News > 2012 > CPM August 2012 Newsletter
CPM August 2012 Newsletter
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CCSS Issues: Why Implementing the Mathematical Practices is Critical for Our Students
Simply put, we live in a much different world than the post-WW II era, when America had advantages over virtually all other countries and thus dominated most facets of the world stage. That era is past. Quiet revolutions in technology and globalization have changed the face of industry and markets along with international politics. The impact of "flattening" the world for goods and services during the 20 years or so at the end of the last century has been accelerated by the ability to generate and share ideas with anyone or any group in the world, thanks to the Internet and World Wide Web. In 2002, one-sixth of the people in the world had cell phones. In 2010, two-thirds had one.
Much of the focus of mathematics in America has been on learning information and procedures. While there is no doubt that there is content to learn, the competent 21st century student needs to learn how to use this content effectively. They need to learn to: (1) think critically; (2) work collaboratively; and (3) communicate clearly. Indeed, take any idea in the K-12 math curriculum and google it. The information is out there. The measure of successful education (and thus productive citizens and employees) will be their ability to think creatively, tackle non-routine, complex tasks, and do it with teams of employees in various venues. The rote jobs are still here, but many are done with technology or by robots. Those that remain are dead-end jobs that rarely pay well. Today, an employee has to have the aforementioned qualities and bring an attitude that asks, "What do I bring to the job that adds value and helps invent better ways to accomplish tasks?" Just showing up is not enough anymore—in school or on the job.
Consequently, the shape of the mathematics classroom needs to be dynamic, where students have opportunities to explore ideas and acquire the skills to move beyond the routine. Teachers need to provide direction and ask good questions to help students navigate their world. Thus, the CCSSM "mathematical practices" are at the heart of what should drive lessons. They, along with other strategies that cultivate students who can think for themselves will help to develop students with the baseline abilities that the world and the workplace now require.
Implementing CCSS Courses at Your Site
One of the issues that received lengthy discussion among the Core Connections editors and CPM's Directors was how sites would make the transition from their current mathematics curriculum to a CCSS-aligned program. They finally determined that there is no single answer to this task. Indeed, they concluded that it is a local matter for which each school or district needs its own plan. In many places, state tests based on their standards will still be given through 2014. Current middle school standards vary from state to state. Yet teachers, students and parents should start the transition to CCSS-aligned materials sooner than the 2014-15 testing year.
For the middle grades, we created a three-year program in which each course offers substantial mathematics with sufficient time to explore ideas in depth. There are about 105 days of instruction in each of the courses. Past experience with the Foundations for Algebra (FFA) series taught us that this is a reasonable amount of material for these grades. Our teacher-authors know that some lessons will need additional time beyond what is recommended. Student presentations will add a few days. They also know the realities of the limited time to teach math in middle school. The courses also provide substantial chapter closure activities that add about three days per chapter. Add in assessment—more than just tests—and you have a full year's course.
We created the Core Connections high school series with enough flexibility so that the books can be used with current standards for one or two years, yet still meet the CCSS content standards in 2014. CCA has an appendix that is a chapter from CC 3 that uses algebra tiles to work with expressions and solve equations if students need these topics. In addition, Chapter 2 in CCA deals with linear relationships, albeit at a faster pace than CC 3. For the next two years, schools will have the option to skip the three new topics—sequences, exponential functions, and statistics—until CCSS testing begins. Likewise, CCA2 will have the chapters from CCA on these three topics as appendices so that teachers can include them now and skip some of the new CCSS topics until students come to Algebra 2 after taking the CCA course.
|Taking CCSS Algebra in the 8th Grade
There is quite a bit to rethink about teaching mathematics in the era of CCSS, and whether to take algebra in the 8th grade is certainly one of them. The CPM Directors and editors have developed a position paper that discourages mandating algebra for every student in 8th grade. The paper is available at www.cpm.org/teachers/standards.htm. Part of the rationale is that the CCSS 6-8th grade curriculum offers solid mathematics to prepare students for high school math. About half of CCA is linear algebra. These foundational topics should not be skipped. Second, these courses are meant to give students time to understand the ideas (hence, fewer topics in
each grade) and to foster mathematical practices. Third, research, not to mention test results, indicate that these grades are NOT the time to accelerate except for a very few students. The paper offers suggestions so that students can take calculus
or statistics in high school. It also outlines a way to get students to 8th grade algebra if that is your local decision.
Editor's note: Now that there are two "Connections" textbook series, references to the various books can be a bit confusing. In this newsletter we usually give specific details as to the courses we are referencing. However, in general, here is what you need to know. Algebra Connections (AC), Geometry Connections (GC), and Algebra 2 Connections (A2C) are the original high school Connections series, now designated the first edition of Connections. Making Connections, Courses 1 and 2 (MC1 and 2) are the first edition of the middle grades Connections series. These books all carry copyright dates between 2006 and 2011.
Core Connections is the CCSSM-aligned 6th grade through Algebra 2 series that is based on and thus designated as second editions of the aforementioned two series. These books all have 2013 copyright dates. The middle grades books are titled Core Connections, Courses 1-3 (CC1, CC2, and CC3), while the high school titles are Core Connections Algebra (CCA), Core Connections Geometry (CCG), and Core Connections Algebra 2 (CCA2). In some cases you may see the phrase "the Connections series" used, which is the most general reference and usually means any of the courses written in the style and format of either of the two editions.
Core Connections course updates
The CC 1-3 and CCA books were completed in June and available by mid-July. The first press run sold out and fortunately our printer in Missouri was able to get a second press run to us so that there was only a temporary delay in shipping CCA books.
The CCA2 course took longer to complete than anticipated. However, the first half of the teacher edition (Chapters 1-5 and appendices A and B) was shipped in time for the workshops. The rest of the chapters, resources and cover sheets will ship by early September. All of the tabs for the chapters were included with the binder that shipped with the first half of the TE. For those who ordered soft bound versions of CCA2, volume 1 began shipping on August 8; volume 2 will ship by the end of August. Everyone who ordered hard bound CCA2 books was shipped complimentary copies of Chapter 1 and Appendices A and B in booklet form on August 6th or 7th. Use them until the hard bound books arrive by about the third week of September. In the event that a site completes these three chapters before the textbooks arrive, or in the case of schools on compressed blocks, we have posted a PDF file of Chapter 2 at http://www.cpm.org/pdfs/CCA2/CCA2Ch2SV.pdf
The CCG edition has been delayed. We shipped everyone who ordered this course in the past 14 months copies of volume 1 of GC. We expect very little change to the first six chapters of the course with respect to scope and sequence. We hope to ship CCG by December. If that is impossible, we will send copies of GC volume 2 and ship the CCG books next spring. Schools on compressed block schedules should contact Jill in the business office in September to arrange to receive volume 2 (email@example.com).
Parent Guides will be available in late September. We will ship copies for teachers to the same address as the one where we shipped teacher editions. The guides will also be available at the CPM website. The CC 1-3 guide will be a single booklet with a table of contents for each course. We combined the three courses so that, especially in CC 2 and CC 3, students would have a resource to review (or learn) ideas from a previous grade if they need such support.
When new books are published there are invariably a few mistakes that survive the editing process. CPM maintains errata files for all of the books at its website. Everyone using one of the Core Connections courses should check these files and have students make the corrections. As of mid-August, we have found three errors of significance in each of CC 1-3, and seven in CCA. From the home page, select "Teaching Resources" from the left menu, then "Resources by Course" on the next page, then use the pull-down menu to select the course you want. You will find an errata file for that course among the resources listed there.
Online homework help is now available for the Core Connections books at www.cpm.org > Homework Help. We are still completing some of the later chapters of the books, but expect to have the work done by the fall. This year students can get help from a computer by clicking on the problem number for a "Java applet" or the letter "m" next to the problem number for mobile devices.
SMART Board files for the Core Connections courses may be accessed through the ebook TE. Since every teacher edition comes with an ebook license, access to an electronic version of the book as well as the online assessment resources is done through the ebook. Consequently, there are no course CDs for the Core Connections courses.
CCSS content correlations for the Core Connections books will be available and posted at the CPM website for CC 1-3 and CCA by September 1. CCA2 will follow shortly thereafter, and for CCG once the book is finished.
For an assessment update, see the "Assessment" section of this newsletter.
For an update about Core Connections technology matters, see the "Technology" section of this newsletter.
Original Connections series
The five books—MC 1, MC 2, AC, GC and A2C—are all available for sites that are continuing to use them and need additional or replacement copies. In addition, previous purchasers may add a three-year eBook license for student texts for $9.00 and teacher editions for $25.00.
FFA, Math 1-4
Copies of these books are still available. In particular, FFA teachers may order toolkits for their classes. The Business Office has full details about what bindings of the student books are available.
Carol Cho, Director of Assessment
Core Connections (CC) eBooks are now available for all of the courses except CC Geometry, which we hope to have available early in 2013. In order to simplify matters with respect to the two editions of Connections, there are only two sets of licenses. The original, first edition licenses will include the materials in the CCSSM supplement booklets. This will avoid having two different sets of licenses for those editions, one with the supplements and one without them. The supplements for the first editions will continue to be available as PDF files for free download at the CPM website as well as in booklet form for purchase. The other Connections licenses will be for the six books in the Core Connections series (second editions).
Every order for a CC teacher edition comes with an eBook license. Teachers now have immediate electronic access to the course itself and the online assessment. This license in part replaces the CD that comes with the first editions of the Connections courses. (It had a PDF copy of the teacher edition and most assessment resources.) These eBooks also have links to mathcasts for most lessons (they are intended to be used with the lesson notes) describing how to present the lesson to students. CC Smart Board files are available through the eBooks. The majority of support files for the books are now easily accessible via links throughout the CC eBooks. These links include study team and teaching strategies, assessment ideas, universal access strategies, closure strategies, and more! Please take time to explore all of the resources. More are being added all the time.
As this newsletter goes to press (8/15), student Core Connections eBooks are 95% complete. The eBook team will continue to add Lesson Teacher Notes for the last half of the Teacher Editions of the eBooks through September. Changes to eBooks take place immediately for all licensed eBook holders. You may notice some changes as we finish the Teacher Notes, add additional eTools and videos, and complete linking tasks.
With Internet access, the CPM eBooks are also viewable on mobile devices such as the iPad. The eBooks have a double link after each homework problem (Hints <=> Help). "Hints" link to a Java App. "Help" links to an HTML5 file viewable on most mobile devices and computers.
Schools not using the eBooks can also find the homework help at: http://www.cpm.org/students/homework. When using the homework site, the problem number links to a Java App while the "m" links to an HTML5 file. The homework help works best with FireFox, Safari, or Chrome browsers. Smart Board files for the first edition Connections series books remain at the CPM website: http://www.cpm.org/technology.
If you need assistance, please use the "Help" pdf files at the Homework, eBook and assessment sites. If, after reviewing the help files for eBooks or assessment you still have questions, additional issues, or corrections to report, please contact Carol Cho (firstname.lastname@example.org). Send feedback and questions about Homework Help to Bob Petersen at email@example.com.
In the spring of 2011 Chris Mikles, Director of Teacher Education, began working with some of CPM's mentor teachers to create five to ten minute "mathcasts" for every lesson in the original Connections (1st editions, five books), PCT and Calculus courses. When this project is completed, each lesson in each of these courses will have tips about how to use each lesson and discussions about any issues unique to the lesson. Most books in the original series are complete. Currently, we are creating Lesson Mathcasts for the Core Connections books. We are following the same procedure of doing the first few chapters of each course and getting them loaded to the website this summer. All of them have at least the first three chapters completed. Our goal is to stay ahead of the regular, nine month school year calendar so that teachers who find this resource helpful will be able to use it all year. The mathcasts are not a replacement for the lesson notes in the teacher edition; rather, they are intended to be used with them. They can be located in two places: online at cpm.org/technology and through a link in the eBooks in the Teacher Notes for each lesson.
Calculators in CCA
Which calculator will Algebra students need when?
Core Connections Algebra assumes, in general, that students have a scientific calculator available as one of the tools they can choose from to strategically solve problems, both for classwork and for homework. Typical inexpensive scientific calculators are those in the Texas Instruments TI-30x family.
Many lessons in Core Connections Algebra, particularly in the second half of the book, also assume that students have daily access to a graphing calculator or other graphing technology in the classroom. Typical graphing calculators are those in the Texas Instruments TI-83+ and TI-84+ families. A graphing calculator makes some of the homework problems more efficient, but with very few exceptions, a graphing calculator is not required for homework.
Chapter 5 of Core Connections Algebra contains some optional opportunities to introduce students to multiple representations of functions (equations, table, graph) on a graphing calculator. We strongly recommend that you include these calculator opportunities in your curriculum, even if it slows down your teaching pace. The extra time spent on calculator use now is well worth it. Students will be more comfortable (and efficient!) when the graphing calculator is relied upon more heavily in future chapters.
The statistical functions and statistical graphing capability of a graphing calculator first become a necessary part of the lesson in Core Connections Algebra Chapter 6, "Modeling Two-Variable Data." Then the ability of a graphing calculator to efficiently create multiple representations of a function is leveraged in the investigations of exponential and quadratic functions in Chapters 7 through 10. Chapter 11 contains challenging, culminating investigations in which students use the skills they learned throughout the course. Strategically choosing a graphing calculator when it is an appropriate tool is an important objective of these investigations.
CPM Stat/Grapher Tool
At home, students may want to choose a graphing calculator to help them investigate andunderstand a problem in more depth. Of course they can use a TI83+/84+ calculator if they have one available. However, on its website, CPM also provides the Stat/Grapher Tool. Although this tool is still under development, it can already be used as an alternative for students that do not have access to a TI83+/84+, or other, graphing calculator.
The Stat/Grapher tool can be found at the www.cpm.org website by selecting "Student Support" and then "Technology Resources," or by going directly to http://www.cpm.org/technology/techtools/grapher/.
The Stat/Grapher tool is intended as a graphing and statistics supplement to a scientific calculator—adding capability that is needed in Algebra but not provided on the typical scientific calculator. At this time, the tool can:
At this time, the Stat/Grapher tool does not have the capability to make an x→ y table from an equation.
- Graph functions typically encountered in Algebra
- Make statistical calculations like mean, median, quartiles, and standard deviations
- Create boxplots and histograms from a list of data
- Create scatterplots from lists of two-variable data
- Make regression calculations like the correlation coefficient and the sum of the squares
- Calculate and display the least squares regression line, residuals, and residual squares.
Calculator Instructions for Teachers
When a graphing calculator is needed, the lesson notes in the teacher binder for Core Connections Algebra, provide guidance for using a Texas Instruments TI83+/84+ graphing calculator. Much more detailed instructions for using a TI83+/84+ calculator is provided in a tab in the front of the teacher binder. A TI-Inspire calculator can be made to emulate a TI-84+. You should note that procedures for other TI graphing calculators (TI-89, TI-73, TI-Inspire not in emulator mode), and calculators from other manufacturers, are very different.
Much more detailed operating instructions for your calculator than are provided in the teacher edition can be downloaded from education.ti.com by clicking on "Downloads & Activities" and then "Guidebooks."
One option for the teacher to demonstrate calculator use to the whole class is a document camera or video visualizer (like an Elmo). The advantage of a document camera is that the teacher can project both the calculator's screen and demonstrate which keypad buttons to press.
Another option for whole-class demonstration is a projector connected to a computer with a graphing calculator emulator. For the Texas Instruments TI-SmartView calculator emulator software, go to http://epsstore.ti.com and click on Computer Software/SmartView Emulator/T1-84. Various free TI-84+ emulators are also available. Most emulators require that you own a TI 83+/TI 84+ calculator to activate the software. Some possibilities are:
While there are two more options for demonstrating calculator use to a whole class, neither of the following options are capable of displaying the keypad. Only the calculator screen in projected; the teacher cannot project which keystrokes are being entered. However, Texas Instruments can provide a wall poster of the keypad to aid a teacher in demonstrating keys pressed. A Texas Instruments TI-Presenter is a piece of hardware that connects a presentation-model TI-84 to the video input of a TV or video projector. The TI-ViewScreen is a large transparent display screen that lies on top of a traditional overhead projector. Both the TI-Presenter and the TI-ViewScreen are available from http://education.ti.com.
- Wabbitmu (http://wikiti.brandonw.net/index.php?title=Emulators:Wabbitemu)
- Virtual TI (http://www.ticalc.org/archives/files/fileinfo/84/8442.html), and
- TilEm (http://www.ticalc.org/archives/files/fileinfo/372/37211.html).
Before teaching any lesson that uses technology, be sure to set up and test your equipment in advance to make sure that batteries, software, and the projection system are working properly. It makes sense to have extra batteries and a replacement projector bulb readily available. It also is a good idea to walk through the activity using the actual technology in the classroom before the day of the lesson to review the keystrokes and anticipate any issues that may arise during the lesson.
In Pursuit of the Unknown:
5 Blogs That are Changing (My) Math Tech World
Bruce Melhorn, International School Bangkok (Thailand)
Here is my collection of the "5 Blogs That are Changing (my) Math World." I'm sure you have others; please share!
- Mindshift: http://blogs.kqed.org/mindshift/
- Edutopia: http://www.edutopia.org/technology-integration
- Dan Meyer's blog: http://blog.mrmeyer.com/
- Richard Byrne's blog: http://www.freetech4teachers.com/
- Will Richardson's blog: http://willrichardson.com/
Karen Wootton, Director of Assessment
Access to the assessment website: Core Connections teachers (and anyone else using an eBook version of Connections) can access the assessment website through the eBook. Anyone else who needs access should contact their Regional Coordinator (contact information is in this newsletter on page 2) for the username and password.
We are continuing to update CPM's assessment website for the Core Connections books. The work is incomplete, but the site is still accessible and very useable during the transition. The original Connections courses listed on the assessment website (MC1, MC2, AC, GC, and A2C) continue to be available, and will not be altered or rearranged. All the sample tests for these courses also remain available.
During the coming school year, problems will be added to the test bank for the CCSS-aligned courses (Core Connections). If you visit the assessment website now, you will see that CC1, CC2, CC3, CCA and CCA2 are listed below the original Connections courses. If you click on any of the CC courses, you will see the chapters listed, and the topics within each chapter. (Note: the one exception is that CCA2 stops at Chapter 7. The remaining chapters of this book will be added during the year.) Some of the chapters and topics are already populated with problems while others have no problems assigned to them yet. As the school year progresses, you will see more and more problems filling the categories within the chapters.
Our goal is to continue to add problems to each course until the CC books are completed, staying ahead of a standard, August-to-June school year timeline. These books are second editions, so many of the chapters in the original Connections books are similar to those in the CC books. Use the first edition resources if you need to see sample tests or are teaching on a compressed block schedule. Likewise, if you find some misplaced problems, typos, or other errors when you use the website, please use the "Comments and Suggestions" link on the bottom of the website to let us know and we will fix the errors immediately.
General reminders for success—for everyone!
- Follow the pacing in the Teacher Editions as closely as you can.
- Read the lesson notes before each class; pair them with the lesson mathcasts.
- Focus on the core problems to meet the lesson objectives.
- Mastery comes over time, not the day after the lesson.
- Use team roles to help each student become an active participant in learning math.
- Ask questions rather than tell answers to help students.
- Prep for class by working each problem, thinking about questions students may ask, and making a list of questions to ask them to help them solve the problems with their team.
Change in CPM Leadership
Last May Lori Hamada, President and Co-Executive Director of CPM, decided to resign from CPM to pursue other opportunities closer to her home in Fresno. CPM wishes her well in her new endeavors and appreciates the contributions she has made to CPM over the last two years. Tom Sallee will serve as the interim President and Brian Hoey as the Executive Director.
Check the CPM website (www.cpm.org > Professional Development > Workshops) for the schedule of follow-up workshops. You can search by course or state. These sessions provide on-going support and preparation for teachers new to a CPM course as they go through the year. They also help with successfully implementing problem-based instruction and developing student study teams, especially using team roles. If you did not attend them the first year that you taught a CPM course, we encourage you to register and attend this year.
Ongoing local support
Every teacher using CPM has a CPM Regional Coordinator (RC) available to respond to questions and provide support for the program. We encourage you to have a person from your site designated to communicate with your local RC. Their contact information is in this newsletter and at the CPM website.
Parent eBook licenses
Some parents may want to have the eBook version available to them. They may purchase a one-year license for $10 by calling CPM and using a credit card. Contact Lorrayne Graham at (209) 745-2055.
Fall professional conferences with CPM speakers and booths
CPM participates in as many as 40 professional conferences each year. CPM mentors offer sessions and host an exhibitor booth at the fall NCTM regional conferences (Dallas and Hartford in October, Chicago in November) and the April national conference (Denver). This fall we will also participate in conferences in October in Idaho, Pennsylvania, Ohio, Florida, Utah and Kentucky; in November in Palm Springs (CA), Portland (OR), New York, Michigan, and Asilomar (CA); and in December in Boston. Please stop by and see us. The complete list with dates is available at: http://www.cpm.org/teachers/announce.htm.
Teacher Registration with CPM
Please be sure that any teachers who are new to the school this year and teaching CPM complete and submit a teacher registration form. If they attended a workshop this summer, they are already registered. Forms are available at www.cpm.org/teachers/apps.htm if there is not one in the front of their teacher edition. Registering with CPM is important, because we use the database to send out new or revised resources and the newsletter. Teachers who wish to use the new web-based assessment program (including the test generator) must be registered to access it.
Purchasing CPM materials
An order form is available at www.cpm.org/teachers/ordering.htm. Fax orders to (916) 444-5263. Address questions to the Business Office at (209) 745-2055 or firstname.lastname@example.org. You may also call the CPM Business Office and make small purchased (under $300) by credit card.
Register for the CPM Discussion Forum
We encourage you to register for the CPM on-line forum for teachers where you may ask questions, offer suggestions, share resources, and generally discuss using CPM in their classrooms. Teachers are able to post ideas for teaching lessons, resource materials they create, or commentaries about how a lesson or problem went with their students. Once something is posted, any registered forum participant may add to it.
The forum is divided into categories by course. In addition, we have created categories for classroom management, assessment, and student learning styles. We will add categories as the discussion forum grows. The forum URL is http://www.cpm.org/phpBB2. Click "register" in order to post messages. Carol Cho, the Director of Technology, is the moderator of the forum (email@example.com).
Chris Mikles, Director of Teacher Education
Sue Freeman Culverhouse says in an article about attention spans that:
Psychologists vary on what they believe the "average" attention span of a child may be. Some assert that the child's age plus two minutes is the average. That means most kindergarteners (most are five years old) have a seven-minute attention span. Others insist that the age of the child multiplied by three to five minutes is the average. These folks think that a six-year-old, or average first grader, can concentrate for 18 to 30 minutes. Few of these people have taught first grade. Sales experts plan on a seven-minute attention span for an executive to listen to a sales presentation. Some college professors plan on a 20-minute attention span for their adult students.
Rae Pica says in an article called, More Movement, Smarter Kids, that:
Thanks to advances in brain research, we now know that most of the brain is activated during physical activity – much more so than when doing seatwork. In fact, according to (Eric) Jensen, sitting for more than 10 minutes at a stretch "reduces our awareness of physical and emotional sensations and increases fatigue." He tells us this results in reduced concentration and, most likely, discipline problems. Movement, on the other hand, increases blood vessels that allow for the delivery of oxygen, water, and glucose ("brain food") to the brain. And this can't help but optimize the brain's performance!
If movement helps the brain to function better, what does this mean for our classrooms? If students' attention spans are not as long as a class period, yet we need their attention so that they will learn, what can we do? My answer is that using study team and teaching strategies can really help. They can be used to change the learning structure within a lesson, so that we can restart the clock on their attention span. In addition, by getting them moving, we can improve their brain function.
Consider the "Carousel" strategy. Students do math problems that are posted around the room, while at the same time they are moving from poster to poster. During a "Walk and Talk," students discuss what they have learned so far in the lesson during a brief walk around the room with a partner. The "Give One, Get One" strategy allows students to share their ideas with classmates while walking around the classroom. A "Swapmeet" has the students get up and change teams at some point during a problem to share ideas and strategies with another team. I could keep on going, but you get the idea.
Think about your students and be mindful about which strategies you can use throughout the lesson to meet their attention span needs and help them to be more effective learners.
Teaching Team Roles to Your Study Teams
Cisco Cox and Linda Giauque, Colorado
Use the strategies that follow to introduce team roles in Chapter 1 of any Connections course. Start by copying the number of each of the Team Role and Team Role Norm cards you will need from this link: http://www.cpm.org/teachers/study.htm
Preparation: Each role should be on a different-colored sheet. Cut the Team Roles apart. Make team packets—one of each Team Role and one of each Team Norm page—and distribute them to your study teams. Each person within the team will have a different Team Role and the page with the matching Team Role Norm.
Jigsaw the initial roles by having all students with the same-color, same role card report to one of the four corners of the classroom. For example, all Recorder/Reporters report to the same corner to discuss how they see themselves handling this role, what questions they will need to ask their team members, and what behaviors they will encourage within their teams. This information is on the Team Norm card. Take only a short time to do this, then have them reconvene in their regular study teams to share their roles with the other team members.
Conduct a whole-class discussion about these roles so that everyone hears what each role requires and has an opportunity to ask questions about them. For example, "Raise your hand if your job is to be the Resource Manager for today. What is one question you will ask your group members today?" Go through all four roles in this manner.
Then launch one of the first lessons in the course and use it to while you introduce students to the team roles. Remember that all Connections courses (1st and 2nd editions) have problems in the first chapter for which the team role cards have been adapted on a resource page to give students specific questions to use for these problems.
Once students start working, circulate among the teams, jotting down examples of appropriate questions and comments you hear as students solve the problem. At first they will probably use only the exact questions from the role cards. Process this with them at the end of the session, reinforcing the positive questions you have heard and how the team roles help make the teams work more efficiently. For example: "What are some examples of responses to the team role questions that helped you to solve the problem?" During the next three days, have students keep the same roles. The goal is to have them ask questions like those on the team role cards as a matter of habit as you work through the lessons in Chapter 1. Support their efforts by sharing some of their questions that you heard with the class.
During the next two weeks, rotate the jobs within each team so that students have a chance to learn and practice each role. You should see students make more productive use of class time as the use of team roles becomes a normal part of their solving process. During this time, the constant, conscious reminders about what each role entails and noting when you hear them in use will help students to internalize them. It is also helpful to display the team roles norms by posting them in the classroom and discussing each one together in class. As part of closure for Chapter 1, ask them to state the evidence they have observed supporting how these norms help teams to function more smoothly and, ultimately, help them to solve math problems.
Continue to work relentlessly throughout the first quarter and the school year to make the study teams improve in their effectiveness. Developing smooth teamwork maximizes the effectiveness of the Connections materials within a student-centered classroom. In particular, it helps students to gain a deeper conceptual understanding of the mathematics.
Finally, student roles and the norms for study teams are discussed in detail in the frontmatter of all course teacher editions. Classroom posters are at the URL above. The roles and norms are listed below.
- Resource manager
- Task Manager
Together, work to answer questions
- Explain and give reasons
- Ask questions and share ideas
- Members of your team are your first resource.
- Smarter together than apart
Saving Some Space
Erin Schneider, Louisville, KY
After you have been teaching CPM for awhile, you realize that CPM supplies can take up a lot of storage space. So when I was preparing for Lesson 8.3.3 (problem 8-104) in Geometry Connections, it required the use of shoe boxes to represent a barn. I wanted to find something that I could use year after year that would actually be to scale. So I took some half-inch wooden poplar boards I had left over from a project at home and cut them into 15 cm by 25 cm rectangles to model the 15 m by 25 m barn in the problem. Now I had something that took up half the space of one shoebox and was also durable. Along with the board, I cut string at 10, 20, and 30 cm, using different colors of string for each length so the students could easily differentiate them. The teacher's edition warns that students may have trouble visualizing what is going on in this problem. Given that I teach advanced students, I was not expecting what I saw.
I found that my students were taking the wood, using it to draw the diagram to scale, and then setting it aside to draw the area the goat could graze. I was getting a lot of answers like p100 m2 for the 10 meter rope. I asked them to draw the possible grazing area again with the barn (board) in place and found that this helped most students catch their earlier mistakes. What had started as an attempt to save storage space turned into enriching the investigation.
As many of you know, advanced students can be a challenging group to teach. At this level, freshmen are excellent at following rote procedures but are very weak when it comes to application and logical discourse. This problem is an excellent opportunity to get students thinking in a more critical fashion and to ask good, simple, logic questions, such as, "What am I being asked to do?" instead of "What is the problem I am being given?"
Making Your Thinking Visible
Theresa Reilly, Louisville, KY
I plan to try out a new norm for my study teams this year that I hope, after some practice, will help my students enhance their ability to construct viable arguments and critique the reasoning of others. We all know this issue: Students just want to state the answer to each problem, then think that they are finished. However, this approach does not allow for the critical thinking and evaluation that the Math Practices require. In order to evaluate and justify their responses, I plan to establish a team norm called, "Make your thinking visible."
Students may do this by showing examples of diagrams, their computations, or writing a justification of an answer. Then another student in the team will review the student's work. This review will give them an opportunity to practice evaluating the responses of others. The teacher will also have the chance to follow the reasoning for both correct and incorrect responses. If the responses are incorrect, the teacher can make a formative assessment and ask some guiding questions to help the students rethink their work.
Something to Smile About...
Rachel Fry, a CPM mentor teacher in Pennsylvania, asks each of her students to write a letter at the end of the school year. The focus is explaining their experiences in her class and advising future students what to expect. She passes out the letters on the first day of class the next year. She shared the following insightful letter from a student in her Algebra 1 class.
I probably should have been in Algebra II this year. Honestly, I can't really blame anyone apart from myself though. When I took Algebra in middle school, I didn't pay too much attention, nobody did. Our teacher was really nice, but he wasn't very good. So, I passed his class with the flying colors of a C. I didn't understand it at all.
So here I am, at the end of Algebra I again. And an Algebra I modified and tailored to the preference of people like me. I know it inside and out now, backwards and forwards. Taking Algebra II would probably have put me on an ideal college track. In fact, I'm actually taking action in getting back on that track because I've got some big dreams. But, I would have hated it. I detest conventional math courses because I never actually understand the material, the goal is not to understand the material. You memorize how to do something. And even in my short fifteen years of life, I, unlike some, have observed the difference in memorization and actually learning something. This book helped me loads, I have to say. It made a point of making sense and I really appreciated it.
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