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Csrqi Nmsa Presentation2
 

Csrqi Nmsa Presentation2

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  • <br />
  • <br />
  • It might be good to have any language we have from the front page of the web site here. <br />
  • Mention the populations up front: <br /> Special learning needs <br /> English Language Learners <br /> Rural Students <br /> <br />
  • Mention the populations up front: <br /> Special learning needs <br /> English Language Learners <br /> Rural Students <br /> <br />
  • These four groups are all groups with extensive experience in middle grades reform. <br />
  • <br />
  • Before getting into the details of individual tools and resources, it would be good to address the common ideas and considerations that we had in developing these resources. <br /> Of primary concern is a need to address the notion that teachers need to focus on developing a deeper understanding of mathematical concepts – not just building simple skills, as is so often the case in classrooms. <br /> A second aspect of the toolkit materials is that the focus primarily on professional development as the mechanism for change, as the most crucial aspect of doing this work is to get teachers to change their practice. And, as a design principle, the PD activities and resources we have all developed incorporate questions, cases, and assessment to help teachers reflect on their teaching. We recognize that this change doesn’t happen without reflecting on one’s own instruction. <br /> Beyond this, it is good to think of these resources as a true toolkit – a collection of materials that each have specialized purposes and approaches, just as a hammer, screwdriver, and wrench do. <br />
  • The first of the toolkit materials was initially designed to address the needs of rural educator. However, the primary challenge for rural educators is not so much the lack of community expertise, differing values toward mathematics, or some other contextual issue for students. It is that rural mathematics teachers lack access to high quality mathematics professional development. In fact, because of the lack of “density” in most rural areas, professional learning opportunities for educators focuses on whole school instructional or procedural issues – not on content. So, when Middle Start, the organization responsible for this component of the toolkit developed their materials, the idea was to provide high quality mathematics professional development through a series of modules focusing on challenging concepts for middle grades mathematics educators. The intent is to get teachers to reflect on their practice by examining student work and the nature of the tasks that they ask students to perform. In addressing depth of understanding, part of the goal is accomplished by getting teachers to use discussion around challenging tasks rather than reliance on skill building alone with lots of repetition (i.e. drill and kill approaches). <br /> <br /> While the original intent was to address needs of rural educators, these resources could easily be used in other sites, as they are not specific to rural educators – they just use a platform that allows teachers with differing locations and schedules to use the tools. We are also going to be field testing these resources in a large urban district as well. <br />
  • A fourth set of tools addresses the specific needs of English Language Learners in mathematics instruction. Same as last slide – Sara should include materials from the STW presentation, such as the example she used there, to address why this is an issue and what their materials support about it. <br />
  • A fourth set of tools addresses the specific needs of English Language Learners in mathematics instruction. Same as last slide – Sara should include materials from the STW presentation, such as the example she used there, to address why this is an issue and what their materials support about it. <br />
  • A fourth set of tools addresses the specific needs of English Language Learners in mathematics instruction. Same as last slide – Sara should include materials from the STW presentation, such as the example she used there, to address why this is an issue and what their materials support about it. <br />
  • This is where you should go into detail about the Turning Points tools, and perhaps show a sample video, or the sample text . <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is one example that the facilitator provides to the workshop participants. It presents the “noticing” along with an accompanying comment. <br /> I notice that the two students in the front of the picture are smiling. I wonder if this means they are engaged in their work. <br /> <br /> Another example could be to list one or two items in the left column and ask participants to write any questions or comments they have about them in the right column. <br /> <br /> Make sure you give time for all participants to write at least two responses on both sides of the columns before you ask for individual responses. This process ensures that everyone is given an opportunity to participate and signals that everyone has something to share with the group – a key strategy used throughout the workshops as well as a key strategy and stance in classrooms that are highly effective in teaching high level math to English language learners. <br />
  • I notice that…I wonder if, I wonder how, I wonder why… <br /> Students are using manipulatives to create models.I wonder if manipulatives allow all students to begin working on the problem. <br /> Students are recording their results in an organized fashion. I wonder if the teacher gave them any sort of template or model. <br /> Students discover how to use manipulatives in a variety of ways.I wonder how the students will work with each other after working separately. <br /> I wonder if it would have been better if the students had worked as a team to <br /> build one model together. <br />
  • You can use one master list of comments for the entire set of slides, simply adding new comments as the participants watch each successive slide. <br /> <br /> For example, in this slide the students might notice that: <br /> There is a “Do Now” posted prominently on the board. A comment connected to that might be “I wonder if there are clear routines established for the class and <br /> if this type of organization helps students focus on the important concepts presented in each lesson, <br /> as well as providing a good example of the importance of organization. <br /> <br /> Other possible “noticings: <br /> The “Do Now” asks a non-mathematical question.” “I wonder what mathematical concept will be the focus on the lesson. <br /> “I wonder why the “Do Now” is not a math problem. <br />
  • I notice that…I wonder if, I wonder how, I wonder why… <br /> Two boys are writing on a piece of paper that appears to have some models orI wonder if the teacher has modified the worksheet for ELLs. <br /> diagrams written on it.I wonder when students work individually and when they work in groups. <br /> I wonder how writing is used in a classroom to support ELLs. <br /> <br /> The two boys are serious, one’s lips are pierced in concentration, both of their eyes are focused solely <br /> On the paper. <br /> <br /> The two boys are sitting close to each other. <br />
  • I notice that…I wonder if, I wonder how, I wonder why… <br /> The teacher is working with one boy.I wonder how the teacher decides what to say to each student as she works with them. <br /> Each boy seems to be working in a different way. <br /> One boy has some money on top of a worksheet. <br />
  • I notice that…I wonder if, I wonder how, I wonder why… <br /> These two students are working in pairs.I wonder if they are taking turns in working on the problem or if one is teaching the other. <br /> One student is writing on another student’s paper. <br /> Both students are using their pencils. <br /> The two students are working side by side, desks close to each other. <br /> Both students are looking at the work, not at each other. <br />
  • I notice that…I wonder if, I wonder how, I wonder why… <br /> Students are excited to compare their results with their peers.I wonder what engages them so strongly that they are excited about sharing with others. <br /> Students show their work to each other as a way of comparing results. <br /> Students share their work with peers who sit next to them and in different groups.I wonder on what basis the teacher groups her English language learners. <br /> Students are writing their work on templates.I wonder how templates help students better understand the concept. <br />
  • This is where you should go into detail about the Turning Points tools, and perhaps show a sample video, or the sample text . <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Turning Points tools, and perhaps show a sample video, or the sample text . <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Turning Points tools, and perhaps show a sample video, or the sample text . <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • The final set of resources addresses the needs of students with special learning considerations. This is not to say that we wanted to focus on these students only. Rather, there is an approach to the design of instructional materials called Universal Design, which can apply to the materials all students use. Based originally on the field of architecture and urban planning, Universal Design was intended to address the needs of people with special challenges, such as blindness or lack of mobility, through such designs of urban spaces that allowed everyone to use the space, such as ramps, curb-cuts, and warning sounds at intersections. In the past decade, these principles have been applied to learners, including those with visual needs, conceptual challenges, and other considerations. These resources include materials for teachers and students that are aligned with reform curricula in mathematics… <br /> <br /> The rest of this should be developed by Talent Development. <br />
  • The final set of resources addresses the needs of students with special learning considerations. This is not to say that we wanted to focus on these students only. Rather, there is an approach to the design of instructional materials called Universal Design, which can apply to the materials all students use. Based originally on the field of architecture and urban planning, Universal Design was intended to address the needs of people with special challenges, such as blindness or lack of mobility, through such designs of urban spaces that allowed everyone to use the space, such as ramps, curb-cuts, and warning sounds at intersections. In the past decade, these principles have been applied to learners, including those with visual needs, conceptual challenges, and other considerations. These resources include materials for teachers and students that are aligned with reform curricula in mathematics… <br /> <br /> The rest of this should be developed by Talent Development. <br />
  • The final set of resources addresses the needs of students with special learning considerations. This is not to say that we wanted to focus on these students only. Rather, there is an approach to the design of instructional materials called Universal Design, which can apply to the materials all students use. Based originally on the field of architecture and urban planning, Universal Design was intended to address the needs of people with special challenges, such as blindness or lack of mobility, through such designs of urban spaces that allowed everyone to use the space, such as ramps, curb-cuts, and warning sounds at intersections. In the past decade, these principles have been applied to learners, including those with visual needs, conceptual challenges, and other considerations. These resources include materials for teachers and students that are aligned with reform curricula in mathematics… <br /> <br /> The rest of this should be developed by Talent Development. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the Talent Development tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • The next set of tools focuses on instructional practices that can support student understanding in mathematics. This refers to the EDC materials. We should have them insert notes or extra slides here, including some examples of video from their resources. <br />
  • The next set of tools focuses on instructional practices that can support student understanding in mathematics. This refers to the EDC materials. We should have them insert notes or extra slides here, including some examples of video from their resources. <br />
  • The next set of tools focuses on instructional practices that can support student understanding in mathematics. This refers to the EDC materials. We should have them insert notes or extra slides here, including some examples of video from their resources. <br />
  • This is where you should go into detail about the EDC tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the EDC tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the EDC tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the EDC tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • This is where you should go into detail about the EDC tools, and perhaps show a sample video. <br /> <br /> You may want to show where this is on the web site, but it is probably better to put the actual media in this presentation file, as it would take a lot of time to download the files from the website. <br />
  • The first of the toolkit materials was initially designed to address the needs of rural educator. However, the primary challenge for rural educators is not so much the lack of community expertise, differing values toward mathematics, or some other contextual issue for students. It is that rural mathematics teachers lack access to high quality mathematics professional development. In fact, because of the lack of “density” in most rural areas, professional learning opportunities for educators focuses on whole school instructional or procedural issues – not on content. So, when Middle Start, the organization responsible for this component of the toolkit developed their materials, the idea was to provide high quality mathematics professional development through a series of modules focusing on challenging concepts for middle grades mathematics educators. The intent is to get teachers to reflect on their practice by examining student work and the nature of the tasks that they ask students to perform. In addressing depth of understanding, part of the goal is accomplished by getting teachers to use discussion around challenging tasks rather than reliance on skill building alone with lots of repetition (i.e. drill and kill approaches). <br /> <br /> While the original intent was to address needs of rural educators, these resources could easily be used in other sites, as they are not specific to rural educators – they just use a platform that allows teachers with differing locations and schedules to use the tools. We are also going to be field testing these resources in a large urban district as well. <br />
  • The first of the toolkit materials was initially designed to address the needs of rural educator. However, the primary challenge for rural educators is not so much the lack of community expertise, differing values toward mathematics, or some other contextual issue for students. It is that rural mathematics teachers lack access to high quality mathematics professional development. In fact, because of the lack of “density” in most rural areas, professional learning opportunities for educators focuses on whole school instructional or procedural issues – not on content. So, when Middle Start, the organization responsible for this component of the toolkit developed their materials, the idea was to provide high quality mathematics professional development through a series of modules focusing on challenging concepts for middle grades mathematics educators. The intent is to get teachers to reflect on their practice by examining student work and the nature of the tasks that they ask students to perform. In addressing depth of understanding, part of the goal is accomplished by getting teachers to use discussion around challenging tasks rather than reliance on skill building alone with lots of repetition (i.e. drill and kill approaches). <br /> <br /> While the original intent was to address needs of rural educators, these resources could easily be used in other sites, as they are not specific to rural educators – they just use a platform that allows teachers with differing locations and schedules to use the tools. We are also going to be field testing these resources in a large urban district as well. <br />
  • The first of the toolkit materials was initially designed to address the needs of rural educator. However, the primary challenge for rural educators is not so much the lack of community expertise, differing values toward mathematics, or some other contextual issue for students. It is that rural mathematics teachers lack access to high quality mathematics professional development. In fact, because of the lack of “density” in most rural areas, professional learning opportunities for educators focuses on whole school instructional or procedural issues – not on content. So, when Middle Start, the organization responsible for this component of the toolkit developed their materials, the idea was to provide high quality mathematics professional development through a series of modules focusing on challenging concepts for middle grades mathematics educators. The intent is to get teachers to reflect on their practice by examining student work and the nature of the tasks that they ask students to perform. In addressing depth of understanding, part of the goal is accomplished by getting teachers to use discussion around challenging tasks rather than reliance on skill building alone with lots of repetition (i.e. drill and kill approaches). <br /> <br /> While the original intent was to address needs of rural educators, these resources could easily be used in other sites, as they are not specific to rural educators – they just use a platform that allows teachers with differing locations and schedules to use the tools. We are also going to be field testing these resources in a large urban district as well. <br />
  • The Middle Start resources are based on an expert or coach-facilitated online set of activities that build trust and communication among several participant teachers that might not otherwise know each other. Activities online are designed like face-to-face professional learning communities, where teachers first work on common tasks, and then share ideas with each other. <br />
  • After some work reviewing student work to better understand what students know and what they don’t, teachers are presented with a variety of tasks on a particular concept to evaluate how these might develop student understanding and what level of understanding they would promote. The goal is to get teachers away from tasks that involve rote memorization or computation alone. <br />
  • After some work reviewing student work to better understand what students know and what they don’t, teachers are presented with a variety of tasks on a particular concept to evaluate how these might develop student understanding and what level of understanding they would promote. The goal is to get teachers away from tasks that involve rote memorization or computation alone. <br />
  • After some work reviewing student work to better understand what students know and what they don’t, teachers are presented with a variety of tasks on a particular concept to evaluate how these might develop student understanding and what level of understanding they would promote. The goal is to get teachers away from tasks that involve rote memorization or computation alone. <br />
  • After some work reviewing student work to better understand what students know and what they don’t, teachers are presented with a variety of tasks on a particular concept to evaluate how these might develop student understanding and what level of understanding they would promote. The goal is to get teachers away from tasks that involve rote memorization or computation alone. <br />
  • After some work reviewing student work to better understand what students know and what they don’t, teachers are presented with a variety of tasks on a particular concept to evaluate how these might develop student understanding and what level of understanding they would promote. The goal is to get teachers away from tasks that involve rote memorization or computation alone. <br />
  • After some work reviewing student work to better understand what students know and what they don’t, teachers are presented with a variety of tasks on a particular concept to evaluate how these might develop student understanding and what level of understanding they would promote. The goal is to get teachers away from tasks that involve rote memorization or computation alone. <br />
  • After some work reviewing student work to better understand what students know and what they don’t, teachers are presented with a variety of tasks on a particular concept to evaluate how these might develop student understanding and what level of understanding they would promote. The goal is to get teachers away from tasks that involve rote memorization or computation alone. <br />
  • <br />
  • <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • Go to second page handout - 5 x 8 grid problem. Let’s look at a sample of student work from the materials. Initially, teachers examine samples of student work on various problems to understand the nature of complex tasks and how they can bring out the level of understanding of students by reviewing their work. These also aim to develop an understanding that there is often not just one correct answer to any such problem. <br /> Here, for instance, we see three different samples where students were asked to use a 5 x 8 grid to show and see what percentage 6 such squares would be of the total. <br />
  • In order to get teachers to reflect on their own instruction, research suggests that the use of case studies, where one can basically “see” or “hear” what is going on in someone else’s classroom can be useful for teachers, in that they begin to make parallel associations with their own instruction. While there are some casebooks out there that do a fine job of this, they often involve lengthy descriptions of a whole class session that could be examined from multiple perspectives. Such approaches are less effective for online instruction, and so cases were developed to isolate instructional practices that focus on a particular issue that teachers might deal with in the module. Such cases are generally 3-4 pages long, and may include artifacts from the class that teachers can review from the online materials. <br />
  • In order to get teachers to reflect on their own instruction, research suggests that the use of case studies, where one can basically “see” or “hear” what is going on in someone else’s classroom can be useful for teachers, in that they begin to make parallel associations with their own instruction. While there are some casebooks out there that do a fine job of this, they often involve lengthy descriptions of a whole class session that could be examined from multiple perspectives. Such approaches are less effective for online instruction, and so cases were developed to isolate instructional practices that focus on a particular issue that teachers might deal with in the module. Such cases are generally 3-4 pages long, and may include artifacts from the class that teachers can review from the online materials. <br />
  • In order to get teachers to reflect on their own instruction, research suggests that the use of case studies, where one can basically “see” or “hear” what is going on in someone else’s classroom can be useful for teachers, in that they begin to make parallel associations with their own instruction. While there are some casebooks out there that do a fine job of this, they often involve lengthy descriptions of a whole class session that could be examined from multiple perspectives. Such approaches are less effective for online instruction, and so cases were developed to isolate instructional practices that focus on a particular issue that teachers might deal with in the module. Such cases are generally 3-4 pages long, and may include artifacts from the class that teachers can review from the online materials. <br />
  • After teachers have gone through all of the other analyses mentioned, a main component of the learning in these modules is through the facilitated community that teachers develop with colleagues over time. Once this understanding and trust has been built (especially difficult for rural teachers who might not have had to share aspects of their own practice before with other teachers), participants are asked to share examples of instruction from their own instruction, including student work, samples of tasks, and questions they might have about particular issues. <br />
  • After teachers have gone through all of the other analyses mentioned, a main component of the learning in these modules is through the facilitated community that teachers develop with colleagues over time. Once this understanding and trust has been built (especially difficult for rural teachers who might not have had to share aspects of their own practice before with other teachers), participants are asked to share examples of instruction from their own instruction, including student work, samples of tasks, and questions they might have about particular issues. <br />
  • After teachers have gone through all of the other analyses mentioned, a main component of the learning in these modules is through the facilitated community that teachers develop with colleagues over time. Once this understanding and trust has been built (especially difficult for rural teachers who might not have had to share aspects of their own practice before with other teachers), participants are asked to share examples of instruction from their own instruction, including student work, samples of tasks, and questions they might have about particular issues. <br />
  • After teachers have gone through all of the other analyses mentioned, a main component of the learning in these modules is through the facilitated community that teachers develop with colleagues over time. Once this understanding and trust has been built (especially difficult for rural teachers who might not have had to share aspects of their own practice before with other teachers), participants are asked to share examples of instruction from their own instruction, including student work, samples of tasks, and questions they might have about particular issues. <br />
  • The eventual goal is to develop a deeper understanding of content. This is addressed in two ways. First, all such tasks, student work, and other artifacts of classroom learning are evaluated with respect to the depth of understanding of the content that students might have, using evaluation schemes like Bloom’s Taxonomy and the Mathematical Task Framework (from Ed Silver and Peg Smith). <br /> (hit return key here) <br /> Second, these tasks are used to develop the teachers’ understanding of middle grades mathematical concepts that are most challenging. After an introductory module, teachers can participate in specialized modules that focus in depth on content in ratio and proportion, algebraic reasoning and functions, geometry and measurement, and data and probability. We are hoping to add an additional module on problem solving processes and strategies. <br />
  • The eventual goal is to develop a deeper understanding of content. This is addressed in two ways. First, all such tasks, student work, and other artifacts of classroom learning are evaluated with respect to the depth of understanding of the content that students might have, using evaluation schemes like Bloom’s Taxonomy and the Mathematical Task Framework (from Ed Silver and Peg Smith). <br /> (hit return key here) <br /> Second, these tasks are used to develop the teachers’ understanding of middle grades mathematical concepts that are most challenging. After an introductory module, teachers can participate in specialized modules that focus in depth on content in ratio and proportion, algebraic reasoning and functions, geometry and measurement, and data and probability. We are hoping to add an additional module on problem solving processes and strategies. <br />
  • The eventual goal is to develop a deeper understanding of content. This is addressed in two ways. First, all such tasks, student work, and other artifacts of classroom learning are evaluated with respect to the depth of understanding of the content that students might have, using evaluation schemes like Bloom’s Taxonomy and the Mathematical Task Framework (from Ed Silver and Peg Smith). <br /> (hit return key here) <br /> Second, these tasks are used to develop the teachers’ understanding of middle grades mathematical concepts that are most challenging. After an introductory module, teachers can participate in specialized modules that focus in depth on content in ratio and proportion, algebraic reasoning and functions, geometry and measurement, and data and probability. We are hoping to add an additional module on problem solving processes and strategies. <br />
  • The eventual goal is to develop a deeper understanding of content. This is addressed in two ways. First, all such tasks, student work, and other artifacts of classroom learning are evaluated with respect to the depth of understanding of the content that students might have, using evaluation schemes like Bloom’s Taxonomy and the Mathematical Task Framework (from Ed Silver and Peg Smith). <br /> (hit return key here) <br /> Second, these tasks are used to develop the teachers’ understanding of middle grades mathematical concepts that are most challenging. After an introductory module, teachers can participate in specialized modules that focus in depth on content in ratio and proportion, algebraic reasoning and functions, geometry and measurement, and data and probability. We are hoping to add an additional module on problem solving processes and strategies. <br />
  • The eventual goal is to develop a deeper understanding of content. This is addressed in two ways. First, all such tasks, student work, and other artifacts of classroom learning are evaluated with respect to the depth of understanding of the content that students might have, using evaluation schemes like Bloom’s Taxonomy and the Mathematical Task Framework (from Ed Silver and Peg Smith). <br /> (hit return key here) <br /> Second, these tasks are used to develop the teachers’ understanding of middle grades mathematical concepts that are most challenging. After an introductory module, teachers can participate in specialized modules that focus in depth on content in ratio and proportion, algebraic reasoning and functions, geometry and measurement, and data and probability. We are hoping to add an additional module on problem solving processes and strategies. <br />
  • The eventual goal is to develop a deeper understanding of content. This is addressed in two ways. First, all such tasks, student work, and other artifacts of classroom learning are evaluated with respect to the depth of understanding of the content that students might have, using evaluation schemes like Bloom’s Taxonomy and the Mathematical Task Framework (from Ed Silver and Peg Smith). <br /> (hit return key here) <br /> Second, these tasks are used to develop the teachers’ understanding of middle grades mathematical concepts that are most challenging. After an introductory module, teachers can participate in specialized modules that focus in depth on content in ratio and proportion, algebraic reasoning and functions, geometry and measurement, and data and probability. We are hoping to add an additional module on problem solving processes and strategies. <br />
  • The eventual goal is to develop a deeper understanding of content. This is addressed in two ways. First, all such tasks, student work, and other artifacts of classroom learning are evaluated with respect to the depth of understanding of the content that students might have, using evaluation schemes like Bloom’s Taxonomy and the Mathematical Task Framework (from Ed Silver and Peg Smith). <br /> (hit return key here) <br /> Second, these tasks are used to develop the teachers’ understanding of middle grades mathematical concepts that are most challenging. After an introductory module, teachers can participate in specialized modules that focus in depth on content in ratio and proportion, algebraic reasoning and functions, geometry and measurement, and data and probability. We are hoping to add an additional module on problem solving processes and strategies. <br />
  • The second resource of the toolkit focuses on the issue of family engagement. While this is not necessarily addressing a special population within the classroom, as the other toolkit resources focus on, it does address a issue often ignored or not considered as vital to mathematics education reform. These resources are also part of the online modules from Middle Start, but include several resources for teachers to use to see how community engagement can play a critical role in improving mathematics education. There are several issues involved here, but the primary ones specific to mathematics are that most parents don’t understand the content to the depth we want teachers to address, and that they approaches parents take when they do help their children with math are often contradictory to the understandings and messages that we want to promote, because they are based on generation-old approaches, antipathy toward mathematics, and stereotypes about abilities in mathematics. <br />
  • The second resource of the toolkit focuses on the issue of family engagement. While this is not necessarily addressing a special population within the classroom, as the other toolkit resources focus on, it does address a issue often ignored or not considered as vital to mathematics education reform. These resources are also part of the online modules from Middle Start, but include several resources for teachers to use to see how community engagement can play a critical role in improving mathematics education. There are several issues involved here, but the primary ones specific to mathematics are that most parents don’t understand the content to the depth we want teachers to address, and that they approaches parents take when they do help their children with math are often contradictory to the understandings and messages that we want to promote, because they are based on generation-old approaches, antipathy toward mathematics, and stereotypes about abilities in mathematics. <br />
  • The second resource of the toolkit focuses on the issue of family engagement. While this is not necessarily addressing a special population within the classroom, as the other toolkit resources focus on, it does address a issue often ignored or not considered as vital to mathematics education reform. These resources are also part of the online modules from Middle Start, but include several resources for teachers to use to see how community engagement can play a critical role in improving mathematics education. There are several issues involved here, but the primary ones specific to mathematics are that most parents don’t understand the content to the depth we want teachers to address, and that they approaches parents take when they do help their children with math are often contradictory to the understandings and messages that we want to promote, because they are based on generation-old approaches, antipathy toward mathematics, and stereotypes about abilities in mathematics. <br />
  • Before teachers can start using remediation approaches with parents or their community, they need to understand the general issues and “state of readiness” of the school and community to work together on these issues. Often, having data from the community and knowledge of challenges in building a positive relationship with parents is a necessary pre-cursor to engaging in deep, sustained work within the community to improve mathematics education. Introductory activities from the tools aim to identify potential conflicts and challenges, and recognize the issues of greatest priority in any particular community, as these are not universal. <br />

Csrqi Nmsa Presentation2 Csrqi Nmsa Presentation2 Presentation Transcript

  • From Wall Charts to Web Sites: The National Forum Mathematics Improvement Sara Freedman Steve Best (in lieu of Deborah Kasak) NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Goals for this Presentation Provide background on the  purpose of the toolkit, and the teaching and learning needs it was designed to meet  Introduce the toolkit and its components  Walk you through some of the actual PD activities embedded within these tools NMSA Conference, Denver, CO 2 Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • What is the Mathematics Improvement Toolkit? NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • What is the Mathematics Improvement Toolkit? Joint venture of four groups to  utilize expertise to address special populations  Provides support for teachers, professional developers, decision makers, and students around middle grades mathematics instruction  Addresses specific instructional NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Goals of the Project NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Goals of the Project Resources to address instructional  needs of: English Language Learners Students with Special Needs Students and Teachers in Rural Settings Communities and Families Develop an online tool to guide  decision makers and educators in planning and implementing professional development NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Partners NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Partners National Forum for Middle Grades  Reform Talent Development  (Johns Hopkins University) Turning Points  (Center for Collaborative Education) Educational Development Center  Middle Start  (Academy for Educational Development) NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • NMSA Conference, Denver, CO 6 Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Common Ideas / NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Common Ideas / Mathematics instruction needs to  focus on building deeper conceptual understanding  Resources are designed for use in professional development with math teachers and others supporting mathematics learning for ALL students  Materials need to focus on getting teachers to reflect NMSA Conference, Denver, CO on practice Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Professional Development NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 1: English Language NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 1: English Language Issues: Teachers need support to  ensure that English Language Learners have access to and are successful in learning high-level mathematics.  Primary Resources: Videos and facilitator materials to guide mathematics instructors in recognizing issues and modifying instructional practices and tasks. NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... What student engagement on a high level looks like for English language learners I wonder if/how/ I notice that... whether... On this side, “talk back to Write down the text” – ask questions, everything you make comments see on this side. NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Wednesday, March 18, 2009
  • Wednesday, March 18, 2009
  • Wednesday, March 18, 2009
  • Wednesday, March 18, 2009
  • Wednesday, March 18, 2009
  • Wednesday, March 18, 2009
  • Wednesday, March 18, 2009
  • What did you think? What student engagement on a high level looks like for English language learners I wonder if/how/ I notice that... whether... NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job? NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... A certain construction job usually takes four workers six hours. Today, one worker called in sick, so there are only three workers. How long should it take them to do the job? What specific challenges do you think an English language learner in the middle grades might have in trying to answer the question posed by this problem? 1) What are some language difficulties in this problem? 2) What are some math difficulties in this problem? 3) What are some cultural features that could cause difficulty in understanding this problem? NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Issues: Curriculum materials do  not support students with special learning needs. NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Issues: Curriculum materials do  not support students with special learning needs.  Primary Resources: Modified curriculum resources, student materials, and instructional practices based on Universal Design for Learning principles NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Issues: Curriculum materials do  not support students with special learning needs.  Primary Resources: Modified curriculum resources, student materials, and instructional practices based on Universal Design for Learning principles  Resources need to be NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Students come into  a class with varying levels of understanding NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Students come into  a class with varying levels of understanding Some students  need explicit instruction to get to a functional level NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Demonstration - I do Students come into  a class with varying 0 - 20% proficiency levels of understanding Guided Practice - We do Some students  20 - 80% proficiency need explicit instruction to get Independent - You do to a functional level 80 - 100% proficiency NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Students come into  a class with varying levels of understanding Some students  need explicit instruction to get to a functional level Students need  support for visual, NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Students come into  a class with varying levels of understanding Some students  need explicit instruction to get to a functional level Students need  support for visual, NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Issues: Teachers need support for  instruction of students with special needs NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Issues: Teachers need support for  instruction of students with special needs  Primary Resources: Videos and facilitator guide for workshops to support co-teaching and literacy strategies to address the needs of all learners NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Issues: Teachers need support for  instruction of students with special needs  Primary Resources: Videos and facilitator guide for workshops to support co-teaching and literacy strategies to address the needs of all learners  Teachers often need to SEE what NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Language Module  ! topics: ! !quot;#$%&'!()*!!+,quot;'-.!/0..0#1! ! 2&3.'0%#*!!quot;!#$$!%&'!(')%#*+$',!%&#%!)#*!-'!quot;.(/'0!quot;(./!12!,34#('!%5$',6!7&#%!#('!  Challenges of %&'!05/'*,5.*,!.quot;!%&'!(')%#*+$'!75%&!%&'!+('#%',%!8'(5/'%'(9! ! ! ! vocabulary in 4'&$3#'!53.6%#.3! !:;&'!,50',!.quot;!%&'!,&#8'!75%&!%&'! mathematics $.*+',%!7#<!#(.4*0!5,!12!#*0!1=! ;&'!,&#8'!75%&!%&'!$.*+',%!7#<! #(.4*0!&#,!#!>'(<!$.*+!,&#8'=?!  instructional ! ! 1= @*0'($5*'!%&'!>.)#-4$#(<!%'(/,!5*!%&'!34',%5.*!#*0!%&'!/#%&!>.)#-4$#(<! strategies 4,'0!-<!%&'!,%40'*%=! ! ! ! !  planning for A= B&#%!>.)#-4$#(<!%'(/,!0.!<.4!quot;''$!#('!/5,,5*+!quot;(./!%&'!,%40'*%C,!7.(D9! ! ! vocabulary ! ! ! ! instruction E= F5,)4,,!<.4(!#*,7'(,!#*0!,./'!8.,,5-$'!,%(#%'+5',!%.!&'$8!%&5,!,%40'*%=! ! !  assessment of ©2008, Education Development Center, Inc. vocabulary NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... Question: Of all of the rectangles that can be formed from 16 square tiles, what are the dimensions of the rectangle of the greatest perimeter? Student response: “The sides of the shape with the longest way around is 16 and 1. The shape with the longest way around has a very long shape.” NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... Question: Of all of the 1. Identify the vocabulary rectangles that can be formed terms in the question and from 16 square tiles, what are the math vocabulary used the dimensions of the rectangle by the student. of the greatest perimeter? 2. What vocabulary terms do you feel are missing Student response: from the student’s work? “The sides of the shape with 3. Discuss your answers the longest way around is 16 and some possible and 1. The shape with the strategies to help this longest way around has a very student. long shape.” NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Language Module  Resources:  Video Clips  Facilitator Notes  Presentation materials  Handouts and other resources NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 2: Students with Special Learning Needs Co-teaching Module topics: • Models of collaboration / co- teaching • Co-teaching strategies • Co-teaching roles • Communication and planning between co-teachers NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Biggest hurdle:  Access to quality mathematics PD NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Biggest hurdle:  Access to quality mathematics PD  Primary Resources: Online professional development program, PD materials focusing on depth of understanding and appropriate instruction NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Biggest hurdle:  Access to quality mathematics PD  Primary Resources: Online professional development program, PD materials focusing on depth of understanding and appropriate instruction  High quality PD in mathematics NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Modifying a Task: Task 1 Online community   Focus on mathematics The Old Farmer’s Almanac suggests that you can tell the temperature outside by tasks as a lens to counting the chirps a cricket makes in 14 seconds and examine teaching adding 40 (to get the temperature in degrees practice and student Fahrenheit). Use this to find how many chirps the cricket understanding makes when it is 72 degrees. middlestart NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Modifying a Task: Task 5 Online community   Focus on mathematics What type of sequence is shown in the figures at the right? Explain. tasks as a lens to a) Linear b) Quadratic 1 3 6 examine teaching c) Exponential practice and student d) None of the above understanding 10 15 middlestart NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community   Focus on mathematics Mathematical Task tasks as a lens to Framework examine teaching (Stein and Smith, 1998) practice and student understanding Tasks as Tasks as enacted they Tasks as by appear in set up by teachers Student curriculum teachers and materials learning students NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... NMSA Conference, Denver, CO 31 Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... Shade 6 of the small squares in the rectangle shown below. Using the diagram, explain how to determine each of the following: 1. the percent area that is shaded 2. the decimal part of the area that is shaded 3. the fractional part of the area that is shaded. NMSA Conference, Denver, CO 31 Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Let’s try a task... Shade 6 of the small squares in the rectangle shown below. Using the diagram, explain how to determine each of the following: 1. the percent area that is shaded 2. the decimal part of the area that is shaded 3. the fractional part of the area that is shaded. NMSA Conference, Denver, CO 31 Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community   Focus on mathematics tasks as a venue for examining student understanding and teaching practice  Review student work NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community   Focus on mathematics tasks as a venue for examining student understanding and teaching practice  Review student work NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community   Focus on mathematics tasks as a venue for examining student understanding and teaching practice  Review student work NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community   Focus on mathematics tasks as a venue for examining student understanding and teaching practice  Review student work NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community   Focus on mathematics tasks as a venue for examining student understanding and teaching practice  Review student work Tasks as Tasks as enacted they Tasks as by appear in set up by teachers Student curriculum teachers and materials learning students NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  middlestart  Focus on mathematics Module 1 - Case 1: David Orcutt tasks as a venue for This mini-case provides an introduction to the use of cases as a reflective professional development tool, and is not intended for sustained use. This also uses student work examples to explore understandings and misconceptions around fractions, percents, and decimals. examining student INTRODUCTION AND CONTEXT David Orcutt is one of two 7th grade mathematics teachers in the lone junior high school for this district. The district serves students from a largely rural agricultural and recreational area which understanding and includes two villages. The school is a 7-8 school in a small school building next to the district’s high school. In fact, a number of teachers are on the faculty of both schools to provide appropriate coverage for topic areas. David has four classes among his other duties as the 7th grade advisor and a track coach. teaching practice In his three years of teaching, he has learned that students coming in from the two K-6 schools in the district (as well as a small but growing migrant labor population that is becoming a more permanent fixture in the area) often have varying skills and understanding in mathematics. To understand each of the student’s abilities and conceptions about basic topics, he has devised a  Review student work two week introduction to his course which addresses a different topic from the grade 4-6 standards each day or two, and uses this to establish norms for classroom participation, work expectations, etc. The following sample of classroom interaction starts by asking students to take out the homework task from the previous day, which was really a pre-assessment of sorts to understand student knowledge of decimals, percents, and fractions.  Use of brief case studies CLASSROOM ACTIVITIES David starts class by greeting all students at the door as they come in, and has a problem on the board, which he reminds students to get a paper out and copy the problem down after they have to encourage reflection taken their homework out from the previous day. Meanwhile, he checks attendance and missing assignments from the previous day, and then begins wandering through the aisles to see what students are doing with the problems on the board, and whether they have their homework out. He quickly scans the homework for each student, noting whether they have all twenty problems done, and whether they have them numbered, the problem written down, and the answer underlined for each. Most do, which results in him writing a “10” on the top of the page, but a couple did not finish, receiving 5 and 7 points respectively, and three others had 3 points deducted from these for not organizing their work properly. For these, David underlined a few of the answers they had in their work that were not already underlined, and had jotted down the words “show your steps” on some of these papers. While doing this, he marked on a copy of a grade sheet the points for the homework assignment for each student. Following this fairly quick review (which took four minutes from the time he started moving around the room), he told the students they would review the answers of the homework. He circled the room as he called out problem numbers, and would look around the room to see who was looking at him (or not) and would call out the names of students to state what their answer was. Once one student gave the answer, he would call on two other students and ask if they came up with the NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  same answer as the original student, or if they had something different. At every problem in which  Focus on mathematics all students agreed on the answer, he would quickly ask if any other answers were out there, and unless a quick response came, he would say “correct” and repeat the problem number and answer and move on. When students disagreed, he would quickly survey students in the room to see which of the stated answers other students got, or, what other answers people came up with, tasks as a venue for and unless it seemed that one was an outlier, would note that problem number of the whiteboard, so that the class could go through it after checking homework. Six of the problems were noted on the board, and he they asked, problem by problem, if there were any volunteers to go to the board and do the problem. Two of the problems had no volunteers, so he asked one student what examining student answer they got for the problem, then asked if anyone had a different answer, and had both (or more if several different answers arose) go up to the board to write their explanation or procedures for the problem. understanding and One of the two problems that had contested answers was the following: ! Emma was asked to order the following numbers from smallest to largest: .43, 8%, and .7 ! Emma’s order was: .7, 8%, .43 ! Is she correct? Why or why not? teaching practice Two students wrote their answers on the board initially as shown below. Student D: No because .43 is just about half and .7 is almost full and 8% is like 8 1s. .43 .7 8% Student F: She is correct because 7 is the smallest and 43 is the biggest  Review student work The following dialog is taken from this activity: DO: “So, what do we think everyone. We have two answers here. What do we think?”  Use of brief case studies Student H: “[D] is right. Emma didn’t get the right answer.” DO: “And why is that?” to encourage reflection H: “Well, sort of right. Emma didn’t get the right answer, but [D] didn’t get it right either.” DO: “[F], what you you think? You said Emma got the right answer. Explain what you said.” F: “Well, the numbers get larger, um, in Emma’s order, and, um, the dots and percents are the same cause you can change from dots to percents and so I, um put them in order, and so, um, 7 is smallest, then 8, then 43.” H: “But they aren’t the same. Dots are two places different.” DO: “[D], what do you think? You said Emma wasn’t right, just like [H], but she said you weren’t either. What do you think?” D: “I was just trying to see what they are close to, and .43 is close to .5, which is a half. .7 is bigger. It is nearly a whole thing, and definitely more than half. The percents don’t have the decimals, so I thought 8% is like 8 whole things. But I think [H] is kinda right, um, ‘cause you have to do move the dot two places.” NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  DO: “Let’s see what someone else says. [G], how about you? What did you say?”  Focus on mathematics G: “I said Emma was wrong. It should be 8%, .43, .7 in that order because I put them all in percents.” tasks as a venue for DO: “Aha. There we go. You put them all in percents. All in the same units. That is exactly what we want to do when we have decimals and percents together is put them in the same units. [H], is that what you meant? Is that what you did?” examining student H: “Yeah, I made them all the same, but I didn’t do percents. I changed percents to fractions, so they were all some part of 100.” DO: “Excellent. There we go. We want to change them all to the same, and the best way is to understanding and change them to fractions. Since we have percents, we should change them to parts of 100. That is what percents really are. They are parts of 100. So, when you have all of your test right, for instance, you have 100%. You get everything out of 100. So, how do we want to change these to fractions of 100?” teaching practice C: (called on after raising hand) “If it is one place. like .7 was, that is 7 out of 10, because the first place is tenths. Then hundredths. so we could add a zero to the end of that, because .7 is the same as .70, and that is seventy out of a hundred.”  Review student work DO: “Great. That’s exactly it. Are we okay? Can we move on?” No responses, so they go on to the next question. Shortly thereafter, David moves through the other answers, and to the boardwork task. This task is written on the board already. It was modified by David from a task he had seen in a workshop focusing on differentiation, which was  Use of brief case studies addressing visual learners. The original task from the workshop is below. Shade 10 of the small squares in the rectangle shown below. Using the diagram, explain how to determine each of the following: a) the percent area that is shaded, b) the decimal part of the area that is shaded, and to encourage reflection c) the fractional part of the area that is shaded. David’s modified version that is on the board is the following: Shade 10 of the boxes in the rectangle shown below (same rectangle). Find the percent area that is shaded. David says that, in the interest of time, he is going to go through it, and asks students to watch. He shades in 10 of the rectangles, picking them at random, and shading individual rectangles. NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community   Focus on mathematics DO: “So, it really doesn’t matter which ones I pick, it will be the same. What I really care about is how many total ones we have. [A], how many total boxes are there?” A: “40” tasks as a venue for DO: “And how did you get that?” A: “I counted ten across, and there are four rows, so it was four times ten.” examining student DO: “Exactly... or you could count everyone of them if you didn’t figure that out. So, what next (looking at A)?” understanding and A: “Well, it is a quarter. There are 10 out of 40, and if we write that as a fraction (DO pauses A with a hand gesture and writes this on the board as the fraction 10/40, and then motions for him to proceed)... so yeah, that’s it. And then you can cross out the zeros, cause 10 out of 40 is like 1 out of 4, and that’s a quarter. And a quarter is always 25%.” teaching practice DO: “Exactly. Does everyone see that? Once [A] got it to a fraction, he could easily change it to a percent. If it was a fraction you didn’t know already, like... suppose we had 12 shaded boxes instead? You could make it 12 out of 40, and then cross multiply to figure out the number out of 100 (as he draws on the board ‘12/40 = n/100’ and then proceeds to write, ’12 x 100 = n x 40’),  Review student work and so in this case you could multiple 12 and 100...[A], what is that?” A: “Twelve and a hundred? That’s one thousand two hundred.” DO: “and divide that by 40 and we would get 30. Thirty percent... if it was twelve out of 100.” Do  Use of brief case studies you all see that? The class seems to agree quietly, and David moves on to the next part of class... to encourage reflection NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  Focus on mathematics  tasks as a venue for examining student understanding and teaching practice Review student work  Use of brief case studies  to encourage reflection Teachers share examples,  observations, and reflections on own and others practice NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community Online discussion  Focus on mathematics  tasks as a venue for examining student Lesson library understanding and teaching practice Review student work Chat/room and live  Use of brief case studies  whiteboard to encourage reflection Teachers share examples,  observations, and Video and reflections on own and artifact upload others practice NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  Focus on mathematics  tasks as a venue for examining student understanding and teaching practice Review student work  Use of brief case studies  to encourage reflection Teachers share examples,  observations, and reflections on own and others practice Develop deeper  understanding of content NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community  Focus on mathematics  tasks as a venue for examining student understanding and teaching practice Review student work  Use of brief case studies  to encourage reflection Teachers share examples,  observations, and reflections on own and others practice Develop deeper  understanding of content NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 3: Rural Education Online community Introductory   Content and Focus on mathematics  tasks as a venue for processes examining student understanding and Ratio/Proportion teaching practice  Review student work  Use of brief case studies Algebraic   to encourage reflection Reasoning/ Teachers share examples,  Patterns/Functions observations, and reflections on own and Geometry and  others practice Measurement Develop deeper  understanding of content NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Issues: Schools struggle with this in  general and many mathematics issues for students arise from parent/ community misunderstandings, stereotypes, and attitudes toward math. NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Issues: Schools struggle with this in  general and many mathematics issues for students arise from parent/ community misunderstandings, stereotypes, and attitudes toward math. Primary Resources:  Online PD tools for schools and teachers that guide them through family engagement NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment  and introductory activities NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment  and introductory activities NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment  and introductory activities Sample discussion  materials (big picture) and communications NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment  and introductory activities Sample discussion  materials (big picture) and communications NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment  and introductory activities Sample discussion  materials (big picture) and communications Strategies to  provide awareness of approaches to learn NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment Family Math Night  and introductory activities Career Sample discussion  awareness materials (big programs picture) and communications Afterschool tutoring Strategies to  provide awareness Regular of approaches to communication learn with parents NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment  and introductory activities Sample discussion  materials (big picture) and communications Strategies to  provide awareness of approaches to NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • Focus 4: Family Needs assessment  and introductory activities Sample discussion  materials (big picture) and communications Strategies to  provide awareness of approaches to NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • For more information… NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
  • For more information… Complete the email signup sheet   Denote any specific tools that you are interested in using  Visit: http://www.mgforum.org NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009