Monday, June 29, 2015
Error Analysis Reflection
After looking and completing the error analysis of problem found in more errors I found it beneficial. I realized after looking into this, this will be something that I will be doing with my students. It is important to find the errors and common mistakes that students are making. Once you can determine the errors the students are making then you can help them fix the problem and explain to them why they are doing it wrong. It is important as a teacher to be able to do this because you want the students to have a valuable learning experience. If you don't catch the errors in the beginning the students will continue to make the same errors and get in a bad habit.
Wednesday, June 24, 2015
Classroom Changes Reflection
As students move through the grade k-8 there are classroom changes. For one, the math concepts build on each other and get more advanced at each grade level. We can see that they continue to build off each other in the Common Core standards. At the younger grades, students are asked to use pictures and words to explain how they got their answer. Students are asked to do this because this allows them to demonstrate they know the answer. As grades builds students are asked to show their calculations and work. Students are then also have to apply what they know about math to the real world. Technology and manipulates is also used throughout the grades. Students start using basic manipulates and technology when they are young. When students get older they used more advanced tools such as a protractor and compass. Throughout all of the grades though, students are to be engaged and always being able to explain their mathematical thinking.
Technology Reflection
During this class I discovered that technology has really grown from when I was in elementary school. There is so many cool things that we can use as teachers to help students grow. The coolest thing that we worked with is the smart board. There are endless things that you can use on the smart board to enhance your lesson. I hope that one day that I have a smart board to work with. It is very interactive. Another thing we discussed in class is apps and applets. I realized that is an app for everything! I will definitely use apps when I am a teacher. Apps and applets allow for students to deepen their understanding through interactive games and supports. It is another more fun way for students to learn a concept rather than using paper and pencil. We used prezi, jing, and videos in the class. These are also nice things to use in the class. As a teacher I could create an interactive prezi with a voice recording like our first project to show to the class. It would be something differernt than just lecturing a class. Videos are also fun projects for students to create and use their creative and artistic abilities. It would show students understand a topic through video presentation. Calculators are also a nice technology to have in the classroom. Although, I would not have students use calculators until students knew how to do a problem and be able to explain how to do it. Calculators are convenient to use and most everyone has one on their cell phone. It is important that students learn how to use a calculator.
Manipulative Reflection
In class I enjoyed exploring the different types of manipulative in class. I discovered that you can use a manipulative in so many ways! All grades and different math concepts can be benefit from using the manipulative. I am a hands-on learner so I really understand why students like to use these. It is visually appealing and allows for students to deepen their undressing of a concept or use the manipulative to be able to understand a concept. I know that students are deepening their understanding of a topic if the student can transfer what they learned on paper and through lecture into the manipulative. For example, the student would be able to show what 2 times 4 looks like using snap cubes. You can assess their understanding by if the student uses a manipulative correctly and is able to show and explain what he or she did with the manipulative. When students work in groups I think the students will tend to want to play with the manipulative. I noticed that even myself wanted to play with the manipulative. So to make sure that students are accountable walk around the classroom making sure students are working and have the students complete a worksheet along with the manipulative so that you know if the student was working or not working. Working with manipulative allows for students to work on their problem solving skills because they have to solve problems using the manipulative. It allows for students to transfer what they work on paper on to the into a manipulative.
Journal Entries
Assessing for Learning
This article focuses on assessment of learning. With the new common core standards assessment are changing. To provide for meaningful assessment items it is helpful to organize expectations of students into learning levels. The learning levels are, construct a concept, discover a relationship, simple knowledge, comprehension and communication, algorithmic skill, application, and creative thinking. These levels describes the types of thinking that are required to learn mathematics. Each level progresses. Each level is assessed a little differently. The CCSSM standards call for a wider range of assessments. Teachers whole follow this model and create their own assessments will cater to the students as individuals.
I thought this article was very relevant and useful. I think that it is logical to organize assessments into learning levels. Each student might be a different learning level so assessing at their level would make most sense. It would help the student succeed in math. I also agree with this article that it is important for teachers to start creating their own assessments. If teachers create their own assessments they will cater to what the students need. And that is the most important thing to do as a teacher.
Area Beyond Formula
Walter Stark is a teacher that had his students explore a the Area beyond the Formula problem to asses the students understanding of the mathematical ideas. He started out with a discussion before giving the students the problem. Students were separated into groups. They were given a notecard and had to determine how many of the notecards would it take to fill up the poster board. Each group presented their strategies to the class. He found that some students had similar strategies while others had different approaches.
I thought this article was interesting. It was interesting to read the different strategies that the students came up with. There were some that I didn't even think of! This type of activity would be really beneficial to students because it allows them to think more deeply about the mathematical ideas. It goes beyond pencil and paper. I also liked that the teacher included many discussions. This allowed for students to generate more ideas. I would like to do something like this in my class one day. It is cool to read about how students are really engaged in an activity and like to learn.
This article focuses on assessment of learning. With the new common core standards assessment are changing. To provide for meaningful assessment items it is helpful to organize expectations of students into learning levels. The learning levels are, construct a concept, discover a relationship, simple knowledge, comprehension and communication, algorithmic skill, application, and creative thinking. These levels describes the types of thinking that are required to learn mathematics. Each level progresses. Each level is assessed a little differently. The CCSSM standards call for a wider range of assessments. Teachers whole follow this model and create their own assessments will cater to the students as individuals.
I thought this article was very relevant and useful. I think that it is logical to organize assessments into learning levels. Each student might be a different learning level so assessing at their level would make most sense. It would help the student succeed in math. I also agree with this article that it is important for teachers to start creating their own assessments. If teachers create their own assessments they will cater to what the students need. And that is the most important thing to do as a teacher.
Area Beyond Formula
Walter Stark is a teacher that had his students explore a the Area beyond the Formula problem to asses the students understanding of the mathematical ideas. He started out with a discussion before giving the students the problem. Students were separated into groups. They were given a notecard and had to determine how many of the notecards would it take to fill up the poster board. Each group presented their strategies to the class. He found that some students had similar strategies while others had different approaches.
I thought this article was interesting. It was interesting to read the different strategies that the students came up with. There were some that I didn't even think of! This type of activity would be really beneficial to students because it allows them to think more deeply about the mathematical ideas. It goes beyond pencil and paper. I also liked that the teacher included many discussions. This allowed for students to generate more ideas. I would like to do something like this in my class one day. It is cool to read about how students are really engaged in an activity and like to learn.
NAEP Reflection
I thought this assignment was very beneficial. It taught me that it can be difficult to grade students work when the rubric is so vague. It taught me that when you create a rubric that it shouldn't be a vague and that someone else that reads it would be able to grade the students work. Looking at all the students wok my group had a lot of discussion. We disagreed upon a couple of what we thought the students deserved. This shows that the rubrics could be interpreted a couple of different ways. I thought of differently than what my groups members thought. It was hard to come to an agreement on some of the students work. I noticed that I tended to give the students higher grades. This assignment also allowed me to stretch my mind to think how I could help the students that were not understanding the questions. As a teacher it is important to be able to help the students to understand what they are not.
Math Applet/Apps Review
Math Applet: Equivalent Fractions
http://illuminations.nctm.org/Activity.aspx?id=3510
In this math applet students have to create two other fractions that are equivalent to the given fraction. There are two boxes, blue and green that students can use to fill in to make a fraction. Students have to make two fractions that have different denominators. The fraction that the students create move along a number line so students can visually see where the fraction they make relate to the fraction the computer gives.
I like this applet because it is interactive and visually appealing. I like that students can see that 1/2 looks the same as 2/4 and 3/6. Students can see this because students fill in boxes as they can see on the number line that the fractions go in the same place. Students who struggle with equivalent fractions I believe would benefit from this. Teachers can use this applet on the smart board so that students can see it and interact with it. Students can also do this on the computer if the teacher doesn't have a smart board.
Math App: Fractions by Brainingcamp
https://itunes.apple.com/us/app/fractions-by-brainingcamp/id471353363?mt=8
This app allows students to work with fractions. There is narrated lessons, virtual manipulatives, fraction activities, practice questions, and interactive challenges. The topics the app covers are fractions introduction, equivalent fractions, common denominators, comparing and ordering fractions, adding and subtraction fractions, multiplying fractions, and dividing fractions. The app is free on the iTunes store. The app has visual models with audio narration. There is questions to practice what has been learned. It is very hands-on because there is manipulatives. Students can apply there understanding through the challenges. It even aligns with the common core.
I think this is a great app! It has everything a student needs to practice fractions. I like that it is very interactive and hands-on. It also allows students to apply their understanding of their learning through challenges. This app would be great to have on iPads for students in the classroom. The app can be downloaded for free which is another bonus of the app. The students can start using the app when fractions are introduced and then continue to use the app when new topics are introduced. Student could use this app in their free time or after they are introduced a lesson.
Math App: 5th Grade Splash Math
https://itunes.apple.com/us/app/splash-math-grade-5/id504807361?mt=8
This app is an innovative and fun way to practice math. There is 9 chapters that cover endless supply of lessons. It is the 2011 "Best Elementary App" winner. There is interactive content, personalized learning, weekly email reports (to track your students learning), and a scratch pad for students to use for their rough work. The topics covered include, place value, number sense, algebra expressions, multiplication, division, fractions, decimals, measurement, and geometry.
I like this app because it contains topics the students will be practicing throughout the whole year. It is interactive which students love. I also really like that it has weekly email reports so that the teacher can track the student learning. The teachers can see if the students are understanding the topics in class. This would be very valuable. This app is free so it wouldn't cost anything to download. Students could practice what they learn in class on their iPads. The app fits in with the common core state standards which is also very good.
http://illuminations.nctm.org/Activity.aspx?id=3510
In this math applet students have to create two other fractions that are equivalent to the given fraction. There are two boxes, blue and green that students can use to fill in to make a fraction. Students have to make two fractions that have different denominators. The fraction that the students create move along a number line so students can visually see where the fraction they make relate to the fraction the computer gives.
I like this applet because it is interactive and visually appealing. I like that students can see that 1/2 looks the same as 2/4 and 3/6. Students can see this because students fill in boxes as they can see on the number line that the fractions go in the same place. Students who struggle with equivalent fractions I believe would benefit from this. Teachers can use this applet on the smart board so that students can see it and interact with it. Students can also do this on the computer if the teacher doesn't have a smart board.
Math App: Fractions by Brainingcamp
https://itunes.apple.com/us/app/fractions-by-brainingcamp/id471353363?mt=8
This app allows students to work with fractions. There is narrated lessons, virtual manipulatives, fraction activities, practice questions, and interactive challenges. The topics the app covers are fractions introduction, equivalent fractions, common denominators, comparing and ordering fractions, adding and subtraction fractions, multiplying fractions, and dividing fractions. The app is free on the iTunes store. The app has visual models with audio narration. There is questions to practice what has been learned. It is very hands-on because there is manipulatives. Students can apply there understanding through the challenges. It even aligns with the common core.
I think this is a great app! It has everything a student needs to practice fractions. I like that it is very interactive and hands-on. It also allows students to apply their understanding of their learning through challenges. This app would be great to have on iPads for students in the classroom. The app can be downloaded for free which is another bonus of the app. The students can start using the app when fractions are introduced and then continue to use the app when new topics are introduced. Student could use this app in their free time or after they are introduced a lesson.
Math App: 5th Grade Splash Math
https://itunes.apple.com/us/app/splash-math-grade-5/id504807361?mt=8
This app is an innovative and fun way to practice math. There is 9 chapters that cover endless supply of lessons. It is the 2011 "Best Elementary App" winner. There is interactive content, personalized learning, weekly email reports (to track your students learning), and a scratch pad for students to use for their rough work. The topics covered include, place value, number sense, algebra expressions, multiplication, division, fractions, decimals, measurement, and geometry.
I like this app because it contains topics the students will be practicing throughout the whole year. It is interactive which students love. I also really like that it has weekly email reports so that the teacher can track the student learning. The teachers can see if the students are understanding the topics in class. This would be very valuable. This app is free so it wouldn't cost anything to download. Students could practice what they learn in class on their iPads. The app fits in with the common core state standards which is also very good.
Tuesday, June 9, 2015
Journal Reflections
Thinking Through a Lesson: Successfully Implementing High-Level Tasks -
Many teachers don't successfully implement high-level math tasks. A high-level math task allows students to use reasoning skills with thinking skills. Tasks also have different ways of solving the problem so different students would solve the problem in their own way. Teachers can make sure to implement high-level math tasks by using TTLP (Thinking Through a Lesson Protocol). It is divided into three parts. Part one is choosing the mathematical task. Teachers plan the lesson in this part. This helps teachers never to loose sight of what they want to teach the students in math. Part two is supporting the students exploration of the task. Part three is sharing and discussing the task. The TTLP is intended to be used periodically. I think that is would be a useful and helpful strategy to have in my classroom. Like the article said it wouldn't be realistic to do it for every lesson every day. But it is important to use this strategy periodically. By then practicing this method periodically it will end up becoming into my everyday lessons because I will end up asking the TTLP questions. Teachers have described and I would probably agree with them that the TTLP is useful for planning, instructing, and reflecting. Three important aspects of teaching. The TTLP I think really allows teachers to think deeper into what and how they are teaching.
A Model For Understanding Mathematics -
What I found interesting, which I have never realized, is that mathematical understanding of a concept is different from understanding a procedure. Concepts are usually single terms such as equations or greater than. It is the most basic subject matter in math. The relationships between two concepts is called a generalization. On the other hand procedures are more in depth. Examples of procedures are constructing proofs, geometric constructions, synthetic division, and solving equations. The article then describes that teacher need to be making moves so that students understand mathematics. Teachers should move from physical to pictorial and then finally to symbolic representations. Students should then be able to take their symbolic representations and make physical and pictorial representations. I agree with this and I think I will implement this while I am teaching students. Making moves also helps teachers in making lessons plans, instructing and testing. So therefore it will be very useful to me when I am teaching an elementary classroom.
Many teachers don't successfully implement high-level math tasks. A high-level math task allows students to use reasoning skills with thinking skills. Tasks also have different ways of solving the problem so different students would solve the problem in their own way. Teachers can make sure to implement high-level math tasks by using TTLP (Thinking Through a Lesson Protocol). It is divided into three parts. Part one is choosing the mathematical task. Teachers plan the lesson in this part. This helps teachers never to loose sight of what they want to teach the students in math. Part two is supporting the students exploration of the task. Part three is sharing and discussing the task. The TTLP is intended to be used periodically. I think that is would be a useful and helpful strategy to have in my classroom. Like the article said it wouldn't be realistic to do it for every lesson every day. But it is important to use this strategy periodically. By then practicing this method periodically it will end up becoming into my everyday lessons because I will end up asking the TTLP questions. Teachers have described and I would probably agree with them that the TTLP is useful for planning, instructing, and reflecting. Three important aspects of teaching. The TTLP I think really allows teachers to think deeper into what and how they are teaching.
A Model For Understanding Mathematics -
What I found interesting, which I have never realized, is that mathematical understanding of a concept is different from understanding a procedure. Concepts are usually single terms such as equations or greater than. It is the most basic subject matter in math. The relationships between two concepts is called a generalization. On the other hand procedures are more in depth. Examples of procedures are constructing proofs, geometric constructions, synthetic division, and solving equations. The article then describes that teacher need to be making moves so that students understand mathematics. Teachers should move from physical to pictorial and then finally to symbolic representations. Students should then be able to take their symbolic representations and make physical and pictorial representations. I agree with this and I think I will implement this while I am teaching students. Making moves also helps teachers in making lessons plans, instructing and testing. So therefore it will be very useful to me when I am teaching an elementary classroom.
Sunday, June 7, 2015
Rich Task Reflection
As I completed this project I learned a lot. I learned that it is important to incorporate rich activities into the classroom. I had a hard time deciding what activities would be a rich activity. You really have to think and plan for a rich activity. I think our final project with the tin man was a great idea. In class it could have been executed better. I think that having pre-cut aluminum would have been best. It took much time to cut out the aluminum. It would also be a good idea to know what the surface area of each object was ahead of time. Ideally in a real class, you would spend more time on each object.
I enjoyed seeing the other groups rich activities. Every group came up with really good ideas. I could see myself using each of the activities if I was teaching at the grade level it was intended for. What I learned through watching the presentations is that you have to reflect on how the lesson went. Each group had something that they could improve on. Reflecting on what you can do better and what went well is important to know to be a better teacher. Your teaching will become better through reflection of your work. The next time that you teach the lesson it will get better and better.
I enjoyed seeing the other groups rich activities. Every group came up with really good ideas. I could see myself using each of the activities if I was teaching at the grade level it was intended for. What I learned through watching the presentations is that you have to reflect on how the lesson went. Each group had something that they could improve on. Reflecting on what you can do better and what went well is important to know to be a better teacher. Your teaching will become better through reflection of your work. The next time that you teach the lesson it will get better and better.
CCSSM SMP Reflection
I thought doing this project was a very useful. I was not familiar with the Common Core standards. It is important to get to know and get familiar with the standards so that I can teach to the standards in my classroom. Doing this project I have a lot more knowledge in the two standards that I worked with. My partner and I worked on standard 3 and 5. I think our final product turned out nice. The handout is easy to read and follow with good information. The presentations we created also show the standards in a nice way.
I think that it was a great idea to show all of the presentations in class. I was really familiar with standards 3 and 5. Seeing the other presentations allowed me to get more familiar with the other standards. Although I still don't know the standards as well as 3 and 5, I have a better understanding of each standard. It was also interesting to see how others decided to do their presentations.
I think that it was a great idea to show all of the presentations in class. I was really familiar with standards 3 and 5. Seeing the other presentations allowed me to get more familiar with the other standards. Although I still don't know the standards as well as 3 and 5, I have a better understanding of each standard. It was also interesting to see how others decided to do their presentations.
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