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Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Data
- Population (in data analysis)
- Random sampling
- Association
- Repeated experiment
- Statistical question
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In middle grades, students examined the processes for generating data and making calculations from data, and they continued these processes to a degree in Algebra I. In Mathematics for College Statistics, students learn about appropriate statistical design for the first time. While some terminology may be unfamiliar to students, these ideas can be related to familiar topics.- When determining the design of a statistical study, students should first decide the type of conclusion that will be made. In order to infer a causal relationship, the design should be based on an experimental study. In order to show a link or an association, the design can be based on an observational study.
- Instruction includes that observational studies should include random sampling in order to select participants, and participants in an observational study are typically given a survey or are asked questions about their opinions or events that have already occurred. Again, an observational study can lead to a conclusion that there is a link or an association between variables.
- Instruction includes experimental studies that are designed such that participants are
randomly assigned to different groups (at least two or more). Different aspects to be
discussed with experimental studies include treatment groups, control groups, placebos,
blinding and double-blinding. An experimental study can lead to a conclusion that there
is a cause-and-effect relationship among variables.
- A treatment group is a group in an experiment that receives the treatment of interest.
- A control group is a group in an experiment that does not receive the treatment of interest.
- A placebo is something that may be similar to the actual treatment but should have no effect on the subjects taking the placebo.
- Blinding occurs when the subjects in the experiment are not aware of which group they are in, or even that other groups exist in the experiment.
- Double-blinding occurs when the subjects in the experiment are not aware of which group they are in, nor do the individual collecting data know which group the subject is in.
- Instruction includes discussions on what questions should be asked, how questions should be asked, the data that will be generated, how this data will be generated and ethics that may be involved in certain observational studies or experimental studies. There should also be a discussion of the advantages and disadvantages of each of these types of statistical study designs.
- Avoiding measurement bias, sampling bias and the presence of non response bias in surveys should be addressed during instruction.
- Instruction includes identifying the benefits of large sample sizes.
Common Misconceptions or Errors
- Students may have difficulty when determining which type of study may be more appropriate for a particular statistical question.
- Students may have difficulty when identifying and including all of the necessary aspects in designing a study.
Instructional Tasks
Instructional Task 1 (MTR.2.1, MTR.7.1)- Suppose that a college professor would like to show that there is a link between using the on campus tutoring center and earning passing grades in college algebra classes taught at her
college.
- Part A. What type of statistical study should the professor use? Explain.
- Part B. How should she design her study? Be specific in the elements that should be present.
- Part C. What questions should be asked of participants, and what type(s) of data would be produced?
- Part D. Suppose that the data show that students who utilize the on-campus tutoring center three or more times in a semester are more likely to earn a passing grade in college algebra. What conclusion can be made?
- Part E. What if the professor wants to show that utilizing the on-campus tutoring center leads to earning passing grades in college algebra; would this study be able to show this result? What changes, if any, would need to be made, and what elements would need to be added in to the statistical study?
Instructional Items
Instructional Item 1- Suppose a pharmaceutical company wants to show that a new medication will reduce the number of migraines in patients who suffer from severe migraines. How could the company design a statistical study to possibly show this? What questions should be asked, and what conclusions could be drawn?
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Lesson Plans
Perspectives Video: Professional/Enthusiast
Problem-Solving Tasks
STEM Lessons - Model Eliciting Activity
Can your school use $5000? What school doesn't?! Well, the money is available, but the student body must decide how the money will be spent!
5K and No More - Producing Data will enable students to fantasize about what they would do to improve their school if allowed to answer the question, "How would $5000 best be spent at your school?" The activity begins with students distinguishing the differences between a sample survey, an experiment, and an observational study through a pre-activity. After this, the students are given five (5) scenarios in which they must discuss the pros and cons of each. In life we want things to be fair, so students must constantly think about bias. The company in this MEA desires the most efficient and effective way to collect information from the students without having to talk to everyone ... who has that kind of time!
Now, just when the students have found the most efficient and effective way to get students to share their thoughts on where the money should go, more information is revealed about the High School. How do we account for the brains and the brawn, the perfect attendee and the most missed days, or for the goth or skater?
Your Savvy Statisticians in the making will figure it out and tell you ALL about it.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
Student Resources
Problem-Solving Task
The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.
Type: Problem-Solving Task
Parent Resources
Problem-Solving Task
The purpose of this task is to assess (1) ability to distinguish between an observational study and an experiment and (2) understanding of the role of random assignment to experimental groups in an experiment.
Type: Problem-Solving Task
