Curriculum Materials
Wisconsin Fast Plants (WFP)
Variation, differences based on both genetics and environmental factors, is a fundamental attribute of life. Individual organisms vary from one another, and organisms vary over time. This investigation allows students to observe, describe, and measure variation using a model organism, Wisconsin Fast Plants (WFPs). Focusing on the guiding question, “how do plants change as they grow?”, students will plant, observe, and measure WFPs. This activity provides opportunities for students to make observations about individual differences in WFPs and how they change as they grow. They then make decisions about how to measure those observations to generate quantitative data and create data displays to make claims about how plants grow. As they make claims, students will have opportunities to explain how different sources contribute to the variation in the data. These explanations help students consider the different inferences you might make about the variation. For example, if we think all the variation is from measurement error then we might interpret it as mistakes or noise. If we think the variation is from errors in a production process, then we might interpret it as things to improve in the process. In this investigation, though, much of the variation comes from differences in environmental and genetic factors, which provides opportunities to use the variation to explore the factors that impact plant growth.
This investigation equips students to understand that quantitative data emerge from decisions they make as they measure, organize, and analyze their data, and how, ultimately, their choices provide evidence to support their claims about plant growth. This activity also provides opportunities to contrast ways of thinking about variation that students may have been exposed to in their mathematics classes.
Inventing Data Displays
Unit 1 focuses on the development of representational and meta-
representational competencies, meaning that students progress from case-
based interpretations of data representations to those involving characteristics of
the aggregate. Students learn that the shape of the data arises from the choices that
designers make to show and hide aspects of the data.
Inventing Center
In Unit 2, a simple question is posed: What is the “best guess” of the real
length of (name-of-person)’s arm span? The activities in this unit involve
students in the design of a measure of center. Students participate in the
important mathematical practice of inventing an algorithm.
Inventing Precision
In Unit 3, students invent a measure of precision—the tendency of the
measurements to agree. Focusing on precision, and not only spread,
invites students to consider how to develop a quantity that measures
“clumpiness” or proximity of the measurements. Focusing on clumps,
especially the center clump, often spurs simultaneous consideration of
center and spread as students focus on distances (deviations) from the
center or consider the neighborhood of values around the center.
Exploring Generalization
This unit focuses on the important mathematical idea of generalization. Do
statistics invented previously work well to describe new samples? When
attributes of the distribution of sample values change, do the statistics also
change in sensible ways? At the teacher’s option, the attribute measured in
Unit 1 (e.g., a teacher’s arm-span) is measured again with another tool
(e.g., a meter stick) that tends to produce less variation in the resulting
collection of measurements. Students use statistics of center and variation
developed in Units 2,3 to characterize this change, usually in variability
(the precision of the measures) but not in center.
Generalization is promoted further by exploring production processes. A
production process is one with a target value and with variation about the
target value that arises just by chance. In manufacturing, products that are
consistently produced to match target specification are valued. Statistics of
center estimate the tendency of the production process to meet its target
specification. Statistics of variability measure the consistency with which
the target value is attained. Production processes featured in this unit are
Toothpick Factory and Rate Walk. Teachers choose one or more
production process for students to explore. Other production processes can
be found in the Teacher’s Corner of the modelingdata.org website.
Investigating Chance (Data Modeling Curriculum)
Probability relies on intuitions about chance events, but unfortunately, our
intuitions are often misleading. This unit addresses everyday intuitions but
provides opportunities for students to elaborate and revise their intuitions
through investigation of the behavior of simple chance devices. Peering
through the lens of the behavior of these devices, the unit develops probability—the
measure of uncertainty--from two perspectives: long- term trends in outcomes of random
events, also called empirical probability, and analysis of the structure of the devices
producing these
long-term trends, also called theoretical probability. In principle, these two
forms of estimation should converge on common values.
Modeling Measurements
Unit 6 introduces students to building and testing models of the process
that produced the measurements of the arm-span (or other attribute)
generated by the class. The measurement process has two components.
The first is the true measure of the arm-span, estimated by a statistic such
as the mean or median. Real measurements tend to clump because there is
a true measure. The second component is random errors of measurement.
The unit assumes that Tinkerplots is available for use.
Making Inferences in Light of Uncertainty
Building on concepts of sampling distribution and modeling introduced in
the previous unit, students develop models, create model-based sampling
distributions, and then make inferences by comparing the values of sample
statistics to model-based sampling distributions. Investigations include
inferences about claims made about (a) changes in person or
improvements in methods for repeated measure of a person’s arm-span,
and (b) the reality of the power of illusion in a psychophysics experiment
that students conduct. Extensions and formative assessments provide
further opportunities for exploring model-based inference.
Investigating Chance (Our Curriculum)
This unit addresses probability, by examining students’ everyday intuitions then providing opportunities for students to investigate, challenge, and refine their intuitions using both simple and chance devices and Tinkerplots.
