Assessments in math can come in all different varieties, just like assessment in any other subject. I remember in middle school we would have daily assessment grades on our homework. In high school we would have homework checks for completion, however homework was a learning tool so we weren't counted off if we had the problem wrong. We were supposed to learn from our mistakes so we could be successful on the tests and quizzes.
In math methods we have learned many more assessment styles and tools other than homework grades, quizzes, and tests. There is a big push for switching classrooms over to inquiry based learning. This learning style is best assessed by a rubric. In methods we have learned about the importance of a strong rubric that isn't biased and the level on the rubric should be clear. I think performance based assessments and portfolio assessments are a great way to assess students. Performance based allows students to take the knowledge of the topic and apply it to a real world situation. Portfolio assessments allow students to see the physical growth of their learning by collecting various assignments throughout the semester or year. These assignments are much more meaningful to students because they are applying what they have learned. The traditional tests and quizzes are also of value, however these mainly assess memorization and don't represent the depth of knowledge a student may have when compared to all the levels of Bloom's Taxonomy.
In my classroom I want to have a variety of assessments for mathematics. Many students get discouraged in a math class, and with allowing students to see the connections of math to the real world, they will have a much better appreciation for the subject.
Thursday, June 25, 2015
Error Reflection
In class we explored different math problems done by students. Each student modeled a different error within solving the problem. Since I am a math concentration, I find this really interesting. I enjoyed looking at each student's work and analyzing it for where they made a mistake. This is something I will have to be comfortable with when I begin teaching math whether it is at the middle school level or at the elementary level.
I thought this assignment was very similar to the NAEP reteach assignment. The only difference was that the NAEP assignment all students were solving the same problem, whereas this assignment each student was solving a different problem.
I thought this assignment was very similar to the NAEP reteach assignment. The only difference was that the NAEP assignment all students were solving the same problem, whereas this assignment each student was solving a different problem.
Tuesday, June 23, 2015
Assessment Readings
Open-Ended: This article talks about using open-ended problems to assess math students' work. I like this idea, because with the many possible solutions to the problem, students may think outside the box to find a strategy to solve the problem. Open-ended problems allow teachers to see the students thinking process and allows them to help the students where they struggle.
Options: This article talks about the different ways math can be assessed. This is often referred to as the menu choice. This article mentions how even though multiple choice may be an okay assessment, performance assessments with accurate rubrics are a much better tool to assess whether or not a student is able to apply the information in a real life situation.
Reasoning: This article is about students' ability to problem solve in mathematics. The teacher in the article had students explain what area was in their own words. This allowed the teacher to see what each student was thinking and how they were able to think or reason throughout the problem based on what the student wrote.
Conversation: This article discusses the importance of assessing student conversations. In the example used in the article, a teacher was able to understand that the students didn't know the properties of rectangles. Then the teacher was able to do an impromptu lesson on what is considered a rectangle before moving on with the area lesson. I think assessing conversations is a great way to assess vocabulary terms. This way teachers will know if students know the correct terms and the teachers are able to clarify to make the topic more clear.
Portfolio: This article is about a teacher implementing the use of portfolios in her classroom. Portfolios are an important tool that allow teachers as well as students and parents to see the mathematical growth of the child. I love this idea of having a folder where the student can reflect back on their work. I also liked how this teacher used a certain criteria to assess the portfolio so that this was a project that encouraged the students in mathematics, instead of discouraging them.
Options: This article talks about the different ways math can be assessed. This is often referred to as the menu choice. This article mentions how even though multiple choice may be an okay assessment, performance assessments with accurate rubrics are a much better tool to assess whether or not a student is able to apply the information in a real life situation.
Reasoning: This article is about students' ability to problem solve in mathematics. The teacher in the article had students explain what area was in their own words. This allowed the teacher to see what each student was thinking and how they were able to think or reason throughout the problem based on what the student wrote.
Conversation: This article discusses the importance of assessing student conversations. In the example used in the article, a teacher was able to understand that the students didn't know the properties of rectangles. Then the teacher was able to do an impromptu lesson on what is considered a rectangle before moving on with the area lesson. I think assessing conversations is a great way to assess vocabulary terms. This way teachers will know if students know the correct terms and the teachers are able to clarify to make the topic more clear.
Portfolio: This article is about a teacher implementing the use of portfolios in her classroom. Portfolios are an important tool that allow teachers as well as students and parents to see the mathematical growth of the child. I love this idea of having a folder where the student can reflect back on their work. I also liked how this teacher used a certain criteria to assess the portfolio so that this was a project that encouraged the students in mathematics, instead of discouraging them.
Thursday, June 18, 2015
2 Articles from our Groups
My first article was: Strategies to Support Productive Struggle. This article explains how teachers should approach students when students don't know how to start a problem, don't know how to continue on with a problem, or if they know the answer but can't explain why. This article showed many examples of dialogue between a teacher and a confused student. In each of the situations, the teacher used guiding questions to help the students break down the more difficult problem into a more simple problem until the student was able to comprehend the problem and move on.
I think this was a nice article on guiding questions. This provides examples for me that I can use as a reference for when I begin teaching. The article also included a chart that explained teacher questions vs. student questions.
My second article was: Counting on Using a Number Game. This article explains the difference between counting all and counting on. Counting all is when a student is given two numbers such as 4 and 2. The student would count, "one two three four, (then move to the next card) five six" to get the total number when these numbers are added together. Counting on is when a student is given the same two cards the student would say, " five six". The student would understand that four was already given to them and would know the number sequencing for the next two numbers.
I liked this article because it was geared towards younger students. With math I usually only work with upper elementary or middle school criteria because I am a math concentration and I will have a middle school endorsement. Having articles will give me resources to use if I do end up teaching in the younger grade levels.
I think this was a nice article on guiding questions. This provides examples for me that I can use as a reference for when I begin teaching. The article also included a chart that explained teacher questions vs. student questions.
My second article was: Counting on Using a Number Game. This article explains the difference between counting all and counting on. Counting all is when a student is given two numbers such as 4 and 2. The student would count, "one two three four, (then move to the next card) five six" to get the total number when these numbers are added together. Counting on is when a student is given the same two cards the student would say, " five six". The student would understand that four was already given to them and would know the number sequencing for the next two numbers.
I liked this article because it was geared towards younger students. With math I usually only work with upper elementary or middle school criteria because I am a math concentration and I will have a middle school endorsement. Having articles will give me resources to use if I do end up teaching in the younger grade levels.
Tuesday, June 16, 2015
Video 2 Reflection
This video started right in with the lesson. I was in the same position as the students because I didn't know what direction the video would take. The first video grouping had a meeting when teachers went over what the lesson would be about and how she would go about teaching the students. I liked how she was trying to get the student to use the term grouping when explaining the work regarding multiplication and division. I also liked how the teacher gave the students to share their ideas with their neighbor. I think these students need a lesson on mathematics terms and vocabulary. When listening to the students' ideas, you could tell some students really didn't know what some terms meant and in other times they would use the wrong word in replace of another term.
I liked how the teacher tied in "A picture is worth a thousand words" into the lesson for drawing a picture to explain their math, however she never explained what the quote really meant to those who didn't understand it. I liked seeing the engagement of the students during the lesson. They were able to drawn their own pictures and then had to explain how the picture related to the story problem. I also liked Charlie's way. I think the diagram could have been written in a clearer way so that the students could better understand what each of the boxes represented. Maybe next time the boxes could have labels such as Maria's money with her boxes, Wayne's money with his boxes, and then the words total money and a box to represent all of their money. The brackets in the initial diagram would have really confused me if I were a 4th grader. I like how in the debrief other teachers commented on the lack of a vocabulary foundation, the engagement during the lesson, and how some of the diagrams got the right answer, but the diagram did not explain what the math story was. If I were to teach this lesson, I would really emphasize the importance of pictures when doing math problems. I would also emphasize the importance of their connection to the math problem. The picture does no good if it doesn't show what is happening in the problem.
I liked how the teacher tied in "A picture is worth a thousand words" into the lesson for drawing a picture to explain their math, however she never explained what the quote really meant to those who didn't understand it. I liked seeing the engagement of the students during the lesson. They were able to drawn their own pictures and then had to explain how the picture related to the story problem. I also liked Charlie's way. I think the diagram could have been written in a clearer way so that the students could better understand what each of the boxes represented. Maybe next time the boxes could have labels such as Maria's money with her boxes, Wayne's money with his boxes, and then the words total money and a box to represent all of their money. The brackets in the initial diagram would have really confused me if I were a 4th grader. I like how in the debrief other teachers commented on the lack of a vocabulary foundation, the engagement during the lesson, and how some of the diagrams got the right answer, but the diagram did not explain what the math story was. If I were to teach this lesson, I would really emphasize the importance of pictures when doing math problems. I would also emphasize the importance of their connection to the math problem. The picture does no good if it doesn't show what is happening in the problem.
Sunday, June 14, 2015
NAEP Reflection
I enjoyed this project. This project is really realistic to what I will be doing as a teacher in the future because I am a math concentration. I enjoyed looking at all of the student work samples and giving them individual feedback on how they could improve their work. Through the process I learned about the importance of a good rubric. The rubrics we were supposed to use were confusing and each person could have given the same student a completely different grade. Rubrics should be so straight forward that it shouldn't matter who grades the work, that the student will always get the same grade because the rubric allows for no guessing.
Thursday, June 11, 2015
Math Apps and Applets Geometry 6-8th Grade
1. The first applet I found is for teaching students about reflections.
http://nlvm.usu.edu/en/nav/frames_asid_206_g_1_t_3.html?open=activities&from=topic_t_3.html
Students can insert different shapes and drag the shapes around to see what the reflection looks like. Axes can be added to have the four quadrants with reflection. The reflection line can also be altered to be at any angle.
I think this is a great applet. It is really user friendly and allows the students to see what the reflection of many shapes would be.
2. The second applet I found is a geoboard for coordinate planes.
http://nlvm.usu.edu/en/nav/frames_asid_303_g_3_t_3.html?open=activities&from=topic_t_3.html
Each page in the geoboard instructs the students on what they are supposed to create. Once the students finish it they can move on to the next problem.
I think this is a fun applet. It is easy to use and is a great way to use geoboards and coordinate planes if these are not available in the classroom.
3. The app I found is a video geometry tutor app.
https://itunes.apple.com/us/app/video-geometry-tutor/id411902469?mt=8
This app has 80 videos teaching the many different aspects of geometry from points and lines to the Pythagorean theorem. Students would be able to access these videos anywhere and don't need access to the internet to do so.
This app is $1.99 to purchase. I think this would be worth the money to have downloaded to tablets for each student to use. This could be a very helpful resource for many teachers, students, and parents.
http://nlvm.usu.edu/en/nav/frames_asid_206_g_1_t_3.html?open=activities&from=topic_t_3.html
Students can insert different shapes and drag the shapes around to see what the reflection looks like. Axes can be added to have the four quadrants with reflection. The reflection line can also be altered to be at any angle.
I think this is a great applet. It is really user friendly and allows the students to see what the reflection of many shapes would be.
2. The second applet I found is a geoboard for coordinate planes.
http://nlvm.usu.edu/en/nav/frames_asid_303_g_3_t_3.html?open=activities&from=topic_t_3.html
Each page in the geoboard instructs the students on what they are supposed to create. Once the students finish it they can move on to the next problem.
I think this is a fun applet. It is easy to use and is a great way to use geoboards and coordinate planes if these are not available in the classroom.
3. The app I found is a video geometry tutor app.
https://itunes.apple.com/us/app/video-geometry-tutor/id411902469?mt=8
This app has 80 videos teaching the many different aspects of geometry from points and lines to the Pythagorean theorem. Students would be able to access these videos anywhere and don't need access to the internet to do so.
This app is $1.99 to purchase. I think this would be worth the money to have downloaded to tablets for each student to use. This could be a very helpful resource for many teachers, students, and parents.
Tuesday, June 9, 2015
article 2
Thinking through a Lesson: Successfully Implementing High-Level Tasks.
This article starts off with a math problem about different bags with different amounts of red and blue marbles. The students are to determine the fractions of each, the percent of blue marbles, to scale up the ratios so all bags contain the same amount of blue marbles and so on. These types of problems are ones that don't have a required way to solve them. Students could be creative and solve these questions in any different ways from their neighbors. The rest of the article discusses TTLP, or Thinking Through a Lesson Protocol. This involves the teachers thinking about what questions they want to ask their students prior to the lesson plan as well as the teachers thinking and listing out all the possible ways students may: solve the problem, run into trouble and not know how to continue, or possible common errors students may make.
I thought this article had a lot of great information for current math teachers as well as students training to become teachers. Its important for teachers to realize that math problems can be solved in a variety of ways. So by the teachers solving the problem in these different ways will allow class time and questions to run more smoothly.
This article starts off with a math problem about different bags with different amounts of red and blue marbles. The students are to determine the fractions of each, the percent of blue marbles, to scale up the ratios so all bags contain the same amount of blue marbles and so on. These types of problems are ones that don't have a required way to solve them. Students could be creative and solve these questions in any different ways from their neighbors. The rest of the article discusses TTLP, or Thinking Through a Lesson Protocol. This involves the teachers thinking about what questions they want to ask their students prior to the lesson plan as well as the teachers thinking and listing out all the possible ways students may: solve the problem, run into trouble and not know how to continue, or possible common errors students may make.
I thought this article had a lot of great information for current math teachers as well as students training to become teachers. Its important for teachers to realize that math problems can be solved in a variety of ways. So by the teachers solving the problem in these different ways will allow class time and questions to run more smoothly.
Article 1
A Model for Understanding: Understanding in Mathematics.
This article is all about how students are able to understand mathematics. The author, Edward J. Davis, created a list of items that people must be able to do in order to understand a topic. These were a list of seven things like, state in own words, state the opposite of the item, and give examples of it. Davis went on to saying that these items do not complete the list of items needed in order to thoroughly understand a topic. I like the format of the article how he would explain one of the items needed in order to understand, and then he would have a chart of questions and examples that would go along with the point needed for understanding the topic.
This is a beneficial article for math teachers because students all understand topics in various ways. With having these tools to help see whether or not a student has grasped the concept, students will be more successful in mathematics in the long run. If a teacher notices that the students do not understand the topic, they will change their teaching style so that everyone is able to get the math concept.
This article is all about how students are able to understand mathematics. The author, Edward J. Davis, created a list of items that people must be able to do in order to understand a topic. These were a list of seven things like, state in own words, state the opposite of the item, and give examples of it. Davis went on to saying that these items do not complete the list of items needed in order to thoroughly understand a topic. I like the format of the article how he would explain one of the items needed in order to understand, and then he would have a chart of questions and examples that would go along with the point needed for understanding the topic.
This is a beneficial article for math teachers because students all understand topics in various ways. With having these tools to help see whether or not a student has grasped the concept, students will be more successful in mathematics in the long run. If a teacher notices that the students do not understand the topic, they will change their teaching style so that everyone is able to get the math concept.
Friday, June 5, 2015
Rich Task Reflection
I enjoyed all three of the rich task lessons. The first activity with the coins is definitely something I would use if I teach math to younger students. These sticks with coins could be used in many different ways by altering the activity to have it coordinate with a slightly different math task. The second activity with the surface area measurement was a very cute idea. I could definitely see the students getting engaged and enjoying the math activity. I thought the Barbie activity was a great way to show students how to scale up an item by using ratios and rates. Overall, all three had many positives to only one or two negatives. These would be great activities to incorporate into math classrooms for students to be engaged in math.
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