Monday, February 28, 2011

Curriculum Analysis

As I promised this is the final project for my Curriculum and instruction course. There are three parts. The Youtube presentation, a template, and a written report.

Assignment #2
Curriculum Analysis Template

Record your responses to each of the questions in the Analysis column based on your review of a curriculum guide.

Part 1: Overview of Format, Organization, and Scope

Which curriculum document are you analyzing?
Title: 8th grade Connected Math 2 textbook
Author: Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N. Friel, Elizabeth Difanis Philips
What documents are you using?
Teachers Edition
For which grade level(s) and specific populations was the curriculum developed? 
8th grade Math regular education.
Who developed the curriculum and what expertise did they have in the content area?
Glenda Lappan-Professor in the Department of Mathematics at Michigan State University
James T. Fey-Professor of Curriculum and Instruction and Mathematics at the University of Maryland
William M. Fitzgerald-(deceased) was professor in the Department of Mathematics at Michigan State University
Susan N. Friel-Professor of Mathematics Education School of Education at the University of North Carolina
Elizabeth Difanis Philips-Senior Academic Specialist in the Mathematics Department of Michigan State University
What materials or other resources did they use in the curriculum development?
Field tested by over 100 classroom teachers at 49 school sites in 12 states and the District of Columbia
Were teachers involved in the development? Did teachers have an opportunity to review or pilot the curriculum before its release? Is there any indication that there will be ongoing support for teachers using the curriculum?
Teachers were instrumental on helping review the textbook and suggest improvements. The University of Michigan runs a training session during the summer. Having spoken to some of the authors I know they are very passionate about quality math education and are continually working towards improvement of the series.
Is the relationship between and among the various sections of the document(s) clear and logical?
The curriculum is broken into 8 separate books. Each book focuses on specific goals. Often skills or strategies used when working on one skill will transfer or be used to discover new skills in another section of the book.
Is there a system that will allow users to add details and set objectives for instruction based on the document?
Lessons are suggested based on either a 40 minute math period or a block schedule. Lessons of course have objectives set, but not all lessons have to be taught (the book even suggests which lessons to skip if necessary)
Does the document have a wide range of content that could be used as a scope and sequence by a curriculum committee at the system or school level?
The series was designed specifically to meet curricular the needs of a school.
How would the document help a classroom teacher plan?
A teacher could just follow the books from cover to cover and teach a decent year of 8th grade math. The books also explain the math concept behind each lesson giving the teacher the opportunity to understand the lesson objective more fully.
If the teacher looks at each individual book as a unit and follows the pacing guide within the book the program plans itself. With the supplemental CD-ROM it will even create a lesson plan complete with alignment to state standards.
It has been my experience teaching this book that some of the lessons examples are kind of contrived, but that the teacher can substitute alternative stories and or situations that can involve the students more. 
Why was the document developed? (Think about: Was there a problem to be solved or a need that had to be filled?)
The Connected Math text was developed specifically as a better method of teaching middle school math. It is completely student-centered, allowing the math students to “discover” math concepts on their own. Each lesson or “investigation” is a mini science lesson asking students to answer questions that will hopefully illuminate a skill. Each section, a group of 4 or 5 lessons, will have an overall theme and connect together to create one concept. Each book has 4 or 5 sections that are all connected with a common theme, such as quadratic relationships.
II:  Content of the Curriculum Document
Does the document describe a philosophical basis for the curriculum document? Does it appear to be connected to a specific learning theory? Is there a statement of vision for the curriculum? What definition of curriculum did the authors use?
“What to teacher” and “How to teach it” are inextricably linked. (p. 2 Implementing and teaching guide) The Connected math curriculum is based on research from cognitive sciences mathematics education and education policy and organization. Overall the curriculum is a problem based curriculum.
Their definition seems to be: what is taught, how it is taught, skills, conceptual understanding and assessments in the form of quizzes, tests, and projects.
Does the document describe in detail the scope and sequence of the curriculum? What content did the authors think was the most important? Does the document describe a time frame for implementing the curriculum?
There is a very detailed scope and sequence chart for all grades 6th – 8th. The 8th grade course of study is almost entirely review of previously learned material It does however have a very broad reach, covering almost every topic in the curriculum.
What skills are needed before the curriculum is taught?
Basic multiplication and division skills are expected before the 6th grade section of the curriculum is introduced. If students learn using the Connected Math curriculum by 8th grade they are expected to have the skills necessary to achieve the tasks.
Is there a clear alignment with national standards in the content area? Describe how they are aligned. 
The Connected Math curriculum is standards based. The books I have are older than the Common Core Standards, but from what I have heard and seen they should already meet the new standards.
Is there an integration of appropriate technologies to maximize teaching and learning?
The original curriculum can be taught using only pen, paper, and an overhead projector.
How could the curriculum and learning environment be designed to meet ISTE’s NETS Standards for Administrators and Teachers?

How is the content of the curriculum aligned with your state curriculum (such as the Maryland Voluntary State Curriculum)? Give examples.
Each lesson has been reviewed by experts and aligned to specific standards in the state curriculum. The curriculum does meet all of Illinois standards, some better than others.

Is there support for differentiated instruction?  For what type of students, e.g. special needs, gifted?  How is the curriculum differentiated?  If there are no suggestions for differentiated instruction, what would you recommend? Are there recommendations for accommodations for students with special learning needs? Are there any suggestions for assistive technology resources?
The curriculum is based on cooperative groups and discovery based learning. Each unit usually begins with concrete hands on activity and builds towards a concept. There is an entire special needs book filled with alternative activities for students who have difficulty with the regular curriculum.
I also suggest suing some video taped lessons for students to watch online when they need or want it. Some teachers do this with Compass Learning and find it very helpful.
Is there a multicultural approach to the curriculum? Is the curriculum appropriate for your school and community? Can you “see” all students in the curriculum?
I don't know if it is intentionally multicultural, but it does work well with our population.
Is there evidence of interdisciplinary connections in the curriculum? Do students have opportunities to apply what they are learning in real world situations?
There is some interdisciplinary connections, but there could be more.
Does the curriculum provide sample lesson plans?
Yes. The curriculum has full lesson plans complete with alignment to the state standards.
Does the curriculum provide assessments (formative and summative) to measure mastery of curriculum?
Yes. The curriculum has full quizzes, tests, and projects for assessments.
Is there a suggested plan for implementing the curriculum?
Yes. The curriculum is separated into 8 books with each book roughly equivalent to a unit.
Is there a recommended textbook or other text resources?
Yes. The curriculum is designed to go with the Connected Mathematics textbooks.
Are additional materials needed so that the curriculum is effectively implemented?  Are suggestions provided, e.g. visual, literature, manipulative, or technology resources?
The curriculum comes complete with blackline masters and overhead transparencies. I think the student-centered curriculum is difficult for most teachers and support in model teaching, suggested lessons, and outside resources might be helpful.
What professional development will be provided to teachers? Who will be responsible for the professional development? How could the professional development be provided to meet Maryland or National Staff Development Council (NSDC) Standards for Professional Development?
Currently our district has none. We can buy some from the publisher. More likely we will develop our own. We are in the midst of planning a Math Coach position. The person in the position would work in a non-evaluative role to observe and help individual math teachers. He/she would create professional development opportunities such as Lesson Studies, Looking At Student Work, and other teacher centric professional development opportunities.

Assignment #2
Curriculum Analysis
Written Report

This paper analyzes the Waukegan Public Schools math curriculum. Waukegan bases their math curriculum almost entirely on the Connected Mathematics curriculum.  The Connected Math curriculum is a full curriculum developed by mathematicians and math educators. It was specifically designed to meet the National Council of Teachers of Mathematics (NCTM) standards for math.  The Connected Math curriculum uses a problem-based approach to teaching mathematics. Students are not taught the procedures for solving math problems, but are instead presented with problem situations that require mathematics to solve. In this way students discover the main concepts fundamental to middle school mathematics.
            Currently Connected Math is in its second edition. The problems and lessons found within the curriculum have been developed and refined through actual use in classrooms around the country. The philosophy of Connected Math begins with the understanding that ”what to teach” and “how to teach it” are inextricably linked. (Fey, Fitzgerald, Friel, Lappan, Phillips, 2006, p. 2). The overarching Goal of Connected Math (Fey, et al, p. 6) is:

All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness, and technical proficiency.

Connected Math describes itself as a problem based curriculum (fey, et al. 2006, p. 3) however the program can be more accurately described as discovery centered or constructivist as it attempts to set up situations for students to discover basic concepts of mathematics. Used as designed Connected Math lessons ask students to work in small groups to explore problems in depth. The emphasis on depth should allow students to build understanding and the ability to transfer knowledge and skills across concepts.
The Connected Mathematics curriculum is designed to be as teacher friendly as possible. In practice however it is not very teacher friendly. The textbook for Connected Math is broken into eight units designed to last on average four weeks. Each unit is designed to cover one major concept in depth, and to develop related skills. Each unit has a student book and teacher book. Within the teacher copy are detailed goals of the unit, an overview of the mathematics in the unit, a background of the mathematics in the unit, and connections between prior learning and future learning.  Each unit has a suggested pacing guide complete with formative and summative assessments, a unit project is suggested instead of the test, but both are provided. This holistic view of math education is radically different than most math textbooks and I think leads to the difficulties most teachers have with teaching Connected Math, at least in my experience.
Many math textbooks divide the math curriculum into discrete skills. Each skill is taught in isolation. The separation of skills makes it easier for the teacher to focus each lesson. On the other hand this seems to lead to a common complaint from math teachers that students just apply procedures to problems in an attempt to find a solution. Often by high school students have memorized so many procedures that they get confused and misapply them. Connected Math asks students to recognize patterns and create their own procedures for solving them. The teacher’s job is more to help students discover and formalize the procedures. Teachers not taking the time to formalize procedures after discovery would seem to lead to the chief Connected Math complaint of students not knowing how to “do math”.
Having worked in several schools that implement this program I can see many areas that are ready for improvement. In the one school I taught in which teachers were given a week long professional development training the implementation of the curriculum was very similar to what is suggested by the authors. In the schools where teachers were never trained on the implementation of Connected Math the implementation varies immensely.
With Connected Math being so radically different from the normal mathematics textbooks professional development and an understanding of the philosophy behind Connected Math is of paramount importance. I see many teachers give up on Connected Math before seeing results because “some students are not highly motivated and tend toward procrastination and socializing rather than doing schoolwork and homework” (Ray, 2011
In an effort to help teachers understand and implement Connected Math I would change the teacher’s manual. The average student lesson might be one to two pages in length while the teacher’s manual will have up to ten pages of dense writing and still leave teachers confused as to what they are actually teaching.
For each lesson the teacher’s manual has a full explanation of the lesson complete with goals, suggested discussion questions, and illustrations of the multiple ways students may solve each problem. The authors then follow that up with, the lesson at a glace, which is the same information in more condensed form. I would do away with the second part entirely. Instead I would include an annotated version of the student text. The annotations would include suggestions for student prompts when they get stuck, what are some of the interesting student thoughts to listen for and share during summary, and information on why these particular questions were asked and how they lead to building knowledge. 
One of the weaknesses of Connected Math is its complete lack of technology. I understand, if I remember correctly from my professional development many years ago, that the authors did this intentionally so that Connected Math could be implemented at any school, but times have changed. There are many ways that technology can be used to enhance the Connected Math curriculum without making it too expensive. One simple way would be the use of multimedia in the launch section of the lesson to create an engaging anticipatory set as described by Madiline Hunter
Dan Meyer explores in depth ways to use multimedia to get students to ask their own motivational questions. In a series of posts on his blog tagged What Can You Do With This?. Dan holds an ongoing conversation with math educators on specific problems that can be posed to students through multimedia to start a math conversation. I find this very similar to the design of the lessons in Connected Math.            
The ongoing conversation with Dan Meyer and other math teachers and bloggers brings up another limitation of the Connected Math curriculum. Connected Math is very static. The books and lessons haven’t changed much in the last five years. There is little supported feedback from educators about using the curriculum in the classroom today. It would be very helpful for teachers to be able to see and discuss the implementation of the Connected Math curriculum in today’s classroom. What ways are teachers including technology? What lessons are more difficult for students to grasp? What discussion starters work? What summaries are most effective? An open and active online forum to share should be included in the purchase of the Connected Math curriculum.
This isn’t to say that Connected Math is completely devoid of any modern technical support. The Connected Math Project at Michigan State University ( does contain many resources ranging from professional development for teachers to homework help for students. The connected math page at Pearson Hall also contains some web links for parents, students, and teachers (
These resources are very nice additions to the curriculum. However, they are additions to the curriculum and not a part of the curriculum. Few of the technologies are designed to be used in the classroom. Rather the technology is mostly designed to be a support for students who need extra help or for teachers who would like to know more about teaching using Connected Math. Some third parties have also created some interactive activities which can also be used in the classroom. If Connected Math were to be funded for a third major revision I would assume that this lack of interactive technology in the classroom would be a major focus of the program.
Many of the initial lessons in Connected Math are based around an exploration or experiment. These are prime areas for inclusion of technology. There is some evidence of technology inclusion by means of web codes in the student books. By visiting the Pearson web site and using the code students can find material extending the classroom learning. This seems to be more of an after thought or an addition in later printings. There is no mention of the web codes in the teacher’s edition.
Much of the web content would be useful in the classroom. At the very least it would be an alternative method of introducing the concepts for students who struggle with hands on activities. Technology could also be used to allow students to share between classes, schools, or even districts. Lastly, the Connected Math curriculum asks students to do a lot of reflection writing. Technology such as wikis and blogs are perfect forums for students to share their mathematical learning.
The most important consideration when using Connected Mathematics, is the support of the teachers. Implementing the Connected Math curriculum requires long term consistency, especially for students that are used to working quietly alone at a desk. Learning how to work in a learner-centered curriculum is the most difficult aspect of the program for most students and teachers.
If I were to write my own mathematics curriculum I would start with Connected Math. I think they identify the important concepts necessary for middle school math and cover them well. I also appreciate the emphasis on depth of knowledge as opposed to a spiraling curriculum. I have always felt that using a spiraling curriculum, where a concept is introduced then revisited again and again in later years, was an effective way to teach mathematics. What I realized after studying this curriculum is that the spiraling model doesn’t allow students to fully integrate the skills and concepts learned. When they spiral back it is necessary for the teacher to reteach basic skills.
This reteaching of procedures for solving problems, I think, is a major contributing factor to student emphasis on brute force attempts to solve problems.  Students learn a procedure for solving a problem, but they don’t fully understand why or how it works before moving on to the next skill. In subsequent years students are asked to recall the procedure for solving those types of problems. If the students don’t remember how to solve the problem they are reminded of one of many possible procedures and expected to use that procedure to develop further knowledge.
As a math teacher I find the philosophy that is the basis of Connected Math to be an excellent match with my own and I would recommend its continued use in our district. I also reviewed the district created pacing guide, which is based on the Connected Math curriculum and also includes some extensions.
I think it would very useful for the district to review the pacing guide and develop a district curriculum team to finish the pacing guide. At the moment the pacing guide does a great job of laying out an outline of the units to be taught during the year. The pacing guide does suggest the schedule and order of the books to be taught, but after talking with the Director of School Improvement, who also headed the writing of the pacing guide, the scheduling and time frames dictated in the guide are not meant to be a strict schedule, but rather a general guideline. She has mentioned on several occasions that she has attempted to communicate to building principals the necessity of a fluid schedule for Connected Mathematics.
The Director of School Improvement, who is my mentor and my direct supervisor, and I have talked often about the math curriculum. During our informal discussions we have brought up the topic of math curriculum and the pacing guide many times.  In general we feel that the guide is a great start, but it is unfinished. Funding has been difficult of find over the last couple of years, which has stalled to completion of the project.
Currently the pacing guide is a table linking the school calendar to the lesson focus, text and supplemental resources, alignment to Illinois State standards, instructional tips, and assessments.  We would like to finish adding supplemental resources and include technological resources. We would like to include an interactive resource such as a wiki that would allow teachers to share what they are using in their own classrooms. Finally, we would also like to create an observation guide for administrators.
Too often we have administrators who look at the pacing guide as a rigid structure for teachers to follow. For example they would look at the pacing guide for day 35 of the school calendar and expect to see teachers teaching a specific lesson. This is not what was intended during the creation of the pacing guide. Instead on a specific day during the school year all math teachers should be near a specific lesson, but there should be variation depending on the strengths and weaknesses of the specific class.
Overall, the Waukegan school district has made a good choice in adopting the Connected Math curriculum. It is a strong student-centered math curriculum that does meet all of the current state standards and soon to be adopted Common Core standards. The district has made a great start in implementing the curriculum by creating a solid pacing guide. There are three areas of concern. The first area of concern is the integration of technology into the curriculum. The second area of concern would be a stronger more systematic implementation of professional development concerning the implementation of Connected Math in the classroom. The final area of concern would be to finish the pacing guide and add an in interactive resource for teachers to share what works in the classroom.
Common Core Initiative (2010). Common core standards for mathematics. Retrieved February 11, 2011from
Fey, James T., Fitzgerald, William M., Friel, Susan N., Lappan, Glenda L., Phillips Elizabeth D., (2006). Implementing and teaching guide. Boston, MA., Pearson Education Inc.
Meyer, Dan. Archives for what can do with this? [Web log]. Retrieved from (2011 February 25).


Saturday, February 19, 2011

Math Curriculum

I know it isn't a protest march in Madison, but I'm thinking about them.


Wednesday, February 16, 2011

Common Core Standards Webinar

Would you like to learn more about common core and its effects on our school. Pearson (yes the people who publish our textbooks) are giving a series of free webinars. If you go to one please write up and add it to a page on our wiki. Here or here


Monday, February 14, 2011

·  As a school administrator and instructional leader, what instructional technology would you expect to see in the written, taught, and tested curriculum of a school or school district striving to meet the needs of 21st century learners?

·       Taught curriculum
o   I would expect to see extensions and resources for the written curriculum online.
o   I would expect that every teacher in my school to create at least one detailed unit complete with differentiations and share it online.
o   I would expect to see a discussion forum for the teachers. A place where they can reflect on each others lessons, share what they learned, make suggestions for improvement, and more.
o   I would expect to see teachers using laptops and projectors on a regular basis.
o   I would expect that students would be given the opportunity to use web 2.0 tools to create, collaborate, and share.
o   I would expect to see a computer based, or preferably game based program designed and used to give students individualized instruction at their own level.
·       Tested curriculum
o   I would expect to see a test generator.
o   I would expect that students would be given the opportunity to use web 2.0 tools to create, collaborate, and share.  Less emphasis on tests and more on authentic assessments
o   I would expect to see digital portfolios
·       Written curriculum
o   I would expect to see the entire published curriculum also in electronic form, even e-book form for my students.
o   I would expect to see curriculum mapping software used to unify the entire curriculum.
o   I would expect to see a discussion forum for the teachers so they can log and suggest revisions to the curriculum
o   I would expect there to be a way for my teachers to get just in time PD if and when they need it.

·  What instructional technology would you promote to differentiate instruction for all learners?  Consider some of the tools and strategies outlined in the Jacobs' text.

Different representation
·       I would promote the use of universal access technology built into most modern computers. Text-to-speech speech-to-text, contrast, zoom, etc…
·       I would promote the use of technology that allows teachers to present materials in a variety of ways such as podcasts, or video.
·       I would promote the use of individual technologies such as tablets, laptops, or smart phones to allow students to receive instructions.
Different engagements
·       I would promote a student centered programming such as Compass Learning or Read 180 that gives student instruction at their level.
·       I would promote the use of individual technologies such as tablets, laptops, or smart phones to allow students to participate in class., voki, voicethread, etc….

Different action and expression
·       I would promote the use of web 2.0 technologies that allow students to publish authentic work to the world. Blooging, schooltube. Etc..
·       I would promote tools that allow students to share and discuss with other students outside their classroom and school. Wiki, google docs, etc….
·       I would promote the use of tools that allow students to participate in authentic activities at times even experts, authors, or other interested parties. Skype, diigo groups etc…



Algebra Tiles

I think most people have heard of these, but not everyone knows what they are and how to use them.  I’m not really going to explain that here. I have however found a great power point that is very easy to explain. A direct link to the power point is here. The Alliance for the Improvement of Mathematics site is here

What I will do is explain how to make your own set of tiles.

Start with four different colors of paper. Card stock would probably be best. Red, blue and yellow green is suggested.  The x tiles will be red and blue and the y tiles will be yellow and green.  One color will be for positive and one color for negative. I would also laminate when done if you can.

When making the tiles the important part to remember is that the long side of the tile should be immeasurable.  This is easily enough to figure out by simple using any sort of diagonal on graphing paper. Make the short side 1cm in length. Make two different size tiles. This is important because the immeasurable length means that the tile is an unknown.  When introducing the tiles to the students for the first time let them measure all they want and eventually they should come to the determination that the length of one is x and the length of the other is y.

The next two tiles to make are squares that are x2 and y2. Finally you will want 1cm by 1cm squares of white. (You can substitute centimeter cubes for this) If you want you can also include 10cm long strips.

The tiles can be used for everything from adding and subtracting integers to multiplying and dividing polynomials.

Finally, I want to end with a great video from Dan Meyer. He is sharing his application video for Apple’s Distinguished Educator Program. It’s a fun watch and because he uses Vimeo it is visible on school computers.

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Sunday, February 6, 2011


Photo from on 2/6/2011

Honestly why do people think of this as cheating?

Added 2/7/11
Perhaps the voices in my head are not coming through. It isn't cheating at school to take the drugs and stay awake longer to study. It is however killing you. 


Tuesday, February 1, 2011


Did you see this cool activity created by our own Mr. Foster? Of course not I haven't shown it to you yet.

A simple excel file Students are to label points on a number line. Then move numbers around to make the columns equal zero. Great for practice in adding integers, but also great for building the concept of finding zeros,
I'm also thinking it can help build the concept of equations, but putting the zero block in the center and asking students to add or subtract from the ends.
Feel free to play with it.
We were also talking about setting up a way for students to access these files and turn them in on their own. We are thinking a separate google doc for each student. You can access the document here. When you share the link (a setting in google docs) your students don't need an account to view the page.
There is also a company with many of the same features as google docs. I uploaded the document there also. I think the formatting looks a lot better than it did in google docs. In Zoho you can share the document with other Zoho users (free plan even) but you can't share outside of Zoho unless you buy the premium plan. They also have an option of sharing to a group.
One idea we did have is to differentiate the lessons and give some students more challenging spreadsheets. This of course would mean sending each one to individual students negating the advantage of a group.
One final thought is that sharing the documents will mean a link somewhere. Either a hyperlink in a class blog (try to find a blog that isn't blocked). The other option I can think of is a URL shortener.
A service like will shorten the URL (the address of the web page) to something such as It is even possible to customize the last part of the link. Perhaps something like a name and a date. Then you can assign each student a different spreadsheet and they can remember the URL easily.
Enjoy your snowday, and share some of your favorite lessons.