I have used the rubric idea on a few assessments now and it seems like the students that use them do a lot better than those that don't. I think that having clear expectations that show what is important has given some students that have been lost in the past a better understanding of what they have to do to problem solve. So many students have a hard time because they get stuck at the beginning and can't break a problem down. By breaking the problem down and emphasizing writing an equation for the parts, they have been doing a lot better than classes in years past.
I think I am going to continue to use the rubric idea because not only does it give students clear expectations, but it also makes grading their assessments a lot easier for me and cuts down on inconsistency in grading. I think that for everyday assignments I can embed the rubric criteria into directions so that students will know at the beginning, middle and end of a unit what they are expected to do when completely any problems.
My current unit is on polynomials which contains one of the dreaded F-words in math: FACTORING (the others being fractions and foiling). I think that giving students specific guidelines for factoring will take some of the pressure off of remembering what to do, so they can focus on figuring out the puzzles pieces. If you remember factoring you should know what I mean by a puzzle. Hopefully by using this idea, my students won't continue to loathe factoring.
Wednesday, December 9, 2009
Tuesday, November 17, 2009
Inquiry Plan
One of the final tasks for this course is to create an Inquiry Plan in which you implement something new into your classroom instruction based on the Domain you researched. My original plan was to create a project bases learning that I could implement with a unit on exponential growth. I was going to spend some time creating a project that would be used throughout the unit and would be a basis for assessment at the end of the unit. Though I thought this was a great plan, I realized that it wouldn't be possible to enact this plan within the timeframe of my graduate course.
So since that time I have been thinking of a way to implement something new in terms of assessment in my classroom. I have decided that I will make a rubric for all the questions on my next formal assessment. I am going to give this to only one of my Algebra 2 classes to see if it makes a differnce in student performance. This way students will have a clear idea of what my criteria is for grading their tests. This will be helpful since they have been problem solving with differnt types of word problems that use systems of equations for solving them. My criteria for these types of problems is pretty clear though many students forget all things required of them. I ask them to define their variables, write an equation, show their work to solve it, and answer the question that was asked in a complete sentence. Many of them think that if they just write down an answer they are fine. But I want to see how they got the answer so I know they understand what was being asked. I also like to see work so that if they made a small mistake I can give them partial credit. Lastly I like them to use complete sentences to answer the question so they get used to using correct units and reffering to what they defined the variables as.
I think that the class with the rubric will perform better because they will know the standards and make sure that they have all parts that I am looking for. Also seeing what is required may jog their memory when they are trying to solve all problems and will help them be more successful. If this assessment tool does help student achievement, then I will probably use a rubric on all further assessments.
So since that time I have been thinking of a way to implement something new in terms of assessment in my classroom. I have decided that I will make a rubric for all the questions on my next formal assessment. I am going to give this to only one of my Algebra 2 classes to see if it makes a differnce in student performance. This way students will have a clear idea of what my criteria is for grading their tests. This will be helpful since they have been problem solving with differnt types of word problems that use systems of equations for solving them. My criteria for these types of problems is pretty clear though many students forget all things required of them. I ask them to define their variables, write an equation, show their work to solve it, and answer the question that was asked in a complete sentence. Many of them think that if they just write down an answer they are fine. But I want to see how they got the answer so I know they understand what was being asked. I also like to see work so that if they made a small mistake I can give them partial credit. Lastly I like them to use complete sentences to answer the question so they get used to using correct units and reffering to what they defined the variables as.
I think that the class with the rubric will perform better because they will know the standards and make sure that they have all parts that I am looking for. Also seeing what is required may jog their memory when they are trying to solve all problems and will help them be more successful. If this assessment tool does help student achievement, then I will probably use a rubric on all further assessments.
Monday, October 12, 2009
Deeper Thinking about Domain One
This week's blog is a little different from past weeks. I was asked for this blog to research an article, video, and blog that had to do with the student assessment component of Domain One. The article that I found is "How Should We Measure Student Learning?: The Many Forms of Assessment" by the Edutopia staff (http://www.edutopia.org/comprehensive-assessment-introduction). It stated that we need multiple forms of assessments to gauge student learning. I also liked their idea of using skills like collaboration and team building when it comes to assessments. This is more like the real-world or business situations that students would face after high school.
The second item I found was an interesting video titled, "Making a Case for Comprehensive Assessment" also located on Edutopia's website (http://www.edutopia.org/urban-academy). This video is about a high school that doesn't use standard state tests as their way of assessing student knowledge. Instead they use a lot of project based tools to show what students have learned. Also in a social studies class, students read real-world law cases and argue one side or the other after researching both sides. Though Urban Academy has recently been pressured to give state regents tests, they are fighting to keep the standards that have been working for their students so far.
The final item I found was a blog by Bill Tucker titled, "Improving Assessment: Getting From Here to There" (http://www.quickanded.com/2009/09/improving-assessment-getting-from-here-to-there.html) about the need for our educational system to try something new. He wrote about how our current testing system is failing us, but that it would be incredibly hard for major changes to happen quickly. He noted that if any change were going to happen, it would have to be in small increments with lots of research going into the correct changes as well as a major investment being made into a new system. I liked the analogy that he gave at the end of the blog that referenced the time and energy it took to get to the moon. NASA put in a huge investment of time and money with many failures and triumphs before they actually met their goals.
All three of these resources talk to the idea that we need a new system of assessment that includes different types of methods. I am definitely open to trying new forms of assessment with my students that would give more students the opportunity to succeed. I really like the idea of trying more project based assessments that would ask students to apply what they have learned in a more hands on way then a multiple choice or free response test. It is a little frustrating though with the push that my district is having for more assessments. We are moving from semester exams to quarter exams as well as making the all common across grade and subject. Though I can see some benefit for having quarter exams (less material for students to remember for one assessment), they are taking away instructional time that can be used for some of these alternate assessment types. We are more pressured to get a certain amount of material in before students have to take their exams.
The second item I found was an interesting video titled, "Making a Case for Comprehensive Assessment" also located on Edutopia's website (http://www.edutopia.org/urban-academy). This video is about a high school that doesn't use standard state tests as their way of assessing student knowledge. Instead they use a lot of project based tools to show what students have learned. Also in a social studies class, students read real-world law cases and argue one side or the other after researching both sides. Though Urban Academy has recently been pressured to give state regents tests, they are fighting to keep the standards that have been working for their students so far.
The final item I found was a blog by Bill Tucker titled, "Improving Assessment: Getting From Here to There" (http://www.quickanded.com/2009/09/improving-assessment-getting-from-here-to-there.html) about the need for our educational system to try something new. He wrote about how our current testing system is failing us, but that it would be incredibly hard for major changes to happen quickly. He noted that if any change were going to happen, it would have to be in small increments with lots of research going into the correct changes as well as a major investment being made into a new system. I liked the analogy that he gave at the end of the blog that referenced the time and energy it took to get to the moon. NASA put in a huge investment of time and money with many failures and triumphs before they actually met their goals.
All three of these resources talk to the idea that we need a new system of assessment that includes different types of methods. I am definitely open to trying new forms of assessment with my students that would give more students the opportunity to succeed. I really like the idea of trying more project based assessments that would ask students to apply what they have learned in a more hands on way then a multiple choice or free response test. It is a little frustrating though with the push that my district is having for more assessments. We are moving from semester exams to quarter exams as well as making the all common across grade and subject. Though I can see some benefit for having quarter exams (less material for students to remember for one assessment), they are taking away instructional time that can be used for some of these alternate assessment types. We are more pressured to get a certain amount of material in before students have to take their exams.
Sunday, October 4, 2009
Question for My Group
Besides tests and quizzes, what other assessment tools could I use at the secondary level in my Algebra classes?
Domain 1: Planning and Preparation
As I talked about in my last blog, the Four Domains of Teaching Responsibility is a great tool for teachers to use when planning lessons and a way for administrators to observe and critique new teachers. I have been given the task to pick a domain that I would like to look more deeply at and have chosen Domain 1: Planning and Preparation. The components of this domain are: 1a) Demonstrating knowledge of content and pedagogy, 1b) demonstrating knowledge of students, 1c) setting instructional outcomes, 1d) demonstrating knowledge of resources, 1e) designing coherent instruction, and 1f) designing student assessment.
The component that I feel the most comfortable with is in demonstrating knowledge of content and pedagogy. I feel that after teaching Algebra for the last few years, I have really begun to understand the themes that run through all of the content and are important for students to learn and understand. I was confident in my knowledge of Mathematics before I started teaching, but I have found that as I teach, I have gained a deeper understanding of the material and have been able to relate the upper level Math courses I took in college with what I teach at the high school level. Though I would have to relearn a lot of the content if I were to teach Geometry or Calculus, I know that with a solid Algebra background, I would be fine.
The second part of this component is about demonstrating a sound pedagogy. Though I went through coursework designed to teach pedagogy, it wasn't until I started teaching that I gained a better knowledge of the art of teaching. It definitely took me a while to find my niche and be able to break down the material so that my students could understand me. Like a lot of first year teachers, I was given classes that most of the other teachers didn't want to teach. I had a hard time relating the material to my students and found that I was teaching over their heads. Once I realized how to uncomplicate my subject, I had success with my students and have been continuing to grow in the area of pedagogy.
In terms of instruction, I think that the third component is most important. This component is about setting instructional outcomes which is very important when designing a lesson. Instructional goals must be clearly stated so that the teacher and students can see if they met the desired outcomes. It is also important because teachers must incorporate school directed curriculum, statewide requirements, community expectations, etc into every lesson that they teach. Setting sound instructional outcomes is a way to integrate all off these outside factors into a lesson so that instruction will most benefit students.
The component that I think I need to focus on in my own instruction the most is designing student assessments. I would like to see myself incorporate higher-level thinking into my assessment as opposed to a procedural type of test. Currently I feel that my assessments (tests and quizzes) are mostly driven by low-level memorization. Can the student factor the binomial like all of the examples? Instead I would like to focus more on problems that would cause the students to apply the facts/procedures that they have learned. Also I would like to get them to think about the importance of the topics that they are learning so instead of them asking when they will need Math in life, they will already have the answer. Lastly, I would like to use different methods for assessing student learning. Instead of always using a test or quiz, I would like to use a project or some other form of assessment. Hopefully using alternate forms of assessment and higher-level thinking problems will help promote student learning and lasting knowledge of the subject.
The component that I feel the most comfortable with is in demonstrating knowledge of content and pedagogy. I feel that after teaching Algebra for the last few years, I have really begun to understand the themes that run through all of the content and are important for students to learn and understand. I was confident in my knowledge of Mathematics before I started teaching, but I have found that as I teach, I have gained a deeper understanding of the material and have been able to relate the upper level Math courses I took in college with what I teach at the high school level. Though I would have to relearn a lot of the content if I were to teach Geometry or Calculus, I know that with a solid Algebra background, I would be fine.
The second part of this component is about demonstrating a sound pedagogy. Though I went through coursework designed to teach pedagogy, it wasn't until I started teaching that I gained a better knowledge of the art of teaching. It definitely took me a while to find my niche and be able to break down the material so that my students could understand me. Like a lot of first year teachers, I was given classes that most of the other teachers didn't want to teach. I had a hard time relating the material to my students and found that I was teaching over their heads. Once I realized how to uncomplicate my subject, I had success with my students and have been continuing to grow in the area of pedagogy.
In terms of instruction, I think that the third component is most important. This component is about setting instructional outcomes which is very important when designing a lesson. Instructional goals must be clearly stated so that the teacher and students can see if they met the desired outcomes. It is also important because teachers must incorporate school directed curriculum, statewide requirements, community expectations, etc into every lesson that they teach. Setting sound instructional outcomes is a way to integrate all off these outside factors into a lesson so that instruction will most benefit students.
The component that I think I need to focus on in my own instruction the most is designing student assessments. I would like to see myself incorporate higher-level thinking into my assessment as opposed to a procedural type of test. Currently I feel that my assessments (tests and quizzes) are mostly driven by low-level memorization. Can the student factor the binomial like all of the examples? Instead I would like to focus more on problems that would cause the students to apply the facts/procedures that they have learned. Also I would like to get them to think about the importance of the topics that they are learning so instead of them asking when they will need Math in life, they will already have the answer. Lastly, I would like to use different methods for assessing student learning. Instead of always using a test or quiz, I would like to use a project or some other form of assessment. Hopefully using alternate forms of assessment and higher-level thinking problems will help promote student learning and lasting knowledge of the subject.
Tuesday, September 29, 2009
Instruction
When I was in the interviewing process to find a teaching job, I was constantly asked, "Do you believe all students can learn?" The answer that they were looking for of course was, "Absolutely!" Sometimes though, in my classroom I find myself wondering if all of my students can actually learn the content I am teaching them. So I think the answer to the question is somewhat tricky. Yes, all students can learn. Can all students learn and apply the concepts from my Algebra class? I don't know. For the most part they can all at least regurgitate back to me the processes that I teach them, but I don't think they would be able to apply these skills out of context.
I think that this is why Laura Resnick and Sharon Nelson-Le Gall wrote the article "Socializing Intelligence". They suggest shifting the focus of intelligence studies from what academic content do students know to what skill sets can students acquire and use properly in the right contexts. This means less focus on assessing content and more focus on assessing a student's learning process. They also suggest that effort can lead to good learning skills which in turn leads to understanding. Putting this all together, I see their theory as a way to redefine intelligence as more of the process of being able to ask the right questions and solve problems with skills that have been acquired.
This new way to think about intelligence also redirects some of the focus from WHAT the teacher is teaching to HOW the teacher is teaching. The Four Domains of Teaching Responsibility is a great tool for teachers to use to 1)plan and prepare lessons that are meaningful and have specific learning goals for individual students, 2)create a classroom environment that is the most conducive for student learning, 3)implement methods of instruction that engages all students, and 4)exhibit professional responsibilities such as reflection and continued professional development.
Working in an Ohio school where the Four Domains are almost as important as the Bible, I have a certain level of familiarity with implementing the components of the domains. Before beginning work in Ohio though, I had never heard of the Four Domains and didn't realize how important they were to the schools I was applying at. I was amazed when some of my colleagues had binders dedicated to the domains and knew each component by heart (Ohio colleges have classes dedicated to the domains). See, in Nashville where I went to school, they teach the concepts that are presented in the Four Domains of Teacher Responsibility, but not in such a formatted way. It was taught as common practice or common sense that we should just use everyday. So when I was a beginning year teacher at Lakota West High School, I was at a major disadvantage to those that had gone to an in-state university. Though I knew that I needed to know what kind of student I was teaching (1b), demonstrate that I know what I am teaching (1a), manage classroom behavior (2d), know how to organize my classroom (2e), clearly communicate with students (3a) and parents (4c), and be flexible and respond appropriately to any given situation (3e), I had no idea there was an organized system to categorize each of those actions (which were common sense to me).
I did struggle a little bit my first year. It wasn't because I didn't know the domains (not that I'm knocking them, they are great for assessing and reflecting on your own teaching), it was more because I hadn't learned yet how to connect what I knew about my subject to things that my students could understand and relate to. I had to deal with the initial question I posed, "Do I believe that all students can learn?" After having a few years under my belt now, I can definitively say, "YES!" A lot of it though is up to me and how I present the content that I want my students to learn.
I think that this is why Laura Resnick and Sharon Nelson-Le Gall wrote the article "Socializing Intelligence". They suggest shifting the focus of intelligence studies from what academic content do students know to what skill sets can students acquire and use properly in the right contexts. This means less focus on assessing content and more focus on assessing a student's learning process. They also suggest that effort can lead to good learning skills which in turn leads to understanding. Putting this all together, I see their theory as a way to redefine intelligence as more of the process of being able to ask the right questions and solve problems with skills that have been acquired.
This new way to think about intelligence also redirects some of the focus from WHAT the teacher is teaching to HOW the teacher is teaching. The Four Domains of Teaching Responsibility is a great tool for teachers to use to 1)plan and prepare lessons that are meaningful and have specific learning goals for individual students, 2)create a classroom environment that is the most conducive for student learning, 3)implement methods of instruction that engages all students, and 4)exhibit professional responsibilities such as reflection and continued professional development.
Working in an Ohio school where the Four Domains are almost as important as the Bible, I have a certain level of familiarity with implementing the components of the domains. Before beginning work in Ohio though, I had never heard of the Four Domains and didn't realize how important they were to the schools I was applying at. I was amazed when some of my colleagues had binders dedicated to the domains and knew each component by heart (Ohio colleges have classes dedicated to the domains). See, in Nashville where I went to school, they teach the concepts that are presented in the Four Domains of Teacher Responsibility, but not in such a formatted way. It was taught as common practice or common sense that we should just use everyday. So when I was a beginning year teacher at Lakota West High School, I was at a major disadvantage to those that had gone to an in-state university. Though I knew that I needed to know what kind of student I was teaching (1b), demonstrate that I know what I am teaching (1a), manage classroom behavior (2d), know how to organize my classroom (2e), clearly communicate with students (3a) and parents (4c), and be flexible and respond appropriately to any given situation (3e), I had no idea there was an organized system to categorize each of those actions (which were common sense to me).
I did struggle a little bit my first year. It wasn't because I didn't know the domains (not that I'm knocking them, they are great for assessing and reflecting on your own teaching), it was more because I hadn't learned yet how to connect what I knew about my subject to things that my students could understand and relate to. I had to deal with the initial question I posed, "Do I believe that all students can learn?" After having a few years under my belt now, I can definitively say, "YES!" A lot of it though is up to me and how I present the content that I want my students to learn.
Thursday, September 24, 2009
Results of Enacting Curriculum (Day 2)
Word Problems. They are generally the most feared thing in Math (besides factoring and fractions). I used the ideas put forth in our readings and started with something the students were familiar with:
If I have 5 ten dollar bills and 3 five dollar bills, how much money do I have?
The idea being that they take the amount of bills and multiply by the worth of each bill. This gets the general idea of what we will be doing with percentage problems and lots of others. So after this easy problem, I gave them:
I have 7 bills (tens and ones) that equal $34. How many of each bill do I have?
They start to think of all the possibilities and for some of the problems like this they have a hard time figuring out the right combination. So we took the original idea of multiply worth by amount and wrote an equation to help us solve. This seemed a lot easier for them from students past because they started with a basic idea. Writing an equation wasn't so bad because they already understood the concept.
This led into being able to solve "solution" problems that involved percents. In years past I just showed students a method to solve and then had them replicate it. But today, they were able to connect the amount and worth together and told me what to do to solve. Even some of my students that usually say, "I don't get it" were getting it. I was so amazed and pumped at the results. An example of the "solution" problems:
A chemist has some 8% hydrogen peroxide solution and some 5% hydrogen peroxide solution. How many mL of each should be mixed together to make a 300 mL solution which is 6% hydrogen peroxide.
Before these problems mesmerized my students, but today they were actually attempting them and solving them correctly. For you math teachers out there, if you haven't tried starting with something basic that your students already know, you need to give it a shot. For those students that struggle, I think it really built up their confidence to start with something easy then work harder.
If I have 5 ten dollar bills and 3 five dollar bills, how much money do I have?
The idea being that they take the amount of bills and multiply by the worth of each bill. This gets the general idea of what we will be doing with percentage problems and lots of others. So after this easy problem, I gave them:
I have 7 bills (tens and ones) that equal $34. How many of each bill do I have?
They start to think of all the possibilities and for some of the problems like this they have a hard time figuring out the right combination. So we took the original idea of multiply worth by amount and wrote an equation to help us solve. This seemed a lot easier for them from students past because they started with a basic idea. Writing an equation wasn't so bad because they already understood the concept.
This led into being able to solve "solution" problems that involved percents. In years past I just showed students a method to solve and then had them replicate it. But today, they were able to connect the amount and worth together and told me what to do to solve. Even some of my students that usually say, "I don't get it" were getting it. I was so amazed and pumped at the results. An example of the "solution" problems:
A chemist has some 8% hydrogen peroxide solution and some 5% hydrogen peroxide solution. How many mL of each should be mixed together to make a 300 mL solution which is 6% hydrogen peroxide.
Before these problems mesmerized my students, but today they were actually attempting them and solving them correctly. For you math teachers out there, if you haven't tried starting with something basic that your students already know, you need to give it a shot. For those students that struggle, I think it really built up their confidence to start with something easy then work harder.
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