For the unit that your Lesson Study lesson plan is situated in, what are your student outcomes (unit topic, understandings, knowledge, skills) and your end of unit assessment? How does your planned instruction & formative assessment for the lesson plan move your students toward that goal?
My video-tapped lesson occurs during our multiplication and division unit. The unit combines three of the major standards on multiplication and division, including Number Sense 3.1 and 3.2 which involve the use of repeated addition and subtraction, counting by multiples, and grouping to solve multiplication and division problems. The unit also covered standards that require students to know their 2, 5 and 10’s times tables.
The goal of the unit was not necessarily for students to have a firm memorization of multiplication and division facts (eg: 6 x 6 = 36), but for students to develop a deep understanding of the concepts of multiplication and division and to learn how to apply those understandings to real life situations and story problems. Ultimately students should be able to score a 90% or higher on the end of unit assessments, which test them not only only being able to solve problems like 6x6 but also on how to choose the correct operation in story problems and how to choose/implement the taught strategies to arrive at an answer.
The particular lesson which was video-tapped introduced students to a strategy for solving division problems, the strategy is known as repeated subtraction. This tied into the unit goals in two ways. First, it added to student’s previous knowledge of what division is. Students already understood that in division you start with how many in all then split them equally into smaller groups. This lesson expanded upon that knowledge and allowed them to view division through a different lens. In multiplication we use repeated addition because in most cases we are trying to find how many in all, consequently the number will increase. In division, we use repeated subtraction because we know how many in all and usually need to find a smaller number. The lesson also provided students with an additional skill. Previously students could only draw pictures to solve division problems, now they have another strategy at their disposal.
The instruct for this lesson was mostly direct, but portions asked students to put their head together to discuss what repeated addition is and why they think we use it for division. It attempted to help students construct knowledge which would in turn promote their deeper understanding of division. The formative assessment, which was a worksheet, was a sheet of story problems with the division problems listed. This assessment not only gave them a chance to practice the newly aquired skill but also gave them more real world context for when to use division.
The challenge activity for early finishers gave students math problems for which they were asked to write division problems. This activity was aimed at promoting critical thought amongst the students.
The differentiation in this lesson for the small (lower) group attempted to lay more scaffolding on how to set up repeated subtraction problems based on a certain division problem. It focused primarily on teaching students the skill so that the students would be able to solve division problems using the skill on their own.
Saturday, February 7, 2009
Tuesday, January 13, 2009
108: Pre-Assessment
The articles on differentiated instruction were slightly overwhelming. Prior to reading, I viewed differentiation merely as making the time to lay more scaffolding for students who were behind and finding ways to challenge students who were ahead. After reading the article, I realized the differentiation goes far beyond merely thinking about what level students are performing at – it is a mindset that should guide every element of instruction. Students not only perform at different levels, but they learn in different ways. They have different interest and different backgrounds. Some have different language needs and some have different behavioral needs. All of these things need to be considered while planning with differentiation.
I generally feel like I have the knowledge to be able to differentiate effectively. I know my students fairly well, although I do have 80 of them. I’ve gone to a number of house visits and am familiar with many of their learning habits. One of the second grade literacy teachers has surveys from each student where they comment on the type of learner they are and whether they learn best by listening, watching or doing. I’ve reviewed all of those surveys and found that students are all over the spectrum; some prefer watching, other prefer doing and many like listening or reading. I also have plenty of assessment data – especially from end of unit exams. For the first two units of the year I also issued pre-assessments, although I did not for the last two – perhaps that is something I should be doing more consistently. That being said, I have plenty of informal data about students prior to beginning units, most of which stems from bell-work share alouds and mini-lessons on future learning items. Although I feel like I have a decent knowledge base, especially in terms of student needs, it doesn’t always translate to the execution of effective differentiation.
Although I do also feel like there are moments where I differentiate fairly well. For example, during the middle of the lesson I have make opportunities to check for understanding… my checks usually consist of some follow up questions, which, for students at lower levels, allows me a chance to lay scaffolding and, for students at higher levels, allows me a chance to provide a challenge. I’ve also recently begun small groups which are based around both formal and informal assessment data and have so far been effective in getting the students who are behind caught up and providing the students who are ahead the opportunity for enrichment. On Thursday I begin centers, and I will further use this as an opportunity for differentiation. Although many stations will cover the same material, I plan on differentiating the work for each group. There will be many folders at each station, each group will have a folder that has work at their level. If this doesn’t occur during my first go-around of centers, it is definitely in the works for the future.
On the whole, there numerous areas for growth in differentiation, too many to list here. But after reading, there are a few changes I think are fairly manageable and easy to implement. I noticed that many of my students, based on their surveys and my own observations, are visual learners. They can be greatly assisted by a simple graphic organization. A graphic organizer, I’ve found, can be made for almost anything in math. For those students, I need to start making one for each lesson, or at least a few per unit. I can also make little word list for students who have issues retaining important vocabulary and look at me like I am crazy when I ask them to find the “product.” These are just a few of the small things I can incorporate to improve my differentiation.
Overall, I would rank myself at the beginning/emerging levels on the rubic. I think that by the end of 108 I could certainly be at the applying level, but it will take time and effort, which, after reading these articles, is definitely worth it.
I generally feel like I have the knowledge to be able to differentiate effectively. I know my students fairly well, although I do have 80 of them. I’ve gone to a number of house visits and am familiar with many of their learning habits. One of the second grade literacy teachers has surveys from each student where they comment on the type of learner they are and whether they learn best by listening, watching or doing. I’ve reviewed all of those surveys and found that students are all over the spectrum; some prefer watching, other prefer doing and many like listening or reading. I also have plenty of assessment data – especially from end of unit exams. For the first two units of the year I also issued pre-assessments, although I did not for the last two – perhaps that is something I should be doing more consistently. That being said, I have plenty of informal data about students prior to beginning units, most of which stems from bell-work share alouds and mini-lessons on future learning items. Although I feel like I have a decent knowledge base, especially in terms of student needs, it doesn’t always translate to the execution of effective differentiation.
Although I do also feel like there are moments where I differentiate fairly well. For example, during the middle of the lesson I have make opportunities to check for understanding… my checks usually consist of some follow up questions, which, for students at lower levels, allows me a chance to lay scaffolding and, for students at higher levels, allows me a chance to provide a challenge. I’ve also recently begun small groups which are based around both formal and informal assessment data and have so far been effective in getting the students who are behind caught up and providing the students who are ahead the opportunity for enrichment. On Thursday I begin centers, and I will further use this as an opportunity for differentiation. Although many stations will cover the same material, I plan on differentiating the work for each group. There will be many folders at each station, each group will have a folder that has work at their level. If this doesn’t occur during my first go-around of centers, it is definitely in the works for the future.
On the whole, there numerous areas for growth in differentiation, too many to list here. But after reading, there are a few changes I think are fairly manageable and easy to implement. I noticed that many of my students, based on their surveys and my own observations, are visual learners. They can be greatly assisted by a simple graphic organization. A graphic organizer, I’ve found, can be made for almost anything in math. For those students, I need to start making one for each lesson, or at least a few per unit. I can also make little word list for students who have issues retaining important vocabulary and look at me like I am crazy when I ask them to find the “product.” These are just a few of the small things I can incorporate to improve my differentiation.
Overall, I would rank myself at the beginning/emerging levels on the rubic. I think that by the end of 108 I could certainly be at the applying level, but it will take time and effort, which, after reading these articles, is definitely worth it.
Monday, December 8, 2008
105: Assignment 2, "How Teachers Learn"
Question:
Most of this article seems like it is directed to school administrations rather than teacher. The article discussion the way by which teachers learn but then quickly transitions into a discussion about which environment teachers can best learn in – which in most cases are outside of the realm of a teacher’s control. At Rocketship and through reach, many of those environments exist in one form or another. But in other schools, where less support is provided, what can teachers do to ensure that they have exposure to such environments?
Quote:
“When student teachers enter their first classrooms, the instructional methods, curricula, and resources can be very different from the ones they learned about in teacher education programs. So although prospective teachers are often anxious to begin their student teaching and find it the most satisfying aspect of their teacher preparation (Hollins, 1995), the dissonance between this experience and their course work supports the belief that educational theory and research have little to do with classroom practice.”
This quote is particularly interesting. Not having been in a typical education program at a 4-year university, my experience is much different than what this article assumes the experience of most new teachers is. This is perhaps a strong point of TFA’s training model. Although it only provides one month of training, it directly couples theory and research with the implementation of such theories and research in the class-room almost immediately. REACH works in a similar way. Once research is discussed as a collaborative group it is implemented in a lesson at some point down the road. That lesson is also observed to make sure that the theories and research are not only implemented, but implemented correctly – which is another point this article makes: observation is important!
Commentary:
Overall, I think this was a useful article to read. It allows us as teachers to see what we are being exposed to and how that helps us learn. It allows provides us for the opportunity to reflect on our learning – are we in each of these environments? Is there anything else we can do to expose ourselves to those environments? Especially looking at the first section, which address HOW teachers learn – most of the items listed in that section are things we can do on our own, like talking with other teachers. By reading this article, we know specifically what to look for when we reflect on our growth (eg: Are we talking to other teachers? Just informally? Or also formally? How often do we do it? Etc.)
Most of this article seems like it is directed to school administrations rather than teacher. The article discussion the way by which teachers learn but then quickly transitions into a discussion about which environment teachers can best learn in – which in most cases are outside of the realm of a teacher’s control. At Rocketship and through reach, many of those environments exist in one form or another. But in other schools, where less support is provided, what can teachers do to ensure that they have exposure to such environments?
Quote:
“When student teachers enter their first classrooms, the instructional methods, curricula, and resources can be very different from the ones they learned about in teacher education programs. So although prospective teachers are often anxious to begin their student teaching and find it the most satisfying aspect of their teacher preparation (Hollins, 1995), the dissonance between this experience and their course work supports the belief that educational theory and research have little to do with classroom practice.”
This quote is particularly interesting. Not having been in a typical education program at a 4-year university, my experience is much different than what this article assumes the experience of most new teachers is. This is perhaps a strong point of TFA’s training model. Although it only provides one month of training, it directly couples theory and research with the implementation of such theories and research in the class-room almost immediately. REACH works in a similar way. Once research is discussed as a collaborative group it is implemented in a lesson at some point down the road. That lesson is also observed to make sure that the theories and research are not only implemented, but implemented correctly – which is another point this article makes: observation is important!
Commentary:
Overall, I think this was a useful article to read. It allows us as teachers to see what we are being exposed to and how that helps us learn. It allows provides us for the opportunity to reflect on our learning – are we in each of these environments? Is there anything else we can do to expose ourselves to those environments? Especially looking at the first section, which address HOW teachers learn – most of the items listed in that section are things we can do on our own, like talking with other teachers. By reading this article, we know specifically what to look for when we reflect on our growth (eg: Are we talking to other teachers? Just informally? Or also formally? How often do we do it? Etc.)
Tuesday, November 25, 2008
105: Pre-Assessment, "How People Learn"
I cannot with absolute certainty say that I’ve experienced “flow” in any academic setting throughout the course of my life. Although I was interested in the subject matter of many classes throughout life, the material and focus of the class was always determined by the teacher or professor. I also found that in most academic settings, even the most exciting material could be turned into a source of boredom when particular types of assignments and papers were assigned; not to mention the horrendously mind-numbing nature of monotone lectures.
The truth is, I learn best and am most excited about learning when I am provided with the opportunity to explore and to explore the things that I choose to explore. Every time I’ve experienced “flow” it’s been outside of a class. Speech and debate in high school consumed my life. I chose my debate case, I researched my debate case, I wrote my debate case and I debated my debate case. I chose a topic I was interested in, and I saturated myself in all the information I could find regarding that topic. It was not an assignment from a teacher, it was not a product of an essay or a lecture – it was my own. Throughout my experience in Young Democrats, I learned so much more about politics, campaigns and elections then I could have ever learned sitting in a lecture hall. I chose what I wanted to learn, and I was able to choose the way I wanted to learn it – I got hands on experience, I read newspapers, I talked to and worked with people in the field – I was in control.
I can imagine to some extent that many of my students learn in a similar manner. They learn better when an element of choice is presented, when they truly feel like they are in control of what they are learning.
The truth is, I learn best and am most excited about learning when I am provided with the opportunity to explore and to explore the things that I choose to explore. Every time I’ve experienced “flow” it’s been outside of a class. Speech and debate in high school consumed my life. I chose my debate case, I researched my debate case, I wrote my debate case and I debated my debate case. I chose a topic I was interested in, and I saturated myself in all the information I could find regarding that topic. It was not an assignment from a teacher, it was not a product of an essay or a lecture – it was my own. Throughout my experience in Young Democrats, I learned so much more about politics, campaigns and elections then I could have ever learned sitting in a lecture hall. I chose what I wanted to learn, and I was able to choose the way I wanted to learn it – I got hands on experience, I read newspapers, I talked to and worked with people in the field – I was in control.
I can imagine to some extent that many of my students learn in a similar manner. They learn better when an element of choice is presented, when they truly feel like they are in control of what they are learning.
Tuesday, November 11, 2008
109: Assignment 2; Step Up to Writing
What do you see as your strengths and areas of growth for writing in your classroom?
Strengths
Although I only teach math, I attempt to incorporate writing into the class structure. We have a math meeting daily where students write to explain what they think the meaning of a particular vocabulary word is. They also solve a problem of the day. After solving the problem they are asked to give a written response explaning how they arrived at their answer. Often I provide them with a writing prompt to get them started. The prompt is often short and to the point "The answer is ________ because ______________________."
Areas for Growth
I have not been using the writing done by students as a way to measure their level of understanding. After reading the articles from Marilynn Burns, I can appreciate the amount of information that a student's writing can give you into their actual understanding of the concept they are working on. I need to be frequently be reading what students write in math meeting and use that information as a window into their rationale for solving certain problems. Intially I had treated such writing activities as only a tool for students, to help them clarify and organize their thoughts about problems. Now I understand it is a tool for the teacher as well.
What is one thing you can implement from the readings?
I really enjoyed the idea of having students write a short essay about a particular mathematical idea. I think it really forces students to try and grasp a deeper understanding of the procedures they do everyday. Often times we talk about what it means to subtract, or what it means when we're regrouping - but I am not sure that student's retain that information because they themselves are not the ones trying to figure out and put into words what they think is going on. It would also be a useful method of assesment and would allow me to see how I can explain these concepts better. I really felt like the samples Marilynn Burns provided gave me a deep insight to her students and not only what they knew, but how well they understood. I feel like this can be easily incorporated into a homework assignment of sorts.
Which section of Step Up for Writing Would you like?
Asking and Answering Questions: 1-38, 1-39, 1-40.
Strengths
Although I only teach math, I attempt to incorporate writing into the class structure. We have a math meeting daily where students write to explain what they think the meaning of a particular vocabulary word is. They also solve a problem of the day. After solving the problem they are asked to give a written response explaning how they arrived at their answer. Often I provide them with a writing prompt to get them started. The prompt is often short and to the point "The answer is ________ because ______________________."
Areas for Growth
I have not been using the writing done by students as a way to measure their level of understanding. After reading the articles from Marilynn Burns, I can appreciate the amount of information that a student's writing can give you into their actual understanding of the concept they are working on. I need to be frequently be reading what students write in math meeting and use that information as a window into their rationale for solving certain problems. Intially I had treated such writing activities as only a tool for students, to help them clarify and organize their thoughts about problems. Now I understand it is a tool for the teacher as well.
What is one thing you can implement from the readings?
I really enjoyed the idea of having students write a short essay about a particular mathematical idea. I think it really forces students to try and grasp a deeper understanding of the procedures they do everyday. Often times we talk about what it means to subtract, or what it means when we're regrouping - but I am not sure that student's retain that information because they themselves are not the ones trying to figure out and put into words what they think is going on. It would also be a useful method of assesment and would allow me to see how I can explain these concepts better. I really felt like the samples Marilynn Burns provided gave me a deep insight to her students and not only what they knew, but how well they understood. I feel like this can be easily incorporated into a homework assignment of sorts.
Which section of Step Up for Writing Would you like?
Asking and Answering Questions: 1-38, 1-39, 1-40.
Sunday, November 9, 2008
109: Assignment 1, Strategies that Work
Question:
On pages 17 and 18 of Strategies that Work, there is a discussion about the importance of celebrating the questions that students have. The section also states that teachers should help facilitate the answers. Although I will always entertain questions that are clearly relevant to the topic at hand, I am often not sure how to address questions that stray away from zone of relevance. How does a teacher go about facilitating such questions? Is it a matter of providing the student with the resources to answer such questions on their own at a later point? Also, is there a way to teach students how to monitor whether or not the question they wish to ask is important to their learning prior to asking it; essentially, is there a way to teach students to distinguish between important questions and an inconsequential questions?
Quote:
"The fact is all readers space out when they read. Kids need to know this, or they risk feeling inadequate when it happens to them. We share these stories of our attention lapses with our students. When they learn that adult readers space out, too, they are less likely to brand themselves poor readers at such times." – Page 27
Ironically, I had to go back a handful of times and re-read parts of these articles. I imagine that I tend to "space out" more than most adult readers. If I read something that perks my interest, my mind suddenly directs its energy to that particular concept rather than to comprehending the material I read thereafter. Luckily I have a variety of strategies at my disposal which allow me to go back and gain an understanding for the material I may have missed on the first go-around. However, the initial panic that hits once I realized that I’ve read a paragraph or two and retained no information is still rather alarming. I never imagined what it such a situation would feel like for a young reader who hasn’t developed the comprehension strategies necessary to go back and figure out exactly what had been read. Even students who are past decoding and can comprehend while reading may encounter situations where they "space out." If they don’t understand that this is normal and they do not have the tools to go back and comprehend what they read, it may become a point of frustration and lower their confidence as a reader.
Commentary:
After reading these excerpts from the book Strategies that Work, I feel like I have an understanding of why comprehension is such an important part of any literacy instruction. I also feel like there is an excellent take way from this article that can be applied to math (or any other subject matter for that matter). When any material is taught it is still important to use many of these strategies discussed. Although students will not be writing questions and connections on sticky notes while solving a specific problem like 4x6; it is important for students in to make connections to how the material effects them beyond the problem they are solving; to ask questions and reach for a more deeper understanding; and to monitor and clarify to make sure they are aware of what is occurring at every step in a problem.
On pages 17 and 18 of Strategies that Work, there is a discussion about the importance of celebrating the questions that students have. The section also states that teachers should help facilitate the answers. Although I will always entertain questions that are clearly relevant to the topic at hand, I am often not sure how to address questions that stray away from zone of relevance. How does a teacher go about facilitating such questions? Is it a matter of providing the student with the resources to answer such questions on their own at a later point? Also, is there a way to teach students how to monitor whether or not the question they wish to ask is important to their learning prior to asking it; essentially, is there a way to teach students to distinguish between important questions and an inconsequential questions?
Quote:
"The fact is all readers space out when they read. Kids need to know this, or they risk feeling inadequate when it happens to them. We share these stories of our attention lapses with our students. When they learn that adult readers space out, too, they are less likely to brand themselves poor readers at such times." – Page 27
Ironically, I had to go back a handful of times and re-read parts of these articles. I imagine that I tend to "space out" more than most adult readers. If I read something that perks my interest, my mind suddenly directs its energy to that particular concept rather than to comprehending the material I read thereafter. Luckily I have a variety of strategies at my disposal which allow me to go back and gain an understanding for the material I may have missed on the first go-around. However, the initial panic that hits once I realized that I’ve read a paragraph or two and retained no information is still rather alarming. I never imagined what it such a situation would feel like for a young reader who hasn’t developed the comprehension strategies necessary to go back and figure out exactly what had been read. Even students who are past decoding and can comprehend while reading may encounter situations where they "space out." If they don’t understand that this is normal and they do not have the tools to go back and comprehend what they read, it may become a point of frustration and lower their confidence as a reader.
Commentary:
After reading these excerpts from the book Strategies that Work, I feel like I have an understanding of why comprehension is such an important part of any literacy instruction. I also feel like there is an excellent take way from this article that can be applied to math (or any other subject matter for that matter). When any material is taught it is still important to use many of these strategies discussed. Although students will not be writing questions and connections on sticky notes while solving a specific problem like 4x6; it is important for students in to make connections to how the material effects them beyond the problem they are solving; to ask questions and reach for a more deeper understanding; and to monitor and clarify to make sure they are aware of what is occurring at every step in a problem.
Tuesday, October 28, 2008
109: Pre-Assessment; My History as a Reader
My History as a Reader:
When/how/where did you learn to read and what was it like for you?
I learned to read at the end of Kindergarten. I had two years of preschool under my belt when I entered K. I knew my letters and I knew the sounds they made, but I often struggled to blend them correctly and recognize letter patterns that made different sounds, like "ch" or "oo." I also struggled with understanding when long vowels and short vowels were used. It took lots of practice at home with help from my mother to finally really start to read. Although I would like to say that I learned to read in school, I really learned at home.
What are some experiences with reading that you remember vividly? Why?
I remember that in Kindergarten, my teacher would let kids who knew how to read, read books from home aloud to the class. I was fairly confident in my abilities toward the middle of Kindergarten, mostly because I knew my letter sounds. I volunteered to read the Little Mermaid, one of my favorite books from home. Well, as long as it took from me to stand up, was as quickly as it took the teacher to sit me back down. I started reading, sounding things out and going slowly only zipping through sight words like "the" and "and". The teacher thought I was taking to long, and after the first page, told me to try it again when I really know how to read. I remember feeling pretty embarassed and down on myself. I could read - it just took me time, and really... for me to be reading anything at Kindergarten, that was pretty good, right? But I felt like I was behind, like I wasn't where I need to be. It was not a very good feeling.
How have your feelings about reading developed over time?
I strongly dislike reading, especially fiction. I am not sure if it stems back to that day in Kindergarten, I am not sure. I only read when I have to. Text books, journal articles for research papers - all of that I don't mind. But I never read for pleasure. Perhaps it goes beyond Kindergarten and extends to all of those fiction novels that we read in classes throughout school. I never remember throughout any of my educational career, being given an opportunity to actually enjoy the material we were reading - just quizes and tests for make sure we did the reading, and comprehended it.
When/how/where did you learn to read and what was it like for you?
I learned to read at the end of Kindergarten. I had two years of preschool under my belt when I entered K. I knew my letters and I knew the sounds they made, but I often struggled to blend them correctly and recognize letter patterns that made different sounds, like "ch" or "oo." I also struggled with understanding when long vowels and short vowels were used. It took lots of practice at home with help from my mother to finally really start to read. Although I would like to say that I learned to read in school, I really learned at home.
What are some experiences with reading that you remember vividly? Why?
I remember that in Kindergarten, my teacher would let kids who knew how to read, read books from home aloud to the class. I was fairly confident in my abilities toward the middle of Kindergarten, mostly because I knew my letter sounds. I volunteered to read the Little Mermaid, one of my favorite books from home. Well, as long as it took from me to stand up, was as quickly as it took the teacher to sit me back down. I started reading, sounding things out and going slowly only zipping through sight words like "the" and "and". The teacher thought I was taking to long, and after the first page, told me to try it again when I really know how to read. I remember feeling pretty embarassed and down on myself. I could read - it just took me time, and really... for me to be reading anything at Kindergarten, that was pretty good, right? But I felt like I was behind, like I wasn't where I need to be. It was not a very good feeling.
How have your feelings about reading developed over time?
I strongly dislike reading, especially fiction. I am not sure if it stems back to that day in Kindergarten, I am not sure. I only read when I have to. Text books, journal articles for research papers - all of that I don't mind. But I never read for pleasure. Perhaps it goes beyond Kindergarten and extends to all of those fiction novels that we read in classes throughout school. I never remember throughout any of my educational career, being given an opportunity to actually enjoy the material we were reading - just quizes and tests for make sure we did the reading, and comprehended it.
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