mathematics initiative office of superintendent of public instructionwera12-7-2006 ospi mathematics ...
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Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
OSPI Mathematics OSPI Mathematics
Mathematics isMathematics is a language and science of patternsa language and science of patterns
Mathematical content (EALR 1) must be embedded in Mathematical content (EALR 1) must be embedded in the mathematical processes (EALRs 2-5) the mathematical processes (EALRs 2-5)
For all students to learn significant mathematics, content For all students to learn significant mathematics, content must be taught and assessed in meaningful situationsmust be taught and assessed in meaningful situations
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERA 2006WERA 2006
12-7-200612-7-2006
Data to Display:Data to Display:Graphs Tell a StoryGraphs Tell a Story
WERA, December 7, 2006
Karen Hall, OSPI Mathematics Initiative Specialist
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Weather StoryWeather Story
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Why do we care?Why do we care?
A numerate person should be able toA numerate person should be able to interpret data presented in graphical forminterpret data presented in graphical form reason with data reason with data evaluate the soundness of conclusions evaluate the soundness of conclusions
based on databased on data draw conclusions/support with data.draw conclusions/support with data.
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
CU02 (Organize, Represent, and CU02 (Organize, Represent, and Share Information)Share Information)
(4.2.1, 4.2.2, 4.2.3)(4.2.1, 4.2.2, 4.2.3)
PS03 (Data RepresentationPS03 (Data Representation and Interpretation)and Interpretation)
(1.4.5, 1.4.6)(1.4.5, 1.4.6)
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Student Weakness- GraphsStudent Weakness- Graphs
Drawing graphs is usually satisfactory. Drawing graphs is usually satisfactory. Students have difficulty interpreting Students have difficulty interpreting information from graph. information from graph.
Students have difficulty knowing when to Students have difficulty knowing when to use which type of graph.use which type of graph.
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Graphs we will examineGraphs we will examine
Bar graphBar graph Line graphLine graph Scatter plotScatter plot Connected Scatter plotConnected Scatter plot
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Components of a graphComponents of a graph
titlestitles labels labels appropriate and consistent scales appropriate and consistent scales an accurate data displayan accurate data display
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Comparison of CategoriesComparison of Categories
Frequency Plots of categorical data:Frequency Plots of categorical data: Bar Graph (categories are attributes or Bar Graph (categories are attributes or
numbers)numbers) Line Graph (categories are time intervals of Line Graph (categories are time intervals of
equal value)equal value)
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Student's Favorite Color of cayons (N = 32)
0
2
4
6
8
10
Red Blue Green Yellow Purple Black
Crayon Colors
Nu
mb
er o
f S
tud
ents
Categorical Data: Non-numerical
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Categorical Data: Equal Time IntervalsCategorical Data: Equal Time Intervals
Cookies Baked in School Cafeteria
010203040506070
1996 School Year
Am
ou
nt
in p
ou
nd
s
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Categorical Data: Equal Time IntervalsCategorical Data: Equal Time Intervals
Cookies Baked in School Cafeteria
010203040506070
1996 School Year
Am
ou
nt
in p
ou
nd
s
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Categorical Data: Equal Time IntervalsCategorical Data: Equal Time Intervals
Cookies Baked in School Cafeteria
010203040506070
1996 School Year
Am
ou
nt
in p
ou
nd
s
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Cookies Baked in School Cafeteria
010203040506070
0 2 4 6 8 10 12
1996 School Year
Am
ou
nt
in p
ou
nd
s
CAUTION: Looks like a scatter plot when months treated as numbers by EXCEL
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Voting Methods 1980 to 2006
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Date from Continuous set of Date from Continuous set of NumbersNumbers
Scatter plotScatter plot Connected Scatter Plot Connected Scatter Plot
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Scatter Plot with line of regressionScatter Plot with line of regression
www.isteve.com/BabyGap-scatterplot2-WV-fixed.gif
www.isteve.com/BabyGap-scatterplot2-WV-fixed.gif
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Connected scatter plot
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Research on Research on “Student thinking about data”“Student thinking about data”
Experts look at data as a collection or Experts look at data as a collection or aggregateaggregate
Students new to the study of data look at Students new to the study of data look at data as individual cases or subgroups of data as individual cases or subgroups of individuals. They tend individuals. They tend notnot to see to see aggregate features. aggregate features.
Chapter 13, NCTM Research Companion to Chapter 13, NCTM Research Companion to
Principles and Standards for School MathematicsPrinciples and Standards for School Mathematics
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Look at student work.
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Improve Student PerformanceImprove Student Performance
Create opportunities toCreate opportunities to Explore meaningful data setsExplore meaningful data sets Use student’s intuitive approach Use student’s intuitive approach Explore scale and interval widthExplore scale and interval width Draw conclusion and then support it with Draw conclusion and then support it with
data from student’s data setdata from student’s data set
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
Exploring Data SetsExploring Data Sets
Understand the context of dataUnderstand the context of data Make a hypothesis about what data might Make a hypothesis about what data might
showshow Investigate their hypothesisInvestigate their hypothesis Choose type of graph to display their dataChoose type of graph to display their data Make conclusion supported by dataMake conclusion supported by data Make conjectures for additional studiesMake conjectures for additional studies
Mathematics InitiativeMathematics Initiative
Office of Superintendent
of Public Instruction
WERAWERA
12-7-200612-7-2006
ResourcesResources
Miller, Jane E, The Chicago Guide to Miller, Jane E, The Chicago Guide to Writing About Numbers, Univ. Chicago Writing About Numbers, Univ. Chicago Press, 2004Press, 2004
Tufte, Edward R., The VIsual Display of Tufte, Edward R., The VIsual Display of Information, Graphics Press, 2001Information, Graphics Press, 2001
Curcio, Frances R., Developing Graph Curcio, Frances R., Developing Graph Comprehension, NCTM, 1989Comprehension, NCTM, 1989
Tinker Plots, Key Curriculum PressTinker Plots, Key Curriculum Press