Purpose for the Activity
In this activity the teacher wanted the students to understand the relationship between a word problem or story problem, a data table that numerically shows the data and the information graphed on a coordinate plane. The students practiced generating ordered pairs. They also worked on identifying and assigning the x and y axes. Next, the students generated the algebraic equation. All in all, the teacher wanted the students to be able to show each problem as a graph, a table and an algebraic expression.
The teacher had the students talk about the graphs as a story. I liked the example she gave, comparing the relationship of the graph to an oven baking cookies. The oven’s temperature slowly climbs at a steady rate until its reached temperature. Once it has reached the temperature it has been set to it fluctuates around that number for the amount of time that it is used. Then as the oven is turned off it slowly looses heat until it has reached room temperature. Good pedagogy suggests that students understand mathematic relationships better when they can apply it to a story or in another context. The students took time to create a story that fix a graph which helped them to understand the foundation which the rest of the assignment built on. As the lesson progressed the students worked with generating tables, graphs and the algebraic equations.
Questions:
#1 Describe how appropriate you think the primary task in this lesson is for developing an understanding of the mathematics being taught.
I feel that the teacher did a thorough job with this topic. She set up a context for the students to explore the concept on their own and attack the problems from different angles; some of the groups started with the tables and progressed onto the graphs and algebraic equations, some of the groups started by making the graph and then generated the table. However, I do feel that the teacher’s initial instructions were a little vague. She spent a lot of time reiterating the directions; I feel that her initial instructions, given to the whole class, should have been more thorough. Furthermore, considering the time constraints, a ninety minute block period every-other day, I think that the teacher balanced the amount of time spend in whole class discussion and group work well.
#2 Describe how the teacher’s questioning, and the manner in which student responses are handled, contribute or do not contribute to a positive classroom learning environment?
The teacher discussed her questioning style at length in the interview section of the video. I was very pleased to see the degree to which she used errors to teach concepts and emphasize ideas and relationships. Furthermore, the teacher acknowledged that the students feel comfortable sharing mistakes and asking questions because of the positive classroom learning environment that she created. Clearly, she was sensitive to the student’s mistakes and very tactfully dealt with errors. Her sensitivity to the student’s mistakes was possible because she clearly understood the types of errors that the students made and why they made the mistakes they did. She quickly addressed misconceptions and mistakes in a very non-threatening manner. However, she never just gave students the answers, she always lead them to the answer through her line of questioning.
#3 Describe what the teacher does to support learning while students are working in groups.
The interview section of this video addressed the strategies that the teacher used to support the individual groups and help them reach the next level of understanding. She knew her students well enough that she knew when a simple question would be enough to redirect their thinking and lead them to the correct answer. However, she knew that some group needed more personal attention and stopped to discuss the problems with them at length. The teacher said that in this lesson they tried a different grouping arrangement, she allowed them to select their own groups. Personally, I would not do this; I feel that having done it once that the students would frequently ask to choose their own group and that it might become a point of contention. Perhaps, had she grouped the students more purposely they would have avoided some of the confusion that may have been caused by the students distraction caused by grouping situation.
Overall Use of the Video
Unlike the last video I felt that this video was less effective because it was broken into so many pieces. The former lesson was shorter, with less parts and the general flow of the lesson was more apparent. In this video series, I was very confused as to the sequence of events and the general progression of the lesson. The video quality was very poor and that detracts slightly from what I, as an observer, get from the lesson. However, the interview section of the video was more valuable in my opinion. Sand Allen provided very specific examples of techniques she used, errors that they students made, the objectives that she had for the lesson and what she believed the students got from the experience. Overall, she spoke about the lesson using specific examples and was less theoretical than Rosemary Klein, the teacher from the previous lesson.
There are some aspects of the video that are frustrating. I wish that I could see the overhead properly. Some of the audio is difficult to understand and the subtitles do not consistently make up for lost on inaudible speech. Being able to see the student work as the video progressed would have been helpful as well. However, overall I feel that the video is very useful. It has certainly given me some ideas about how to best teach this information in my own classroom.
Monday, February 22, 2010
Saturday, February 13, 2010
Math Applet: How Many Under the Shell: Grade K-2
How Many Under the Shell
K-2
http://illuminations.ncthttp://illuminations.nctm.org/ActivityDetail.aspx?ID=73m.org/ActivityDetail.aspx?ID=198
Summary:
This is a very simple application that allows young students, from kindergarten to second grade, to practice with addition and subtraction. It is a very straightforward game that will help the students with their counting, addition and subtraction skills. The bubbles pop up, as each one appears it is counted, then the shell covers the bubbles and some of the bubbles are pulled away or added, and some remain under the shell. Then the octopus asks, “How many bubbles are under the shell?” and the equation appears. The students then answer the question using the number pad. If the students select the correct answer the applet dings that the answers is correct, if it is incorrect an angry buzz is heard and the student has another opportunity to answer the question. In general, it is a very simple applet, ideal for the young student just learning to use these types of tools.
Critique:
I feel that this is a very useful application that can be used to introduce young children how to use math applets. The interface is very friendly and the program is very intuitive. Again, I feel that the biggest problem is that the program does not record student responses in any way to show how many questions that a student has answered in a session. Unlike the applet for the third for fifth grade student this application does not have a “help” option, which I feel might be helpful for the students. Furthermore, the instructions are a very small font and are not appropriate for the kindergarten through second grade student. It is obvious that the parent or teacher would have to explain the directions if the students didn’t automatically get it and that the instructions are there for the adult audience. This applet is especially useful in the young grades as the teacher can have the student select a specific skill; the questions can have either, all addition, subtraction or a random assortment of both addition and subtraction. The program can also be test specific numbers, any number one through nine. This would be useful if you were working with a student who had a strong understanding of addition and subtraction with the numbers one through five but needed assistance with five through nine.
K-2
http://illuminations.ncthttp://illuminations.nctm.org/ActivityDetail.aspx?ID=73m.org/ActivityDetail.aspx?ID=198
Summary:
This is a very simple application that allows young students, from kindergarten to second grade, to practice with addition and subtraction. It is a very straightforward game that will help the students with their counting, addition and subtraction skills. The bubbles pop up, as each one appears it is counted, then the shell covers the bubbles and some of the bubbles are pulled away or added, and some remain under the shell. Then the octopus asks, “How many bubbles are under the shell?” and the equation appears. The students then answer the question using the number pad. If the students select the correct answer the applet dings that the answers is correct, if it is incorrect an angry buzz is heard and the student has another opportunity to answer the question. In general, it is a very simple applet, ideal for the young student just learning to use these types of tools.
Critique:
I feel that this is a very useful application that can be used to introduce young children how to use math applets. The interface is very friendly and the program is very intuitive. Again, I feel that the biggest problem is that the program does not record student responses in any way to show how many questions that a student has answered in a session. Unlike the applet for the third for fifth grade student this application does not have a “help” option, which I feel might be helpful for the students. Furthermore, the instructions are a very small font and are not appropriate for the kindergarten through second grade student. It is obvious that the parent or teacher would have to explain the directions if the students didn’t automatically get it and that the instructions are there for the adult audience. This applet is especially useful in the young grades as the teacher can have the student select a specific skill; the questions can have either, all addition, subtraction or a random assortment of both addition and subtraction. The program can also be test specific numbers, any number one through nine. This would be useful if you were working with a student who had a strong understanding of addition and subtraction with the numbers one through five but needed assistance with five through nine.
Math Applet: Concentration: Grades 3-5
Concentration
3-5
http://illuminations.nctm.org/ActivityDetail.aspx?ID=73
Summary:
The concentration math applet, available through the NCTM Illuminations, resources for teaching mathematics, is a game which requires students to use matching skills in a memory game. The program allows for a great deal of flexibility of the content being taught. The students can elect to play the game with simple number relations, numbers represented as blocks, dots, words or numbers. Then the students can graduate to more difficult numbers. You can set the program to test the understanding of geometrical shapes, multiplication, fractions and even percentages. At each skill level the students can play solo or with a partner. In the way that the program responds; beeps, shows correct answers and resets the game, it feels very much like a game. It is very user friendly and easy to understand. However, despite its ease of use, the applet is able to test students on a variety of skill levels.
Critique:
I feel that this applet is a very useful tool. Because it fees so much like a game I feel that students would enjoy using the program. Furthermore, because the program is interactive the students are motivated to continue to the more difficult levels. In a number of the other applets I noticed that they allowed the students to manipulate; however, without a focus I can see the students becoming bored and giving up. As a teacher, I appreciate that the program is self sufficient, with the other programs I would have to create a problem or purposeful context for the students were they to use the applet for any prolonged period of time. Having tested the program I feel that the fractions version of the game is the most challenging. It requires the students to match the numerical fraction to a visual representation. Students who struggle with this concept can use the “glass pained window” to make the process easier. It makes the task much easier. Then the students can really focus on identifying the correct fraction pair with less focus on the time constraint. The only thing I would change about this applet is that it does not record the student’s results. Were I to use this applet in the classroom, as a reward, during computer time or to get a feel for the student’s prior knowledge on the subject, it would impossible to know their results unless you sat and watched each student play the game.
3-5
http://illuminations.nctm.org/ActivityDetail.aspx?ID=73
Summary:
The concentration math applet, available through the NCTM Illuminations, resources for teaching mathematics, is a game which requires students to use matching skills in a memory game. The program allows for a great deal of flexibility of the content being taught. The students can elect to play the game with simple number relations, numbers represented as blocks, dots, words or numbers. Then the students can graduate to more difficult numbers. You can set the program to test the understanding of geometrical shapes, multiplication, fractions and even percentages. At each skill level the students can play solo or with a partner. In the way that the program responds; beeps, shows correct answers and resets the game, it feels very much like a game. It is very user friendly and easy to understand. However, despite its ease of use, the applet is able to test students on a variety of skill levels.
Critique:
I feel that this applet is a very useful tool. Because it fees so much like a game I feel that students would enjoy using the program. Furthermore, because the program is interactive the students are motivated to continue to the more difficult levels. In a number of the other applets I noticed that they allowed the students to manipulate; however, without a focus I can see the students becoming bored and giving up. As a teacher, I appreciate that the program is self sufficient, with the other programs I would have to create a problem or purposeful context for the students were they to use the applet for any prolonged period of time. Having tested the program I feel that the fractions version of the game is the most challenging. It requires the students to match the numerical fraction to a visual representation. Students who struggle with this concept can use the “glass pained window” to make the process easier. It makes the task much easier. Then the students can really focus on identifying the correct fraction pair with less focus on the time constraint. The only thing I would change about this applet is that it does not record the student’s results. Were I to use this applet in the classroom, as a reward, during computer time or to get a feel for the student’s prior knowledge on the subject, it would impossible to know their results unless you sat and watched each student play the game.
Sunday, February 7, 2010
100 Students by Riskowski, Obricht and Wilson Mathematics Teaching in the Middle School
Summary
This article is a great example of project based learning and its use in a middle school classroom. The learning goals were that students would learn to talk about and analyze statistical data, collect a representative sample of a population and analyze the results in proportion. The project was modeled after 100 people world, which was a project by The Miniature Earth that sought to analyze how the earth would look if only 100 people lived on it, a representative 100 people that proportionally represented the Earth’s population from the 2001 statistics. The students set out to discover what their school would look like if a representative 100 students were chosen according to proportion to represent the entire school. Students were really responsible for carrying out the activity. They came up with the research questions, examined the questions in depth to analyze for bias, administered the surveys, collected the results, entered the data, analyzed the data and made an informational video about their project. In the end the teacher reported that not only did the students learn about statistics and data but that they learned about respect for others. At the end of the project the students sat down and talked about things they would have done differently and it was clear from their conversation that they understood how to get more accurate results from the school had the changed their questions, their sample and how they interpreted their data.
Application
This type of activity is so wonderful. In high school, these are the types of activities that I loved and still remember. These students were actively involved in the project because it was about them, their school, their peers and their lives. The students were involved in complex tasks that required a lot of planning and reflective practice. I admire the way the teachers taught this lesson, they allowed the students a lot of freedom; yet, they were there to ask thought provoking questions and prompt the students to analyze their research methods. I feel that this project is multidisciplinary and incorporates many advanced tasks; for instance, the students edited their own video, I have worked with editing software and that is not small feat for middle school students. I also appreciate the way that this project required students to work with their peers in coorporative groups. By the end of the project the students reported that they felt they had a better attitude toward their peers and felt that they should be less quick to judge and kinder to their classmates. If for that reason alone I feel that it was a time worthy project and its amazing how much they learned as well.
Riskowski, J. Olbricht, G. and Wilson, J. (2010) 100 students. Mathematics Teaching in the Middle School. 15(6) p 320
This article is a great example of project based learning and its use in a middle school classroom. The learning goals were that students would learn to talk about and analyze statistical data, collect a representative sample of a population and analyze the results in proportion. The project was modeled after 100 people world, which was a project by The Miniature Earth that sought to analyze how the earth would look if only 100 people lived on it, a representative 100 people that proportionally represented the Earth’s population from the 2001 statistics. The students set out to discover what their school would look like if a representative 100 students were chosen according to proportion to represent the entire school. Students were really responsible for carrying out the activity. They came up with the research questions, examined the questions in depth to analyze for bias, administered the surveys, collected the results, entered the data, analyzed the data and made an informational video about their project. In the end the teacher reported that not only did the students learn about statistics and data but that they learned about respect for others. At the end of the project the students sat down and talked about things they would have done differently and it was clear from their conversation that they understood how to get more accurate results from the school had the changed their questions, their sample and how they interpreted their data.
Application
This type of activity is so wonderful. In high school, these are the types of activities that I loved and still remember. These students were actively involved in the project because it was about them, their school, their peers and their lives. The students were involved in complex tasks that required a lot of planning and reflective practice. I admire the way the teachers taught this lesson, they allowed the students a lot of freedom; yet, they were there to ask thought provoking questions and prompt the students to analyze their research methods. I feel that this project is multidisciplinary and incorporates many advanced tasks; for instance, the students edited their own video, I have worked with editing software and that is not small feat for middle school students. I also appreciate the way that this project required students to work with their peers in coorporative groups. By the end of the project the students reported that they felt they had a better attitude toward their peers and felt that they should be less quick to judge and kinder to their classmates. If for that reason alone I feel that it was a time worthy project and its amazing how much they learned as well.
Riskowski, J. Olbricht, G. and Wilson, J. (2010) 100 students. Mathematics Teaching in the Middle School. 15(6) p 320
Storyboards for meaningful patterns by Dubon and Shafer Teaching Children Mathematics
Summary
This article is about Dubon, a Novice teacher who works in a kindergarten classroom in a Title 1 school in northwestern Indiana. While the class frequently uses patterns and predictability, in classroom management as well as in following the daily routine, the students were unable to generate patterns on their own and were not able to discuss or talk about the patterns that they saw or had created. Dubon’s principal eventually paired her with a professor, Shafer, from the local college who arrived at the school armed with manipulatives and ideas on how to teach the children patterns. Initially, Shafer tested the student’s ability to generate a simple pattern, a topic that they had studied in class; few of the students were able to perform the task. So Shafer began her lesson, she used multiple examples using, people (boy-girl-boy-girl), sounds (snap, clap, snap, clap) and other patterns. She then introduced storyboards to the children. The storyboards require the students to start story problems and then introduce the snap cubes as a way to visually represent the objects in the story. The image shown in the article as cats and dogs in an alternating AB pattern; one of the students made up a story about the cat and dogs kissing and fighting, etc. Where all the other strategies had failed this one was successful. The students were able to take this model and extend it to many other situations and stories. Eventually the students were able to successfully use pattern blocks to present many things, assign meaning and tell a story. The key to the strategies success is that it allows the students to assign meaning to an otherwise meaningless activity.
Application
I feel that this article is a wonderful example of how a reflective teacher solves a problem in the classroom. Dubon’s students did not understand the material the way that she approached it, so she approached it a different way and sought the help and guidance that she needed. It can be difficult for a teacher to admit that she dose not know how to help her students and I feel that it is a mark of professionalism to admit when you need help. This article is also very helpful in that it reminds teachers that what we teach must always carry meaning in students lives. The best lessons appeal to student’s interests and common knowledge, are holistic and allow students to participate in a meaningful way. In this article the students spend a lot of time coming up with the problems that they then solved; which, in part was why they remembered the material.
Dubon, L. and Shafer, G. (2010). Storyboards for meaningful patterns. Teaching Children Mathematics. 16(6) 325.
This article is about Dubon, a Novice teacher who works in a kindergarten classroom in a Title 1 school in northwestern Indiana. While the class frequently uses patterns and predictability, in classroom management as well as in following the daily routine, the students were unable to generate patterns on their own and were not able to discuss or talk about the patterns that they saw or had created. Dubon’s principal eventually paired her with a professor, Shafer, from the local college who arrived at the school armed with manipulatives and ideas on how to teach the children patterns. Initially, Shafer tested the student’s ability to generate a simple pattern, a topic that they had studied in class; few of the students were able to perform the task. So Shafer began her lesson, she used multiple examples using, people (boy-girl-boy-girl), sounds (snap, clap, snap, clap) and other patterns. She then introduced storyboards to the children. The storyboards require the students to start story problems and then introduce the snap cubes as a way to visually represent the objects in the story. The image shown in the article as cats and dogs in an alternating AB pattern; one of the students made up a story about the cat and dogs kissing and fighting, etc. Where all the other strategies had failed this one was successful. The students were able to take this model and extend it to many other situations and stories. Eventually the students were able to successfully use pattern blocks to present many things, assign meaning and tell a story. The key to the strategies success is that it allows the students to assign meaning to an otherwise meaningless activity.
Application
I feel that this article is a wonderful example of how a reflective teacher solves a problem in the classroom. Dubon’s students did not understand the material the way that she approached it, so she approached it a different way and sought the help and guidance that she needed. It can be difficult for a teacher to admit that she dose not know how to help her students and I feel that it is a mark of professionalism to admit when you need help. This article is also very helpful in that it reminds teachers that what we teach must always carry meaning in students lives. The best lessons appeal to student’s interests and common knowledge, are holistic and allow students to participate in a meaningful way. In this article the students spend a lot of time coming up with the problems that they then solved; which, in part was why they remembered the material.
Dubon, L. and Shafer, G. (2010). Storyboards for meaningful patterns. Teaching Children Mathematics. 16(6) 325.
Wednesday, February 3, 2010
PBL Student Work Analysis
1-1) Creating Candy- imagine that you are a candy company who is struggling to compete with another company who has just released their most successful candy ever! That is the problem the fifth grade students in my first selection were asked to do. The students needed to determine what kind of candy they were going to create, based on consumer feedback, how it should be packaged, and how much they can charge for their candy.
1-2) After School Special: A PBL Unit for Grades 7th- 8th-in this PBL a group of students is being asked to design a space in their town’s community center. The center is designating the space to be used as a teen center; however, they do not know what the space should become. They are eliciting the help of local teenagers to create a plan that is educational and yet recreational. The students need to budget, create a floor plan, determine what materials will be needed and be ready to defend why their plan was the best.
1) The two plans are very different. In the Creating Candy PBL one of the strengths was the range of mathematic objectives and extension objectives. Overall, the Candy group put a lot of detail and guidance in the project, which allows for the wide range of math concept covered. However, there are a couple of weaknesses in the project. The group’s guided questions were not very helpful. The guided questions are intended to prompt students when they are stuck or confused. The guided question in this project more or less reiterated the instructional goals of the assignment. Furthermore, the group left very little flexibility in the assignment, every day was meticulously planned out, perhaps so much that it began to detract from the meaning of the assignment. The second PBL, After School Special, was strong in that it allowed for a lot of creativity and independence though out the entire process. This group chose to incorporate journaling, as a means of assessing the students reasoning methods and justification for their decisions regarding the youth wing. Each day of their lesson outline included the activities and the possible guided questions that would be helpful to the students as they worked through the process. Overall I felt that the After School Session PBL is a cohesive project, I didn’t recognize any major flaws in the assignment.
2) The Creating Candy PBL is a very restrictive PBL assignment. However, After School Special allows the students a lot of independence and flexibility in their work. At this point I don’t know what level of flexibility is best for students; however, it is clear that these two groups choose two very different approaches to this assignment. When comparing the two PBL’s I noticed a substantial difference in the way each group incorporated mini lessons in the overall project. I felt that the Creating Candy mini lessons did not fit well with the flow of the project; whereas, the budgeting assignment in the After School Special PBL, was a logical assignment that helped the students complete the rest of the project.
3) In general I feel that both assignments are rather restrictive. My understanding of the Problem Based Learning assignment is that it should allow students flexibility and creativity. In the second project, the School Special PBL, the group used journaling to help make the students accountable for their work. I like this idea; however, I would change the assignment a bit, I would have the students keep a learning log, all their mathematic problems and scratch work would be done in their learning logs and the students would write their feelings, reactions and frustrations. This would also help the teacher have a log of the areas of the project that were problematic which might need revision in the future.
4) In the Creating Candy the students were clearly focused on incorporating as many mathematic concepts as possible. There are many content standards involved in the project; however, the group seemed to neglect the many process standards, they are clearly present in the work; however, the group did not call attention to them or specifically assess them. In the second project, After School Special, it’s clear that the students were attentive to both the content standards and the process standards; each was addressed numerous times in three separate rubrics that the students created to assess the PBL.
5) The Creating Candy PBL was very thorough in assessing all the mathematics objectives that were taught in the lesson. However, there are some specific problems with the rubric. For instance students who have earned an “excellent” in the rubric must have demonstrated “much evidence” supporting the mathematic topics covered. I question a teacher’s ability to measure “much evidence.” My experience is that rubrics should be much more explicit. However, in the second group no specific mathematic concepts are assessed, merely that the group was neat, organized and that their final product was effective.
1-2) After School Special: A PBL Unit for Grades 7th- 8th-in this PBL a group of students is being asked to design a space in their town’s community center. The center is designating the space to be used as a teen center; however, they do not know what the space should become. They are eliciting the help of local teenagers to create a plan that is educational and yet recreational. The students need to budget, create a floor plan, determine what materials will be needed and be ready to defend why their plan was the best.
1) The two plans are very different. In the Creating Candy PBL one of the strengths was the range of mathematic objectives and extension objectives. Overall, the Candy group put a lot of detail and guidance in the project, which allows for the wide range of math concept covered. However, there are a couple of weaknesses in the project. The group’s guided questions were not very helpful. The guided questions are intended to prompt students when they are stuck or confused. The guided question in this project more or less reiterated the instructional goals of the assignment. Furthermore, the group left very little flexibility in the assignment, every day was meticulously planned out, perhaps so much that it began to detract from the meaning of the assignment. The second PBL, After School Special, was strong in that it allowed for a lot of creativity and independence though out the entire process. This group chose to incorporate journaling, as a means of assessing the students reasoning methods and justification for their decisions regarding the youth wing. Each day of their lesson outline included the activities and the possible guided questions that would be helpful to the students as they worked through the process. Overall I felt that the After School Session PBL is a cohesive project, I didn’t recognize any major flaws in the assignment.
2) The Creating Candy PBL is a very restrictive PBL assignment. However, After School Special allows the students a lot of independence and flexibility in their work. At this point I don’t know what level of flexibility is best for students; however, it is clear that these two groups choose two very different approaches to this assignment. When comparing the two PBL’s I noticed a substantial difference in the way each group incorporated mini lessons in the overall project. I felt that the Creating Candy mini lessons did not fit well with the flow of the project; whereas, the budgeting assignment in the After School Special PBL, was a logical assignment that helped the students complete the rest of the project.
3) In general I feel that both assignments are rather restrictive. My understanding of the Problem Based Learning assignment is that it should allow students flexibility and creativity. In the second project, the School Special PBL, the group used journaling to help make the students accountable for their work. I like this idea; however, I would change the assignment a bit, I would have the students keep a learning log, all their mathematic problems and scratch work would be done in their learning logs and the students would write their feelings, reactions and frustrations. This would also help the teacher have a log of the areas of the project that were problematic which might need revision in the future.
4) In the Creating Candy the students were clearly focused on incorporating as many mathematic concepts as possible. There are many content standards involved in the project; however, the group seemed to neglect the many process standards, they are clearly present in the work; however, the group did not call attention to them or specifically assess them. In the second project, After School Special, it’s clear that the students were attentive to both the content standards and the process standards; each was addressed numerous times in three separate rubrics that the students created to assess the PBL.
5) The Creating Candy PBL was very thorough in assessing all the mathematics objectives that were taught in the lesson. However, there are some specific problems with the rubric. For instance students who have earned an “excellent” in the rubric must have demonstrated “much evidence” supporting the mathematic topics covered. I question a teacher’s ability to measure “much evidence.” My experience is that rubrics should be much more explicit. However, in the second group no specific mathematic concepts are assessed, merely that the group was neat, organized and that their final product was effective.
How to but a car 101. Problem Based Learning in Action
1) This journal article was about a middle school class, who used Problem Based Learning to work on and solve a problem that would interest them; selecting a car to purchase. The students were presented with very specific restrictions, Mr. Jones, their ‘client’ needed to buy a car that would be affordable on his budget, have good gas mileage and be appropriate for Mr. Jones and his wife. The project was full of mathematic content. The students had to determine Mr. Jones’s monthly payments, which included the price of gas and take into account the interest rate. The project was involved, holistic and the students were engaged and excited about it. One of the most challenging things for the teacher is learning to let the students work on their own and not giving them the answers; rather, the teacher needs to act as a facilitator and resource.
2) The article definitely addressed the strengths and weakness of the project. Firstly, the teacher needs to have established an environment where the students are capable of working independently with others. Secondly, the teacher must learn restraint and allow the students to struggle and make decisions on their own. Finally, the project requires very specific assessment tools, if the teacher is not clear about the requirements initially the students will struggle. The teacher must be attentive to the point which the students struggle with and make alterations as the project develops which is a process which takes a lot of time and effort. As a reader, I appreciate all the visuals that the author included in the article. It defiantly helps me to visualize and understand the process and final products when I see examples.
3) APA Citation: Flores, C. (2006). How to buy a car 101. The National Council of Teachers of Mathematics. 12(3), 161-164.
2) The article definitely addressed the strengths and weakness of the project. Firstly, the teacher needs to have established an environment where the students are capable of working independently with others. Secondly, the teacher must learn restraint and allow the students to struggle and make decisions on their own. Finally, the project requires very specific assessment tools, if the teacher is not clear about the requirements initially the students will struggle. The teacher must be attentive to the point which the students struggle with and make alterations as the project develops which is a process which takes a lot of time and effort. As a reader, I appreciate all the visuals that the author included in the article. It defiantly helps me to visualize and understand the process and final products when I see examples.
3) APA Citation: Flores, C. (2006). How to buy a car 101. The National Council of Teachers of Mathematics. 12(3), 161-164.
Problem Based Learning
Problem based learning is really a holistic approach of teaching. I have personally experienced problem based learning in two of my teacher education mathematics classes. However, this is the first time that I have really had to look at the instructional objectives that an instructor would set when designing a problem based learning assignment (from here on referred to as a PBL).
Problem based learning exercises require the students to work on several different skills that are typically aimed at solving a problem outside of the classroom. In some examples I have seen the students were attempting to solve an actual problem that effected their daily lives, in some instances the students were attempting to solve a fictitious problem, and in some instances the students were competing to find the most efficient, most creative or most effective ways of solving the problem.
When a teacher grades the PBL work the assessment is very important. This is a project when the process is as important as the product and the teacher should be aware of how well the group members worked together, how effective their plan or solution was and how creative they were in accommodating the constraints.
Problem based learning can be used in any discipline; however, I especially like its application in mathematics. In science classes I have experiences units when I was completely immersed in the content. Yet, in math courses I rarely spend more than thirty minutes filling out the assigned work sheet. Imagine how much more engaged in mathematics students can become when you make it a project that requires teamwork, discussion and application.
One of my favorite examples of problem based learning was from an article in a science journal. One student was fed up with recess being canceled due to flooding on the playground. The teacher used the situation as an opportunity to have a PBL assignment. He divided the class into teams, assigned budgetary constraints, time constraints, material constraints, labor constraints and asked that the students come up with the most creative use for the diverted water. The students were sent out to collect the data; they measured the slope of the playground and collected all the measurements they needed. Each group proposed their idea and the teacher selected the winning plans. In the end, the students were able to get their playground back as well as have a small pond and water collection tanks for the school’s garden.
Another instance when I have encountered PBL’s is at the Science Olympiad competitions. Students compete in different areas; they build robots, solve simulated crimes, build model cities from the future (solving problem like recycling and exponential population growth), they have even taken the egg drop to the next level. The response that you see from students when you present them with this type of project proves that it is not the mathematics that they don’t like, it’s the way that it’s taught.
Problem based learning is important because it really incorporates all of the process skills. One of the most important things, in my opinion, is that it teaches students perseverance, dedication and when the students are finished there is a huge sense of accomplishment. It promotes that intrinsic motivation, which will help the students be successful even when they are not encourages by parents or by their peers.
Problem based learning exercises require the students to work on several different skills that are typically aimed at solving a problem outside of the classroom. In some examples I have seen the students were attempting to solve an actual problem that effected their daily lives, in some instances the students were attempting to solve a fictitious problem, and in some instances the students were competing to find the most efficient, most creative or most effective ways of solving the problem.
When a teacher grades the PBL work the assessment is very important. This is a project when the process is as important as the product and the teacher should be aware of how well the group members worked together, how effective their plan or solution was and how creative they were in accommodating the constraints.
Problem based learning can be used in any discipline; however, I especially like its application in mathematics. In science classes I have experiences units when I was completely immersed in the content. Yet, in math courses I rarely spend more than thirty minutes filling out the assigned work sheet. Imagine how much more engaged in mathematics students can become when you make it a project that requires teamwork, discussion and application.
One of my favorite examples of problem based learning was from an article in a science journal. One student was fed up with recess being canceled due to flooding on the playground. The teacher used the situation as an opportunity to have a PBL assignment. He divided the class into teams, assigned budgetary constraints, time constraints, material constraints, labor constraints and asked that the students come up with the most creative use for the diverted water. The students were sent out to collect the data; they measured the slope of the playground and collected all the measurements they needed. Each group proposed their idea and the teacher selected the winning plans. In the end, the students were able to get their playground back as well as have a small pond and water collection tanks for the school’s garden.
Another instance when I have encountered PBL’s is at the Science Olympiad competitions. Students compete in different areas; they build robots, solve simulated crimes, build model cities from the future (solving problem like recycling and exponential population growth), they have even taken the egg drop to the next level. The response that you see from students when you present them with this type of project proves that it is not the mathematics that they don’t like, it’s the way that it’s taught.
Problem based learning is important because it really incorporates all of the process skills. One of the most important things, in my opinion, is that it teaches students perseverance, dedication and when the students are finished there is a huge sense of accomplishment. It promotes that intrinsic motivation, which will help the students be successful even when they are not encourages by parents or by their peers.
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