concord g...glimpse into student thinking and an opportunity for mean-ingful assessment. using...

Why Are ProgressionsImportant?

There is a disturbing tendency to treat edu-cational materials as building blocks thatcan be assembled in any convenient order.“Knowledge engineers” think they canstart with “learning objects” that can beautomatically assembled into meaningfulinstruction.

Such designs ignore the central role ofsequences of content and the importanceof the progressive integration of ideas thatcreates knowledge and expertise. Core con-tent needs to be returned to again andagain, with each encounter deepening stu-dent understanding and increasing theweb of associations that is a critical attrib-ute of true knowledge.

At each step, a curriculum designer must

consider what the student already knows,what misconceptions are likely, what canbe learned now, and what is important forsubsequent steps. This need not precludeinquiry, but is required to make learning ofkey ideas and processes successful.

Creating a coherent progression in sci-ence areas that are changing is particularlychallenging. For instance, advances inmolecular science in general and in molec-ular biology in particular are happening sorapidly that simply memorizing the tenetsof yesterday no longer ensures true fluencyin the field. Even biology’s vaunted CentralDogma (DNA codes RNA, which codes pro-teins)—a cross between classical geneticsand modern molecular science—is show-ing cracks. To truly understand newadvances in molecular biology, studentsneed molecular literacy that includesunderstanding the molecular conceptsunderlying the constructs of modern biol-ogy and the ability to apply these concepts

A sequence of model-basedactivities supports student understanding.

BY BORIS BERENFELD AND ROBERT TINKER

org

REALIZING THE EDUCATIONAL PROMISE OF TECHNOLOGY

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Perspective: STEM EducationNeeds a Major OverhaulIt’s time to act. Existingresearch shows ways scienceeducation can be improved.

How Can Assessment BeImproved? DigitalPerformance AssessmentMay Be the AnswerComputer simulations canassess student performance.Now it’s time to help teachersput assessment to work.

What is 21st CenturySecondary Engineering?The engineering curriculumshould be built around a progression of math and science projects focused oncore concepts.

Monday’s Lesson: WhatFlows When Heat Flows?Unlock the mystery to heat flow with a dynamicmolecular model.

What is 21st CenturySecondary Math? Concepts,Not ComputationNew tools and new assess-ment models make mathaccessible to all.

Interactive Models: HelpingStudents Learn and HelpingTeachers Understand StudentLearningInteractive models provide aglimpse into student thinkingand an opportunity for mean-ingful assessment.

Using Sensors and Models toAnswer Discovery QuestionsUsing a simple web-basedinterface, teachers can designprobeware activities for theirclassrooms.

Inside@Concord

continued on page 4

www.concord.org vol. 10, no. 2 Fall 2006

Science education could be so much better if onlywe implemented it based on what we know aboutteaching and learning. Decades of research, pilotstudies, and innovations have conclusivelydemonstrated how science education could beimproved. We should also include changes in thedisciplines and newly discovered science content,and most importantly, we should exploit themany opportunities that technology provides tofundamentally change what is taught and howstudents learn. These changes could result inhuge advances in student understanding.

There is wide agreement that somethingshould be done about science, mathematics, andengineering education. Increasingly, industry

is high-tech,jobs demandtechnologicalsavvy, civicdecisions arebased on mod-

els and statistics, and personal health requiresmedical expertise. Societies that implement a 21st

century science education will flourish whilethose that cling to antiquated models will be leftbehind. This was recognized recently in a flood ofpassionate and reasoned calls for improvementsin science education from business leaders, acade-mia, futurists, commentators, and even the mili-tary. Clarity about what to do, however, has beenlacking. Most plans involve some combination ofhigher standards, harder tests, more requiredcourses, more AP courses, better teachers, higherpay, or smaller schools. These changes simplyresult in more of the same old instructional prac-tices. They fail to support needed change in whatis taught, how it is taught, and how it is assessed.

A new, comprehensive and coherent curricu-lum is needed from kindergarten through thefirst years of college in all STEM subjects (sci-ence, technology, engineering, and mathemat-ics) that focuses on fewer and deeper conceptstaught conceptually, coherently, and in mean-ingful contexts. These core concepts can providetouchstones around which a profusion of math,science, and engineering topics can be organizedin a far more interdisciplinary way

A good place to start a reform effort is the sec-ondary STEM curriculum. Success at the second-ary level would have a profound effect on bothelementary and college education. Such a radical

design for STEM education reform must be basedon the following principles:

• Research Based. There is a growing consensuson how to teach STEM subjects. Studentsneed to be actively engaged in thinking criti-cally about key topics, so that they examinetheir own ideas and build associations.

• Unified. Mathematics, engineering, and the sci-ences should be linked as much as possible.An integrated math-science sequence shouldtake advantage of a spiral curriculum. Tech-nology and engineering, usually orphaned,should be woven throughout these courses.

• Conceptual. There should be far less emphasison facts and algorithms, and far more on coreconcepts. For instance, the calculus conceptsof derivatives and integrals would be coveredin science and engineering contexts withoutfocusing on their proofs or calculation.

• Technology Enhanced. A reformed STEMeducation would exploit many advantages ofcurrent technology for experimentation, mod-eling, collaboration, and resource acquisition.

• Standards Compliant. STEM reform canadhere to the national standards and go farbeyond them in many cases by emphasizingfundamental concepts and featuring anemphasis on inquiry, applied math, and engi-neering found in the standards.

• Teacher Friendly. Teachers should haveextensive support for teaching the new con-tent and adopting new instructional tech-niques. The technology should give teachersdetailed and timely feedback about studentlearning so they can adjust instruction.

This vision will be difficult to achieve. Fewschools have the resources and flexibility toimplement these recommendations. Not all theneeded curriculum pieces currently exist, andfew have been subjected to classroom testing.And teachers will be required to learn new con-tent and better instructional strategies. Still, thisvision cannot be dismissed simply because of thechallenges to its implementation. We hopeadventurous educators, schools, and institutionscan agree on an agenda for comprehensivereform of STEM education, along these lines.

Robert Tinker ([email protected]) is President of theConcord Consortium.

2 @Concord Fall 2006 vol. 10, no. 2

P E R S P E C T I V E

STEM Education Needs a MajorOverhaul BY ROBERT TINKER

A new curriculum is needed that focuses on fewer and deeper concepts.

Assume that you are selecting items foran assessment leading to certificationof electronic technicians. Which ofthese would you choose?• Define the term “digital multimeter”

and give two examples of its use.• An RC circuit consists of a 100-ohm

resistor in series with a 10-microfaradcapacitor. What is its time constant?

• Using a function generator and anoscilloscope, find out what is wrongwith this power supply and fix it.

It’s a trick question, of course. Thefirst of these assessment items stressesirrelevant language skills and the sec-ond involves plugging numbers into amemorized equation. The third clearlycomes closest to simulating the condi-tions a technician might actuallyencounter on the job. Nevertheless, thequestions on certification exams forelectronic technicians are far morelikely to resemble the first two itemsthan the third. The reason is simple:“performance assessments” like itemthree are much more costly to adminis-ter and score.

Or are they?Computers can simulate any elec-

tronic circuit or measuring device;moreover, they can monitor and reporton the actions of their users. All that’smissing, then, is the ability to analyzethose actions and make valid infer-ences from them concerning a stu-dent’s knowledge, understanding, andskill, and her ability to combine thoseassets to solve realistic problems.

For several years, the ConcordConsortium has been experimentingwith computer-based models of real-

world phenomena. The computersets up a challenging problemthat involves manipulationof a model to achieve aspecific goal. It thenmonitors what the stu-dent does, possiblyoffering hints or ask-ing questions at crit-ical junctures. Mostimportant, the com-puter logs the stu-dent’s actions—answers to ques-tions as well asexperimentationwith the model. Byaggregating suchdata from thou-sands of students, wehave been able todetect statistically sig-nificant patterns in theirperformance that corre-late to their learning gainsas measured by other means(see “Interactive Models,” page12). Thus, we can use performancedata to make valid inferences concern-ing students’ content knowledge aswell as their ability to explore and rea-son with models.

To date, our work with these modelshas involved science students, not bud-ding technicians, but that’s about tochange. With support from the NationalScience Foundation’s Advanced Techno-logical Education Program, we areadapting our technology to assess stu-dents as they troubleshoot computermodels of faulty electronic circuits,using models of standard measuringequipment. This will enable us to posechallenges similar to the one describedabove, and to monitor, for instance,whether the student knows where toplace the probes of the oscilloscope andhow to set its time scale.

3The Concord Consortium www.concord.org

How Can Assessment BeImproved?Digital PerformanceAssessment May Be theAnswer

BY PAUL HORWITZ

We have developed the technologynecessary to give teachers those tools,but so far we have concentrated ourdata reporting tools on the needs ofresearchers, not teachers. The chal-lenge now is to adapt our technologyto create formative assessments thatcan identify the struggling studentsand describe their difficulties inenough detail so the teacher can helpthem, long before they are confrontedby that high-stakes, multiple-choicecertification exam.

Paul Horwitz ([email protected]) isDirector of the Computer-Assisted Perfor-mance Assessment Project.


to various biological phenomena. Yet literacy in any field, particularly

in molecular science, cannot be taughtby treating curriculum components asbuilding blocks assembled in any order.Proper sequencing that guides studentsto construct a rich molecular world-view useful for explaining a wide rangeof phenomena is critical.

Students Need More than “The Chemistry of Life”In the traditional biology curriculum,molecular science is presented in a frag-mented way, highlighting limited con-cepts. Most, if not all, ninth gradebiology textbooks include a section typ-ically entitled “The Chemistry of Life.”Students are introduced to atoms, ions,and small molecules. This chapter tradi-tionally includes a colorful picture ofwater molecules, with dotted linesbetween them referred to as hydrogenbonds. Another picture shows sodiumand chloride ions attracted into a crys-talline structure due to opposite chargescarried by the ions, though this maycreate a misconception that attractionsexist only between ions. There is noth-ing or very little about polarity or vander Waals forces.

In the “Chemistry of Life” chapter,macromolecules come next. Here car-

bohydrates, lipids, proteins, andnucleic acids are introduced. Studentsmemorize the four nucleotides—A, C,G, and T—that make up DNA, look upthe chemical formulas of 20 aminoacids capable of combining intopolypeptide chains, and learn that pro-teins have primary, secondary, tertiary,and quaternary structures.

To address the genetic code, such achapter has a table linking 64 possibletriplets of nucleotides to 20 aminoacids. As the finale, it mentions thatwhen DNA code is translated into pro-teins, the proteins determine traits.Since Mendelian genetics usuallycomes much later in the course, stu-dents cannot question at this pointhow traits are linked with proteins. Acouple of months later, by the timethey study Mendel’s Laws, “The Chem-istry of Life” looks like a distant anddisconnected mirage.

While this approach refers to atomic-scale interactions, it doesn’t develop theconnections necessary to build a strongunderstanding or reasoning skill at themolecular level. Because many criticalmolecular principles underlying theseideas had been considered hard toteach, they were often skipped, lightlytouched upon, or taught quantitativelythrough mathematics. But unless stu-dents were mathematically literate, thiswas not an effective approach.

Stepping Stones to MolecularLiteracy With the support of the NationalScience Foundation, we have devel-oped a sequence of model-based activi-ties to support student understandingof key concepts that underpin modernbiology. The Stepping Stones to MolecularLiteracy helps students reason aboutmicroscopic and macroscopic phenom-ena using what they learn about atoms,molecules and their interactions, andthe resulting emergent phenomena.The specific sequence is critical becauseeach activity builds upon the onesbefore it. Like Russian nesting dolls,each activity encompasses the priorones, thus building a progression ofmolecular understanding.

The following is an example of amodel-based progression of activities.(For the complete list of The SteppingStones to Molecular Literacy activitiessee: http://molo.concord.org/database/browse/stepping-stones/)

1. Atomic Movement Never Stops.Students start with a single molecule ina virtual container and gradually addmolecules to the system. As they addheat energy, they observe increased fre-quency of molecular collisions.Students can select a single moleculeand trace its path to see how its motionis affected by collisions with other mol-

Progressions—continued from page 1

Using the DNA to Protein model, students can compose any sequence of nucleotides, transcribe it into mRNA, and then translate that into a small pro-tein. They can then view the protein folding in water or oil. This is how nature makes a 3D protein from a one-dimensional DNA sequence.Experimenting with such a model allows students to explore the relationship between a DNA sequence and the resulting protein structure, arguably themost important concept in molecular biology.

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ecules. By changing the amount of heatin the system, students can addressissues of thermal motion, averagekinetic energy of molecules, and tem-perature. This dynamic picture of mat-ter composed of constantly moving andcolliding molecules must be a founda-tion of students’ mental models.

2. It’s a Sticky, Sticky MolecularWorld. Few students realize that allatoms attract one another. This funda-mental idea is central to an under-standing of the atomic scale. It isquite common for students to thinkthat only opposite charged ions areattracted to each other. Our modelallows them to experiment with sys-tems that depict attractive forces,such as van der Waals and hydrogenbonds that exist between atoms andmolecules.

3. Relating to Water: Hydrophiliaand Hydrophobia. The earlier modelsof random thermal motion and theattraction and repulsion betweenatoms and molecules are now appliedto understanding the unique propertiesof water and aquatic solutions.Students simulate the attractive forcesbetween water molecules called hydro-gen bonds, experiment with addingionic and non-ionic compounds, and

observe the interactions between watermolecules and the solute.

4. Protein Chains and Water. Withthe above knowledge, students investi-gate how a protein chain made of acombination of hydrophobic andhydrophilic amino acids behaves inwater and lipids (the cell’s environ-ment). Students see how hydrophilicamino acids pull the chain towardwater and how the hydrophobic aminoacids are excluded by water and thusmove inside the chain. Students learnhow these processes shape the protein.

5. Genetic Code and Proteins.Students are ready to embark on exper-iments based on the Central Dogma.Using a model that contains a DNAcoder and is capable of generating pro-teins according to the genetic code,students can create any sequence ofnucleotides, launch protein synthesis,and observe the resulting compositionof the chain of amino acids; they alsocan predict and observe the resultingshapes of the polypeptide chain inwater, and develop a conceptual under-standing of the genetic code and itsconnection with the shapes of theresulting proteins.

6. Molecular Self-Assembly. Whenstudents explore the folding of thepolypeptide chain into a specificthree-dimensional shape, and theassembly of proteins in a complexquarternary structure, they usefundamental ideas of physics andchemistry, including the idea thatkinetic motion brings the piecesin contact and the charge and

shape knits units together, creatingshapes with biological consequences.

7. Mutations and Illness. If one trulyunderstands the concepts leading tothe Central Dogma, one should be ableto reason about the molecular natureof mutations. To grasp the concept ofmutations, students are able to alterthe genetic code and compare howdeletions, insertions, or substitutionsof the coding sequences affect theamino acid composition and the shapeof the protein. This molecular hands-on learning allows students to tacklethe cause of a genetic disease, such assickle cell anemia.

Thus, from simple concepts of ran-dom motion and the stickinessbetween particles, a sophisticated viewof the molecular world emerges.Generations of biology teachers usedtheir eloquence and tons of chalk toconvey these ideas. For our students,modeling and visualizing the processesof molecular interactions are only aclick away. The Stepping Stones toMolecular Literacy builds a unique pro-gression of understanding. Armed withthis foundational understanding, stu-dents can take on more complex explo-rations, all the way to the CentralDogma, and further, to new discoveriesin molecular biology.

Boris Berenfeld ([email protected]) isthe Principal Investigator of the MolecularWorkbench projects and Director of theInternational Center. Robert Tinker([email protected]) is President of theConcord Consortium.

The Stepping Stones toMolecular Literacy http://molo.concord.org/database/browse/stepping-stones/

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In the Brownian Motionactivity, students observethe motion of a single par-ticle, and then increase thenumber of particles in themodel, as well as theamount of heat energy.They follow the motion ofparticles as they collideand discover the cause fortheir apparent randommotion.


What is 21st Century SecondaryEngineering?Increasingly in society, much of whatsurrounds us has been engineered. Wewear clothing designed to wick mois-ture from the body, stretch, stay wrin-kle free, and protect us from UVradiation and insects. We live in struc-turally sound buildings with optimizedlighting, heating and cooling, smokedetection, and numerous other tech-nologies. We use cellular phones thatknow the correct time in every zone,can download digital media, and runon a rechargeable battery for severaldays. But how does all this work?

Relative to its importance, engineer-ing is greatly underrepresented in ele-mentary and secondary education. As aconsequence, many high school stu-dents are unaware of engineering-related careers and unable to make theinformed civic decisions demanded ofcitizens in a technological society.

In this era of teaching to standards,it is important to note that nationalstandards have clearly defined theskills and knowledge expected of sec-ondary students in engineering andtechnology. Engineering is treatedextensively in the National Science Edu-cation Standards and the InternationalTechnology Education Society. The bold-est statement about secondary engi-neering is found in the AAASBenchmarks, in which two of the twelvedescribe engineering topics: Bench-mark 3, “The Nature of Technology”and Benchmark 8, “The DesignedWorld.”

To illustrate the detail and speci-ficity of these benchmarks, considerjust one in the “Energy Sources andUse” sub-section of Benchmark 8 formiddle grades: “Students should knowthat…electrical energy can be pro-duced from a variety of energy sourcesand can be transformed into almostany other form of energy. Moreover,electricity is used to distribute energyquickly and conveniently to distant

locations.” This example shows theclose association between science andengineering and suggests that the 21stcentury curriculum should integrateengineering topics with scienceinstruction. The following sectiondescribes how this can be done.

Projects in Science, Math, andEngineering Easy access to information and compu-ter technologies (ICT) can revolution-ize secondary engineering education.Of course, ICT can be studied as animportant engineering topic—studentscan learn about the computer, pro-gramming, interfacing, and network-ing. But just as importantly, ICT canfacilitate learning all engineering top-ics, in the way that ICT supports majorinnovations in math and science edu-cation, as described throughout thisnewsletter.

The two uses of ICT are mutuallyreinforcing: students who learn aboutICT technologies are also empoweredto use these technologies to expandtheir math and science learning. Andthe ability to make one’s own tech-nologies gives students insights intootherwise “black boxes,” expands therange of possible investigations, andreduces equipment costs.

Student projects are the provenstrategy for engineering education.This approach provides a hands-on

learning experience, where studentsget a genuine opportunity to be inquis-itive and come up with solutions.Projects are best undertaken in smallteams with defined roles, much theway most science and engineering isdone. The potential pitfall in the use ofprojects is that they can be too open-ended, and consume time andresources. To avoid getting mired inlow-yield projects, the curriculumneeds to focus on well-defined activi-ties that provide guidance and haveclear educational purposes. This can be done with highly interactive computer-based activities that providemotivation, opportunities for reflec-tion, guidance, hints, and support forsharing reports.

The following two projects illustratethe power of projects and the role ofICT technologies.

Taking Measurements: NaturalFrequency and Resonance Did you know that the human stom-ach resonates at a frequency of 4-8 Hz(cycles per second), and that your headresonates around 20-30 Hz? Fortu-nately, the engineers designing cars areaware of this (or you might get car sickif the car’s vibrations occurred at thesame frequency as your head or stom-ach). The topic of natural frequencycan be investigated using a two-dollarmicrophone connected to a computer,

BY BRADLEY HEILMAN

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Figure 1. The natural frequencyof a glass bottle can be meas-ured with a $2 sensor and a com-puter. The top graph shows thewaveform of the natural fre-quency within the bottle. Thebottom graph shows the frequen-cies present at resonance.


a glass bottle, and free software devel-oped by the Concord Consortiumcalled the Sound Grapher (see@Concord, Fall 2005). Figure 1 showsthe natural frequency of the bottle, asdepicted by the Sound Grapher. Usingfree tone generation software from theWeb or installed on your computer,this activity teaches the fundamentalsof resonance and tuning, and can beextended to investigate mechanicalprinciples in construction, car andinstrument design, and electrical prin-ciples in circuit or cell phone design.

Understanding Systems: TheClassroom Thermostat Is the air temperature in your class-room constant? Inside air temperaturesare always changing as air is heated orcooled by objects within the class-room, air mixes from sources such aswindows and doors, and other factors.Figure 2 shows a student-made fast-response temperature sensor, whichcosts under $10 in parts. This sensorcan quickly measure small changes inair temperature. The graph shows thefluctuations caused by a room air heat-ing system. The air temperature gradu-ally drops, the heating system turnson, the temperature rises, andthe system turns off. Studentscan measure these changes,then build their own heatingsystem using a temperaturesensor and a switch-operatedheating element or fan. Thisfeedback loop is part of everyheating and cooling system.Such feedback loops are allaround us, from nightlights tothe radiator fan in a car.

Core ConceptsThe 21st century secondary engineer-ing curriculum should be built around acarefully designed progression of proj-ects such as these. The projects wouldincrease in sophistication throughoutthe grade levels and be selected to focuson core engineering concepts:• Hands-on design and construction of

both mechanical and electrical systems.Students need to develop a range oftechnical skills and common con-struction sense. They should learnabout materials, time and financialconstraints, and flexibility and com-promise in project planning and exe-cution.

• Taking measurements and testingdesigns. Some measurements may bedone with mechanical tools (e.g., aruler), but often the best approach isto use sensors and computers.Thermisters, phototransistors, Halleffect probes, and other inexpensivesensors can interface to a computerwith a general-purpose voltageinput. This do-it-yourself approachgreatly expands the range of applica-tions of probeware while also intro-ducing students to the rudiments ofelectronics and interfacing.

• Using mathematical models and simu-lations. Students can extend theirunderstanding and investigate situa-tions not easily explored throughother means. Models also introducestudents to a widely used engineer-ing tool. Almost every large-scaleengineering project is modeled priorto production, which helps deter-mine feasibility, safety levels, andcosts of construction and operation.

• Understanding engineering systems.Systems are collections of componentsthat work together to achieve a result.A system can be compact—such as thecomponents in a pair of pliers or amechanical clock—or as complex andwidespread as the phone system.Students aware of the bigger picture—the components, the interactionsbetween components, and the overallgoal—are equipped for innovating ormanaging better solutions.

ConclusionEngineering and technology are contin-ually advancing in our society. Suchadvances are a call for more attention to21st century secondary engineering.They are also an indispensable enabler:as computer technologies become moreprevalent, they can be leveraged toteach concepts of engineering in ameaningful, effective, project-based cur-riculum. This type of curriculum neces-sitates an understanding of science andmath as building blocks for engineering.

The Concord Consortium is taking afirst step at developing aspects of sucha curriculum, funded by the NSF underan ITEST (Information TechnologyExperiences for Students and Teachers)grant. Teachers nationwide will help ususe both computational models andreal-time data acquisition to createactivities appropriate for their class-rooms and their communities. These

activities will merge engineer-ing with science and math, tothe benefit of all STEM sub-jects, and more importantly,the benefit of the 21st centurystudent.

Bradley Heilman ([email protected]) is a curriculumdeveloper focused on the useof sensors and mathematicalmodels.

National Science Education Standardshttp://www.nap.edu/readingroom/books/nses

International Technology Education Societyhttp://www.iteaconnect.org/TAA/PDFs/xstnd.pdf

AAAS Benchmarkshttp://www.project2061.org/publications/bsl/online/bolintro.htm

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M o n d a y ’ s L e s s o n

Heat energy is hard to understand. You can-not see it, you cannot measure it directly, and itis not a material. In fact, you can only infer heatenergy indirectly from its ability to heat or coolthings. No wonder everyone—including the emi-nent scientists Lavoisier and Laplace—had it sowrong for so long. They thought that somethingcalled “phlogiston” flowed like a gas from hotsubstances where it was dense, to cold oneswhere it was less dense.1

But no one ever found phlogiston.Scientists concluded that if it existed, it had nomass, or maybe a negative mass. They got itconfused with fire, oxidation, and other sourcesof heat. It’s no wonder students have prob-lems understanding heat. The following lessoncan help your students to unlock the mystery.

OverviewThis computer-based lesson uses the MolecularWorkbench (MW) software to make heat visi-ble and to provide a playground where stu-dents can interact with heat and temperature,pose questions, run experiments, and see whathappens. MW is a computational model thatsimulates how atoms and molecules interact.Understanding atomic interactions is essential

for understanding heatflow, so experimentationwith MW gives students aunique way to figure outwhat’s happening on theirown.

Kinetic energy is madevisible in MW by coloringatoms. When still, atomsare white, but as theyspeed up, they becomepink and then red.Students learn that kineticenergy is associated withspeed and that it can betransferred through colli-sions. From there, it’s ashort step to see that

atoms will share some of their kinetic energywith any other atoms they contact and thatthe average kinetic energy is temperature.

Step One: Why Are Those AtomsRed?Go to the Molecular Workbench database ofactivities at: http://molo.concord.org/

Jump to Activity #292, “What is Heat Flow?”This activity consists of a series of pages,

each containing a model. On the first page is anactivity (see Figure 1) designed to familiarizestudents with the Molecular Workbench soft-ware, and the association between kineticenergy and the color of the atom. Using thekeyboard’s arrow keys to apply force, the usercan “steer” an atom. One warm-up challengeconsists of turning the white atom red and thenwhite again as fast as possible.

What Flows When Heat Flows?ROBERT TINKER

Figure 1. This model starts with three atoms at rest. The stu-dent can steer the one atom with arrow keys. As it speeds up,it turns red. The challenge is to get the steered atom whiteand the other atoms red.

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Figure 3. A series of snapshots of the MWsimulation of Newton’s Cradle.

NoteÊ For more information, see

http://en.wikipedia.org/wiki/Caloric_theory

Step Two: Newton’s CradleThis model mimics that familiar pendu-lum toy called the Newton’s Cradle(Figure 2). Four atoms in a row are hit byanother atom. All the atoms are red ifthey have kinetic energy. The model—likethe desktop toy—dramatically illustrateshow kinetic energy moves from one atomto the next, down the line to quite distantatoms (Figure 3).

In real substances, of course, atomsare not in perfect lines, so the energydoes not flow quite so rapidly, but theidea is the same.

Step Three: Heating byHittingIn this step, students are challenged togive kinetic energy to the last atom onthe lower left (Figure 4), starting witheverything at rest. This is an importantstep—and a natural progression fromNewton’s Cradle—because it introduces asolid crystal and shows that kinetic energycan spread among its atoms.

The obvious way to achieve the goal isto steer the big atom to the right at maxi-mum speed. After two hits, the nearbyatoms have a lot of kinetic energy, andthe kinetic energy begins to spread downthroughout the solid. As you run the MWmodel, you can see the red atoms ripple

outward from the point of impact. Askyour students to explain in detail why thered color seems to hop from one atom toanother at random.

Step Four: Heat FlowExperimentsStudents are now prepared to understandenergy flow from one object to another.The final step uses a model of two sub-stances, one with lots of kinetic energyand one with none. The model has thetwo in contact and gives the resultsshown in Figure 5. This might represent ahot cup placed on a counter. Have stu-dents experiment with ways to increaseand decrease the rate of energy flow by

changing the starting positions of theatoms. Can the heat flow be stopped?

These experiments show that kineticenergy will transfer from atom to atomuntil all atoms have the same averagekinetic energy. Since heat flows until tem-peratures are equalized, this justifiesthinking of temperature as the averagekinetic energy, and heat flow as the trans-fer of kinetic energy at the atomic level.This is a profound result with many impli-cations in chemistry, biology, and techni-cal fields.

Closing ThoughtsThe Molecular Workbench allows studentsto explain and connect a wide range of

concepts. In this short activity, stu-dents use guided inquiry to learnabout kinetic energy and atomiccollisions. They learn two founda-tional concepts: temperature isaverage kinetic energy and heatflow is simply the spread of kineticenergy. No equations or numbersare required; a purely conceptualapproach can get the ideas acrossbetter than pages of equations andnumbers.

Robert Tinker ([email protected])is President of the ConcordConsortium.


ows?

Figure 5. A solid with a lot of kinetic energy isplaced on top of one in which the atoms are atrest. The left illustration shows the startingpoint. The right shows what happens after ashort time has elapsed. The graph, which isgenerated in real time during the simulation,shows that the average kinetic energy of thetwo kinds of atoms converge to a single value.

Figure 4. The starting condition (left) and after the big atom has hit the solid crystalline atoms twice(right). The atoms are held together by mutual attraction. The arrowheads in each atom indicatevelocity. On the right, the leftmost atoms have been given some kinetic energy as indicated by theslight shading and their velocity vectors.

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Twenty-first century secondary mathematics callsfor a very different curriculum. The demands onworkers and voters to make informed decisionsrequire greater knowledge of concepts related to

data, models, computers, and rates of change. But ubiq-uitous access to computers in schools, work, and homemeans that procedural and computational techniquesare far less important, while learning more sophisticatedmathematics concepts is possible. A transformation isrequired that results in greater emphasis on the manyways math helps us understand the world, and less onmath for its own sake. We need to focus on concepts,not computation.

In the coming decade, developing and using real-world content will require new technology tools andnew approaches to teaching and learning. It will alsorequire new assessment methods and a commitment toteacher professional development.

New Content and Technology ToolsEducators must bring the ideas of mathematics to stu-dents so that they can recognize the power and poten-tial of the deepest ideas of mathematics. New contentincludes a greater emphasis ona conceptual understanding offunctional relationships, as inrates of change and accumula-tion. It also includes the use ofmodeling to develop and illus-trate ideas. And it must demon-strate ways mathematics cansupport decision making, for

example, understanding graphs and percentages couldhelp a voter interpret a political candidate’s views onglobal warming or the budget deficit.

Over ten years of research by Jim Kaput and col-leagues1 with a large number of middle school and sec-ondary students has shown that students can grasp andapply calculus concepts without first mastering formalnotation. Using SimCalc software, students can creategraphs of data obtained from a real motion detector orfrom simulations of the motion of an elevator, a car, orother object to explore the relationship between func-tion and its derivative and integral.

Research has shown that using visualization toolssuch as TinkerPlots and Fathom, elementary throughhigh school students can achieve sophisticated levels ofstatistical understanding. Computer-based models suchas StarLogo, NetLogo, and AgentSheets are all environ-ments in which students can create a set of rules (e.g.,evolution, global climate change, phases of matter, orschools of fish) and watch for emergent behavior. Thistype of learning provides students with a broad concep-tual understanding needed by everyone, not just thosestudents planning a mathematics or technical career.

The Seeing Math algebra interactives developed by theConcord Consortium support an approach to algebrausing the function concept as a central theme. Withtraditional approaches that offer exercises requiringmanipulation of symbols and equation solving, teachersand students miss many opportunities to make connec-tions to real-world, practical mathematics. The functionconcept unifies later study in algebra and the study ofchange in calculus; introducing functions earlier aidsstudent understanding of mathematics significantly.

New Professional DevelopmentIn order to understand and use new content and newtechnology tools, mathematics teachers need a newtype of professional development that mirrors the stu-dent experience by being grounded in student work aswell as a cognitive theoretical framework.

Seeing Math online case stud-ies2 integrate videos of studentsat work, expert commentary onstudent thinking, online interac-tives that target key mathemati-cal ideas, and threadeddiscussions. Within the coursedesign, teacher participantswatch online video clips of stu-

What is 21st Century Mathematics?Concepts, Not ComputationBY ROBERT TINKER AND GEORGE COLLISON

NotesÊ See http://www.simcalc.umassd.edu/

library.php

Ë Seeing Math courses are available atTeachscape and PBS TeacherLine.

NewCurricularContent

New TechnologicalTools

New Methodsfor Assessment

New ProfessionalDevelopment Models


dents working through the same or similaractivities to those the participants areworking on. Participant collaboration anddiscussion of the activities helps illuminatekey elements of mathematics and mathe-matics teaching. In contrast to olderdesigns of online professional develop-ment in which an expert moderator acts asa “sage on the stage,” in Seeing Mathcourses expert knowledge is imparted intwo ways: using videotaped expert com-mentary targeting specific ideas in the stu-dent work and participants’ experiencegained by working through the activitiesthemselves. As a result, participants makeconnections related to their own learningof mathematics as well as important newconnections among graphic, symbolic, anddynamic representations that are critical inorder to teach algebra effectively. Theimportant aspects of mathematics theylearn through these case studies are notaccessible through traditional methods orrefresher algebra or calculus courses.

Another powerful professional development tooldeveloped at the Concord Consortium is theVideoPaper Builder™, which enables teachers or admin-istrators to author their own web-based video cases. Justas students need to learn how to learn, teachers need tosustain their own professional development.

New Assessment ToolsDifferent forms of assessment must accompany thesecurricular and instructional innovations. The goal ofthe assessment should be to inform students and teach-ers about the level of understanding achieved, and ofthe next necessary steps in instruction. Large-scale stan-dardized assessments provide information about anaggregate of student performances; they are of little usein addressing individual student needs. Extensiveresearch by Paul Black at the Open University hasshown that ongoing formative assessment that guidesteaching and learning brings about increased learningas well as increased self-esteem for students.

The Concord Consortium’s MW Platform offers anexample of a highly innovative design for ongoingformative assessment. MW Platform allows teachers tocreate their own stand-alone or web-based lessons usingSeeing Math interactives, or other Java-based software.

The highly innovative report feature of the MWPlatform enables students to create a series of annotatedscreenshots with explanations of their work. The MWreport includes annotated graphs and student commen-tary that can be sent to the teacher or other partici-pants. With MW, teachers can set up lessons using anyof the above applets and customize activities and ques-tions to suit their students’ local needs (for example, tochange the context of the question or to meet specificlocal standards). The report feature enables students tocapture dynamic “footprints” of their work and sharethem with other students and with a teacher for thepurpose of formative assessment.

An Integrated VisionThis integration of new content, new tools, new profes-sional development, and new methods of assessment isnot just a dream realizable ten years down the road. TheConcord Consortium has assembled and tested in class-room settings all of these components. Using softwaredeveloped by the Concord Consortium and its collabo-rators, including an elegant case study professionaldevelopment design and the formative assessmentcapacity of the MW Platform, high-quality mathematicswill be accessible to all students.

Robert Tinker ([email protected]) is President of theConcord Consortium. George Collison ([email protected]) is an Associate of the Concord Consortium and SeniorCurriculum Author for the Seeing Math project.Seeing Math algebra interactives

http://seeingmath.concord.org/sms_interactives.html

LINKS 21st Century Math

Linear Piecewise Grapher saved state example

The Seeing Math interactive “Piecewise Linear Grapher” in the MW Platform.This puts all instructions, challenges, help, and assessments in the same environ-ment that can be easily edited and delivered to students.

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SeeingMathby The Concord Consortium

Piecewise Linear Grapher


If a picture is worth a thousandwords, then for science learningan interactive model may well beworth a thousand pictures. Why

are models such powerful learningtools? And what can we learn byobserving how students experimentwith them?

In October 2001, in partnershipwith Harvard University, NorthwesternUniversity, and Massachusetts publicschools in Lowell and Fitchburg, theConcord Consortium launchedModeling Across the Curriculum (MAC), agroundbreaking, five-year researchproject. Since then we have developeddozens of model-based activities thatcover such diverse topics as Newtonianmechanics, gas laws, atomic structure,and genetics. We have also built anextensive suite of tools for collecting

and analyzing the data generated asstudents use the models. Over the lastthree years approximately 400 schoolsin over 20 countries have registeredwith us and downloaded the MAC soft-ware. Each time students ran an activ-ity, if they were online, we collecteddata—over 1.5 GB of log files. In all,over 18,000 students have contributedto our research in this way. As we wrapup the project this fall, our data analy-sis algorithms are converting those logsinto useful information for researchersand teachers.

So what are we learning from all thatdata? First of all, students learned the sci-ence content from models. For instance,98% of the physical science classes thatused our Dynamica activities (whichmodel Newtonian mechanics) showedsignificant learning gains on a post-test

to pre-test comparison. More important,the students who ran more models alsolearned more—in our genetics classes,the number of activities attempted bythe students in a class accounted for17% of the learning gains. That’s not toosurprising, but it’s gratifying nonethe-less—a “proof of principle,” if you will.But the really interesting part comeswhen you consider how the studentsused the models.

Actions Mirror Understanding: Performance Predicts LearningLet’s distinguish “process” data from“outcome” data. Outcome datadescribes what a student learns. It oftenappears in the form of answers to ques-tions or solutions to numerical prob-lems—whether presented as a post-testor embedded within an activity. Processdata, on the other hand, describes howa student goes about solving a problem.For example, one of our genetics activi-ties requires students to figure out thegenotype of two dragons given that allof their offspring have two legs. Stu-dents could perform “thought experi-ments” on the computer, altering thegenes of either parent, and then breed-ing them and observing the result.They could also use a special kind of“magnifying glass” to view the chromo-somes of any organism. We loggedwhat steps the students took, and whattools they used.

Looking over the process data fromthe two-legged dragon challenge, wefound a wide variation in the way stu-dents went about the task. Some stu-dents bred the same two parents overand over, apparently hoping for successjust by chance; others perseverated onan incorrect model (e.g., if both parentshave two legs, so will their offspring),seemingly unable to think outside the

Interactive Models: Helping Students Learn and HelpingTeachers Understand Student LearningBY PAUL HORWITZ, JANICE GOBERT, AND BARBARA BUCKLEY

Teacher and Student Use

Activity: Motion Graphs

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box. Still others approached the tasksystematically, examining the chromo-somes of parents and offspring, varyingonly one parent at a time, and reason-ing their way to the correct answer.

Once we had identified these differ-ent behaviors, we developed algo-rithms that enabled us to classify everystudent’s investigations along aspectrum from “systematic” to “hap-hazard.” We found a statistically signif-icant correlation between a student’sprocess score on this task and her sub-sequent learning gains as determinedfrom the post-test. Moreover, this cor-relation persisted whether or not thestudent actually succeeded—in otherwords, the process variables predictedlearning gains1 even when the studentfailed to accomplish the task. Evenmore surprising—and gratifying—wasthe extent of the “transfer effect” fromthis task. The post-test included someitems that were directly related to thecontent underlying the two-leggeddragon task (i.e., monohybrid inheri-tance, or the inheritance of a singlecharacteristic), together with manyother items that were not. One mightexpect a student’s process score to cor-relate more strongly with the proximalitems than with the test as a whole. Infact, the reverse was true: performanceon the task was more predictive of theoverall post-test score than of the scoreon the directly relevant items.

The task described above is notunique; many of our activities containsimilar “hot spots”—tasks that areopen-ended and complex enough toengage students in authentic inquirywhile giving us a glimpse into theircognitive processes. We have identifiedsuch “teachable moments” in each ofthe science areas covered by the proj-ect. And each of the hot spots exam-ined so far shows the same intriguingcorrelation with learning gains, asmeasured by conventional assess-ments. The next step is to look for“learning progressions.” Do studentsimprove their model-based reasoningskills as they progress from one activity

to the next? And do such skills transferbetween scientific domains? Does thetenth grader who learns to reason withmodels in genetics apply that skillwhen he encounters the model-basedgas laws unit in junior year chemistry?We don’t know yet, but we haveenough data to find out.

Any Number Can PlayThe IERI program that funded this workimposed two nearly mutually contra-dictory constraints. The research was tobe methodologically rigorous and care-fully controlled, yet it had to be poten-tially scalable to very large numbers ofstudents and schools. We addressedthese contrasting requirements by con-straining our intervention to be entirelycomputer-based, thus minimizing localvariability and the need for extensiveprofessional development. We thenmade it freely available on our websiteto any school. When schools down-loaded the software, they were giventhe option to register with us and allowus to collect data from them. In return,we reported to each of these “contribut-ing” schools regarding the performanceof their students2.

Over the period of the project,nearly 400 schools, located in over 20countries, took advantage of this offer.However, many of these appear to haveused the software offline (thus generat-ing no data), and many others did notadminister the pre- and post-tests.Nevertheless, 41 of the contributingschools did comply with these require-ments, and we have subjected theirdata to the same analysis that we usedfor the 10 “member” schools that wereofficially part of the project. We weresurprised to discover, in fact, that thecontributing schools actually per-formed better than the memberschools. For example, the 18 contribut-ing classes that used the geneticsmodel averaged a learning gain of 6.8points, versus 5.8 for the memberschools. This is a remarkable achieve-ment, considering that the contribut-

ing schools received no support ofany kind from the project3. Evenallowing for the fact that the con-tributing schools were self-selected,their stunning success demon-strates the scalability of the tech-nology and pedagogy.

ImplicationsIn Massachusetts students are not per-mitted to graduate from high schoolunless they achieve a minimum scoreon a largely multiple-choice test calledthe Massachusetts ComprehensiveAssessment System, or MCAS. Manyother states have similar requirements.Reliance on such traditional assessmenttools can have two adverse effects: (1)the tests are artificial and at best serve asimperfect markers for real-world skillsand abilities, and (2) an over-emphasison improving test scores is causingmany schools to spend so much timegetting students ready for the MCASthat they have precious little left forteaching.

The experimentation with modelsdemanded of students in the MACproject is a task much more analogousto real-world scientific methods thanthe act of answering a collection ofunrelated multiple-choice questions.The inferences we make by observinghow students perform model-basedtasks turns them into insightful forma-tive assessments that can guide teach-ing without disrupting it.

Some day, perhaps, the MCAS will beredesigned and the question-and-answeritems of today will be recast as tasksinvolving manipulable models. Whenthat happens “teaching to the test” willbe the right and proper thing to do.

Paul Horwitz ([email protected]) is thePrincipal Investigator of the MAC project.Janice Gobert ([email protected]) is aCo-Principal Investigator and ResearchDirector of the MAC project. BarbaraBuckley ([email protected]) is aResearch Scientist on the MAC project.

Modeling Across the Curriculumhttp://mac.concord.org

LINKS Modeling Technologies

NotesÊ The process variable score on this task

accounted for approximately 10% of thevariance in learning gains.

Ë We encrypted all log files before transfer-ring them from the schools to our server,and we maintained strict anonymity byassigning each student a unique ID numberand stripping names from our database.

Ì We conducted professional developmentworkshops and provided monetary compen-sation to teachers at the member schools.


Science is a social construction of knowl-edge and practices based on observation,analysis, modeling, experimentation, andtheorizing about the physical worldaround us. The National Science EducationStandards states, “From the earliest grades,students should experience science in aform that engages them in the active con-struction of ideas and explanations thatenhance their opportunities to developthe abilities of doing science.” Too often,however, science is treated only cursorily,if at all, in elementary grades and in a pas-sive format: reading from a textbook. Buteven very young students can do muchmore, particularly when the science class-room includes probes and models. Andthat’s just what the Technology EnhancedElementary and Middle School Science (TEEMSS2) projecthas been doing: designing activities with probes and mod-els for students in grades 3-8.

In the Classroom: Temperature and HeatAsked to study an event in which temperature changes andto think about how the changes relate to the flow of energy,fifth-grade students took temperature sensors and interfaceshome from school for the weekend. Some compared thetemperature of their dog’s mouth to their sibling’s mouth.

Others compared the temperature of the sidewalk to thegrass beside it. One young man tested the temperatureunder the covers of his bed throughout the night. His ques-tion was, “Why is it so much warmer when I wake up thanwhen I first crawl into bed?”

He started the temperature sensor and tucked it under hisblankets as he went to bed. Throughout the night, the inter-face recorded the temperature; when he woke, he had a graph-ical and tabular representation of the data. The graph showedan increase of temperature from the time he laid his head onthe pillow to the time he woke. Questions surfaced as hereported to the class. Was the change in temperature due tothe blankets? What was the temperature in the bedroom? Didit get colder as the night went on? Did he really become hot-ter throughout the night or did he just feel warmer?

The class discussion of his and other experiments pro-duced a complex dialogue. The teacher guided the studentsto frame their new questions in forms that could beanswered by further experiments. After collecting more datafrom numerous experiments, class discussions grew richerand more nuanced as brittle models of temperature andenergy gave way to more robust models.

For instance, a commonly identified misconceptionregarding heat and temperature is based on the fact that ametal object at room temperature feels cooler than awooden object, which in turn feels cooler than a foamobject. The cognitive dissonance of a student’s experience oftemperature differences and the “scientific” explanationthat the objects are the same (room) temperature can lead toa student developing separate categories of “science” and“real” knowledge. A NetLogo model demonstrates this.

Using Sensors and Models toAnswer Discovery QuestionsBY CAROLYN STAUDT AND STEPHEN BANNASCH

Figure 1: Two runs of a NetLogomodel with a heater on the left in contact with a block that hasdifferent thermal conductivities.Color indicates temperature.

Figure 2: Results of students touching blocks made from three different materials (skin temper-ature vs. time).

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The block on the left (see Figure 1) isa simple model of a finger, which isboth warm and generating heat.Students can change the thermal con-ductivities of the blocks with whichthe finger is in contact and indirectlyinvestigate the flow of heat by lookingat the temperature gradients thatdevelop over time.

After viewing the model, studentsused a fast-response temperature probeto investigate the temperature of theirown fingers, and discovered a widerange of finger temperatures amongmembers in their class. Finally, studentsheld the very small temperature probesbetween their fingers and three differ-ent blocks: aluminum, wood, and foam.

By collecting temperature data witha probe, students were able to easily seewhy the metal block felt colder (seeFigure 2). The temperature data vali-dated their experience. Indeed, theirfingers did get colder touching themetal block. The aluminum block con-ducted heat away from their fingersmuch faster than the wood or foamblocks. In our NetLogo model the fin-ger is modeled as a perfect heater with infinite thermal con-ductivity and mass. An improvement would be to model thefinger with a finite thermal mass, specific conductivity, anda limited amount of heat input. This would allow the modelto simulate the cooling and warming at the skin surface.However, using even our simple NetLogo model and theexperiments with sensors, students learn that their bodiesare heat engines and that heat flows faster through somematerials than others.

Creating Your Own Probeware ActivitiesIn addition to TEEMSS2 curriculum activities we createdfor three grade levels (3-4, 5-6, and 7-8) in five contentstrands, we adapted the technology so anybody can makeand publish their own probeware activities (see “Do ItYourself” sidebar). The software is compatible with MacOS X, Windows, and Linux computers, and with sensorsand interfaces from five different companies. With a sim-ple user interface—it’s as easy as filling out a form—the

power of probeware is at your fin-gertips. You and your studentscan answer your own discoveryquestions.

Carolyn Staudt is Director of theTEEMSS2 and ITSI projects. StephenBannasch is Director of Technology.


Concepts Benefits

Graphing Real-time graphs connect a student’s physical sense of the worldwith an immediate abstract representation. The meaning of differ-ent curves and rates of change become more concrete as patternsare associated with physical events and processes.

Understanding Sensors can measure and display trends that inform deeperphenomena and understanding of physical phenomena. Experiments with sensors issues of scale can be repeated quickly.

Formulas and data By manipulating scales and axes, students implicitly begin totransformation understand how a set of data can be transformed. By applying

functional transformations to the data in graphical and tabularforms, higher-level connections are made between mathematicalthinking and science.

Calibration Calibration is a specific subset of data transformation, which isoften very hard for students to understand. When students maketheir own probes, calibration is an inherent part of the activity.

Experimentation When students are actively engaged with models and sensors,experimentation is a natural byproduct. Formulating a testablehypothesis is one of the hardest science process skills to learn.Repeated authentic inquiry-based experimentation is the only waythese skills are developed.

Value of Probeware in the Classroom

Register for free at the TEEMSS2 Do It Yourself (DIY) site to create your own activity.Start by viewing the Activity Listing for a list of already published activities, like

“Mixing Different Temperature Water.” Show will preview an activity in a webbrowser, while Run will create a custom Java webstart application, which willdownload and run the activity from your computer.

You can try the activity without a sensor by selecting the Simulated Data item inthe Probeware Interface link on the left, and then clicking Run in the activity. Orselect from one of five supported sensor companies.

When you first run an activity, select New. After using the activity and enteringtext or collecting data, choose Save in the file menu to save your work. To print theactivity, first export it as HTML, then open and print it from your browser. You canalso email or share any saved portfolio documents.

To create a new activity, choose the link on the Activity Listing page. A series oftext fields allows you to add an Introduction/Discovery Question, materials, proce-dure, safety notes, and so on. Select a probe type from the pull-down menu. ClickCreate to save your new activity. Be sure to make it public so others can see andrun it.

National Science EducationStandardshttp://www.nap.edu/readingroom/books/nses/6c.html#csak4

TEEMSS2 curriculumhttp://teemss2.concord.org/curriculum/

TEEMSS2 Do It Yourself (DIY) http://teemss2diy.concord.org/

LINKS Sensors and Models

Do It Yourself

TheConcord

Consortium25 Love Lane

Concord, MA 01742

NONPROFIT ORG

US POSTAGE

PAID

PERMIT NO 54601

BOSTON, MA

NEWS at Concord ConsortiumPost-Textbook UDL Materials

The National Science Foundation hasfunded our plans to develop technology-rich science curriculum modules for grades3-6, which acknowledges that stu-dents learn in different ways. Thework at CAST, the Center forApplied Special Technology,has defined a flexibleapproach to teaching calledUniversal Design forLearning (UDL) that hashad considerable success inteaching the language arts.This new project extends theseideas to science. The goal of thisproject is to use UDL principles tocreate practical science materials for stu-dents and teachers in inclusive classrooms.

The project will create seven inquirymodules around the theme of energy. Theywill ask questions such as “Why are thereclouds?” and “What do plants eat?” Probeswill support lab investigations and compu-tational models will allow students toexplore virtual environments. We will alsodevelop graphing and modeling softwarethat express data and relationships in textand language. Twenty-five classrooms inActon, MA, Anchorage, AK, Maryville, MO,and Fresno, CA, will test the effectivenessof this approach through formative andsummative evaluation. We hope thesemodules will inspire additional content andfurther development.

The Science of Atoms andMolecules

Because the theme of atoms and mole-cules runs through physics, chemistry, andbiology, it provides a single framework that

unifies these subjects. Our new “Science ofAtoms and Molecules: Enabling the NewSecondary Science Curriculum” project,funded by NSF, will develop four strands of

atomic-scale materials thatunify the curriculum

sequence of physics,chemistry, and biol-ogy. The project willprovide materialsand professionaldevelopmentresources that

allow high schoolsto implement a suc-

cessful sequence ofphysics, chemistry, and

biology as a unified and consis-tent progression. Curriculum materials willprovide a progressive understanding of theimportance of atomic-scale phenomenafrom fundamental atoms to complex biol-ogy. This approach is designed to guaran-tee better pedagogy, deeper learning, andlonger retention.

Probes and Models Across theCurriculum

With our new NSF-funded “Probes andModels Across the Curriculum: InformationTechnology in Science Instruction” project,the Concord Consortium will prepare mid-dle and high school students for careers ininformation technologies by engaging themin designing inquiry-based science activitiesthat use computational models and real-time data acquisition and analysis.

Teachers from Boston, MA, DesertSands, CA, and Olathe, KS, will meet in thesummers of 2007 and 2008, plus onlinethroughout the academic year to learn

@ConcordEditor: Robert Tinker

Managing Editor: Cynthia McIntyre

Design: Susan W. Gilday

www.concord.org

The Concord Consortium25 Love Lane

Concord, MA 01742

978-405-3200 | fax: 978-405-2076@Concord is published two times a year by TheConcord Consortium, a nonprofit educationalresearch and development organization dedicated toeducational innovation through creative technologies.

Copyright © 2006 by The Concord Consortium, Inc.All rights reserved. Noncommercial reproduction isencouraged, provided permission is obtained andcredit is given. For permission to reproduce any partof this publication, contact [email protected] on p. 1 by Laurie Swope.

Eighty-seven percent of the contents of this publica-tion were developed under several National ScienceFoundation grants (REC-0115699 for $7,024,406over five years; ESI-0352522 for $2,706,805 overthree years; DUE-0402553 for $947,386 over threeyears; DUE-0603389 for $891,937 over three years;ESI-0624718 for $1,256,303 over three years; ESI-0628181 for $1,139,836 over three years; and ESI-0628242 for $2,163,796 over three years), for which1% of funding is provided by non-governmentalsources. The remaining 13% of the contents weredeveloped under a five-year $14,882,925 project ofthe U.S. Department of Education (R286A000006),of which 23% of its funding is provided by non-governmental sources. These contents do not neces-sarily represent the policies of the funding agencies,and you should not assume endorsement by theFederal Government.

basic electronics, programming, anddesign skills. They will learn how to teachstudents to install, configure, and use awide range of sensors for measuringexperiments with computers, and to use,modify, and create computational models.The skills learned will enhance each par-ticipant’s teaching, while giving students asolid foundation for IT-based careers inprogramming, computer hardware, andsoftware engineering.

concord g...glimpse into student thinking and an opportunity for mean-ingful assessment. using...

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