology, because, from what I understand, they are being integrated into almost all classrooms throughout the state and country. Meaning, once I am in my own classroom, I will surely need to work with one. So, the basic knowledge that I gained will give me a leg up on learning the more advanced functions later on in my professional life.
Another important piece of technology we used on many occasions was the google docs program. While this was not the only class that I used the program in, this was the first semester in which I used it. This was also the course in which I used the program the most. While it is basic in format, and can be grasped and even mastered in a days time, it is an important piece of technology to understand, as it will be used many times throughout the duration of my education and career. Therefore, I am grateful for the extended opportunities to work with the program.
These are only two pieces of technology used in this course, and if I were to truly discuss all, this blog may never end. This course really was completely centered around technology, and I found that to be nothing but beneficial. We live in an ever expanding technological world, and it is only right that our classes and educational environment does everything possible to keep up. I feel that this class accomplished that and more.
To begin, the smart board. While I had seen smart boards, and even written on them once or twice, before coming to class, I had absolutely no idea of their actual capabilities. We used them to do everything from take and discuss notes as a class, to creating our own interactive manipulatives for student use. We were required to sign in on the smart board each and every day, using new ways to do so, forcing us to explore some of the most basic functions and options the smart board provides. I am very grateful for the opportunity to work with this piece of technology, because, from what I understand, they are being integrated into almost all classrooms throughout the state and country. Meaning, once I am in my own classroom, I will surely need to work with one. So, the basic knowledge that I gained will give me a leg up on learning the more advanced functions later on in my professional life.
Another important piece of technology we used on many occasions was the google docs program. While this was not the only class that I used the program in, this was the first semester in which I used it. This was also the course in which I used the program the most. While it is basic in format, and can be grasped and even mastered in a days time, it is an important piece of technology to understand, as it will be used many times throughout the duration of my education and career. Therefore, I am grateful for the extended opportunities to work with the program.
These are only two pieces of technology used in this course, and if I were to truly discuss all, this blog may never end. This course really was completely centered around technology, and I found that to be nothing but beneficial. We live in an ever expanding technological world, and it is only right that our classes and educational environment does everything possible to keep up. I feel that this class accomplished that and more.
Errors Blog
Going through and revising and reviewing the math errors blog was, in my opinion, the most beneficial activity of the semester. It gave us one of our only opportunities to witness and work with actual student work. By observing the errors that many students committed in the classroom, we were able to see not only where the students went wrong (while observing patterns that could be observed in the classroom), we also learned multiple ways in which to curb these math behaviors and help the students correct their individual errors.
Another large part of the errors process was learning new ways in which to teach students the mathematical concepts that they obviously struggled with. I found this portion to be just as beneficial, as these are strategies and technology resources that I otherwise would not have been aware of. Many students learn in many different ways, and therefore it is important to be able to teach the same concept in various ways to make up for this.
Another large part of the errors process was learning new ways in which to teach students the mathematical concepts that they obviously struggled with. I found this portion to be just as beneficial, as these are strategies and technology resources that I otherwise would not have been aware of. Many students learn in many different ways, and therefore it is important to be able to teach the same concept in various ways to make up for this.
Monday, April 12, 2010
April MTMS Article - Map Scale, Proportion, and Google Earth
The article, "Map Scale, Proportion, and Google Earth", written by Martin C. Roberge and Linda L. Cooper, is rather self explanatory via the title, but still very interesting. It focuses on the idea of using the revolutionary Google Earth software to teach students about the concepts of creating map scales and proportions.
I found this to be a very interesting concept. As we all know, we live in a rather technology driven society, and this is something that we should incorporate into our every day lessons and instruction. It is simple knowledge that if we can play to our students interests (technology being a major interest of many of todays students) then we will be more successful in providing beneficial instruction to said students. Google earth is a very interesting and user friendly software, and by incorporating it into this mathematical instruction, it has been ensured that these students will be given a better opportunity to connect to this particular lesson.
I found this to be a very interesting concept. As we all know, we live in a rather technology driven society, and this is something that we should incorporate into our every day lessons and instruction. It is simple knowledge that if we can play to our students interests (technology being a major interest of many of todays students) then we will be more successful in providing beneficial instruction to said students. Google earth is a very interesting and user friendly software, and by incorporating it into this mathematical instruction, it has been ensured that these students will be given a better opportunity to connect to this particular lesson.
TCM April Article - Supporting Language Learners
The "Supporting Language Learners" article, written by Jo Ann Candy, Thomas E. Hodges, and Clara Lee Brown, discusses the various benefits of incorporating various instructional practices and techniques into mathematical lessons to help support English language learners. The article goes on to discuss the additions to the educational programs that the incorporation of these programs provides, and its ability to ensure the providing of an excellent and equitable program for all.
I personally feel that this is a very important topic, and this is the reason that I chose to focus on it. Many people underestimate the struggles that English language learners face every day in the educational environment. Not only are these students facing set back in a social setting but an academic one as well. On top of making extra efforts to learn the English language, the students must also incorporate the differences in subject instruction from their native language. Mathematics is one subject that is very diverse and taught in many different ways in different countries. This difference in instruction makes it difficult for students to grasp seemingly basic concepts when learning a new language and a new system of instruction.
I personally feel that this is a very important topic, and this is the reason that I chose to focus on it. Many people underestimate the struggles that English language learners face every day in the educational environment. Not only are these students facing set back in a social setting but an academic one as well. On top of making extra efforts to learn the English language, the students must also incorporate the differences in subject instruction from their native language. Mathematics is one subject that is very diverse and taught in many different ways in different countries. This difference in instruction makes it difficult for students to grasp seemingly basic concepts when learning a new language and a new system of instruction.
Wednesday, March 24, 2010
Assessment: Interviews Journal Article
The article, "Using Student Interviews to Guide Classroom Instruction: An Action Research Project" outlines a very unique "action research project". In an action research project, as opposed to traditional research projects, a designated school research staff partakes in various types of research in an effort to change and improve varying aspects of the school and the daily school lives of the students. The overall goal of an action research project is to initiate and guide further change in the structure of the school.
In this particular situation, many teachers from Jefferson Elementary School ranging from kindergarten to fourth grade had noticed that they were struggling in teaching problem solving in the classroom. They found that this concept was not only hard for them to teach, but even harder for the students to learn. The staff realized that the number one hurdle was lack of knowledge as to the individual learning styles and practices of certain students. Therefore, they chose to investigate the following two questions...
"Do student interviews provide teachers with a more detailed, accurate, and complete picture of children's mathematical understanding?"
and
" Does this knowledge help teachers improve the way that they teach mathematics?"
The action research plan unfolded as follows, team members conducted interviews with individual students while the rest of the class partook in extension activities. Two sets of interviews were conducted, one in the fall and one in the spring. The team members then shared the results of their interviews with the rest of the team and the staff and described the possible impact of using the results of these interviews to guide classroom instruction.
In this particular situation, many teachers from Jefferson Elementary School ranging from kindergarten to fourth grade had noticed that they were struggling in teaching problem solving in the classroom. They found that this concept was not only hard for them to teach, but even harder for the students to learn. The staff realized that the number one hurdle was lack of knowledge as to the individual learning styles and practices of certain students. Therefore, they chose to investigate the following two questions...
"Do student interviews provide teachers with a more detailed, accurate, and complete picture of children's mathematical understanding?"
and
" Does this knowledge help teachers improve the way that they teach mathematics?"
The action research plan unfolded as follows, team members conducted interviews with individual students while the rest of the class partook in extension activities. Two sets of interviews were conducted, one in the fall and one in the spring. The team members then shared the results of their interviews with the rest of the team and the staff and described the possible impact of using the results of these interviews to guide classroom instruction.
Monday, March 22, 2010
TCM March Article - Sand and Water Table Play
This article discusses a study in which the authors observed pre-school children at play. These particular children were engaged at the classrooms sand and water play table, and the authors wanted to determine if mathematics could be found in their simply daily play routines. The authors goal was to understand how these particular children would interact with the provided materials and what basic math ideas and concepts would be evident even in their early play. The authors end the article by providing and discussing how this type of play can provide and encourage current and future mathematical learning and exploration.
I found the subject of this article very interesting, because of the concept of these children starting their mathematical explorations at such a young age. The idea is so simple yet seems to be so commonly overlooked, that the exploration of basic math concepts starts in simply play at a young age. If these students can be provided with even more opportunities to begin exploring math through fun play activities at the pre-school age, then there is no telling how far we as educators can take the positive promotion of math in future students.
I found the subject of this article very interesting, because of the concept of these children starting their mathematical explorations at such a young age. The idea is so simple yet seems to be so commonly overlooked, that the exploration of basic math concepts starts in simply play at a young age. If these students can be provided with even more opportunities to begin exploring math through fun play activities at the pre-school age, then there is no telling how far we as educators can take the positive promotion of math in future students.
MTMS March Article - Poematics
In this creative recount of a unique concept in the area of teaching mathematics, Abraham Ayebo and Lynda Weist describe a classroom in which students are encouraged to connect mathematics with other areas of academic exploration. In this particular example, students are taught via a lesson that integrates poetry and mathematics allowing students to connect their mathematics knowledge with their writing skills and create mathematical poems, or poems describing mathematical concepts and situations/poems with mathematical origin. Essentially, students were asked to describe the mathematical concepts and situations that they were learning through the context of a poem, while being encouraged to use informal, creative and expressive language.
I found this concept and article to be very intriguing. This is a perfect example of a teacher who is at the forefront of the movement to take mathematics outside of the traditional plug and chug memorization context, and allow students to make connections to other academic and real life situations. This allows the students to see how mathematics can apply to a variety of situations and subjects that they will experience every day, and allows them to better connect to the subject in a fun way.
I found this concept and article to be very intriguing. This is a perfect example of a teacher who is at the forefront of the movement to take mathematics outside of the traditional plug and chug memorization context, and allow students to make connections to other academic and real life situations. This allows the students to see how mathematics can apply to a variety of situations and subjects that they will experience every day, and allows them to better connect to the subject in a fun way.
Wednesday, March 3, 2010
Video Reflection - Grade 7 Graphs
In this grade seven on graphs, and the sequence of patterns found in tables, the teacher poses an interesting challenge to the students. She explains that she has created a number of different graphs representing different quantities and functions. She allows the students to break themselves off into their own groups and then provides them all with a transparency of a graph. The task is for the students to create a story to go along with what is represented in the graph. She gives a few examples such as the relationship between time and temperature, however, she leaves the final decision of what their story will revolve around up to them. She goes in, especially in her own reflection or explanation of the lesson, to explain that she then wants the students to show the pattern of the graph in a table form, and come up with an equation for finding unknown values based off of the known ones represented in the table.
1. Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
I personally believe that this task in particular is very appropriate for the lesson that the teacher is providing. By allowing the students to group up and come up with individual stories she is allowing them to connect to the content that she has provided. By doing this she is helping to ensure that the students will possibly take more of a personal interest in the graphs that they are studying because of the fact that are connecting to it on a personal level. By then taking the stories that they have created and further tying them into another math concept closely related to graphs, in this case, tables and the idea of creating an equation to find further numbers in the sequence, she is further ensuring that the students will take these prior connections that they have made and apply them to related topics and hopefully build off of the knowledge that they have gained to build their overall math skills.
2. Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.
I am not entirely sure how well this would have worked, but it may have benefited the students to come up with alternative stories for work with the tables after they were done with their graphs. The only issue I see arising with the original task is that if the students original stories were designed solely for the relationship represented in the graphs and did not lend themselves well to the idea of creating tables and predicting future variables, then the students may struggle with connecting personally to this concept. By allowing students the choice of creating a new story to go with their tables then the teacher may have further ensured that the students would be able to do this.
3. What criteria do you use to determine whether or not to use a particular task with your class?
While I obviously do not have a class of my own at the current time, I can think of what I may do with my future class. I do not have a specific list of criteria, however, I can say that if I did, the number one thing would be the students ability to connect to the topic. I am a firm believer that if the students cannot find some way to connect to a lesson personally, even on the smallest of levels, then they will not be truly engaged in what they are learning. If this is the case, then the learning will simply become a process that they go through and many despise. If students despise the processes of learning math then how can we expect to encourage their further explorations? Outside of this, I would ensure that the lesson allows students room to build on further concepts, this is represented well in this lesson when the teacher has them move from graphs to tables.
1. Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
I personally believe that this task in particular is very appropriate for the lesson that the teacher is providing. By allowing the students to group up and come up with individual stories she is allowing them to connect to the content that she has provided. By doing this she is helping to ensure that the students will possibly take more of a personal interest in the graphs that they are studying because of the fact that are connecting to it on a personal level. By then taking the stories that they have created and further tying them into another math concept closely related to graphs, in this case, tables and the idea of creating an equation to find further numbers in the sequence, she is further ensuring that the students will take these prior connections that they have made and apply them to related topics and hopefully build off of the knowledge that they have gained to build their overall math skills.
2. Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.
I am not entirely sure how well this would have worked, but it may have benefited the students to come up with alternative stories for work with the tables after they were done with their graphs. The only issue I see arising with the original task is that if the students original stories were designed solely for the relationship represented in the graphs and did not lend themselves well to the idea of creating tables and predicting future variables, then the students may struggle with connecting personally to this concept. By allowing students the choice of creating a new story to go with their tables then the teacher may have further ensured that the students would be able to do this.
3. What criteria do you use to determine whether or not to use a particular task with your class?
While I obviously do not have a class of my own at the current time, I can think of what I may do with my future class. I do not have a specific list of criteria, however, I can say that if I did, the number one thing would be the students ability to connect to the topic. I am a firm believer that if the students cannot find some way to connect to a lesson personally, even on the smallest of levels, then they will not be truly engaged in what they are learning. If this is the case, then the learning will simply become a process that they go through and many despise. If students despise the processes of learning math then how can we expect to encourage their further explorations? Outside of this, I would ensure that the lesson allows students room to build on further concepts, this is represented well in this lesson when the teacher has them move from graphs to tables.
Monday, February 15, 2010
Math Applets - Grade 3 - 5
The following math applet for grades 3 - 5 deals with communicating about mathematics using games. The specific game in this applet is entitled the fraction track. In this game, students use the interactive board provided in the applet, and play by moving their markers on the various levels of the track. The overall goal of the game is to have all positive and negative distances add to the total amount shown in the final fraction box. The game can be played in competition, awarding the first student to correctly move all of his/her markers to the right side of the fraction board the winner. The applet moves on to outline possible discussion to be used in playing this game, stating that teachers should ask students questions before the game is played. These questions could range from how the game board was constructed, to how the game tracks are related. To further extend the game students could even be allowed to design their own boards and incorporate a combination of fractions and decimals.
In reviewing this game, I found basically nothing but positives. This applet provides a fun way for students to learn about a subject that many students of this particular age seem to struggle with. By providing an interactive game like this, you as the teacher provide a fun yet structured activity that allows the students to explore the subject of fractions and equivalence in an independent way that still carries the guidelines that you as a teacher can control and provide. Essentially it allows for guided independent exploration, and helps to ensure that students will be interested in their learning.
http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm
In reviewing this game, I found basically nothing but positives. This applet provides a fun way for students to learn about a subject that many students of this particular age seem to struggle with. By providing an interactive game like this, you as the teacher provide a fun yet structured activity that allows the students to explore the subject of fractions and equivalence in an independent way that still carries the guidelines that you as a teacher can control and provide. Essentially it allows for guided independent exploration, and helps to ensure that students will be interested in their learning.
http://standards.nctm.org/document/eexamples/chap5/5.1/index.htm
Math Applets - Pre K - Grade 2
The math applet that I reviewed for the Pre K - Grade 2 level deals with learning number relations and properties of numbers. To complete this lesson students use calculators and hundreds boards to display these number patterns. In summation, the lesson requires students to compare counting sequences, they can generate these sequences using both their calculators and their hundreds boards. Students were asked to count in 2's, 5's, and 10's. This sequence could be done on the calculator, and show on the hundreds board where the students came to the number 100 when using these specific sequences. To further extend the lesson, student were asked to think of other numbers and use them in the same style of sequence once again representing it on their calculators and their hundreds board. Specifically, one group chose to use the number 3, showing that they did not reach one hundred on their hundreds boards. The goal of the applet was to allow students to recognize the patterns in sequences of numbers along with making predictions of what numbers would be marked off on the hundreds boards.
I found this applet to be beneficial and informative initially. It allows students to learn the sequences of numbers in multiple formats, and allows them a chance to collaborate and explore independently by plugging their own numbers in. It also provides a good opportunity for students to use additional tools to make predictions and further extend their knowledge of number patterns. The one outlying flaw I can see is the limited nature of the overall use of the applet. From what I can see, students would only be able to repeat this process for a certain amount of numbers and the overall process may become repetitive after a certain amount of time, resulting in students not being satisfied with the task.
http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm
I found this applet to be beneficial and informative initially. It allows students to learn the sequences of numbers in multiple formats, and allows them a chance to collaborate and explore independently by plugging their own numbers in. It also provides a good opportunity for students to use additional tools to make predictions and further extend their knowledge of number patterns. The one outlying flaw I can see is the limited nature of the overall use of the applet. From what I can see, students would only be able to repeat this process for a certain amount of numbers and the overall process may become repetitive after a certain amount of time, resulting in students not being satisfied with the task.
http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm
Wednesday, February 10, 2010
MTMS February Article - 100 Students
The article entitled "100 Students", published in the February edition of the "Mathematics Teaching in the Middle School" journal, was written by the following authors, Jody L. Riskowski, Gayla Olbricht and Jennifer Wilson. The journal discusses a specific project performed by a group of students in the area of statistics and data analysis. The students were assigned to construct a specific survey to administer themselves to their peers. After the construction of the survey it was the students responsibility to conduct it effectively and professionally in ways allowing them to most effectively gather the necessary information to complete the remainder of the project. Once this aspect was complete the students moved on to collaborate and explore the data that they had collected using it to study concepts in area of statistics. This was achieved by considering and exploring the data in various ways such as cultural and gender distribution. Upon completion of the study of the data the students finished their projects by creating and presenting a multimedia display of their choice. Their challenge in this was finding a creative, fun, and most importantly effective way of displaying the spread and range of their data in a way that their peers could understand and connect with.
While the background ideas of this article were seemingly obvious ones (the ideas on the effectiveness of group work and collaboration) I enjoyed the opportunity to read about a specific example of this through the documentation of this specific project. I gained ideas that I can use as a future teacher in my own classroom and further learned about the benefits of multi-level projects along with teaching mathematics through interactive work. By allowing these students to learn about the areas of data analysis and statistics through group work, collaboration, and even interactive media, they were allowed to connect with the subject on a more personal level. Instead of simply memorizing and regurgitating formulas and facts, they were given an opportunity to employ their mathematics skills in their every day lives. This article further solidified my ideas that this really is the most effective way of teaching mathematics.
While the background ideas of this article were seemingly obvious ones (the ideas on the effectiveness of group work and collaboration) I enjoyed the opportunity to read about a specific example of this through the documentation of this specific project. I gained ideas that I can use as a future teacher in my own classroom and further learned about the benefits of multi-level projects along with teaching mathematics through interactive work. By allowing these students to learn about the areas of data analysis and statistics through group work, collaboration, and even interactive media, they were allowed to connect with the subject on a more personal level. Instead of simply memorizing and regurgitating formulas and facts, they were given an opportunity to employ their mathematics skills in their every day lives. This article further solidified my ideas that this really is the most effective way of teaching mathematics.
TCM February Article - Techniques for Small Group Discourse
The following article, found in the February 2010 issue of the "Teaching Children Mathematics" journal, entitled "Techniques for Small Group Discourse" was written by a culmination of authors including, Hulya Kilic, Dionne I. Cross, Filyet A. Ersoz, Denise S. Mewborn, Diana Swanagan and Jisun Kim. The article focused on the following three general areas, communication, reasoning, and teaching. Specifically it discussed the various types of instructional facilitation that you as a teacher can use to positively influence your students' thinking. The article stressed the idea of small group participation and roles that can positively influence students peer interactions, along with their overall levels of participation and learning. Moving beyond the students benefits, the article discussed the positive aspects of small group communication for teachers. The article stressed the idea that participating in small groups as a teacher can help teachers to reflect on their own practices, discuss with their peers and co-workers and reflect on what is working inside and outside of the classroom and what is not. By participating in this type of group reflection, educators can further determine their role as teacher and the effect they are having on their students education, along with increasing their overall level of competence in the area that they are teaching.
Overall I have to say that I found this particular article to be very insightful and helpful. While the basic ideas behind it were not foreign to me, and were closely interwoven with the personal ideas that I hold on the issue of small-group collaboration, it was refreshing to read a professional article such as this reiterating and confirming my own ideas. One area that this article discussed that I had never really thought of before was that of the benefits for teachers. While in hindsight those benefits seem obvious, I had personally never gone as far as to think of the benefits of peer small group collaboration for teachers and had always left it inside the classroom for the students. By reading about the benefits for teachers, and exploring the higher levels of effectiveness it can help you achieve as an educator, I can confidently say that positive and effective small-group collaboration will not only be a goal of mine inside the classroom, but also outside of it with my fellow educators.
Overall I have to say that I found this particular article to be very insightful and helpful. While the basic ideas behind it were not foreign to me, and were closely interwoven with the personal ideas that I hold on the issue of small-group collaboration, it was refreshing to read a professional article such as this reiterating and confirming my own ideas. One area that this article discussed that I had never really thought of before was that of the benefits for teachers. While in hindsight those benefits seem obvious, I had personally never gone as far as to think of the benefits of peer small group collaboration for teachers and had always left it inside the classroom for the students. By reading about the benefits for teachers, and exploring the higher levels of effectiveness it can help you achieve as an educator, I can confidently say that positive and effective small-group collaboration will not only be a goal of mine inside the classroom, but also outside of it with my fellow educators.
Wednesday, February 3, 2010
PBL Review - Step Three
To begin with the first PBL example provided in the documents section of Sakai. Titled "Lounging Around" this, at least in my opinion (with my limited knowledge of the entire PBL process) seemed to be a relatively effective example of a PBL activity. The students were provided with an interesting and relatable topic or problem. They were given a certain budget and a certain area in which they were allowed to design a new lounge for the 7th and 8th grade students. As long as they stayed within their budget and their set area of space they were allowed to design it in any way they wished. This is a problem that will intrigue the students because it relates directly to them, and it provides a fun issue that could peak and hold their interest. The group laid out the math that the student would be using in the exploration of this problem, along with specific examples of each type of math, and for the most part I was impressed. They covered everything from geometry (the shapes and the actual set up of the items to be placed in the student lounge, maximizing the total space) to data analysis (the actual budgeting). One area that I thought seemed a bit weak was the algebra, as their description of the algebra to be used did not totally seem to match up with the difficulty of the project. Outside of this issue though, they did an excellent job of tying their goals for the students into the NCTM objectives, while providing an intriguing question that would be fun for the students to explore, and setting to an appropriate age level.
The second PBL example provided, entitled "Redo the Zoo" seemed equally impressive. In this one, students were basically asked to design their own ideal zoo, budgeting the space, time, and money that it would take to complete this. I was impressed right off the bat with their rationale and the ideas from outside of the mathematics classroom that they were able to tie in. To begin with, the students will take a trip to their local zoo, giving them ideas as to how a zoo is set up and a basis of operations for how they may want to set up (or not set up) their own. I thought this was a great idea as it seems like a great way to get students involved and excited right away in the introduction of this problem. By providing a field-trip to begin the PBL, you are providing a fun experience that can peak students interest and further encourage them to get involved in the problem. For further connections outside of this, I was impressed with the idea that after their zoo was completed, the students were to write a full proposal to the ficitonal Mathmaticsburg Zoological Society. This is a great way to tie in the Language Arts classroom and allow students to practice their higher order thinking skills. For work inside the math classroom, I feel that this group did an excellent job of including multiple areas of mathematics in their PBL, including everything from geometry, to algebra, to data analysis. The one thing that I was unsure about was the degree of difficulty for the age group. While I think that a problem regarding the zoo is excellent for the fifth-sixth grade level, I think that the idea of re-desigining an entire zoo while writing a full business proposal may prove a bit difficult.
The second PBL example provided, entitled "Redo the Zoo" seemed equally impressive. In this one, students were basically asked to design their own ideal zoo, budgeting the space, time, and money that it would take to complete this. I was impressed right off the bat with their rationale and the ideas from outside of the mathematics classroom that they were able to tie in. To begin with, the students will take a trip to their local zoo, giving them ideas as to how a zoo is set up and a basis of operations for how they may want to set up (or not set up) their own. I thought this was a great idea as it seems like a great way to get students involved and excited right away in the introduction of this problem. By providing a field-trip to begin the PBL, you are providing a fun experience that can peak students interest and further encourage them to get involved in the problem. For further connections outside of this, I was impressed with the idea that after their zoo was completed, the students were to write a full proposal to the ficitonal Mathmaticsburg Zoological Society. This is a great way to tie in the Language Arts classroom and allow students to practice their higher order thinking skills. For work inside the math classroom, I feel that this group did an excellent job of including multiple areas of mathematics in their PBL, including everything from geometry, to algebra, to data analysis. The one thing that I was unsure about was the degree of difficulty for the age group. While I think that a problem regarding the zoo is excellent for the fifth-sixth grade level, I think that the idea of re-desigining an entire zoo while writing a full business proposal may prove a bit difficult.
PBL Review - Step Two
Problem Based Learning, according to Keyong Roh author of "Problem-Based Learning in Mathemtaics. Eric Digest" is essentially a learning environment driven by the exploration of problems. Basically what this means is that learning begins when the students identify a problem to be solved, a problem that requires investigation and the gaining of knowledge in order to be solved. A key component is that students do not simply look for one key correct answer, instead, they explore ideas, propose possible solutions, evaluate their options, and eventually present their conclusions. The use of Problem Based Learning encourages the growth of students heuristic knowledge, which aids in their growth as problem solvers. The final key component addressed in this article is that of peer cooperation. In Problem Based Learning exercises, students are encouraged and required to work as a team, with each student playing a different part in cooperation with the whole. This adds an air of reliability, while refining their peer communication skills, all of these are essential to their growth as learners.
Keyong, R.H. (2003). Problem-based learning in mathematics. eric digest. ERIC Clearinghouse for Science Mathematics and Environmental Education , Retrieved 3 February, 2010, from http://www.ericdigests.org/2004-3/math.html doi: ED482725
Keyong, R.H. (2003). Problem-based learning in mathematics. eric digest. ERIC Clearinghouse for Science Mathematics and Environmental Education , Retrieved 3 February, 2010, from http://www.ericdigests.org/2004-3/math.html doi: ED482725
PBL Review - Step One
PBL's which stands for probelm based learning, are effective teaching problems that allow students to draw from relevant and topical issues to facilitate connections with the outside world. To begin facilitate the choosing of a relevant topic issue that has good solid connections with the worlds current events and issues. Following the choosing of a problem, you must determine the problem based learning adventure. This involves, determining the seperate roles of students and clarifying how they will interconnect to produce the finished product, along with determining the possible outcomes and developing the problems documents. In these problem based learning experiences students should assume the roles of stake-holders, promoting a vested interest in the problem being studied and a drive to develop an effective solution. It is essential when working on these not only for the students to identify and design the problem they will work on, but for the teacher to aid in this design and coach the students critical thinking skills. When an effective problem based learning experinece has been provided it wields many benefits for the students involved. It is effective in increasing student motivation along with a personal responsibility for completeing one's one work in order to aid the entire group. These problems are also effective in emphasizing and fine tunig a students higher order thinking skills, which is a beneficial function for all students and educators.
Friday, January 29, 2010
Journal Article - Turning the Mathematics Classroom into an Intellectual Playground Using Poetry
To start, this article, written by John E. Hammett III, I thought was a perfect choice for relating to our process standard of connections. The article implies the importance of connections right in the title, by implying the connection of mathematics and poetry. The author begins by introducing the appropirate poetry, and more importantly how it can be used inside the mathematics classroom (specifying that the most appropriate classrooms to use this form of connections in are at the middle school level). The author moves on to provide an array of varying examples of successful integration of poetry inside the mathematics classroom, offering up examples of historical mathematical poems, and various poetic mathematical illustrations created by students. Hammett closes by suggesting opitonal instructional methods for the classroom implelmentation of this particular idea, and even offers two seperate examples of mathematics poem problems.
As outlined in my previoius posting, the NCTM has identified three major ideas in their process standards - connections section. While I will not reiterate all three concepts, I would like to reiterate the one that I feel applies best to this particular article. That being, students should be able to use connections to apply mathematical ideas in other subject and life skills areas outside of the mathematics classroom. By suggesting that studnets can use poetry to help them connect with and solve mathematical problems and concepts, Hammett is proving to be a direct advocate of this particular idea. His examples of poem problems show the benefits of moving math somewhere outside of the math classroom, and allowing students to take a subject or concept that they may struggle with or simple find to be unappealing, and connect it to antoher subject area in which they may excell or enjoy. This will mutually benefit both the student and the teacher, as the student will be able to make legitimate outside connections with mathematics to further their understanding of the concepts. This in turn will aid the teacher in teaching these same concepts.
As outlined in my previoius posting, the NCTM has identified three major ideas in their process standards - connections section. While I will not reiterate all three concepts, I would like to reiterate the one that I feel applies best to this particular article. That being, students should be able to use connections to apply mathematical ideas in other subject and life skills areas outside of the mathematics classroom. By suggesting that studnets can use poetry to help them connect with and solve mathematical problems and concepts, Hammett is proving to be a direct advocate of this particular idea. His examples of poem problems show the benefits of moving math somewhere outside of the math classroom, and allowing students to take a subject or concept that they may struggle with or simple find to be unappealing, and connect it to antoher subject area in which they may excell or enjoy. This will mutually benefit both the student and the teacher, as the student will be able to make legitimate outside connections with mathematics to further their understanding of the concepts. This in turn will aid the teacher in teaching these same concepts.
Process Standards - Connections
The connections portion of the process standards section of the NCTM website, outlines three major ideas for educators. The first, students should become framiliar with mathematical ideas and use this framiliarity to make connections amongst these ideas. Students should understand the interconnections of varying seperate mathematical ideas, eventually using these connections to combine these ideas into one whole. Finally, students should be able to use these connections to both recognize and apply these mathematical ideas in other subjects and life skills areas outside of a mathematics classroom.
Thursday, January 28, 2010
Grade 3: Lesson on Patterns (Videos)
In this grade 3 lesson, students were first introduced to a story in which the main character had a magic pot that could double the 5 coins he had in his purse every time the coins were put into the pot. The teacher then took this story and adapted it to a math lesson designed to help the students with their basic multiplication skills along with logical reasoning. In the math question that the teacher proposed, the students were given a sceneario with two options. Option one was to be given five coins and a magic doubling pot that they could use no more than ten times. Option two was to simply be given 1,000 coins right then. Following the teachers original proposition of the question the students immediately chose option two (1,000 coins) in unison. However, the teacher then worked with them to do the math involved in option one, showing the students that eventually, after doubling the number ten times, they would come out with 5,120 coins. Once again, the purpose of the lesson seemed to be to provide the students a chance to interact as a whole group and use their multiplication skills to answer a fun question that could have some real world applications.
Question 1: Describe the primary task in this lesson and identify the mathematical skills and concepts that this task is designed to develop.
As mentioned in the overview of the lesson, the primary task was getting the students to use their multiplication and logical reasoning skills to solve a fun and interesting math porblem. As opposed to simply allowing the stuents to do guess work and choose the first answer or option that seemed appealing, they were given the chance to remend their original choices after completing the work as a whole group and realizing that option number one (doubling the coins ten times) was actually more appealing in the long run. By providing the students with a real world applicable and fun math problem to solve, the teacher has successfully contributed to the building of their multiplication and logical reasoning skills.
Question 2: Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
I feel that this particular task is very appropriate given the age group the teacher is working with. In many cases, simply drilling math facts, more specifically multiplication facts, into young childrens minds is a way to get them maybe to remember these facts in time for a timed test. However, it does not teach them to make connections with the math skills behind these answers. By simply teaching kids facts over and over without giving them some type of situation in which they can use the facts, and draw from to provide them with a "why" to the "what" (a reason that these facts are what they are) does not aid in their learning of mathematics, and only causes more problems in the long run. So, by allowing these children to make those connections through this sceneario, this particular teacher has both helped them learn the basic facts, and provided them a framework for future exploration of mathematics.
Question 3: Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.
I honestly would not propose a completely different alternative assignment or task, as I feel that the teacher did an excellent job (as I previously mentioned) in providing a fun and meaningful connection for these students, along with tying the mathematics to other lessons in other subject areas (reading most prevalently). However, I do feel that the students would benefit if the same concept or task was used again with different numbers. By providing the same style of task with different numbers, you are ensuring that the students will enjoy it once again, make the same connections to aid in their futher learning, and also have the chance to further explore their multiplication and math facts with different numbers.
Question 1: Describe the primary task in this lesson and identify the mathematical skills and concepts that this task is designed to develop.
As mentioned in the overview of the lesson, the primary task was getting the students to use their multiplication and logical reasoning skills to solve a fun and interesting math porblem. As opposed to simply allowing the stuents to do guess work and choose the first answer or option that seemed appealing, they were given the chance to remend their original choices after completing the work as a whole group and realizing that option number one (doubling the coins ten times) was actually more appealing in the long run. By providing the students with a real world applicable and fun math problem to solve, the teacher has successfully contributed to the building of their multiplication and logical reasoning skills.
Question 2: Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
I feel that this particular task is very appropriate given the age group the teacher is working with. In many cases, simply drilling math facts, more specifically multiplication facts, into young childrens minds is a way to get them maybe to remember these facts in time for a timed test. However, it does not teach them to make connections with the math skills behind these answers. By simply teaching kids facts over and over without giving them some type of situation in which they can use the facts, and draw from to provide them with a "why" to the "what" (a reason that these facts are what they are) does not aid in their learning of mathematics, and only causes more problems in the long run. So, by allowing these children to make those connections through this sceneario, this particular teacher has both helped them learn the basic facts, and provided them a framework for future exploration of mathematics.
Question 3: Propose one or more alternative tasks that might have strengthened the lesson or helped to clarify the key mathematical ideas being developed, and justify the use of this task or these tasks.
I honestly would not propose a completely different alternative assignment or task, as I feel that the teacher did an excellent job (as I previously mentioned) in providing a fun and meaningful connection for these students, along with tying the mathematics to other lessons in other subject areas (reading most prevalently). However, I do feel that the students would benefit if the same concept or task was used again with different numbers. By providing the same style of task with different numbers, you are ensuring that the students will enjoy it once again, make the same connections to aid in their futher learning, and also have the chance to further explore their multiplication and math facts with different numbers.
Friday, January 22, 2010
Trusting Students Journal Article
To sum this article up in brief form, the main topic of discussion is the importance of trust in the teacher - student relationship. It is this trust that truly motivates teachers to understand and work with their students to the fullest extent, and further allows teachers to develop positive instructional approaches that will benefit both themselves and their students. The article ends by discussing the results that come from a teachers understanding of students overall goals for educaitons. These results generally coming in the form of student actions, teacher learning, and instructional change.
Upon reading this article, it definitely made me rethink my idea of the best possible student - teacher relationship, and more importantly the role that trust plays in this relationship. It gave me further insight into what have a good level of trust in your students can provide for the educational atmosphere, and the overall nature of your classroom. Having this trust with your students allows the teacher to further modify their curriculum and environment in a way that is mutually beneficial. This article pointed this all out to me, and it was all information that I was glad to have learned.
Upon reading this article, it definitely made me rethink my idea of the best possible student - teacher relationship, and more importantly the role that trust plays in this relationship. It gave me further insight into what have a good level of trust in your students can provide for the educational atmosphere, and the overall nature of your classroom. Having this trust with your students allows the teacher to further modify their curriculum and environment in a way that is mutually beneficial. This article pointed this all out to me, and it was all information that I was glad to have learned.
The Learning Principle
The Learning Principle, from the Principles and Standards for School Mathematics, and the NCTM (National Council for Teachers of Mathematics) discusses the importance of conceptual knowledge in a student's ability to understand any subject and any content, i.e. mathematics. It states that, "When students understand mathematics, they are able to use their knowledge flexibly." They can then combine their factual knowledge with their conceptual understanding to fully harness their ability to comprehend and grow in mathematics.
The section then moves on to discuss that while learning the basics is important, as these lay the groundwork for a students further growth and knowledge apprehension, in many cases the students who simply memorize the facts without actually understanding the reason behind these facts (essentially the why behind the what) often struggle when trying to apply the mathematical concepts behind these facts in other settings. More simply put, these students can solve the problems that they have memorized but cannot use the math skills required to solve these problems to solve those that they have not encountered yet. On the other hand, the students that have conceptual knowledge of mathematics can often time apply the skills they have learned in solving these problems to help them solve those problems of which they are unframiliar with.
This section later discusses the importance of becoming autonomous learners. This is important because it allows students to take control of their own learning, instead of simply being told what and when to do things, they can apply the knowledge that they have been taught to their own problems and solve them on their own, further allowing them to grow in their understanding and conceptual knowledge of mathematics.
The section closes by stating the simple principle that the school setting should not inhibt students ability to grow in their knowledge of mathematics by limiting them to the memorization of basic facts, but should provide them the framework to flourish.
The section then moves on to discuss that while learning the basics is important, as these lay the groundwork for a students further growth and knowledge apprehension, in many cases the students who simply memorize the facts without actually understanding the reason behind these facts (essentially the why behind the what) often struggle when trying to apply the mathematical concepts behind these facts in other settings. More simply put, these students can solve the problems that they have memorized but cannot use the math skills required to solve these problems to solve those that they have not encountered yet. On the other hand, the students that have conceptual knowledge of mathematics can often time apply the skills they have learned in solving these problems to help them solve those problems of which they are unframiliar with.
This section later discusses the importance of becoming autonomous learners. This is important because it allows students to take control of their own learning, instead of simply being told what and when to do things, they can apply the knowledge that they have been taught to their own problems and solve them on their own, further allowing them to grow in their understanding and conceptual knowledge of mathematics.
The section closes by stating the simple principle that the school setting should not inhibt students ability to grow in their knowledge of mathematics by limiting them to the memorization of basic facts, but should provide them the framework to flourish.
Subscribe to:
Posts (Atom)