Cole, K.A. (1999). Walking around: getting more from informal assessment. Mathematics Teaching in the Middle School 4(4), 224-227.
In this article, Walking Around: Getting More From Informal Assessment, the author, Karen A. Cole, addresses walking around the classroom and using frequent informal observation as a component of her teaching approach. Her research was funded by the National Science Foundations in corporation with the Middle School Math through Applications Project. This program was targeted toward middle school mathematics classes and was a comprehensive curriculum that was project-based and student centered. The teacher described the two most important aspects of the process; observation and conference. Observation is fairly straightforward; the teacher must listen to the student’s conversation and stay attuned to potential misconceptions, clarifications and opportunities to ask more in depth and higher order thinking questions.
A possible weakness or problem with this strategy is that it can be very difficult to observe all students equally. Thus, the teacher must be very deliberate when it comes to this type of assessment. The teacher must allow every student the opportunity to talk, provide the students with regular excellent examples of proper discussion and explanation. Furthermore, the teacher can use one-on-one conferences as a time to catch up with students and offer them individualized instruction and attention. I feel that this article might have benefited from some specific suggestions that the author of Informal Assessment: A Story from the Classroom, used. I feel that this technique is more effective if the teacher selects specific students to observe and specific traits to observe.
Wednesday, March 24, 2010
Informal Assessment: A Story from the Classroom
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.
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.
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.
Subscribe to:
Posts (Atom)