Vincent, M.L. and Wilson, L. (2006). Informal Assessment: A story from the classroom. Mathematics Teacher 89 (2), 284-292.
In this article, Informal Assessment: A Story from the Classroom, Mary Lynn Vincent, a twenty year veteran mathematics teacher, worked in collaboration with Linda Wilson of the University of Delaware to revitalize her means of assessment in the classroom. Vincent experimented with various means of observation and documentation, in the form of rubrics and checklists, to determine a holistic and effective way to document not only the student’s procedural, factual and computations knowledge, as traditionally assessed through written assessments, but to assess their problem solving, communication and critical-thinking skills. In the end, she choose observation and checklist as the preferred means of recording and assessing these skills.
I felt that this article was most useful as the teacher offered excellent examples of how, when and why she choose the types of assessment that she used. Furthermore, she referenced the NCTM standards multiple times throughout the article, indicating that she is attuned to the best teaching practices and makes good pedagogy a daily part of her teaching repertoire. I also appreciated that the author provided examples and non-examples of how to use each strategy. The reader is able to learn through Mary Lynn Vincents mistakes and triumphs in the classroom and apply the information to his/her own subject and grade level.
Wednesday, March 24, 2010
Sunday, March 7, 2010
Assessing Understanding through Reasoning Books
Assessing Understanding through Reasoning Books
Mathematics Teaching in Middle School.
Summary
This article starts in on a very theoretical note. As teachers do we sometimes avoid the difficult questions? Do we choose to opt for the easy answers? Are we doing a disservice to our students? Asking difficult questions gets overlooked because it’s an investment. Asking difficult questions requires time, effort, a deep understanding of the material and adequate exploration and communication.
This article focuses o the use of mathematical reasoning books as a tool which will help students develop vocabulary, reasoning and proof skills, communication skills and a forum in which to explore and answer the “difficult questions.” The introduction on page 408 can be used with students; it illustrates the purpose of the assignment and the format that is to be used. I also think that figure four and five on page 412 can be used to help students with the assignment. Figure 4 is a feedback checklist that students can use to evaluate if their answers and responses are through enough. Figure 5 is a self reflection rubric that will help the teacher and students reflect on the process.
The article is really a series of prompts and student responses. The authors then analyze the student’s responses for understanding. There are student samples at each level of achievement. Some students fell upon the belief that there was not enough information to reach a conclusion, which is typical of students who are struggling when it comes to transferring the information into a new context. Some students had the right idea but lacked the justification to support their answer. Other answers were very sophisticated and showed a true understanding of the question, answer and the terminology.
In conclusion, the mathematical reasoning book is a very useful tool that, when used properly and taught correctly, can be used to assess students reasoning and proof skill at the middle school level.
Application
I liked this article. Seeing the types of errors and understanding why the student made an error is an important step. Furthermore, I was surprised by the degree of difficulty of some of the problems and how well some students preformed with their math reasoning books. However, I am suspicious of the article as a whole because it is clearly a plug for the NCTM Reasoning and Sense Making book. While I liked the questions that were provided as an example I don’t know that I need a text book to teach me this strategy. It seems to me that this article did a fair job explaining the math reasoning book, which is really a glorified learning log. Personally, I have been using this technique in my classroom without an actual notebook. The students have been preparing for their ISAT exams and my novice teacher has been using the opportunity to review the mathematics extended response, which requires the students to defend their problem solving strategies in paragraph form. My teacher uses a t-chart to teach this concept. The students write the problem at the top and use the right column for the math- diagrams, equations, etc and explain what and why they did what they did in the left column. I like this approach. I feel that with the t-chart approach as prior knowledge that it would be fairly easy to teach the students to keep a mathematic reasoning book or leaning log.
Roberts, S. & Tayeh, C. (2010). Assessing understanding through reasoning books. Mathematics Teaching in Middle School. 15(7) 406.
Mathematics Teaching in Middle School.
Summary
This article starts in on a very theoretical note. As teachers do we sometimes avoid the difficult questions? Do we choose to opt for the easy answers? Are we doing a disservice to our students? Asking difficult questions gets overlooked because it’s an investment. Asking difficult questions requires time, effort, a deep understanding of the material and adequate exploration and communication.
This article focuses o the use of mathematical reasoning books as a tool which will help students develop vocabulary, reasoning and proof skills, communication skills and a forum in which to explore and answer the “difficult questions.” The introduction on page 408 can be used with students; it illustrates the purpose of the assignment and the format that is to be used. I also think that figure four and five on page 412 can be used to help students with the assignment. Figure 4 is a feedback checklist that students can use to evaluate if their answers and responses are through enough. Figure 5 is a self reflection rubric that will help the teacher and students reflect on the process.
The article is really a series of prompts and student responses. The authors then analyze the student’s responses for understanding. There are student samples at each level of achievement. Some students fell upon the belief that there was not enough information to reach a conclusion, which is typical of students who are struggling when it comes to transferring the information into a new context. Some students had the right idea but lacked the justification to support their answer. Other answers were very sophisticated and showed a true understanding of the question, answer and the terminology.
In conclusion, the mathematical reasoning book is a very useful tool that, when used properly and taught correctly, can be used to assess students reasoning and proof skill at the middle school level.
Application
I liked this article. Seeing the types of errors and understanding why the student made an error is an important step. Furthermore, I was surprised by the degree of difficulty of some of the problems and how well some students preformed with their math reasoning books. However, I am suspicious of the article as a whole because it is clearly a plug for the NCTM Reasoning and Sense Making book. While I liked the questions that were provided as an example I don’t know that I need a text book to teach me this strategy. It seems to me that this article did a fair job explaining the math reasoning book, which is really a glorified learning log. Personally, I have been using this technique in my classroom without an actual notebook. The students have been preparing for their ISAT exams and my novice teacher has been using the opportunity to review the mathematics extended response, which requires the students to defend their problem solving strategies in paragraph form. My teacher uses a t-chart to teach this concept. The students write the problem at the top and use the right column for the math- diagrams, equations, etc and explain what and why they did what they did in the left column. I like this approach. I feel that with the t-chart approach as prior knowledge that it would be fairly easy to teach the students to keep a mathematic reasoning book or leaning log.
Roberts, S. & Tayeh, C. (2010). Assessing understanding through reasoning books. Mathematics Teaching in Middle School. 15(7) 406.
Paint Bucket Polygons
Paint Bucket Polygons
Teaching Children Mathematics
http://my.nctm.org/eresources/view_media.asp?article_id=9163
Summary
This article is presented as the combined efforts of intermediate-level school teachers and college methods instructors. The group worked together to determine a series of lessons that would help the students develop a more sophisticated understanding of geometric concepts. In this particular lesson the fifth grade class was attempting to build an understanding of polygons and what the characteristic of a polygon are. The goal of the lesson: to use the pain bucket function of popular photo editing software, which is also located in the paint application of virtually every computer, to allow students to explore and build an understanding of polygons. The intent was the students would understand if a shape was not closed due to the fact that the paint would “spill out” and color not only the shape but also the background. Also if a shape had intersecting lines inside the shape only part of the image would be colored. As a result, the students would build an understanding of the closed and similar shapes.
The students gathered together and worked with several prototypes and non prototypes. In this instance popular prototypes are triangles, squares, rectangles and pentagons. Typical non prototypes are crescents and circles. While this can be a useful tool it can greatly limit students thinking and the intent of the lesson was to introduce the shapes and quickly graduate to more complex and less typical shapes. However, there was a more difficulty than expected. The students spent much more time than expected defining the word polygon and had considerably difficulty with distinguishing the prototypes and non prototypes.
Eventually the students were able to get to the main focus of the lesson, the use of the software to explore the attributes of polygons. The students were clearly able to understand the distinction of simple and closed using the software but there were limitations of the software and still areas which would need to be addressed using another medium.
Application
This article brings to light a problem that exists in many instances across Mathematics curriculum. Terms and definitions are used in student text books that are ambiguous and vague. Some texts use language that is clearly not student friendly or is all together too broad. When the authors of this article researched 80 different curricula they identified over 21 different definitions. This is clearly a point of confusion and dissension. If students are going to understand the concepts they need an understanding of the vocabulary and precise, student-friendly definitions. While, I like this lesson as a whole, I am surprised by the general tone of the lesson. The authors present the paint tool like a wonderful, unheard of, very creative approach. I consider paint to be old software and I am surprised by the notion that this is a new or novel idea. As soon as I get to school on Monday I want to see if the same tool can be used on the Smart Board, as I believe it can, as that could be another way to teach this lesson. Furthermore, with software like Geometers Sketchpad and other more student oriented applets and programs I feel that the approach is outdated. Like we’re discussed in class, manipulatives and software can not save the subject if it is to be held back by poorly written definitions, text books and lack of inventiveness with upcoming software and technology.
Edwards, M. & Harper, S. (2010). Paint bucket polygons. Teaching Children Mathematics. 16(7) 420.
Teaching Children Mathematics
http://my.nctm.org/eresources/view_media.asp?article_id=9163
Summary
This article is presented as the combined efforts of intermediate-level school teachers and college methods instructors. The group worked together to determine a series of lessons that would help the students develop a more sophisticated understanding of geometric concepts. In this particular lesson the fifth grade class was attempting to build an understanding of polygons and what the characteristic of a polygon are. The goal of the lesson: to use the pain bucket function of popular photo editing software, which is also located in the paint application of virtually every computer, to allow students to explore and build an understanding of polygons. The intent was the students would understand if a shape was not closed due to the fact that the paint would “spill out” and color not only the shape but also the background. Also if a shape had intersecting lines inside the shape only part of the image would be colored. As a result, the students would build an understanding of the closed and similar shapes.
The students gathered together and worked with several prototypes and non prototypes. In this instance popular prototypes are triangles, squares, rectangles and pentagons. Typical non prototypes are crescents and circles. While this can be a useful tool it can greatly limit students thinking and the intent of the lesson was to introduce the shapes and quickly graduate to more complex and less typical shapes. However, there was a more difficulty than expected. The students spent much more time than expected defining the word polygon and had considerably difficulty with distinguishing the prototypes and non prototypes.
Eventually the students were able to get to the main focus of the lesson, the use of the software to explore the attributes of polygons. The students were clearly able to understand the distinction of simple and closed using the software but there were limitations of the software and still areas which would need to be addressed using another medium.
Application
This article brings to light a problem that exists in many instances across Mathematics curriculum. Terms and definitions are used in student text books that are ambiguous and vague. Some texts use language that is clearly not student friendly or is all together too broad. When the authors of this article researched 80 different curricula they identified over 21 different definitions. This is clearly a point of confusion and dissension. If students are going to understand the concepts they need an understanding of the vocabulary and precise, student-friendly definitions. While, I like this lesson as a whole, I am surprised by the general tone of the lesson. The authors present the paint tool like a wonderful, unheard of, very creative approach. I consider paint to be old software and I am surprised by the notion that this is a new or novel idea. As soon as I get to school on Monday I want to see if the same tool can be used on the Smart Board, as I believe it can, as that could be another way to teach this lesson. Furthermore, with software like Geometers Sketchpad and other more student oriented applets and programs I feel that the approach is outdated. Like we’re discussed in class, manipulatives and software can not save the subject if it is to be held back by poorly written definitions, text books and lack of inventiveness with upcoming software and technology.
Edwards, M. & Harper, S. (2010). Paint bucket polygons. Teaching Children Mathematics. 16(7) 420.
Monday, February 22, 2010
Video #7 Lesson on Graphs
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.
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.
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
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