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T£C+lNOLOGY IN MAT+I£MATICS
AND SCI£NC£ INSTRUCTION
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The terms and circum?t
man existence can be expected to change
radically during the next human life span. Science, mathematics, and technology
will be at the center of that change-causing it, shaping it, responding to it.
Therefore, they will be essential to the education of today's children for
tomorrow's world.
......._
...._
8encilmorXs for Scientific l.iteracy (American Association for the Advancement of Science, 1993)
GY INT£GRATION £XAMPL£
HOT AND COlD D).T).
Based on: Canig\ia,J. (l997),The heat is on! Using the calculator-based laboratory to integrate math. science. and technology_ Leoming and Leading with
Technology. 25(1), 22-27.
Grade Levels: Middle to high school· Content Areaffopic: Physics, graphing, and measurement· Length ofTime:
Three weeks
etermine relative advantage
Ms. Belt and Mr. Alter, the physics and mathematics teachers.
respectively, at Pinnacle High School, were excited about the
new calculator-based laboratories (CBLs) that had just
arrived. As they learned about how CBLs can "grab" temperature data and display it in graphs and spreadsheets, they
realized that activities with CBLs provide a natural link between science and mathematics studies. Having students use
CBLs would be an ideal way to give them hands-on insights
into the relationship between these two important skill areas.They also agreed that CBl activities would address an ongoing challenge of making abstract science and math
concepts more concrete and visual. Having students collect
and analyze their own data, they felt, would give them authentic, hands-on application of these concepts.They decided
that a unit on heating and cooling experiments would be a
good first activity. Students could take temperature measurements with the CBL probes, then use mathematical procedures to graph and analyze the resulting data.
out the steps in an assigned experiment and write summaries of their findings by achieving a rubric score of at
least 85% on their work. Assessment: A checklist with
points assigned to each step done correctly; a rubric to
assess quality of written summaries.
Outcome 3: Interpreting data from experiments.
Objective: All students will demonstrate the ability to
review and interpret data derived from experiments by
correctly answering at least 8 of 10 questions requiring
data interpretation. Assessment: A mid-unit test with
each student reviewing example charts and answering
questions on how to interpret the data.
Outcome 4: Completing and reporting on scientific
experiments, without teacher assistance. Objective:
All students demonstrate they can replicate and interpret data from a CBl experiment by working in pairs
to complete the reqUired tasks without assistance.
Assessment: A checklist with points assigned to each
step done correctly; a rubric to assess quality of written summaries.
I
eo e on 0 Jecdves anel assessments
The teachers decided they would assess student progress in
each of four areas: CBl performance tasks, carrying out scientific experiments, investigating physics principles, and using
mathematics to analyze and display data.They decided on the
following outcomes and objectives they hoped students
would achieve, and outlined assessment methods to measure
students' performance on them:
Outcome I: CBl procedures. Objective: Each stu·
dent will score at least 85% on a performance test designed to measure competence with CBl procedures.
Assessment: A checklist with points assigned for successful completion of each task.
Outcome 2: Completing and reporting on scientific
experiments, with teacher assistance. Objective: All
students demonstrate they can work in groups to carry
n
t
ration strate ies
The teachers decided to team-teach the unit to draw together even more the links between the two content areas.
Working together, they designed the following sequence of
activities:
Week I: Introduce unit activities and CBLs and provide
hands-on practice. Introduce the unit with a Consumer
Reports-type scenario. Makers of camp stoves each claim
their product heats water faster than the competitors'
stoves. The various stoves used three different fuels:
white gas, kerosene, and butane.The students have to establish which manufacturer is correct and write up their
findings for the CR magazine. Demonstrate how students
can use the CBl to grab data and how it displays temperatures in graph form. Hold a discussion about inter-
I
preting CBL data. Students carry out the introductory
experiment in three large groups. Using camp stoves
borrowed from a local sporting goods store, students
use the CBLs to heat water to boiling. They go through
the step-by-step procedures for hands-on experiments,
write up their findings, and present them to the whole
class. Hold a whole-class discussion to interpret results
and write up a summary for CR.
Week 2: Carry out heating/cooling experiments and
present findings. As Ms. Belt helps small groups prepare
materials for the next set of experiments, Mr. Alter has
students do individual performance checks on CBL procedures and provides additional instruction, as needed.
Each small group is assigned a heating/cooling experiment, for example, which cup holds heat longest: styrofoam, paper, or ceramic? Which color container holds
heat longest: white, black, or metallic? Each group completes its assigned experiment, answers: the question,
writes up findings, and presents them to the class by inserting spreadsheet and graphed data into a PowerPoint
presentation.
Week 3; Do mathematical analyses and presentations;
take final tests. Each group works with the data to explore linear, quadratic, and exponential functions of
graphed data. Finally, students work in pairs to do their
replication experiment and answer questions on the
meaning of the graphs.
repare
-e Instructional environment
The teachers get a local sporting goods store to loan them
three different camp stoves for the first experiment/demonstration. They tested each of the CBLs and calibrated them,
as needed. They designed and copied each of the performance measures and made copies of lab sheets they needed
during the experiments.
Phase 5:;1
uate and revise
At the end of the unit, the teachers reviewed the students'
products and discussed how the unit had worked. Mr. Alter
and Ms. Belt were happy with the overall performance of
the class. They were impressed at how engaged students
had become in using the CBLs to gather and analyze data.
Perhaps most encouraging, two female students seemed
especially excited by the work they had done on the sci-
entific experiments; they asked Ms. Belt to give them information on careers in science and mathematics. The teachers concluded that this kind of multidisciplinary unit
worked very well.They decided to plan other CBL experiments to be carried out on a long-term basis and at locations outside the classroom.
OSJ£CTlves
After reading this chapter and completing the learning activities for it, you should be able to:
I. Identify some of the current issues in mathematics and
science instruction that may impact the selection and
use of technology.
2. Describe key strategies for integrating technology into
mathematics and science curricula.
3. Identify example software and web resources required
to carry out each integration strategy.
4. Create instructional activities for mathematics and
science instruction that model successful integration
strategies.
Key TeRMs
calculator-based laboratories (CBLs)
interactive or dynamic geometry software
scientific inquiry
virtual manipulatives
For more information on Key Terms, go to the Key Terms module for this chapter of the Companion Website at
http://www.prenhall.comlroblyer.
INTRODUCTION
Science and technology have a unique relationship. Technology supportS science and science makes new technology possible. Both will playa critical role in our students'
future. Thus, it is not surprising that efforts to reform
teaching and learning in these £wo areas have been at the
cenrer of me national standards movement. U.S. elementary students perform well compared to students in other
nations, hut that performance: diminishes as our students
progress through school (Bearon ct al., 1997-1998). Technology provides many opponuniries to build students'
conceptual knowledge of mathematics and science, as well
as ro connect their learning to problems found in OUt
world. This chapter highlights current issues and problems in mathematics and science education and describes
slf3.tcgies for integrating technology imo teaching and
learning processes for these areas.
Take 'advantage of these 10 powerful strategies for using technology
and sqence.
to
enhance the teadling of mathematics
Mathematics Strategies
I. Graphing ca.lculatol"S give students hands-on practice in solving mathematical problems These handy tools help students do mathematical calculations and visualize algebr.lic concepts in a
ma.nne~ that enhances understanding and problem-solving skills.
2. Interactive geometry software such as the Gl!Ometer"s Sketchpad makes abstract concepts
easier to nderstand - These software tools make geometric concepts more concrete. visual, and
inre cdVe so students with limited mathematical background can understand them more readily and
students with more advanced knowledge can explore them more deeply.
,I
3. Spreadsheets help students carry out "what if" problem solving manual calculations involved in solVing higher order problems.
I
Spreadsheets do the
4. Students use the Internet to obtain useful math-related information - Internet sites are rich
sources of data sets and mathematical infonnation to answer questions, and they help students see realworld applications of mathematical principles.
S. Reasoning and skill-building software increases students' fluency with prerequisite subskills
while developing logic and comprehension - Instructional games. puules. and drills offer private,
personal feedback in a motivating environment to help students build fluency.
i
": i
Science Strategies
I. The GLOBE program offers opportunities for doing authentic science activities - This webbased resource is a rich collectioo of hands-on activities in which students can apply science concepts.
2. NASA Internet sites keep students in touch with scientific events - Through web-based
activities, students participate in events. such as the landing of the Mars Rover, that they would otherwise
be unable to observe.
3. Calculator-based labs give students ha.nds-on practice with scientific data analysis tools let students collect and analyze data to support science experiments.
These
4. GPS and GIS tools let students make observations and anatyze data to support scientific
investigations - Students use these tools to study the weather. land COYer, soil. and hydrology.
5. Digital imaging tools and simulations slow down or speed up processes for easier
observation - These activities allows students to study phenomena they would otherwise be unable
to see or could not see well with the naked eye.
326
www.prenhall.comJroblyer
IssUES AND PROllL£MS IN
• C<>mmunication
MATttEMAncs INSTRUCnON
• Connections
Accountability for Standards
in Mathematics
I
The Principles and Standards fOr School Mathematics, released in 2000 by the National Council of Teachers of
Mathematics (NCfM), serves as a primary resource and
guide for all who make decisions that affect the mathematics education of students in pre~kindcrgarten through
grade 12. Through this document, mathematics educators
describe a vision of mathematics teaching and learning.
Achieving this vision requires "solid mathematics curriculum, competent and knowledgeable teachers who can in~
regrate instruction with assessment, education policies
that enhance and support learning, classrooms with ready
access to technology, and a commitment to both equity
and excellence" (NCfM, 2000, p. 3). The Principles and
Standdrds document calls for a common foundation of
mathematics to be learned by all students. Six principles
address crucial issues fundamental to all school mathematics programs:
• Equity
• Curriculum
• Teaching
• Learning
• Assessment
• Technology.
In the technology principle, NCTM stresses that
"technology is essential in teaching and learning mathematics" and "it influences the mathematics that is taught
and enhances students' learning" (NCTM, 2000, p. 24).
"In the mathematics classroom envisioned in Pn'ncipks
and Standards, every studem has access to technology to
facilitate his or her mathematics learning under the guidance of a skillful teacher" (NCfM, 2000, p. 25).
There arc 10 mathematics standards for pre~
kindergarten through grade 12:
Content Standards
• Number and Operarions
• Algebra
• Geometry
• Measurement
• Data Analysis and Probability,
Process Standards
• Problem Solving
• Reasoning and Proof
• Representations.
Through these principles and standards, NCTM provides
guidance on how to prepare studentS for a society that requires mathematical knowledge for filling crucial economic, political, and scientific roles in a highly
technological workplace.
Challenges in Implementing the Principles
and Standards for School Mathematics
Helping teachers change their teaching styles to meet the
vision described in the NCTM standards is not an easy
task. The standards seck a fundamental shift: in the way
most teachers work (Burrill, 1997), Technology can serve
as a catalyst to move teachers toward an instructional style
that is more student cemered, active, and relevant to the
world we now live in. Technology also provides learners
with the opportUnity to visualize and make more concrete
the generally abstract world of mathematics.
Research points to three implications for the selection
and use of technology related to mathematics education.
First, teachers should consider an appropriate combination of off- and on-computer activities, Second, they
should consider technology as a mathematical tool rather
than as a pedagogical tool. Third, they should view technology as a tool for developing student thinking. One way
to accomplish these goals is to use computer software and
applications that can be extended for long periods of time
across topics to engage students in meaningful problems
and projects, rather than provide a variety of applications
with no internal coherence (Clements, 1998),
In "Great Expectations: Leveraging America's Invest~
ment in Educational Technology," researchers at the Benton Foundation concluded that after more than tWO
decades of research on the benefits of technology, mounting evidence exists to document the posidve influence of
technology on student achievement in mathemadcs
(Benton Foundation Communications Policy Program,
2002). The researchers concluded that mathematics software, particularly programs that promote experimentation and problem solving, enables students to embrace
key mathematical concepts [hat are otherwise difficult to
grasp. This research-based evidence has also been described more metaphorically by mathemarics reacher Dan
Kennedy (1995) in his article "Climbing the Tree of
Mathematics~ in which he articulates how technology
provides his students with a means of achieving mathe~
matical understanding previously unknown, Both
through systematic research and common wisdom de~
rived by accomplished teachers, ample evidence exists to
Chapter I I - Technology in Mathematics and Science Instruction
327
ror Mameroatia
Students with disabilities and students who are at risk often fail [0 achieve high Ic:vds of
competency in m;lth due: to problems ",irh completing accur.lu:: calculations. This may involve:
procedural knowledge about wb;u Steps to complete in what seqUtna. as wdl as lack of fluency in
manipulating numbers during'" aleu1arion. An obvious (a1oot controVersial) soluDon is to t('2ch
them how to me: a ca:JcuJatOr. .A Y:lSt numbc:r ofonline calculato~ are available;
• Calculator: hnp:flwww.caleu1ator.coml
• Online Conveners: hup:llonlincconven:ers.comf
• Martindale's CalculatOrs On-line Ccnrer.-htrp;IIWW'\'o'.manindaiecenreuoml
Calculators.html.
A different tactic is to combine an online caladation lool with iMttUcdotW support. WebMath
(http://www.webmath.eom) provides how-to help ;Jtacitculadl1g5Uppon~rstudentS 5~
with alIlevcls of math by providing step-by-step guidance Oil how to oomptete a spl..-dfic problem.
For Science
Students with disabilities often struggle in science due 10 an in:.lbiliry (0 manipulate me science lab
c:quipmenr or bc:ctuse they are unable ro read me to:tbook. ~r tc:chnology adV,lnces can address
both cono::ms.
The Intel Pbr QX3 Computer Miaosco~ (hup:11WWY.·.imelpl:.ly.com) is a powerful Alicroscope
that anaches to the computer so that studo1ts can view the: images on
microsoope slide vIa the:compurc:r or:.l projection sysrem. For students unible: to:.lCCCSS the Iensc:s of a miaosoope.. this tool
provides an opportunity for stud('nts;rnd teachers to point to a specificpanoEihe image to ensure:
thaI all students all:: observing the same phenomena.
BrainPop (lmp:/Iwww.bra.inpop.com) provides instrucrion in a multimedia. format that is very
helpful for students who are ul12ble to n-.ad me tc=nbook.....' irudents sdea: science from a menu of
curriculum areas and see <l vast array ofscience instructional topics. After xkcrin~ a particular
topic, for example. dcetricity, BrainPop offers stre:anUng video, lab activities. an<J.fesouroes
engage stucleon in the topic and provide fundamental infonnation and skills.
me
support srrategies for integrating technology into the
teaching and learning of mathematics to increase: student
undemanding and achievement.
skill building and practice. Figure 11.1 summarizes mese
strategies and gives examples ofsome of the technology resources that make them possible.
TEC~OLOGY INTEGR.l'.TION STR.l'.TEGIES
Using Virtual Manipulatives
fOR M.l'.TtlEH.l'.TICS INSTRUCTION
Technology resources have made: possible a variety of
teaching and learning strategies to help address the
Prinripks and Standanh for School Ml1thmuuics. These in~
dude using virtual manipulatives, fostering mathematical
problem solving, allowing represe:nt:ttion of mathematical
principle:s, implementing data-driven curriculum, suppaning math-related communications, and motivating
328
Computet software can play an imporram role in the way
students perceive mathematics. At the elementary level,
teachers can display models for numbers and operations
on the: computer screen so that stude:nrs can derive and
construct their own meaning for mathematical concepts.
At higher levels, they can use software: models to make ab·
Stract concepts more: concrete. Both of these strategies are
called virtual manipulatives be:cause students usc them
www.prenhall.comfroblyer
Figure I 1.1
Summary of Technology Integration Strategies for Mathematics
• Supports hands-on ac:tivlties for
learning mathematics.
• Offers flexible environments for
exploring compleX concepts..
.. Pro'o'ides a concrete representation
of abstract concepts..
... National UbIwi ofYlt'tUaI HanipuI..mes for Interactive ~tics
at Utah State University
httpllmatii.usu.edulnlvrnfmdex.hi:ml
"- .. National Ubrary oIVartuaI Haniputadves at the Shodor I=oundatfon
_""""_........... ltathWlthjM·
...... lIwww.le<oo.jp(~tml
• Hathemapcs;Sdence,and
l'ecbnology EdU«tioa' at U1UC
m.;11www......._.edUt. ....do&~
Fostering mathematical
problem solving
R~produced with p~rmj .. ion.
Texu
Helps students gather data to use
in problem solving.
Provides rich, motivating problemsolving environments.
Gives students opportunities to
apply mathematical knowledge and
skills in meaningful contexts.
CBls
Software (e.g., Riverdeep's Zoombinis,
Thinkin' Things)
Programming languages
Also see Technology Integration
Idea II, I: What If? Problem Solving with
Spreadsheets
C 2006
I"'trum~"t>.
http://education.ti.com/us/productltech/
datacollection/featureslfeatures,html
Allowing representation of
mathematical principles
• Makes abstract mathematical
COncepts more visual and eaSter
to """""""'.
• Gives· students environments in
Which to make discoveries and
.c:ooJeentres relateCl t6 ~
w
Gr.aphing cakuJatots
.. Software (e.g.• Geometers SktWtpad.
_J
. s,x..""-
Also seeTechnology Integration
Jdea 11.1: Studying Graphs and fun<;dons
concepts and objectS..
~ Key
0nicuIumJ>?Ss.
lIS06Sth~ ~ CA 'H6OB;
1-8OQ.'1'9~TH.www~
http://_.~ss.cofrif
=10<1"""_'_'"
Pro(U<aleidoManlahtml
Implementing data..cJriven
curriculum
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F.!i--;::-I
'1.11.·
·- .....·H -1 ... !
~t~~ ~~~~ il;~.;.J
"'--=-_.
-!-
-
~.
Fathom. K~y Curriculum ~ ...
1150 65th Street, Em~ryvtll~. CA 9#08:
1-800_995_MATH. """"",.keyp.-~'Hom.
Provides easy access to many data
sets.
Provides real statistics to support
investigations that are timely and
relevant.
Supports development of student
knowledge and skill related to data
analysis.
Allows for exploration and presentation of data in a graphical form.
Software (e.g., Fathom, Tabletop, Tabletop Jr.)
U.S. Census
http://www.census.gov/
Spreadsheets
Statistical software (e.g., StatCrunch,
http://www.statcrunch.coml)
Also see Technology Integration
Idea 11.3: Measuring Up
http://www.keypress.com/catalogl
productsfsoftwareiProd_Fathom.html
(continued)
329
Figure I 1.1
(continued)
Sup~ngmath~ated
communicatfons
....
_._._-- ~~-­
~-
:..
_.=E::'
Motivating skill building and
practice
•
PLATO
J\
lEARNING·
COUf'te>y of Pt..ATO Learn;ng.
httpJlwww.plato.com
Provides motivating practice in
foundation skills needed for higher
order learning.
Provides gUided instruction within
a structured learning environment.
Delivers instruction when teacher
may not be available.
Figure 11.2 Sample Virtual Manipulatives
.•
jI
ii i I
t
I. ! I
1
i'i 11
i
i
,
-o
~.
~
I ~ I Mll<1i«lllRmlwl
"-'PlOI_lOOO~Al.lll""_
Source: httpJlarcytech.orgljavaJpatterns/patterns.J.shtml.
Reprinted courtesy ofArcytech.
to do simulated activities they used to do with real objects
(Moyer, Bolyard, & Spikdl, 2002). These simulated activities offer more flexibility than actual objects in the way
teachers can use them to illustrate concepts.
Mankus (2000) describes and provides several examples ofhow online interactive manipulatives can be used to
develop understanding. Utah State University maimains a
library of virtual maniplilatives for all grade levels that are
tied to each of the standards' content strands. Figure 11.2
330
is an example of a virtual manipulative. For other examples, see the websites listed in Figure 11.1.
Fostering Mathematical Problem Solving
~
,
Boxer Math
http://www.boxennath.com
PLATO Learning
httpJfw-NW.plato.com
Waterford Eady Science and Math
http://www.pearsondigital.com
NCTM defines problem solving as "... engaging in a task
for which the solution method is nO[ known in advance. In
order to find a solution, students must draw on their knowledge, and through this process, they will often develop new
mathematical understandings. Solving problems is not only
a goal of learning mathematics but also a major means of
doing so" (NCTM, 2000). Regardless of how many mathematical facts, skills, or procedures students learn, the true
value of mathematics is realized only when students can apply theit knowledge to solve problems. 1Cchnology, by its
definition, is a tool for solving problems. To prepare mathematically powerful citizens for the future, learning to solve
problems using mathematics and appropriate technological
tools is essential to education at all levels.
AI; students acquire number sense, they can begin to
make generalizations that lead them to conceptS in algebra.
'lOChnology tools provide students with a variety of means
for exploring the critical concept of functions. Through
graphing calculators and computer algebra systems, students
can graph functions accurately, explore mathematical models of real-life phenomena, and explore symbolic representations and panerns. Calculator-based labs (a.k.a. probeware)
provide a means to link either calculators or computers to
scientific data-gathering instruments stich as thetmometers
www.prenhall.com/roblyer
Figure 1 1.3 Data Gathering and Analysis
Devices: (a) Graphing Calculator, (b) CBl. and
(c) ImagiProbe Sensor Interface System with
PalmOne Handheld Computer
i e with other students
Case module for
h'l'4.~1",ionWebsite (http://
choose the Message
....
I. The Mathematical Sciences Education Board
offers a view on refonning mathematics
•
instruction: "The national call for the refonn in
mathematics eaching and leaming can seem
o~rwhelming. ecause it f'equires a complete
redesign of the content of school mathematics
and the way it is taught. e basis for refonn is
the widespread belief that the United States
must restructure the mathematics curriculum..
Simply producing new texts and retraining
teachers wil~.(Iot be sufficient to address the
major changes being recommended."
How migh1jvarious technolOgies and
technology-based methods be able to shape and
.suppoq a restructured mathematics curriculum~
2. Cavanagh's 004) article "NelB Could Alter
Science li ching" presents contrasting beliefs
about eft: tive science instruction:
Quote #1: "Advocates of discovery learning say
direct instruction can easily regress into lecturesn:le teaching, heavy on rote recitation of scientific
facts and memorization. 'It's cheaper, faster, and not
as effective: contended Wayne Carley, the
executive director of the National Association of
Biology Teachers, in Reston,Va. 'If you want kids to
memorize a bunch of facts, it's a great way to learn
... (however) science is not just a set of facts, but a
process for discovering more facts.'" (p. 12).
Quote #2: "Directors of the Baltimore
Curriculum Project. a nonprofit program that works
with three schools serving both elementary and
middle school students in that city, have been using
direct instruction for the past six years in subjects
from reading and language am to mathematics.
Leaders of the project, which largely serves students
from low-income families and has seen an
improvement in test scores among its participants in
recent years. plan to use direct instruction in
science over the next few years..... (p. 12).
Why do these groups have such different beliefs
about effective science instruction? How might
technology be able to merge these seemingly
disparate methodologies?
(0)
(e)
Sources: (a, b) Reprinted with permission. © 2006 Texas
Instruments; http://education.tLcom.(c) Reprinted with pennission
of Pasco Scientific; http://www.imagiworks.com.
or pH meters, which allows students to gather data and then
analyze it. Probes are also available for Palm-powered handheld devices (http://www.imagiworks.com). A selection of
these data-gathering devices is shown in Figure 11.3.
As Technology Integration Idea 11.1 shows, spreadsheets can be a powerful means of supporting problem~
solving exercises. Computer programming can help develop
problem-solving abilities by allowing students to analyze
and de-compose a problem and use systematic trial and error to find solutions. A modern (and free) language such as
Python (Van Rossum, 2001) ean provide students with a
means of learning to write computer code for the purpose
of solving problems.
Mathematical problem solving does not have to resem~
ble work. To many learners, young and old, it can actually be
a form of recreation. Software resources have been developed
to create problem~solving environments that require the exercise of mathematical ideas in a COntext that resembles a game
or pUTLIe. Riverdeep's Zoombinis Logical Journey for young
learners is made up of numerous puzzles in a colorful and engaging environment that allow students to use logic, data
Chapter II - Technology in Mathematics and Scienee Instruction
331
fOSTERING MATff£M1I.nCAL PROBL£H SOLVING
Title: What If? Problem Solving with Spreadsheets
ContentAreaITopic: Algebra
Grade Levels: 6-9
NETS for Students: Standards 3.5,6
Description: Students tend to solve math word problems by using an intuitive "guess and check"
strategy. Spreadsheets are a narural tool to support this strategy because they allow srudents to find
patterns, guess and check, and set up tables. Spreadsheet-based strategies are illustrated for several
different kinds of algebra word problems, including "How many coins of each kind in a given tota!!" and
"What is the temperature when Celsius and degrees Fahrenheit are equal?"
Source: Feicht, L. (2000). Guess and check.:A viable problem solving strategy. Learning and Leading with Technology;
27(5),50-54.
Figure 11.4 Thinldn'Things and Zoombinis
Problem-Solving Software
I
Source: Courtesy of Rlverdeep Interactive learning limited and its
licensors.AlI rights reserved. http:/{www.riverdeep.com.
analysis, algebra, and graphing concept.~ as if they were play~
ing a game. Similarly, software like the Rivetdeep Thinkin'
Thing} series integrates mathematics and science into an entertaining problem-solving environment. (See Figure 11.4.)
Different titles in the series focus on young (preK-3), elementary (grades 2-5), and middle (grades 3-8) learners.
Allowing Representation
of Mathematical Principles
'I
I
Mathematics is an abstract subject. Our understanding of
mathematictl ideas and concepts is closely ded to how we
represent the abstractions of mathematics. To some, the concept of "five" is literally five objects (apples, pennies, etc.); to
ochers, it is the numeralS; to the anciem Romans it was represented by the numeral V. Technology has gready enriched
the way the abstractions of mathematics can be represemed,
and today students mlL~t learn mathematics using several
332
represemations: symbolic (with numerals, variables, equations, etc.), verbal (with words such as "\Vhat percent increase is needed to reach $32,000?"), graphictl (using twoor three-dimensional graphs), or nwnerictl (using tables of
numbers or spreadsheets). For each of these representations,
technology resources have been developed to allow learners
to explore mathematics within that representation and to
explore the interaction among representations.
Research has shown that the use of graphing calculators can improve students' understanding of functions
and graphs as well as [he interconnections among the
symbolic, graphical, and numerical representations of
problems (Dunham & Dick, 1994). Without technology,
it is difficult, if not impossible, to have studenrs move
from the symbolic realm of f(x) = Y! - 3 to the equivalent graphical rendering shown in Figure 11.5a to the numerical representation in Figure Il.5b that resembles a
spreadsheet.
In addition to calculators, many computer-based programs such as Green Globs (Sunburst), Derive (TI), and
Tllnteractive provide learning environments across three
differem mathematical realms. Interactive or dynamic
geometry software provides students with an environment in which to make discoveries and conjectures related
to geometry concepts and objects. Here abstract ideas can
be played our on a computer screen, making concepts
more real and providing a doorway imo mathematical reasoning and proof. As Renne (2000) illustrates, Internet re~
sources also can help students make connections between
abstract geometry and real objects in the world around
them. (See Technology Integration Idea Il.2.)
Instead of memorizing geometric facts or concepts,
students can explore and arrive at conclusions on their
www.prenhall.comfroblyer
~LLO~ R£PRESerTATIOH Of MATH PRt-4CWLES
Tide: Studying Graphs and Functions
Content AreafTopic: Algebra graphs and functioos
Grade Levels: 7-11
NETS for Students: Standards 3.5.6
Description: In this activity, students use spreadsheets and graphing calculators to graph the pattern in a
scenario that describes a morning run taken by a boy named julio.Aher each student presents a
spreadsh~-generated graph of Julio's run. small groups work together to deckle which graph is the best
representation of the data in the scenario.This leads to a class investigation 00 two topics: the best fit
functioo for the data and the families of curves and the effects of parameters 00 the behavior of the
defined function.They use graphing calculators to do these investigations. discussing questions such as
"Can a linear function, a quadratiC function, a thinklegree poIynominal. or an equation in exponential form
describe the data adequately and accuratelyr The activity can be extended by doing the same investigation
of other scenarios.
Source: Manoucherhri.A., & Pagnucco. L (1999-2000). Julio's run: StIJdyi"l ~ V1d functions. Leoming cmd Leading
with TtchnoIogy. 27(4), -42-45.
Figure I 1.5
Principle f (x)
(a) Graphical Representation and (b) Table or Numerical Representation of Mathematics
= xl -
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own. For instance, using a program like the G~om~ter's
Sketchpad (Key Curriculum), students can conStruct and
measure the interior angles of a polygon (Stt Figure 11.6)
and determine the formula that rdates rhe measure of the
angle to the numbtr of sides.
Software capable ofdepicting solid or tlutt-dimensional
objects on a screen provides lcamus with a way to visualiU'
objectS that are difficult to imagine. Undemanding the nature and properties of transformacions and symmetry has btcome increasingly important and can be found in nearly all
state mathematics standards. Again. software packages can
f.J.cilitate learning and insuuct students in this area. Websitcs
are available that teach symmetry (Dorsey et al., 200 I) and
software such as KAkidoMania!(Kcy Curriculum), shown in
Ftgure 11.7, goes funher inco me process ofusing symmetry
and geometric tranSformations to create artistic objects.
Figure 1 1.6
Activity
Example of a Geometer's Sketchpad
•
I
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An~e(BACI'
iI
,I I
108·
c----J
Source: Courtesy of Ed Dickey.
Chapter I I - Teehnology in Mathematics and Science Instruction
33]
Figure 11.7
Illustrating Transformations and
Symmetry with KoleidoManio!
Figure 11.8 Fathom: An Example
for Mathematical Problem Solving
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Source: Courtesy of Key Curriculum Press. 1150 65th Srreet,
.Emeryville. CA 9"'608; 1-800-995·MATH, _.keypress.com.
Source: COUlUsy of Key CulTiculum Press. 1150 65th Street,
Emeryville. CA 94608; l..aoo-995-HATH. www.keypreu.com.
Figure 11.9 Spreadsheet for Solving "What If"
Problems
Implementing Data-Driven Curriculum
U.S. srudcms scored well in the area of data analysis on
the Third International Mathematics Science Study
(Beaton cr aI., 1997-1998). The importance of statistical
inference and probability has already had an impact in
U.S. schools. Technology provides an ideal means of de-
vdoping srudenr knowledge and skill related to data
analysis. Fathom (Key Curriculum), an example of which
:I
I
,
I
I, i
I :
! :I
I,! I·
"
I
. 1.rl
l'
is shown in Figure 11.8, is a comprehensive package designed for schools ro analyze and repr~nt statistical data
in a wide range of forms.
Data resources from the Imcrnet also provide students
with realistic statistics and the opportunity ro conduct in·
vestigations that are timely and rdevam. Examples SA and
5.5 from the NCfM Principl~J and Standards for School
Mathematia websitc illustrate how data collection and
represemation might occur (NCfM, 2001). Dixon and
Falba (1997) also describe activities for producing graphs
using Internet data.
Computer spreadsheets also providc environments in
which children can aplon: number concepts, operations,
and patterns with data they obtain from various sources.
(Stt Technology Integration Idea 11.3.) Students can
work with the basic operations, explore '"what if" type
problems, and build a foundation for algebraic thinking.
Activities such as planning a fund.raising activity (Zisow,
2001) or analyzing M&M's data (Drier, 2001) provide
teachers with an imponam software tool to help build students' number scnse. (See Figure 11.9.)
7
11
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Source: Used by permission from Drier, H. (200 1, January "').
Collecting and numerically analyzing M&M's chra.A......HabIe online:
PER:fNTS
http://curry.edschool.virginia.edultNcheriinklmathiaetivitieslexteV
M&MnumericaVhome.hrm.
Supporting Math-Related Communications
The Internet offers students the opportunity to communicate with each other or even with experts in different
fields. Expressing ideas in written form is ~ntiaI; therefore, students must convert their mathematical thinking
334
Using aJcutaton in small-group settings also promotes social
Interaction and discourse.
www.prenhall.comJroblyer
lMf'Lfl1f><It<G D.. A-Df/IV£N CURRlCLU.t1
Tide: Measuring Up
ContentAreafTopic: Measurement: ratios and proportions
Grade Levels: 7-10
NETS for Students: Standards 3.5.6
Description: Students create a spreadSheet to calculate ratios and proportions, using the
measurements of sWdencs in the class as a database.They begin by taking measurements of each student
in the class and entering these data into a spreadsheet. They use their own data and compare it to
Leonardo da Vinci's calculations based on his 1492 drawing "The Proportions of the Human Figure" to
predict "the perfect numbers." After they compare their results, they discuss their conclusions about da
Vinci's hypothesized "perfect proportions."
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in Education). iste@iste.org,www.iste.org.A11 rights reserved.
Source: Morgan, B., & jemigan,J. (1998-1 9'J9).A technology update: Leonardo cia Vinci and the search
body. Learning and Leading with Technology, 26(oi), 22-25.
into words. Projects such as the Math Forum's different
Problems of
\&l"k (http://mathforum.orglpow/) allow
teachers to pose problems mar their srudents must solve
and men communicate the solution. (Sec Figure 11.10.)
Ask Dr. Math (also from me Mam Forum at hITp:/I
marhforum.orgldr.mathl) provides contactS with experts
who can answer questions.
As Technology Integration Idea 1104 shows. srudent~
created websites can be a va.luable form of communication for student projects. Using computers and
calculatOrs in smaU-group settings also promotes social
interaction and discourse. Teachers often find that
grouping students in pairs greatly enhances learning,
augmenting communication from teacher-lO-srudenr or
computer-fo-student ro a richer student-to-studcnr-lOcomputer type of communication.
tm
Figure I 1.10
fOI"
the perfect
Math Forum Problems of the Week
\l'C. The Math Forum.~
fi'Eifl
Problems 01 the Wed:
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Source.' Reproduced with permission from Drexel Univer;ity, ©
2006 by the Math Forum@ Drexe1.AII rights reserved.
Chapter 1I - Technology In Mathematics and Science Instruction
335
I~
I
SUf>POflTI<G M~TH-RfL1>,TID COtHHC~TIONS
Title: Taking Shape----l.Jnking Geometry and Technology
ContentAreaITopic Geometry
I I
II
Gr-ade Levels: 3-$
NETS (or Students: SClI1dards 3,4,5.6
Description: Teachers often help students understand geometry concepts by having them make lists and
draw items with various shapes in the world around them, for example, basketball hoops for circles and
monkey bars for rectangles.This activity expands on that strategy. Students bring in pictures of objects
with various geometrical shapes and scan them into files to create a Geometry in the World virtual book. By
reviewing all of the pictures as a whole class, they create categories to account (or all of the pictures:
cones, angles, horizontals and verticals, multiple shapes, and circles. Each category becomes a chapter for
the book.. Students work in small groups to do a web page for their chapter.They end with a class
presentation of the whole site and a discussion of the geometry concepts they leamed.
Source: Renne, C. (2000).Taking shape: linking geometry and teeMoIogy. Leomin£ and l.eoci1g with Technology, 27(7), 58--62
Motivating Skill Building and Practice
Although the ament emphasis is on learning higher order
mathemarics skills. studems often neW. more resources to
support practice of basic skills. Th~ skills provide an important foundalion on which they can build more advanced skills. Some technology resources that can support
this practice include the following:
• Boxer Math (http://W\VW.boxermath.comf) provides
interactive and dynamic software addressing fundamental mathematics (grades K-3) as well as high
schoollcvel concepts in algebra, geometry, trigonometry, and orher areas.
I
,
I
, !I
I',
,
.I' ,
I,
1
!
I
I
i
• The Plato Learning Company (http://www.plato.com)
has been devdoping tutorial and skill-building software
for more than 40 years, making it one of the longest
standing companies in the computet industry. Courseware is available ar all levels, from orly childhood to
adult, and across numerous contenr areas. Its mathematics tides address fundamental skills as well as problem solving and c:x:plorations.
• Waterford Early Math and Sdtnu software (http://
www.pearsondigital.com) includes daily instructional activities that address mathematics and science standards for elemenrary grades. These
curriculum materials fosrer exploration and inquiry
while providing a foundation in basic skills, problem solving, and science.
Figure 11.11 (p. 337) lists some useful wcbsites for math.
ematics IOstruction.
n6
ISSUES AND PROllL£HS
IN SCI£NCE INSTRUCTION
Several neros and problems specific to the teaching of sci·
ence ropics help shape the uses of technology in this area.
Th~ issues include meeting science standards, a "'nar.
rowing pipeline" of scientific talem. me increasing need
for scientific literacy, difficulties in reaching K-8 science.
and a new emphasis on teaching scientific inquiry.
Accountability for Standards in Science
In 1989 the American Association for the Advancement of
Science published Scimce fir AUAmmcam. This document
set out recommendations for what all students should know
and be able to do in science, mathematics, and technology
by me time they graduate from high school. In 1993,
Bmchmarks fir Scinu~ Literacy was published. This documem tranSlated the science literacy goals in Scimc~ fir AU
.AmnUanrinro learning goals or benchmarks for students in
grades K-12. The Natio7lll1 Scitnu £duration Standards
(NSES) were released in 1995 by me National Research
Council. Th~ standards define me content that all students should know and be able to do and provide guidelines
for assessing student learning in science. The NSES provide
guidance for science teaching strategies, science teacher professional devdopmem, and support necessary ro deliver
high-qualiry science education.loe NSES also describe the
policies to bring coordination. consistency, and coherence
to science educarion programs. Many of the state standards
documents have drawn their content from the &nchmarks
and/or the National Science l:.aucl1tion Stand4rds.
www.prenhall.com/roblyer
Recommended Websites for Mathematics Instruction
The Narrowing Pipeline of Scientific Talent
There is growing concern about America's ability to compete
in science, mathematics, and technology in the futute. With
the declining number of students----especially females and
minorities pursuing studies in math, science, and engineering fields-America faces a growing crisis in leadership for
much-needed scienceltechnology/mathematicslenginccring
initiatives. This trend could have serious consequences for
the long-term economic and national security outlook ofour
country. (See Fueling the Pipeline: Attracting and Educating
Math and Science Students [EMC Corporation, 2003].)
Increasing Need for Scientific Literacy
As the science benchmarks and standards reflect, there is a
need for all citizens to be scientifically literate in order to
make informed decisions that affect our country's future.
More than ever before, America's economic and environmental progress depends on the character and quality of
the science education that the nation's schools provide.
Difficulties Teaching K-8 Science
In a study conducted by the Educational Testing Service,
Gitomer, Latham, and Ziomek (1999) compared SAT scores
for teacher candidates passing the Praxis II exam with the average score for all college graduates. The researchers concluded that elementary education candidates have much
lower math and verbal scores than other college graduates.
Part of this problem may stem from the minimal content
preparation in mathematics and science. As a result, teaching science for understanding becomes difficult due to the
lack of a deep understanding of the discipline on the part of
the teacher. One way [Q assist teachers in science is through
increased professional development. The Eisenhower Na-
tional Clearinghouse offers a guide to improving professional development in the areas of math, science, and technology. The site, entitled "By Your Own Design," is at
http://www.enc.org/professional/guide/?ls = ho.
New Emphasis on and Controversies About
Scientific Inquiry
As many educators place increasing emphasis Oil hands~on
science s1cills, as opposed to rote learning of concepts,
technology can playa special role in improving classroom
practice in teaching scientific inquiry, or the processes of
approaching problems scientifically. Describing this trend,
Rubin (undated) says, "When learning with technology
focuses on doing inquiry-based learning, the following approaches are commonly adopted in classrooms:
II
i
• Technology is viewed as a cool, much like a pencil or
pen, but considerably more powerful.
• Use of the technology is primarily taught in the con~
rext of solving problems.
• Students help one another with the mechanics of the
technology; in fact, in many classrooms, students are
the local experts on tcchnological details.
• Talk about and around technology is as important as the
technology itself, JUSt as talk about how one finds and
uses information is as important as the informacion itself.
• Technology is used co augment communication by
expanding audience (e.g., ovcr networks and by producing hard copy) and expressive options (e.g., mixing graphs and words)."
This new emphasis is not without controversy. Cavanagh (2004) reports on a new study by the Carnegie
Chapter II - Technology in Mathematics and Science Instruction
337
,,.
Figure 11.12
Summar-y of Technology Integration Strategies for Science
Technology
Integration Strategies
I.
experiences
,I I 1
i I 'I
I.
Sample Resources
and Activities
Benefits
doing each phase d authentic
science aetmties-.
• Some Internet projects proride
hap:JIwww.globe.gov
NASA
http-JI_~
enrironment:s dJat support: ..
• Jason Project
phases of an authentic science
http://_.jason.orgf
• Archimedes Laboratory
..-..
http://_~rchimcdes.bb.orgl
index.-optical.html
o ~torium. Reprinted by permIAlon.
http1/www.exploratorium.edu
Supporting scientific
inquiry skills
-''--
Helps students locate and obtain
information to support inquiry.
Makes data collection and analysis
easier and more ~nageable.
Makes it easier to visualize and
understand phenomena.
Supports communicating I'"e$ults
Courtesy of ~ Oobn.
of inquiry.
Astronomy Depuvnent. ~
of WISCO:'lSin.
• GIS Population Data
http://www.esri.com
• Joumey North project
hap:Jfwww.learner.orgljnorthl
• Red Rover Goes to Mars
http://pJaneury.orglrrgunJ
Also see Technology Integration
Idea II.S: Measuring with Precisioo
versus Accuracy
http;//www.astro.wisc.edu
Supporting science
concept learning
• AlIow< ............... """"""" of
scientific proa!SSeS.
• Pn:Mdes opponunides to ~
in probIem-soMng activities.
Idaho. IMlTS.
hap-jlwww.pe:.1cecorps~researchl
hap:l/nova.ed.uidaho.edu/library/
inectechnology/java_3.flpleu.asp
C 1"1-200sWheer""C~
~a(lhefuan.""
ri&hu raerved. ~ with penrlismn.
hap:llwww.cotf.edulete/modules/
modules.html
def.wk.""
• UniYer5ity of Idaho VlStAIs
http://nova..ed.uidaho.edullibraryl
inel:._teehnologyfjava_appIets..asp
• DrinkingWater project
Coonesy ofNQVA,. ~ a(
Accessing science
information and tools
• Web-based Chemistry Simul<ttions
tmp-Jlcse.edc.oryproduaslsimubtionsl
waterlindex.htrnl
Also see Technology Integration
Idea 11.6: Diginllmaging on the
(Butter)f1y
Allows access to unique tools and
collections of infOfmation.
Expands opportunities for learning.
Information on space at NASA
hnp:l/spacelink.nasa.gov
Information on weather i t NOAA
hap:llwww.nou.gov
NIH
http;//www.nih.gov
InfOfmation for science teachers i t the
Eisenhower N<1Ition<1l Clearinghoul;e
hnp;//www.enc.OI'l
Expk>ring the Environment Curricul...-n
hnp;//www.cod.edulete
National Aademy Press
hnpllwww.nap.edu
Also see Technology Integration
Idea 11.7: Collecting Science in il Net
Mdlon University and the University of Pirrsburgh which
found that students taught through diKCt insrruction (rather
than inquiry or discovery learning methods) were more likely
on average to become "experts" in designjng scientific experiments----an important step in the development of scicntificreasoning skills. Also, Cavanagh noted that "The students
who showed expertise in designing those experiments
through direct instruction performed just as weU as those
who developed simiJar expertise through discovery paths on
a separate tCSt of their broader scicmific judgmemcountering some previous claims that direct instruction pra.
duces weaknesses in that area" (p. I). As a result of such
srudies, the National Science leachers Association (NSTA)
~mmends a combination of direct and inquiry methods.
Figure I 1.13 Atmosphere Investigation in the
GLOBE Environment
TECtlMOLOGY INTEGRATION STRATEGI£S
Source: From the GLOBE website (http://www.globe.gov).
0-·0 liil&J'-
:
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fOR SCI£NCE INSTRUCTION
Technology resources support many kinds of teaching and
lcaming Strategies to hdp address science standards. "fbese
strategies include supporting authemic science experiences,
supporting scientific inquiry skills, supporting science concept learning, and accessing scicnce information and tools.
Figure 11.12 summarizes these strategies and gives examples
ofsome ofthe technology resources that make them possible.
Supporting Authentic Science Experiences
Authentic science in the classroom is when srudents "do
science" as a scientist would, not simply hear it discussed
or see a demonstration. Authentic science is also referred
to as Kienrific inquiry. thc process of asking questions and
investigating those questions by making hypotheses, collecting data, analyzing the data, and communicating the
results, which arc then peer reviewed. Scientists use a vari·
ety of technologies to create amhemic sciencc cxperiences.
The GLOBE program is an excellent example of utilizing
technologies to do authentic science. GLOBE is an environmental science program that utilizes remOte sensing
and ground.based observations to study the local environ·
memo The program makes use of a number of technola.
gies to conduct local investigations. Teachers and students
can investigate the weather, land cover, soil, and hydrol·
og}'. Students utiJize Global Positioning Systems (GPS),
Geographic Information Systems (GIS), and information
technologies to collect and analyze data. Figure 11.13 is an
example activity from thc GLOBE program.
In this example, students take ground observations
using traditional and state-of-the-art technology. They lise
tempcrature data~loggers, a GPS unit, and traditional
technologies such as a weather shdtcr and aU-tube thcrmometer. Then they record their dat2 in a notebook and
enter the dara into a database at the GLOBE site. They
manipulate data with online graphing and visualization
tools. The dat2 can also be displayed in a graphical form.
allowing students to look for patterns over time. To complete the process, students write up their results and post
them to the GLOBE Student Research website. In the
write-up, students report on their research questions, discuss their procedures, communicate the results using
graphs and charts. and make conclusions. Dna: posted on
thc website. the report is peeHeviewed by GWBE participants. Additional information on this powerful learning environment can be found at hrrp:llwww.globe.gov.
Supporting Scientific Inquiry Skills
The preceding section describes one cxarnple of authentic
science using a combination of technologies. Teachers do
nOt always have time to complete long-term investigations
that encompass the entirc scientific process. However,
technology can be: used to teach specific dements of the
scicntific inquiry process, as discussed next.
Locating informAtion to investigate scientific issues and
questions. The Internet has become an indispensable
tool for investigating important scientific questions. Science teachers and students have access to a number of excicing resources for teaching and learning sciena:. For
many of the science areas, teachers and students can access
information from good sources such as NASA (http://
www.nasa.gov) or museums such as the Exploratorium
(hrrp:/!www.explofatorium.org).
Thc National Science Foundation (NSF) has funded
the ctcation of digitallibrarics for science. The Digital Library for Earth Science Education (DLESE) is a wonderful resource for teachers and studcnts. The DLESE is a
community of educators, students, and scientists working
to improve the teaching of and learning about the Earth
system at all levels. DLESE provides access to a number of
collections of educational and scientific resources. Digital
libraries provide a starling point for the investigation of
scientific questions.
Chapter II - T«hnofogy in Mathematics and Science Instruction
339
Title: Measuring with Precision versus Accuracy
Content AreaITopic: Scientific methods
Grade Levels: 5-7
NETS for Students: Standards J, S, 6
Description: In this activity students Jearn the difference between precision and accuracy by comparing
the reading of a scale of temperature with its physical meaning.
Instructions: Have a container of hot W<l.ter and one of cold W<l.ter to use as high and low reference
points. Students make twO kinds of readings: one from a scale marked every 10 degrees centigrade. and the
other from a scale marked every I degree centigrade. Although both are accurate. the second reading
reflects greater precision. Have the students work in groups to use the probes to take VMious readings
using each scale. Alter all groups have completed and recorded their readings. calculate the range for each
scale. Half the range is the precision. The difference between the reference thennometer and the
temperature probe is the accuracy. Discuss the difference with the students.
Source: Flick, L (1989). "Probing" temperature and heat. The CompulingTeocher, /7(2), 15-19.
Collecting data. Data collection and archiving are important partS of til(: scientific inquiry process. Science bases itS
conclusions on daet. A nwnber of (Ools are available for
data collea:ion and archiving. The calculator or computerbased laboratory (CSt) is an ideal tool for middJe school
through high school scicnce. CBL sensors collect data and
the data can be downloaded into a compurer or calculatOr,
and then manipulated in a spreadshecL By archiving data
in a spreadsheer, the data can be used at anorher time or
compiled for long-term investigations. Technology Integration Idea 11,5 provides an example of how probes can
be used to gather data for an inquiry activity.
Vuualizing data and phenomena. A number of visualization tools exist that allow studenrs to see representations of data and phenomena that may be difficult to see
directly. Computer simulations diffcr from illustrations
and pictures in that studenrs can manipulate e1emenrs in
them. These include tools that help studenrs visualize
macroscopic phenomena, such as the phases of the
moon, that are difficult to understand because they cannO[ be seen directly.
Visualization rools can also be used to examine mi~
croscopic or other phenomena that would otherwise be
difficult or impossible to observe, for example, molecular
structure Ot growth of planrs or animals. Technology Integration Idea 11.6 illustrates how digiral imaging can help
students study butterfly metamorphosis.
Some tools make it possible to roette and examine strUcrures from multiple viewpointS to help srudents understand
340
them (see, e.g., hrrp:llwww.rcciprocaInet.org). Visualizarionscan be used in a varieryofteachingsiruations. Theycan
be used by teachers as a tool for lecture. a demonstration. or
as a way to invite students to describe what they see. leading
students to explain concepts for themselves. VISUalizations
can also be used as a remedial tool for tutorials. Visualizations are used in the workplace as weU. Meteorologists regularly show oompurer-generated visuali2.:uions on television
to help t:Xplain weather phenomena. City planners use GIS
to plot population growth (sr."e, e.g., hrtp:llwww.esri.com).
Analyzing data. Analyzing data can be done with a numocr of existing programs thar come sr.andard on comput~
ers. Spreadsheers alJow data to be cntered and analyzed
using simple statistics or algorithms supplied by the students. In the GLOBE program, Mu/tiSp« software provides students with the ability to identify land cover types
on a landSat image. GIS software allows students to analyze faCtOrs in an image by temoving or adding attributes
and looking for connections among attributes.
Communicating results. Once dara arc anal)'7.ed, scientistS write up the results and submit them for publication
using standard productivity software (e.g., word process~
ing). Scientists collaborate on scientific problems, and the
Internet facilitatcs the communication process. In addition
to graphs and visualizations. scientisrs use images from digir.a.l cameras and other digital instruments to record dara
and compare and contraSt ovec time.lbis is especially useful in land cover investigations and in asuonomy.
www.prenhaJl.eom/roblyer
SUPPORT... SCI£NTlflC
I...,"RY SKILLS
Title: Digital Imaging on the (Butter)f1y
Content AreaITopic: Biology
Grade Levels: 9-12
NETS for Students: Standards 3.5,6
Description: This lesson shows how digital imaging can support scientific inquiry by letting students do
observations better than they could with the naked eye.To better understand the process of
metamorphosis, the teacher shows students how to set up a digital camera to take time-lapse images.They
focus the camera on the caterpillar as it is about to emerge and take the video. By speeding up the
completed footage. students can see and discuss each phase of the process.
Source: Bowen,A, & Bell, R. (2004).Winging it Using digital imaging to investigate butterfly metamorphosis. Learning
and Leading with Technology, 3/ (6), 24-27.
Figure 11.14 Colors Simulator Created by IMITS
at the University of Idaho
Figure I 1.15
....... - ~ ...
Chemical Mixing Simulations
•
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Source: Images © Hurray Roberston 1999-2004. Reproduced by
permission ofThe Royal Society of Chemistry.
Source: Reprinted with permission from NOVA, University of
Idaho,IHITS.
The Internet also provides a medium for communication among scientists. Data can be c-mailed to teseatchets
around the globe. Classroom teachers can also have scientists interact in their classroom by participating in webcasts. NASA regularly has webcasts in which schools can
participate.
Supporting Science Concept learning
Technology-based Strategies thar simulate and model scientific processes can help students develop rhe foundation
1
knowledge and skills they need to engage in inquiry. Srudents often have difficulty understanding complex scientific
concepts, especially when such concepts are only ptesented
and explained in tcxt as nonmoving stacic images. Simulations and animations can make mese concepts clearer by
showing how they work in action. These include animations where students can see and sometimes manipulate applets to learn a sciemific concept. For example, mixing
coloted light is an elementary science activity that is often
confusing to students. Utilizing rhe "colot mixet" simulation tool shown in Figure 11.14, learners can use rhe RG B
screen as a mechanism to clarify these abstract concepts.
Other simulations, like me one shown in Figure 11.15,
allow students to mix chemicals and simulate the results, saving dollars and providing a safe environment for chemistry
Chapter II - Technology;n Mathematics and Science Instruction
i[
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341
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Title: Collecting Science in a Net
Content AreaITopic: Earth science
Grade Levels: 2-12
NETS for Students: Standards 3.4.5,6
Description: This activity focuses on gathering daD. to investigate greenhouse gases in the atmosphere
and global warming. Students use two Intemet sites to obtain datil. on global temperatures and
atmospheric concentrations of carbon dioxide and use the data to answer questions about these topics.
Students plot monthly average carbon dioxide concentrations for a given year and observe pattems in
increases and decreases.Then they graph the temperature data for a year and compare these dau with the
carbon dioxide data.They discuss possible links between the biosphere and atmosphere. Finally, they use
the Internet to gather other infonnation on ~ warming and discuss the current trends.
Source: Slattery. w.. Hundley. S., Anegan-StoIl. c.. & Becker, M. (1998). CoDeaing science in a net.1b;Iming ortd kOOf(lg
with Technology, 26( I), 25-30.
Figure 11.16
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Mars Rover Online
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Source: Reprinted with permission from The P'bnetary Society
(http://planeury.orgfrrgtmfRrsites.php).
and ph)'5ical science study. Virtual diss«xions also allow students to examine anatomy without coming intO contaa
with presC'I'V<l.tion chemicals. In ph)'5ics, smdents can use
simulacions 10 condua historical experiments.
Accessing Science Information and Tools
The Internet has opened up a world of opportunities for
learning beyond the classroom. Forcxample. students can
control a Rover like the ones on Mars (see Figure J 1.16)
or opcnue a telescope or a camera from the space shuttle.
It is also an unlimited source ofdata for classroom experiments and investigations. (Sec TecllOology Integration
Idea 11.7).
The Internet also is an invaluable resource for up-tOdate science information. Science knowledge changes
faster than most school libraries can keep up. Books are
Out of date the minute they are published. Ifyou want the
latest information on space, you can access NASA; the
weather. NOAA; medicine. the NIH. Most of these sites
provide content targeted for teachers and students. A
number of curriculum projccts arc also available online to
teachers and students. NASA's classroom of me future pro~
vides a frtt Exploring the Environment curriculum
(hnp:llwww.cotfedulete) that integrates science and s0cial studies to examine current issues.
Teachers can also use the Internet for assistance with
content knowledge and for professional development opportunities that may not be available locally. They can also
achange ideas and teaching strategies with other teachers.
The Eisenhower National Clearinghouse (ENe) provides
a comprehensive website to connect teachers with re~
sources and training. The ENe provides a number of on~
line publications containing the latest research on
teaching and learning science. lcachers can also utili1.e the
National Academy Press website (http://www.nap.cdu) to
examine the most current publications in science and sci~
ence education available online for free. Figure 11.17 lists
additional useful websites for science instruction.
!I
ii
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342
www.prenhall.comlrobtyer
Figure 11.17
Recommended Websites for Science Instruction
• The Eisenhower National Clearinghouse (ENC) (http://www.enc.org}-This science organization provides many teaching
resources and training opportunities.
INTERACTIVE SUMMARY
The following is a summary of the main points covered in
this chapter. To see addirional examples and informarion
on these points. go to this textbook's Companion Website
at hup:llwww.prenhall.com/roblyer and click on the
Chapter 11 Interactive Summary module to visit each of
the recommended websites.
1. Issues in mathematics instruction: These include:
• Challenges in implementing the Principles and
Standards for School Mathematics.
2. Integration strategies for mathematics instruction:
Six strategies ate described for integrating technology
into this area:
• Using virtual manipulatives (see exampks)
(see
• Allowing representation of mathematical principles
(C;eomct!.:r's Sketchpad)
• Implementing data-driven curriculum (see Fathom
example)
• Supporting math-related communications
• Motivating skill building
Dr. Math website)
and
practice
• Supporting authentic science experiences (see the
GLOBE project)
• Supponing scientific mqUiry skills (see the Ek
plQratorium)
• Supporting science concept learning (see example
simulations)
• Accessing science information and tools.
• Accountability fot Srandards in Mathematics
• Fostering mathematical problem solving
Riverdcep products)
4. Integration strategies for science instruction: Four
strategies are described for integrating technology
into this area:
(sec
3. Issues in science instruction: These include:
Online Activities
Visit this text's Companion Website at http://www.
prcnhall.cQmlroblyer to gain access to a variety of ques~
tions, acrivities, and exercises to help build your knowledge of this chapter's content.
Online Chapter I I Self-Test
To review terms and concepts fQr this chapter. click on
the Self-Test module for this chapter of the Companion
Website.
Software Skill-BuilderTutorials
To access practical tutorial and skill-building activities and
to build skills using popular software and hardware, click
on the Sofrware Skill-Builder Tutorials mQdule for this
chapter of the Companion Website.
• Accountability for standards in science
• The narrowing pipeline of scientific talent
Web·Enrichment Activities
• Increasing need for scientific literacy
To complete activities that connect to chapter content and
provide web-based resources, click on the WebEnrichment Activiries module for this chapter of the
Companion Website.
• Difficulties tcaching K-8 science
• New emphasis on and controversies about scientific
inquiry.
Chapter I t - Technology in Mathematics and Science Instruction
343
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III:11
,, ,
T£CHNOLOGY INT£GRATION
WORKSHOP
~ Mr. Brino was trying to show
CUf'S fROM THE CLASSROOM:
~ r e business education program
LElIRNlNG WITH TECHNOLOGY
how they could figure OUt quicldy how much car they
Go to the 1~chno/Qgy lnugration Workshop OVD 10- could buy with the moncy they had. He wanted to show
cared in the back of this tat and click on Clips them !.he relacionship among the down payment. interest
from Ih~ Clam-oom. View me video clips listed rare. and length of the loan and how this all affected
below that support this chapter's content:
• LaptoP! fOr Data in 5th Cram
• Qui7.dom System fOr Practice
• Chnlkngu Crour Prollidn Probkm~Based uarning
• Geometer's Sketchpadftr Inductive Reasoning
• Tttbtet Computers in Fourth-GrlUk Scimce
• Tablet Computers in Fjrst~Grade Mathnnatics
• E~Z Geometry Websiu Supports Stutknt Work
• Graphing CakulatoTJ in Trigonometry.
Now, visit this tat's Companion Website :u
to answer
\...;-~!OIi~", hupillwww.prcnhaJl.comlroblycr
questions and complete activities that will
.C\ t guide you in analyzing each clip.
THE TIP MODEL IN ACTION
Read each of the following scenarios related to implementing the TIP Model, and go to the Companion Website to answer the questions that follow it based on your
Chapter II reading and activities.
Ms. Waldrup. the AP matheto ave her students do simple corrclations with two data sn.s to demonstrate the
mathematical principles involved. However. it took Students tOO long to do these calculations by hand and there
were tOO many data enrry errors using a calculator.
1.1 What technology-based strategy couJd Ms.
Waldrup use to address this problem?
1.2 What would be the relative advantage of using
this strategy?
1.3 Would it be berrer to carry Out this strategy as a
whole class or with students working individually
or in groups? Explain how you would do it.
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344
momhly payments and the total they would spend on the
car at the end of the loan period. However. he wanted
them to be able to do the calculations quickly. so they
could focus on the underlying math concepts.
2.1 What technology-based strategy could Mr. Brino
use to address this problem?
2.2 What would be the relative advantage of using'
this strategy?
2.3 Describe the steps you might use to carry out a
simple lesson using this stearegy.
Dr. Ahmed wanted his stuents to t e rea mgs at a local stream to do an experiment on acid and alkaline subStances in water. He wanted
to use the handheld probcware devices when they went on
the field trip. With these devices, they could collect the
data, bring the readings back in a data file. and download
the file to the computer for analysis. However. he had 27
students and only 15 handhdds.
3.1 What grouping strategy could Dr. Ahmed usc to
make the available devices work well wi!.h this
many students?
3.2 How you would advise Dr. Ahmed about his
studentS carrying out the sU'ategy?
3.3 What would be the relative advantage of using
this strategy as opposed to manual methods of
collecting the readings?
Ms. Lyndia was the school
counse or in arge a e ping students prepare for the test
her school district had developed to select those students
eligible for the special math/science magnet program.
which offered all expenses paid to those who were selected.
She knew a lot about the kinds of items thar would be on
the test. and she knew some of the students needed to
prnctice some of the skills.
www.prenhall.comlroblyer
T
4.1 What technology-based strategy would you
recommend Ms. Lyndia use to address this
problem?
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INT£GRATION £XAMf'L£S
4.2 W'hat would be the relative advantage of using
this strategy, as opposed to a paper-and-pencil
format?
The Technology Integration Example that opened this
chapter (Hot and Cold Data) showed how a teacher might
have students use CBLs and spreadsheet activities to carry
out experiments. Ai> each group completes its assigned experiment, it presents the results to the class by displaying
the graphed data in a PowerPoint presentation. With the
knowledge you have gained from Chapter 11, do the following to explore this strategy:
4.3 Should srudents practice individually, in pairs, or
in small groups? Explain.
~
Mr. Cardillo's ninth-grade
~ems understanding geometry
concepts. They seemed to understand them better when
he drew the figures and angles for them as he explained the
concepts, bur this was not feasible for every problem. It
cook too long, and he couldn't draw well enough to show
everything clearly.
1. Create a spreadsheet graph like the example shown
here. Create this example graph by clicking on the
Hands-On with Technology tmorial section on the
DVD that accompanies this text.
2. Answer the following questions abour the Hot and
Cold Data example:
5.1 Whar technology-based strategy would you
recommend Mr. Cardillo use to address this
problem?
• Phase I - What kinds of relative advantage did the
teachers feel the usc ofCBLswould bring to the learning activity? How would using spreadsheets help~
5.2 What would be the relative advantage of using
this strategy~
5.3 If Mr. Cardillo has 32 students in his class and
only one computer, what would you recommend
he do to carry am this strategy most effectively?
• Phase 2 - Outcomes 2 and 4 are very similar state~
ments. Why are they stated as separate outcomes?
How would the assessment for them differ? How
would it be similar?
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• ••
•
• •• .1":
-- Styrofoam
• Paper
---Ceramic
Time in Min
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ii
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Example Graph Created to Insert in Powerfoint (Create this product using the Honds-On with Technology tutorial
section of the DVD,)
Chapter I I - Technology In Mathematics and Science Instructjon
345
III
• Phase 3 - Smdems may nor be familiar with
Consumn &pom and its approach ro comparing
products. If the reachers did nO[ have access to the
magazines themselves. what could they do to help
students understand mis approach?
1. Locate lesson ideas - The DVD has ~eral aamples
• Phase 4 - What could the teachers do with me pe:r-
2. Evaluate the lessons -
formance measures and lab sheers to make them
more accessible to studems both inside and outside
class?
oflessons that use the mathematics and science integration strategies described in this chapter. Locate an
example integration idea for at leasr twO of these
strategies for each content area.
Use the Evaluation CheckliJt
for a Technology-Inugmud Lmon (located on rhe
DVD and the Companion Websire) to evaluate each
of these lessons.
• Phase 5 -In evaluating the outcomes of me activity. the teachers found that all students showed
compe:tence wim CBL procedures and were able to
carry out the experiments with teacher assistance.
How~er. some students still had difficulty with the
final outcome. How might they change the imple~
mentation to help students bener achieve this OUtcome?
3. Modify a lesson - Select one of the lesson ideas and
adapt its strategies to meet a need in your own content area. You may choose to use the same approach in
the original or adapt it to meet your needs.
4. Add descriptors - Create descriptors for your new
lesson like those found on the darabase (e.g.• grade
I~el. content and topic areas, technologies used, relative advantage. objectives. NETS standards).
3. What NETS for Students skills would students learn
by working on the Hot and Cold Data project? (See
the from of the book for a list of NETS for Students.)
5. Add the new lesson -Add your modified lesson wirh
all its descriptors
fOR
TECHNOLOGY INTEGRATION
LESSON PLANNING
The ftchnology Inugmtion Workshop DVD includes a set
of technology integration ideas and links to online
lessons. arranged as a searchable database. The
DVD comes packaged in rhe back of this
tcxtbook. Click on the Haruis-On with Tah·
nology section of me DVO and complete the following
exercISeS.
II
346
[0
rhe lesson idea database.
YOUR TEACHING PORTfOUO
For this chapter's contribution to your reaching portfolio,
add the following products you created in rhe Technology
Integration Workshop:
• The sample gra.ph and p()UIVPoint frame you creared
• The ~uations you did using the Evaluation Check·
lin for a 7tchnology--Intq;raud Lesson
• The new lesson plan you developed, based on the one
you found on the DVO.
www.prenhaJl.comlrobtyer