math link Fall 1999 ELC’s Newsletter for Secondary Mathematics Teachers Vol. 3, No. 1 everyday learning corporation’s CONTENTS Pacing Considerations in a Contemporary Mathematics in Context Classroom 1 Mathematics Bookshelf 5 Mathematics in the News 6 Techlink 7 Interview: Using Baseball Statistics from the Internet 8 New and Revised Products 12 ELC News 14 Suggestion Box 15 The Last Word: Write for ELC’s Mathlink! 16 Pacing Considerations in a Contemporary Mathematics in Context Classroom by Beth Ritsema, Professional Development Coordinator, Core-Plus Mathematics Project The courses in the Contemporary Mathematics in Context (CMIC) cur- riculum are designed to be presented at a realistic, flexible pace. Some teachers implementing the curriculum, however, express concerns about not completing all the material in a course during the academic year. Beginning CMIC teachers often raise the following questions: ➤ How can I pick up the pace in my classroom? ➤ How do I decide what is most important in each unit and in the course? ➤ How do I know that students understand the concepts so I have the confidence to move on? These questions stem from teachers’ concerns for student learning. Since pacing issues can affect student learning, which in turn affects evaluation of both the mathematics program and the classroom teacher,it is worth- while to think carefully about these issues. District decisions as well as individual teacher decisions affect the amount of material that can be effectively taught each year. Districts and teachers who are implementing the CMIC program have found effective strategies for addressing pacing issues. KNOWING THE CURRICULUM Elementary schools, middle schools, and high schools sometimes make cur- riculum decisions in isolation, without considering the common goals for a K–12 mathematics program. Because a district invests time, energy, and financial resources in implementing CMIC, it is advisable to think about the mathematics curriculum from Kindergarten through high school. (Pacing, continued on page 2) ISSUESinMATHEMATICS EDUCATION
Transcript
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C O N T E N T SPacing Considerations in a Contemporary
Mathematics in Context Classroom 1
Mathematics Bookshelf 5
Mathematics in the News 6
Techlink 7
Interview: Using Baseball Statistics from the Internet 8
New and Revised Products 12
ELC News 14
Suggestion Box 15
The Last Word: Write for ELC’s Mathlink! 16
Pacing Considerations in a Contemporary Mathematics in Context Classroom
by Beth Ritsema, Professional Development Coordinator,Core-Plus Mathematics Project
The courses in the Contemporary Mathematics in Context (CMIC) cur-riculum are designed to be presented at a realistic, flexible pace. Someteachers implementing the curriculum, however, express concerns aboutnot completing all the material in a course during the academic year.Beginning CMIC teachers often raise the following questions:
➤ How can I pick up the pace in my classroom?
➤ How do I decide what is most important in each unit and in the course?
➤ How do I know that students understand the concepts so I havethe confidence to move on?
These questions stem from teachers’ concerns for student learning. Sincepacing issues can affect student learning, which in turn affects evaluationof both the mathematics program and the classroom teacher, it is worth-while to think carefully about these issues.
District decisions as well as individual teacher decisions affect theamount of material that can be effectively taught each year. Districts andteachers who are implementing the CMIC program have found effectivestrategies for addressing pacing issues.
KNOWING THE CURRICULUMElementary schools, middle schools, and high schools sometimes make cur-riculum decisions in isolation, without considering the common goals for aK–12 mathematics program. Because a district invests time, energy, andfinancial resources in implementing CMIC, it is advisable to think aboutthe mathematics curriculum from Kindergarten through high school.
Questions for each district to considerinclude the following:
➤ Are students developing mathe–matical habits of mind and goodwork habits in earlier grades?
➤ How do mathematical expectationsfor students align fromKindergarten through high school?
Middle school backgroundsIf students come to high school know-ing how to collaborate with class-mates, to investigate complex prob-lems, to explain their mathematicalthinking, use graphing calculators, andunderstand more than arithmetic, theyare well prepared to complete theCMIC courses in a timely manner.
In cases where the middle schoolmathematics programs have not pre-pared students well or when class-room hours for mathematics instruc-tion have been reduced (in someblock scheduling formats), completingCourse 1 in a single year may not be areasonable goal.The mathemati-cal content inCourse 1 waschosen becausethe authorsconsidered it tobe the mostimportant math-ematics for stu-dents to knowby the end ofninth grade.Each coursesets high butattainable stan-dards that were tested prior to publi-cation.To provide even greater pacingflexibility, the materials are publishedin two parts. A second-year class cancomplete Course 1, Part B, while anew, first-year class begins with Part A.Developing understanding of impor-tant mathematics should not be sacri-ficed to “covering” the content.
Resources of CMICBecause the CMIC curriculum is anintegrated curriculum, careful study isnecessary to determine where con-cepts and methods are introduced,developed, formalized, and revisited. Itwould be unrealistic to expect that allteachers would have time to study thefour years of the curriculum beforebeginning to teach Course 1.Thereare, however, resources to help teach-ers begin to understand the full cur-riculum.The Scope and Sequencepamphlet identifies the course leveland unit in which topics are taught inthe three-year curriculum and whichmajor topics are reserved for Course 4.Information about the development ofmathematical ideas across mathemati-cal strands and across courses is also contained in the Teacher’s Guide.Having access to the Teacher’s Guidefor all courses allows teachers tounderstand the detailed developmentof mathematical concepts within thecurriculum.
MANAGING A NEW PEDAGOGYThe CMIC curriculum requires thatstudents make sense out of problem
situations andexplain theirthinking. Ifone of themajor goals ofyour mathe-matics pro-gram is todevelop stu-dents’ prob-lem-solvingabilities,increasing theclassroompace may take
away opportunities for students tothink deeply about mathematicalideas.Whether deciding to move stu-dents along more quickly by askingprobing questions, providing hints, ordirectly instructing students about anidea, each instance should be carefullyanalyzed in terms of decreased oppor-tunities for problem solving and criti-cal thinking.
(Pacing, continued from page 1)
Having access to the
Teacher’s Guide for all
courses allows teachers to
understand the detailed
development of
mathematical concepts
within the curriculum.
3
(Pacing, continued on page 4)
Time for collaborationOne factor that some teachers indicate slows theirprogress is the number of interesting questions that stu-dents ask. Decisions regarding whether to follow up onadditional questions need to be made in light of thedesire to encourage ownership of learning by valuingstudents’ questions, the mathematical value of the ques-tions, and time constraints.
Efficient group workOf course, groups of students who collaborate efficient-ly will complete their investigations more quickly thanother groups. Organizing and facilitating productivegroup investigations is an important key in successfulpacing of a course. Some districts provide additionalprofessional development for their mathematics teach-ers in collaborative learning. Information on collabora-tive group work is provided in the Implementing theCore-Plus Mathematics Curriculum booklet includedwith the Teacher’s Resource Package. Group self-assess-ment prompts are provided in the Teacher’s Guide foruse following Checkpoints. Often, students will havegood insights into ways to make their own groupsfunction well.
Efficient plans for technologyAnother implementation decision that affects pacing isthe availability of graphing calculators for students’ use.Students frequently need access to graphing calculatorsto complete homework. Some districts provide studentswith an “at-home” graphing calculator along with thetextbook. Other districts make multiple calculatorsavailable for overnight check-out from a classroomteacher or from the school librarian. Business or indus-try contacts may be willing to adopt a classroom andprovide technology resources. In some cases, districtsrequest that students purchase their own calculatorsand may provide financial assistance with rent-to-ownprograms. By having access to technology at all times,students become more efficient with technology.Theyare then able to complete more work during the classsession as well as more homework.
TIPS AND STRATEGIES FROM CMICTEACHERS Experienced CMIC teachers have developed a variety ofspecific strategies to assist them in pacing courses,units, and daily investigations. Some of these strategiesare listed below:
• In Course 1, assess students’ understanding of material from their middle school mathematicsprogram to avoid repetition.
• With other teachers in your department, create aschedule for completing units for the year.Collaborate so that all teachers of the same course continue at about the same pace.
• Know the objectives for each lesson so that you do not get sidetracked. Know whether a concept or skill is being introduced or whether mastery is expected.
• Students should not need to write complete answersto every activity in an investigation. Some activitiesare for scratch work and discussion. Complete write-ups should be made for Checkpoint questions,in students’ Math Toolkits, and for MORE tasks.
• Selectively facilitate mini-checkpoints before the main Checkpoint to consolidate the learning and allow students to move efficiently through theremainder of the investigation. (This may also help bring a lagging group up to speed.)
• If an investigation is not completed during the classperiod, students may begin the next activity at homeand discuss results with their group at the beginningof the following class period.
• Assessment of student understanding by listening to group work may prompt instructional decisions suchas omitting an upcoming activity because students already understand the concept or facilitating a whole-class discussion to clarify student thinking.
• Assign On Your Own tasks for outside class work.
• Assign MORE tasks selectively as students are workingthrough the lesson.
• Resist the temptation to go over all the assigned MORE tasks in class. Reserve class time for the important Organizing tasks. If students have chosen different tasks, students who have chosen the same task could present their solutions for the entire class.
Organizing and facilitating
productive group
investigations is an important
key in successful pacing
of a course.
(Pacing, continued from page 3)
BELOW ARE SOME SPECIFIC SUGGESTIONS FROM CPMP TEACHERS:
Pacing Considerations in a CMIC Classroom➤ Knowing the curriculum➤ Managing a new
pedagogy➤ Using strategies from
other CMIC Teachers
• “Become very familiar with the new curriculum.”– Cathy Helmboldt, Sparta High School
• “Trust the curriculum.You can move on.The important topics will come back again.It took me a while to figure this out. In fact, itwas my students who finally enlightened me.They said,‘Dr.Triezenberg, you don’t need totell us things after we do the investigation.’I was losing valuable time by ‘reteaching’concepts.”– Don Triezenberg, Holland Christian
High School
• “Emphasize group roles daily. Otherwise,students quit using them and subsequently quit working together.”
• “Sit back and let your students do the thinking. I am constantly amazed at what students can do and figure out when I letthem work.”– Karen Fonkert, Orchard View High School
• “When assigning an investigation, give timelimits. Say, for example:‘You have 12 minutesto do Problems 1 through 5,’ or ‘Two moreminutes on this Checkpoint.’ Students reallypush it when they have a limit.”
Teaching the second, third, and fourth courses inCMIC helps teachers understand the developmentof concepts and methods, the retention of con-cepts by students across courses, and the varyinglevel of mathematical understandings gained bystudents at any given time.These understandingsgive teachers the confidence to make many spe-cific teaching decisions that affect pacing.
Helping students develop mathematical habits ofmind requires students to have many opportuni-ties to wrestle with problems, justify their reason-ing, and explain their thinking. Understandinghow concepts are developed and how skills aremastered during the CMIC three-year coreprogram of study, using some of the strategiesabove, and making judicious choices in facilitating
• “Make sure that you do every problemyourself before assigning it. Don’t feel likeyou need to assign every MORE task anddon’t go over every homework problem youassign. Make yourself available before schoolfor questions.”– Jennifer Diekevers, Caledonia High School
• “Don’t change your groups too often. Giveyour groups time to gel. Members fromgroups that finish more quickly can be usedas resources for the other groups.”
• “Don’t wait for every group to complete aninvestigation every time.”– Bob O’Connor, Lakeview High School
• “Some topics can be chunked. One groupcould do #1, another group could do #2,and so on.”
• “Using overheads or the Checkpoint at thebeginning of the hour to wrap up things Iobserved students doing the previous day hashelped get students quickly back into theinvestigation. It has also helped clarify someof the misconceptions students have.”– Mark Tompson, Kent City High School
collaborative work will enable teachers to help stu-dents learn important mathematics in sense-makingways so that students can, in turn, make sense outof new situations and solve new problems.
4
5
mathematicsbookshelfBook Review
Bringing the NCTM Standards to Life: ExemplaryPractices from High Schoolsby Yvelyne Germain-McCarthy(1999, 193 pages, $29.95 paper, ISBN 1-883001-58-7)Published by Eye on Education,6 Depot Way West, Suite 106Larchmont, New York 10538
Review by Susan Halko
More teachers are becomingaware of the NCTM Standards,but are they implementing theStandards into classroom activi-ties? Bringing the NCTMStandards to Life: ExemplaryPractices from High Schools is agood resource for anyone inter-ested in gaining insight on howto successfully implement theNCTM Standards into their ownpractices. In this book,YvelyneGermain-McCarthy profiles 10teachers who have incorporatedthe NCTM Standards into realand workable classroom lessons.
McCarthy begins by summarizingthe NCTM Standards along with some of the researchand philosophy that grounded the Standards. She identi-fies four Standards that are common to all grade levels:mathematics as problem solving; mathematics as com-munication; mathematics as reasoning; and mathematicsas connections. In addition to these four Standards, sheidentifies the Standards for middle grades and highschool and suggests ways to apply them so that stu-dents realize the interconnectedness of mathematics.
McCarthy then describes the elements of exemplarypractice. By exploring two different classrooms, shepoints out that what looks like reformed teaching mayactually lack key elements of reform. For example, stu-dents seated in groups of four busily working with alge-bra tiles and calculators might not be extending theirlearning any more than students in a traditional class-room. Similarly, students sitting in straight rows busilyworking individually on worksheets could be applyingvalid problem-solving techniques to problems that aresuitable for individual work. McCarthy thoroughlyexplains how each of these scenarios could be possible.
The heart of the book consists of the 10 profiles ofStandards-based units. Each profile includes a descrip-tion of the unit, a “discussion between colleagues” sec-tion that clarifies or expands on the ideas presented inthe lessons, a commentary that walks readers throughspecific Standards and other research applied in thelessons, and a unit overview. Secondary teachers willespecially appreciate the unit overview at the end of
each profile; it allows teachers toadapt each unit to their own settings.
Although the 10 profiles incorpo-rate a number of differentStandards, they all demonstratethat Standards-based mathematicsshould include problem solving,communication, and reasoning.Other Standards incorporated intothe 10 profiles include the follow-ing: computation and estimation;patterns and functions; algebra;measurement; trigonometry; con-nections; statistics; geometry froman algebraic perspective; and dis-crete mathematics.
McCarthy devotes the last sectionof her book to planning ahead forthe 21st century. She suggests waysfor parents, teachers, and adminis-
trators to change their thinking about the nature ofthinking and learning.Teachers, for example, can readreform-based articles in journals, revise and reflect onlessons, participate in conferences, and listen to andassess students as a basis for informing instruction.Thesuggested Web sites and bibliography will motivate “tra-ditional teachers in transition” who want to implementreform-based practices.
Have you read any good books about mathemat-
ics lately? In Mathematics Bookshelf, tell
other
teachers about what you’ve been reading. We
welcome book and article reviews about math-
ematical concepts, current research in mathe-
matics
education, and first-hand experiences of
mathematicsbookshelf
6
MATH
EMAT
ICS in the news
CMIC Cited as ExemplaryProgram by U.S.Department of Education
The Core-Plus Mathematics Project hasbeen notified by the U.S. Departmentof Education that ContemporaryMathematics in Context is one of fiveK–12 mathematics programs in thecountry to be designated as“Exemplary” by the Department’sExpert Panel on Mathematics andScience.This is the highest possiblerating for a program.The panel is com-prised of experts in mathematics andscience, including academics, associa-tion representatives, regional lab repre-sentatives, and practitioners.
The Expert Panel was established as aresult of the Educational Research,Development, Dissemination, andImprovement Act of 1994. Its charge isto oversee a process for identifyingand designating both “Promising” and“Exemplary” programs in mathematicsand science education so that practi-tioners can make better-informed deci-sions in their efforts to improve thequality of student learning in mathe-matics and science.The Expert Panelreviewed comprehensive elementary,middle, and high school programs likeCMIC as well as individual coursetexts in mathematics and science.
The panel’s process required curricu-lum programs to undergo an extensiveevaluation process. Each programfaced a stringent review process builton four criteria:
➤ Quality of Program
➤ Usefulness to Others
➤ Educational Significance
➤ Evidence of Effectiveness and Success.
Two Quality Review Panels of practi-tioners with content expertise andclassroom experience evaluated eachprogram based on the first three crite-ria. Programs that satisfied these crite-ria then went to an Impact ReviewPanel of evaluation experts whichevaluated the program on the fourthcriterion. Ratings by all three panelswere then considered by the ExpertPanel in making a final selection.
The criteria against which CMIC andother programs were evaluatedinclude the following:
Quality of ProgramCriterion 1The program’s learning goals are chal-lenging, clear, and appropriate for theintended student population.
Criterion 2The program’s content is aligned withits learning goals and is accurate andappropriate for the intended studentpopulation.
Criterion 3The program’s instructional design isappropriate, engaging, and motivatingfor the intended student population.
Criterion 4The program’s system of assessment isappropriate and designed to informstudent learning and to guide teachers’instructional decisions.
Usefulness to OthersCriterion 5The program can be successfullyimplemented, adopted, or adapted inmultiple educational settings.
MATHEMATICS in the news
offers news on research find-ings, mathematical discoveries,and events that concern sec-ondary mathematics teachers. If you would like to submit anews item to Mathematics inthe News, whether it is some-thing you have read or an eventin which you have participated,please complete the SuggestionBox form on page 15.
7
LINKtech
techLINKIn Techlink, mathematics teachers find out aboutsoftware,Web sites, calculators, and creative com-puter and calculator projects. If you want to shareyour ideas, please complete the Suggestion Boxform on page 15.
Educational SignificanceCriterion 6The program’s learning goals reflect the vision promot-ed in national standards in mathematics education.
Criterion 7The program addresses important individual and soci-etal needs.
Evidence of Effectiveness and SuccessCriterion 8The program makes a measurable difference in student learning.
To be rated as “Promising,” a program had to satisfy spe-cific indicators for each of criteria 1–7.To be rated as“Exemplary,” a program also had to fulfill Criterion 8 byproviding “convincing evidence of effectiveness in mul-tiple sites with multiple populations” using several indi-cators of student gains.
Information about programs designated as “Promising”or “Exemplary” is being disseminated through theEisenhower National Clearinghouse for Mathematicsand Science Education, the Eisenhower RegionalMathematics and Science Education Consortia, and theNational Education Dissemination System.Teachers ofContemporary Mathematics in Context may wish toshare this recognition of CMIC with local schoolboards, administrators, and parents.
Contemporary Mathematics in ContextAssessment and Maintenance Builder
CD-ROMs
ELC recognizes that teachers ofContemporary Mathematicsin Context (CMIC) can bettermeet the needs of their stu-dents if they can easily pre-pare and customize theassessment and mainte-nance items used withCMIC. Early next year,
CMIC Assessment andMaintenance Builder CDs will be avail-
able to specifically meet this need.The CMICCDs, formatted for both Macintosh and IBM platforms,offer an electronic environment that enables teachersto choose and customize the assessment items that nowappear in print format in the Assessment Resources.TheAssessment and Maintenance Builder CDs will makeassessment and maintenance preparation easier, faster,and more effective for use in individual classes.
Teachers will be able to cut and paste, delete, or add toexisting quizzes and exams in Courses 1, 2, and 3.TheCDs will also suggest which items can be adapted for amultiple-choice format or “cloned” (recreated withminor modifications). In addition to all of the assess-ment items from the Assessment Resources, the CDswill also include Maintenance Master items along withsupplemental maintenance items.
A CD sampler for the Contemporary Mathematics in Context Assessment and Maintenance Builder CDs will be available this winter.To request a sampler,call 1-800-382-7670.
Exemplary
8
interviewinterviewUSING BASEBALL STATISTICS
FROM THE INTERNET
Tim Kaltenecker has been teaching mathematics inNew York City for twelve years and has been at theLittle Red School House and Elisabeth Irwin HighSchool for nine of those years. He received his bache-lor’s degree in Math and Computer Science Educationat Bowling Green State University in Ohio and is cur-rently pursuing his master’s degree in MathEducation at New York University. In this interview,he describes a project involving baseball statistics thathe and his students completed using the Internet.
ML: Describe your project involving baseball statis-tics. How did you come up with the
idea? What were you goals for thestudents?
TK: The first unit inContemporary
Mathematics inContext introduces statistics, and thisproject followed
that unit. I wantedstudents to researchdata using theInternet and to finddifferent ways to look
at the informationgiven. I also wanted stu-
dents to realize that theymust look carefully at the information
in order to determine what the data tell them, and that inmany cases, they can interpret the data differently. Finally,I asked students to communicate their understanding inwriting.
I was introduced to the idea in a graduate course in sta-tistics at New York University.At the time, the headline-making news involved the greatest number of homeruns in a single season.The players, Mark McGwire andSammy Sosa, were making headlines each day, and thedebate centered on the question,“Who is the betterplayer?”
I wanted students to use the concepts of average,center, and spread to analyze information. Given a set of
baseball statistics, I wanted them to organize data anddraw conclusions based on the way in which theymade their observations.We looked at baseball statisticsfor Sammy Sosa and Mark McGwire from the ESPN Website.We found that looking at total home runs within acareer was one way to judge the better player … butwas it the only way?
ML: How did you organize time, space, and usingthe Internet? Did students work in groups?
TK: I planned three days for this project.The first dayincluded an introduction to the debate over who is thebetter player, a discussion of methods to use in order todetermine the better player, and an introduction tousing the Internet.There were several students in myclass who had experience using the Internet, so it wasconvenient to match those students with other studentswho had never used the Internet.
On day two, students arrived having done some numbercrunching and presented their initial findings.Aftereach student gave a presentation, I asked students towrite a one-page argument presenting either SammySosa or Mark McGwire as the better player.
On the third day, I asked several students to read theirarguments.An interesting class discussion followed dur-ing which students fully began to realize how statisticscan be manipulated to any opinion, and that one mustpay close attention to what is actually being consid-ered. I also introduced box and whisker plots using thehome run data that initiated the discussion in the firstplace. I asked the students,“Why is there so much fan-fare over Sammy Sosa when Mark McGwire clearly hasmore home runs than Sammy?” By analyzing the boxand whisker graph, students could look at the spread ofthe data.
ML: How did the students analyze the data theyfound on the Internet?
TK: The students had been studying mean and median,and would soon be looking at mean absolute deviation.They had two options for analyzing their data: Theycould enter the data from the Web site into their graph-ing calculators and use the methods studied to deter-mine the appropriate measures; or they could transferthe data from the Web site to a spreadsheet and use thespreadsheet operations to find the appropriate measures.
9
In doing this, students were not onlyusing their knowledge of the mea-sure of center and spread, but theywere also using the technologyavailable in an efficient manner to
assist them in their calculations.
Students discussed their ideas in groupsafter a class discussion on the meaning of
each column in the statistical chart. However, they wererequired to come up with their own unique look atdetermining the better player.The advantage of begin-ning in a group was that the students could discuss anddebate different approaches.Additionally, they helpedeach other use the technology.
ML: How did the students use calculators?
TK: First they entered the data into a data list.Then,they used various functions, such as “SUM (listname)” tohelp them find the mean. Some students explored thecalculator on their own and found that they could auto-matically calculate the mean.This was allowed; I wasprimarily interested in the interpretation of mean at thispoint.There were other homework assignments thatasked for the procedures for calculating the mean.
ML: So … who is the better baseball player? Whatresults did your students find?
TK: After the students presented their results to theclass on the second day, they determined that identify-ing the better player depends upon how one looks atthe data. Each student justified that each player is betterwhen one looks at the data from a certain perspective.Once they made an argument for one player, I askedthem to write an argument for the other.They had tosupport their arguments using statistics as well as showhow they arrived at their numbers. By writing these argu-ments, students learned to communicate with mathemat-ics and justified their thinking in an analytical way.
The first thing to do in any data set is to determine ifthere are any outliers that need to be eliminated.Students sometimes had trouble discarding data; theyfelt that everything should count. However, it was avaluable discussion.As a class, we decided to eliminatethe rookie year.We did not feel the first year was repre-sentative of their “career” stats.Then, we noticed some
very low numbers for each player.A student in the classinformed us that there were a few seasons duringwhich each player had an injury, and therefore, they didnot play the entire season.We decided to throw outthose numbers, too.
With the remaining data of each player’s career statis-tics up to and including 1998, the batting average statis-tics are as follows:
Mean Median Number of Seasons
Mark McGwire .264 .271 10Sammy Sosa .271 .268 7
From this data, one could conclude that Sosa is the bet-ter player by looking at the mean; his average is .271while McGwire’s average is .264. However, by looking atthe median data, McGwire is the better player with anaverage of .271 compared to Sosa’s .268.
So … who is the better player? Of course, the studentsrealized that it depends!
ML: How did this discovery help your studentslearn about using the mean and median?
TK: Students discovered that using the mean and medi-an can result in different conclusions, and that one mustdetermine which system of measurement should beapplied to each situation.Throughout the project, theygained practice in finding these values and in thinkingabout what these values actually represented. Studentswere more careful in their choice of words when talk-ing about “average” after this lesson. For example, afterthis project, a student approached me and asked if Iwould use her median test score instead of her meantest score when calculating her grade; she had discov-ered that her median score was higher!
ML: How did this project fit in withCMIC?
TK: The project fit in withthe philosophy of CMICin many ways. First, studentsengaged in a discussion aboutthe different ways to determinethe better player.They had to
10
articulate their ideas to their class-mates while listening to others.Theydebated and discussed their ideas—they were communicating about mathe-matics.Then, students searched for waysto justify their argument through the useof mathematics. In doing so, they learnedthe different interpretations of mean andmedian.And finally, students communicatedtheir findings to their classmates. Overall, stu-dents were acting like statisticians, searching formeaningful ways to interpret real-life, up-to-date data that had relevance to them.
ML: Do you do any other projectsthat incorporate statistics fromthe Internet?
TK: In another class, a senior electiveon mathematical modeling, students use theInternet to search for real-life data that can be modeledusing regression equations.They must find data that canbe modeled using a few of the many types of regressionequations: linear, quadratic, cubic, quartic, exponential,and so on. Once they gather their data, students gener-ate an equation and justify that it is a good fit usingresiduals and the correlation coefficient. Once they are sure that they have a good fit, students interpret the meaning of their model, use it to make predictions,and determine the accuracy of their predictions.Thisinformation is presented in a written paper usingMicrosoft Word with graphs and charts imported fromMicrosoft Excel and the graphing calculator with theTI-Graph Link.
ML: What tips do you have for other CMIC teacherswho want to incorporate the Internet as a
resource for projects like these?
TK: Using the Internet can be tricky. I recom-mend that once teachers have a plan, that
they follow the plan themselves and deter-mine how well it works.The Internet can
be unpredictable. First, make sure thatyour system is working well; you don’t
want to get your class to the comput-er lab to find that the Internet is
down.You will be faced with aroomful of angry students!
Second, if you plan to use thevarious search engines, show
the students the differentmethods of searching that
narrow down the topic.You can spend hours
searching for some-thing without finding
it.Also, avoid using theInternet if the data can be
found somewhere else. I havehad students spend long periods of time searching theWorld Wide Web for data that can be found in two min-utes in the World Almanac. Finally, if you are doing thisfor the first time with a class, have Internet addressesavailable so that the students can go directly to the sitethat is relevant. Unless you are teaching a class on howto use the WWW, identifying the site you want studentsto visit will save you a lot of time and frustration.Andone final point (this happened to me this year): Even ifyou have used an Internet location previously, checkthe location before using it again; the sites sometimeschange or disappear!
Want to know more?The career statistics for Sammy Sosa can be
“Having been frustrated with traditional textbooks,I found myself drifting away from the book moreand more each year until I was finally without atextbook. I decided it was time to explore new cur-riculum projects that supported the NCTMStandards and assessment methods. During a sum-mer workshop on math and technology at thePhilips Exeter Academy, I studied five curriculumprojects, including the Core-Plus project that hasbecome CMIC.
I brought three of the five projects to the mathdepartment at LREI, and after much research andinvestigation, we chose CMIC.
We began to phase in CMIC during the 1998–99school year with our ninth grade algebra class. Ialso used various units throughout the three-course sequence in other classes in order to testthem out, and I have been very pleased with theresults.As a test, I taught two sections of atrigonometry unit this year—in one section, Iused my traditional, college-level trigonometry
Tim Kaltenecker
book; in the other, I used the trigonometry unitsfrom CMIC. The difference in the two sections wasapparent.Although I covered slightly more contentin the traditional class, the students in the CMICclass seemed more confident in their understand-ing of the topics, and they were more engaged inthe work. I can think of one student in the CMICcourse in particular who had been struggling allyear—not because of a lack of ability, but becauseof his apathy for school. After working with CMICfor about two weeks, I asked him to explain aproblem to his teammate who needed help. Iknew he understood the problem, because I hadseen the work he was doing. He looked at mequizzically, took a deep breath, and said,‘I don’tthink that I have ever been in the position of help-ing another student in math.’ This is what CMICis all about!”
11
A B O U T T H Eteacher
A B O U T T H E
12
Introducing Impact Mathematics:Algebra and More for the Middle Grades
Developed in cooperation with Education DevelopmentCenter, Inc., Impact Mathematics:Algebra and Morefor the Middle Grades is designed to make more mathe-matics accessible to more middle grades students. Theprogram features:
• Full and rigorous coverage of Algebra I by the endof Grade 8
• Informal to formal concept development especially designed for middle grades students
• Number, measurement, algebra, geometry, probability,and statistics integrated throughout
• Problem-solving and engaging contexts that promotemathematical thinking
• Appropriate attention to and practice with computational skills and symbolic manipulation skills
• Balanced use of direct instruction and student discovery in whole-class discussions, collaborative group work, and individual student tasks
• Notes keyed directly to student lessons help teachers play anactive role in instruction
• Lesson plans that accommodate traditional or block schedules
• Comprehensive assessment
new & revised PRODUCTS PRODUCTS PRODUCTS
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Impact Mathematics Course 1 will be available in 2001.
Student Text 42.00 39855 October 1999 39860 April 2000
Teacher’s Edition,Vol.A 39.00 39856 February 2000 39861
Teacher’s Edition,Vol. B 39.00 39857 July 2000 39862 September 2000
Teaching Resources,Vol.A 22.00 39859 February 2000 39864
Teaching Resources,Vol. B 22.00 39875 July 2000 39877 September 2000
Assessment Resources,Vol.A 36.00 39858 February 2000 39863
Assessment Resources,Vol. B 36.00 39874 July 2000 39876 September 2000
Impact Mathematics 15.00 39865 October 1999 39865 October 1999Implementation Guide
Impact Mathematics 230.00 39884 October 1999 39884 October 1999
Manipulative Kit
Teacher’s Resource Package 190.00 39879 July 2000 39880 September 2000
(Includes Teacher’s Edition,Vols. A & B,Teaching Resources,Vols. A & B,Assessment Resources,Vols. A & B, and Implementation Guide)
ITEM DESCRIPTION Price ELC Availability ELC AvailabilityOrder # Order #
Course 2 (Grade 7) Course 3 (Grade 8)
IMPACT MATHEMATICS:Algebra and More for the Middle Grades
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Assessment and MaintenanceBuilder CD-ROMs for ContemporaryMathematics in ContextContemporary Mathematics Context Assessment andMaintenance Builder CD-ROMs will be available nextyear. They will allow teachers to choose and cus-tomize the assessment items that now appear in printformat in the Assessment Resources.
A CD sampler for the Contemporary Mathematics inContext Assessment and Maintenance Builder CDswill be available this winter.To request a sampler, call 1-800-382-7670.To find out more about the CMICCDs, see Techlink on page 7.
A P R I L 2 0 0 0NCTM Annual Meeting Blows into the Windy CityApril 13–15, 2000Plan to attend this year’s national NCTM meeting in thecity that is home to Everyday Learning Corporation.Themeeting will take place at historic Navy Pier and will pro-vide many learning opportunities from thousands of math-ematics educators from around the world.Also, NCTM’supdated Standards, Principals and Standards of SchoolMathematics, will be presented at the meeting.We hopeto see you this spring!
eLcnewsEveryday Learning Corporation
Contemporary Mathematics in ContextReference and Practice BooksWhat are the Reference and Practice(RAP) Books?
The Core-Plus Mathematics Project is currently pro-viding draft versions of CMIC Reference and PracticeBooks.The books provide Core-Plus students withsummaries of previously learned concepts and skills,maintenance practice to review previously learnedconcepts and skills, and test-taking practice for stan-dardized tests, college admission tests, and collegeplacement tests.There is one Reference and PracticeBook per course (Courses 1–3), and each studentbook contains an answer key.
How are the RAP books organized?Each RAP book contains three sections.
Section 1 Reference section of key ideas and con-cepts from previously learned courses or units.Thissection includes examples and short exercise sets toaccompany the text.
Section 2 Mixed-skills practice sets for previouslylearned concepts and skills.
Section 3 Test-taking practice in standardized testformats drawing from key content on college admis-sion and placement tests.
Draft versions of the RAP books are currently available.
ComingSoon
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Name ____________________________________ Position ________________________________
School __________________________________ City & State_____________________________
Secondary Mathematics Program ___________________________________________________
Home Phone ______________________________ School Phone ___________________________
Check all that apply. Below is my
❑ Question for the Ask the Authors section (Please be specific.)
Share your ideas and experiences in ELC’s Mathlink
Have you ever thought that you might like to contribute toELC’s Mathlink but have some questions? Below are somecommonly asked questions and our responses.
Who writes the articles for ELC’s Mathlink?Secondary mathematics teachers and administrators writeabout their ideas, research, and experiences in the classroom.The curriculum authors also write articles for the newsletter.Each contributor offers a unique perspective on secondarymathematics curricula, including algebra, geometry, precalculus,calculus, and integrated mathematics; and current issues inmathematics education.
I would like to contribute an article, but I haven’t written fora publication before. Will I receive input from ELC’s Mathlinkeditors as I write the article?We will be available to answer your questions and offer input onyour writing from the time you propose a topic to the time youturn in that well-crafted final draft. Contributing to ELC’s
Mathlink is a valuable opportunity to write for an audience offellow teachers. You have the option of writing an article, abook or software review, classroom management hints, or aninterview. Or, if you have another idea, tell us about it.
What should I do if I want to write an article for ELC’sMathlink?Write down your ideas and send them in! Either send in arough draft of an article or just jot down a few notes about thetopic you would like to address. Don’t forget to include yourname, school name, address, and phone number. E-mail address-es work, too! You can send ELC’s Mathlink a note addressed [email protected].
I want to comment on an article that was in the last issue ofELC’s Mathlink. Do you print a “Letters to the Editor” column?Yes, we welcome your input on the articles and features in thenewsletter. You can send all letters and other submissions toEveryday Learning Corporation, attn: ELC’s Mathlink Editor,Two Prudential Plaza, Suite 1200, Chicago, IL 60601. You maychoose to use the Suggestion Box form on page 15 of thisissue to share your ideas.
