Performance Benchmark N.8.A.7
Students know there are multiple methods for organizing items and information. E/S
Have you ever thought about all of the information that science has discovered? Scientists have collecting
information and representing their information for millennia; how do scientists represent this information?
What criteria must all information fit into? What is the best way to represent information? In order to
make information accessible to all observers, scientists seek ways of representing information, such as
data, in organized, meaningful structures. Various systems have been established and form a foundation
of organization. Developing systematic structures on this foundation, has allowed the field of science the
opportunity to display both visual and written information within a series of comprehensible formats.
Systematic structures such as; tables, graphs, charts, organizers, and webs are supportive devises that
signify data from one source to another.
Data Tables
One of the most commonly used conventions throughout the many disciplines of science is the data table.
The data table, simple or complex, offers a standardized format for organizing data. The typical structure
for a data table is the first row represents the type of data collected and the units of measure for the
collected data. The first column typically represents the number of trials, or the different types of material.
For example, look at the Index of Refraction data table below. The title is clear and meaningful, the top
row represents the type of information presented, and the first column represents the type of material.
Table 1. Sample data table
(From http://hyperphysics.phy-astr.gsu.edu/HBASE/tables/indrf.html#c1)
Please note that the index of refraction is a unitless value. If this value had a unit, the unit would need to
be either placed in parentheses after the index in the title bar or after each value.
Graphical Representations of Data
One of the most prevalent ways to display relationships between data is the graph. There are many
different types and looks to graphical representations of data, however most of the types fit into one of
three categories; scatter plot, bar, and pie.
Scatter Plot Graphs
The scatter plot graph is one of the most common graphical systems used when analyzing data for
relationships. Commonly referred to as a “line graph,” the scatter plot’s typical convention is for the
independent variable (controlled by the experimenter) to be placed along the “X” axis, and the dependent
variable (the variable examined by the changes in the independent) to be placed along the “Y” axis. Other
convention components of a scatter plot graph are the title (always presented as the dependent vs.
independent variable), labeled axes with units, and a proper scaling so the data spans the graph.
John’s Varying Weight through the Years
Figure 1. Weight versus Years for John
(From http://www.mathleague.com/help/data/data.htm)
The graph above shows how John's weight varied from the beginning of 1991 to the beginning of 1995.
Notice that the individual points of data (datum) in this graph are connected. Dependent on the
appropriateness of the data, connecting the points can be a useful tool for a quick identification of the
trend in the data.
The slope of the line (or the angle at which the data shows a change) is an extremely important and useful
tool in quantitatively examining the trend of a graph. For example, John’s weight increase from 1992 to
1993 can be quantified by calculating the slope of those specific data points. The slope is calculated by
taking the change in the Y axis over the change in the X axis, or 74kg – 70kg / 1993 – 1992 = 4kg/year.
This data could be used to calculate the average change per month, or the data could be used to predict
future events. The slope of a scatter plot graph is often referred to as a “line of best fit.” Under this
meaning it is NOT necessary for the line to cross all, or any, of the data points. The line of best fit only
needs to average the data to show a trend as in the graph below.
Figure 2. Cost of Ticket versus Speed of Automobile
(From http://misterguch.brinkster.net/graph.html)
For additional information on scatter plot graphs visit
http://www.mste.uiuc.edu/courses/ci330ms/youtsey/scatterinfo.html
For more information about graphs, independent and dependent variables, and line of best fit go to
http://www.worsleyschool.net/science/files/scatter/plots.html
Bar Graphs (Histogram)
A bar graph is similar to a scatter plot graph in title and axes labeling. However, rather than using a point
on a plane to define a value, a bar graph uses a horizontal or vertical rectangular bar that ends at an
appropriate level indicating value. There are many characteristics of bar graphs that make them useful for
displaying data for comparison purposes.
Figure 3. Bar Graph Format
(From http://www.omnis.net/technews/030206/)
Notice the features of the hypothetical bar graph above. The height of the line represents the value of the
data, and that value is easily comparable to the other bars.
For more information about bar graphs go to http://cstl.syr.edu/FIPSE/TabBar/RevBar/REVBAR.HTM
Pie Charts
A pie chart is a circular representation of data where the circle represents 100% of the data. The circle is
divided into “slices” called sectors that illustrate the magnitudes of the represented data. In a pie chart, the
size of the sector is proportional to the percentage of data the sector is intended to represent. Together, the
sectors create a full disk, or 100% of the data. For example, the pie chart below shows basic methods of
household trash disposal. The fraction of each sector of the pie should equal 100. From our pie chart we
can see that only about 31% of the total household waste is recycled.
Figure 4. Pie Chart Representing Household Waste Disposal
(From http://www.eia.doe.gov/kids/energyfacts/saving/recycling/solidwaste/landfiller.html)
Models
Models are one of the most commonly used tools for examining relationships between information,
displaying information and making predictions based on information. From posters to computer applets,
there are a wide range of models that are applicable throughout the disciplines of science. Maps, globes,
molecular modeling kits, etc. are all examples of models. All models have benefits in that they attempt to
define or simplify a process, as well as costs, in that they are only a representation of a phenomenon. A
typical model, with respect to organizing thoughts, is commonly referred to as a graphic organizer. There
are many different types and styles to graphic organizers; however, they all share a common
characteristic in that they attempt to make a wide range of information accessible and coherent. Basically,
a graphic organizer is a visual representation created to display understanding by organizing details.
Below is a general representation of some of the many types of graphic organizers.
Examples
Venn diagram
Decision Making
Cycle
T-Chart
Vocabulary
Flow Chart
Chain
Fact/Opinion
Cause & Effect
Tree
Concept mapping is one such way of organizing information. Concept maps differ from most other types
of graphic organizers in that the relationships between concepts (information) is intended to be well
illuminated in the linking phrases (connections between concepts). A concept map is a representation,
mental model, of a learner’s understanding at a given point in time. The following is a concept map
displaying a student’s understanding of seasons on Earth.
Figure 5. Seasons Concept Map
(From http://cmap.ihmc.us/Publications/ResearchPapers/TheoryCmaps/Fig5CmapSeasons-large.png)
For more information about concept mapping go to
http://cmap.ihmc.us/conceptmap.html
For more information about the various types of graphic organizers go to
http://olc.spsd.sk.ca/DE/PD/instr/strats/graphicorganizers/
Performance Benchmark N.8.A.7
Students know there are multiple methods for organizing items and information. E/S
Common misconceptions associated with this benchmark
1. Students incorrectly believe that there is not a structure to a data table.
Students often think that a data table is a collection of data without any organization. They think that
data is just placed within a table at random. Students must be made aware that the purpose of a data
table is to organize data. Data should be in order (ascending or descending), and all columns must
have a label and a unit.
For a basic set of guidelines to follow in constructing data tables go to
http://www.sedl.org/afterschool/toolkits/science/pdf/ast_sci_data_tables_guidelines.pdf
For a checklist of the various components of a data table go to
http://www.sedl.org/afterschool/toolkits/science/pdf/ast_sci_data_tables_checklist.pdf
2. Students incorrectly believe that a line of best fit, on a scatter plot graph, must connect all of the
data points.
Students often think that the line of best fit must cross the collected data points. While the line of best
may pass through some, or many of the data points, it is not necessary for the line of best fit to pass
through any of the data points. In statistics, a linear line of best fit can range from -1 to 1 in correlation
with the data. A -1 indicates that there is a negative relationship between the independent and
dependent variable. A correlation of 1 indicates that there is a positive relationship between the
independent and dependent variable. The closer the correlation is to 0, the less the data shows any
predictable trend.
For a basic overview of the line of best fit visit http://regentsprep.org/Regents/Math/data/linefit.htm
For more information about correlations and regression go to
http://richardbowles.tripod.com/maths/correlation/corr.htm
3. Students incorrectly believe that any graph could be used to represent data.
Students often incorrectly think that any graph can be used to represent the same data, and that the
“prettiest” graph is the graph that is ultimately chosen. The type of graph that is selected to represent
the data is based on the type of data that needs to be represented. For example, the relationship
between an independent and dependent variable typically is placed on a scatter plot graph. If the data
to be represented is divided into sections of a whole (100% of the data is collected and different
sectors are to be represented) then a pie chart is the most appropriate graphical method.
For a list, with examples, of various graphical representations along with the reasons for selecting the
graphic type, go to
http://www.ais.msstate.edu/AEE/Tutorial/graphictypes.html
4. General graphing difficulties
Students generally have difficulties in following convention such as the placement of independent and
dependent variable, titling the graph, calculating the slope and transferring appropriate units, and
labeling the axes with descriptors and units. The general convention states that the independent
variable is placed on the “X” axis and the dependent variable is placed on the “Y” axis. The break
from this convention comes when the dependent variable is time. Time, independent or depended, is
generally placed on the “X” axis. The convention for the title of a graph is the dependent vs.
independent variable. All axes must be labeled with units, and the units need to be appropriately
represented in the slope of a scatter plot graph. Some students also incorrectly believe that all lines of
best fit must pass through the origin (0, 0). The line of best fit can go through the origin, however the
intercept (place where the line crosses the “X” or “Y” axes) most often has a Y value referred to as a
Y-intercept.
For step-by-step instruction on the components of the scatter plot graphical method see
http://staff.tuhsd.k12.az.us/gfoster/standard/bgraph.htm
5. Students incorrectly believe that modes are the real thing, or that models are an accurate
example, in every aspect, of a phenomenon.
Students incorrectly believe that models are completely accurate copies of real phenomenon. Models
in science are used to mimic a phenomenon, predict events, make inferences, examine relationships,
etc. All models have some degree of accuracy, and some degree of inaccuracy. Of the models
discussed above, graphs are often used to predict or extrapolate. The quality of the graph and data
collection allows a scientist to more securely make a prediction based on the model of the data.
However any prediction that can be made has some degree of inaccuracy. Of the graphic organizers
discussed above, some are intended to model thought. Using that model to make predictions invokes a
degree of inaccuracy as well. Other models, globes, maps, diagrams, etc. have degrees of limitations.
For example, all two-dimensional maps must resize the three-dimensional Earth in order to
accommodate the change from the real Earth to the model. Because of this all maps have a degree of
inaccurate portrayal of the real land masses, however carrying a globe while hiking would prove
rather difficult. Educators must explain to students that all models have accurate and inaccurate
components, but the strength of a model lies in its convenient use and its ability to accurately
represent the intended part of the true phenomenon. This can be done as a new model is introduced to
the student. The educator can point out the valuable parts of the model and the reason for its use, and
then the issues with the model and why they are acceptable.
To learn more about models in Science go to http://plato.stanford.edu/entries/models-science/
For a student-centered reading on models in science go to
http://genesismission.jpl.nasa.gov/educate/scimodule/SSWPrOptPDFs/2HowHotIsIt/ModelsInScience
-ST-PO.pdf
Performance Benchmark N.8.A.7
Students know there are multiple methods for organizing items and information. E/S
Sample Test Questions
Questions and Answers to be inserted from separate document
Content Benchmark N.8.A.7
Students know there are multiple methods for organizing items and information. E/S
Answers to Sample Test Questions
Questions and Answers to be inserted from separate document
Performance Benchmark N.8.A.7
Students know there are multiple methods for organizing items and information. E/S
Intervention Strategies and Resources
The following is a list of intervention strategies and resources that will facilitate student understanding of
this benchmark.
Graphing
A. All the Parts Interactive Graphing Tutorial
This site offers a step-by-step student appropriate tutorial for graphing. This site could be used as a
review of graphing or the start of graphical instruction. For more information about the site go to
http://www.beaconlearningcenter.com/Weblessons/AllTheParts/default.htm#page4
B. Identifying Parts of a Line Graph by Wisc-Online
This site offers an in-depth tutorial about line graphs, the students are lead through each section of
the graphing process and examples are shown at every step. The reading is appropriate for the
middle school learner. For more information about the site go to
http://www.wisc-online.com/objects/index_tj.asp?objID=SOC302
C. Line of Best Fit Applet by MSTE program at University of Illinois
This site offers an applet that allows students to enter data points on a scatter plot graph and
calculate the line of best fit. For more information about this site go to
http://www.mste.uiuc.edu/users/carvell/PlotPoints/default.html
D. Line Graph Tutorials by Mrs. Glosser's Math Goodies
This site offers a quick check for mastery of graphing definitions and reading the graph to predict.
For more information about this site go to http://www.mathgoodies.com/lessons/graphs/line.html
E. Create a Graph site from NCES KIDS’ ZONE
This site offers the chance for students to select the type of graph they would like to construct and
then input their data. The program generates the graph then students provide axes labels and units
to create a completed graph. To access this resource go to
http://nces.ed.gov/nceskids/createagraph/
F. Graphing Examples and Fun Activities from Educational Resources for K-8 Students,
Jefferson County Schools
For students new to graphing the Math Graphing website offers a list of graphing games. Most of
the graphing games are written appropriately for the 6th grade level. To access this resource go to
http://classroom.jc-schools.net/basic/math-graph.html
G. Science Graphing Overview from the Science Education Resource Center (SERC)
Basic but effective overview of scatter plot graphs with resources for scatter plot practice and
material can be found at http://serc.carleton.edu/quantskills/methods/quantlit/basicgraph.html
H. Making Sense of Graphs and Interpreting Data
To evaluate your student’s ability to read and interpret graphs, the Making Sense of Graphs and
Interpreting Data site offers a quick check for mastery using different types of graphs. To access
this resource go to http://staff.tuhsd.k12.az.us/gfoster/standard/bgraph2.htm
Graphic Organizers
There are a wide variety of sites offering graphic organizer templates; most of which are valuable if used
for student instruction throughout a unit, and are revisited and reevaluated by the students as the unit of
instruction unfolds.
A. Classroom Resources – Graphic Organizers from Houghton Mifflin Harcourt
For a wide variety of graphic organizer methods and templates that are ready to be printed off and
use immediately go to http://www.eduplace.com/graphicorganizer/
B. Graphic Organizers from Thinkport
For a sampling of graphic organizers with printable templates for immediate use go to
http://www.thinkport.org/Technology/template.tp
C. Graphic Organizers by Subject/Content (Biology, Physics, Chemistry…)
For graphic organizers that are sorted according to discipline and subject go to
http://www.science-class.net/Teachers_Graphic_Organizers.htm#GeneralScience
D. Modeling the Electromagnetic Spectrum by Chandra
Modeling is one of many teaching tools, and using models in science is a ubiquitous practice.
Models typically are used to represent various components of a complex phenomenon, and the
Chandra site offers a resource for modeling the electromagnetic spectrum. To access this resource
go to http://chandra.harvard.edu/edu/formal/ems/
E. C-Map Tools from the Institute for Human and Machine Cognition (IHMC)
Student thought can also be modeled throughout a unit of instruction. There are many great
resources that aid in the process such as Inspiration and C-maps. To access the modeling resource
C-maps, go to http://cmap.ihmc.us/conceptmap.html