LinkedIn emplea cookies para mejorar la funcionalidad y el rendimiento de nuestro sitio web, así como para ofrecer publicidad relevante. Si continúas navegando por ese sitio web, aceptas el uso de cookies. Consulta nuestras Condiciones de uso y nuestra Política de privacidad para más información.

LinkedIn emplea cookies para mejorar la funcionalidad y el rendimiento de nuestro sitio web, así como para ofrecer publicidad relevante. Si continúas navegando por ese sitio web, aceptas el uso de cookies. Consulta nuestra Política de privacidad y nuestras Condiciones de uso para más información.

Se ha denunciado esta presentación.

¿Recomiendas esta presentación? ¿Por qué no compartes?

669 visualizaciones

Publicado el

Sin descargas

Visualizaciones totales

669

En SlideShare

0

De insertados

0

Número de insertados

4

Compartido

0

Descargas

3

Comentarios

0

Recomendaciones

2

No insertados

No hay notas en la diapositiva.

Special learning needs

English Language Learners

Rural Students

Special learning needs

English Language Learners

Rural Students

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.

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.

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.

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.

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.

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.

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.

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.

Students are using manipulatives to create models.I wonder if manipulatives allow all students to begin working on the problem.

Students are recording their results in an organized fashion. I wonder if the teacher gave them any sort of template or model.

Students discover how to use manipulatives in a variety of ways.I wonder how the students will work with each other after working separately.

I wonder if it would have been better if the students had worked as a team to

build one model together.

For example, in this slide the students might notice that:

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

if this type of organization helps students focus on the important concepts presented in each lesson,

as well as providing a good example of the importance of organization.

Other possible “noticings:

The “Do Now” asks a non-mathematical question.” “I wonder what mathematical concept will be the focus on the lesson.

“I wonder why the “Do Now” is not a math problem.

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.

diagrams written on it.I wonder when students work individually and when they work in groups.

I wonder how writing is used in a classroom to support ELLs.

The two boys are serious, one’s lips are pierced in concentration, both of their eyes are focused solely

On the paper.

The two boys are sitting close to each other.

The teacher is working with one boy.I wonder how the teacher decides what to say to each student as she works with them.

Each boy seems to be working in a different way.

One boy has some money on top of a worksheet.

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.

One student is writing on another student’s paper.

Both students are using their pencils.

The two students are working side by side, desks close to each other.

Both students are looking at the work, not at each other.

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.

Students show their work to each other as a way of comparing results.

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.

Students are writing their work on templates.I wonder how templates help students better understand the concept.

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.

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.

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.

The rest of this should be developed by Talent Development.

The rest of this should be developed by Talent Development.

The rest of this should be developed by Talent Development.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

(hit return key here)

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.

(hit return key here)

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.

(hit return key here)

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.

(hit return key here)

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.

(hit return key here)

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.

(hit return key here)

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.

(hit return key here)

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.

- 1. 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
- 2. 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
- 3. What is the Mathematics Improvement Toolkit? NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 4. 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
- 5. Goals of the Project NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 6. 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
- 7. Partners NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 8. 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
- 9. NMSA Conference, Denver, CO 6 Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 10. Common Ideas / NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 11. 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
- 12. Professional Development NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 13. Focus 1: English Language NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 14. 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
- 15. 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
- 16. Wednesday, March 18, 2009
- 17. Wednesday, March 18, 2009
- 18. Wednesday, March 18, 2009
- 19. Wednesday, March 18, 2009
- 20. Wednesday, March 18, 2009
- 21. Wednesday, March 18, 2009
- 22. Wednesday, March 18, 2009
- 23. 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
- 24. Let’s try a task... NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 25. 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
- 26. 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
- 27. Focus 2: Students with Special Learning Needs NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 28. 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
- 29. 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
- 30. 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
- 31. Focus 2: Students with Special Learning Needs NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 32. 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
- 33. 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
- 34. 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
- 35. 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
- 36. 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
- 37. Focus 2: Students with Special Learning Needs NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 38. 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
- 39. 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
- 40. 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
- 41. 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;!%&'!,'!75%&!%&'! mathematics $.*+',%!7#<!#(.4*0!5,!12!#*0!1=! ;&'!,'!75%&!%&'!$.*+',%!7#<! #(.4*0!&#,!#!>'(<!$.*+!,'=?! 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
- 42. Let’s try a task... NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 43. 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
- 44. 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
- 45. 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
- 46. 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
- 47. Focus 3: Rural Education NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 48. Focus 3: Rural Education Biggest hurdle: Access to quality mathematics PD NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 49. 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
- 50. 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
- 51. Focus 3: Rural Education Online community NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 52. Focus 3: Rural Education Online community NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 53. 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
- 54. 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
- 55. 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
- 56. Let’s try a task... NMSA Conference, Denver, CO 31 Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 57. 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
- 58. 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
- 59. 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
- 60. 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
- 61. 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
- 62. 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
- 63. 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
- 64. 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
- 65. 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
- 66. 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
- 67. 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
- 68. 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
- 69. 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
- 70. 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
- 71. 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
- 72. 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
- 73. Focus 4: Family NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 74. 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
- 75. 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
- 76. Focus 4: Family Needs assessment and introductory activities NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 77. Focus 4: Family Needs assessment and introductory activities NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 78. 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
- 79. 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
- 80. 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
- 81. 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
- 82. 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
- 83. 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
- 84. For more information… NMSA Conference, Denver, CO Mathematics Improvement Toolkit Wednesday, March 18, 2009
- 85. 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

No se han encontrado tableros de recortes públicos para esta diapositiva.

Parece que ya has recortado esta diapositiva en .

Crear un tablero de recortes

Sé el primero en comentar