What are some resources for teaching about scatter plots?

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This question was posted to the Numeracy list (numeracy@world.std.com) and what follows are some ideas and suggestions for teaching about scatter plots or diagrams.

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Date: Fri, 30 Sep 2005 10:56:33 -0400
From: Esther Leonelli <eleonelli@ndecboston.org>
To: numeracy@world.std.com
Subject: Seeking lessons on scatter diagrams

Please respond to the list as I think this would be of interest to members of this list. Thank you. Esther

Original Message-----


From: jataylor mailto:jataylor@utk.edu
Sent: Wednesday, September 28, 2005 10:35 AM
To: eleonelli@ndecboston.org
Subject: scatter diagrams


Hello Esther, I have a question from a teacher, and I was wondering what you or the numeracy listserv might recommend. Here is her question:

"One of the Official GED Practice Tests has two questions that require understanding scatter plots. We use both the Steck-Vaugh and Contemporary series, and neither covers this skill. Does anyone have a source for an actual lesson on this? I have printed some things off internet sites, but they are explanations and not work to apply the skill."

Do you have suggestions for classroom activities that might help teachers help learners better understand scatter diagrams?

Thanks so much,

Jackie



Date: Sat, 01 Oct 2005 14:30:26 -0500
From: Fancher Wolfe <Fancher.Wolfe@metrostate.edu>
To: numeracy@world.std.com

This is an excellent resource:

Rossman, A., Chance, B., & von Oehsen, J. (2002). Workshop Statistics: Discovery with Data and the Graphing Calculator 2ed. Emeryville, CA: Key College Publishing.

For a good beginning discussion of scatter plots see pages 161 ff. Any other questions, please write me. Also graphing calculators handle scatter plots. Regards Fancher


Professor Emeritus Fancher E. Wolfe, Ph. D. Metropolitan State University Department of Mathematics 1501 Hennepin Ave. Minneapolis, MN 55403 Office Phone 612-659-7155 Cell Tel. 612.598.8359 Home Tel. 952.544.5105



Date: Fri, 30 Sep 2005 13:13:32 -0400
From: Ed Wall <ewall@umich.edu>
To: numeracy@europe.std.com
Subject: Re: Seeking lessons on scatter diagrams


Well, in a sense, all plotted point data is a scatter plot. An 'official' definition of a scatterplot is "the graphical representation of a joint distribution." In somewhat English this means roughly, for example, that you have some data that can, more or less, be sorted by two characteristics - e.g. height and weight. If you plot this in two dimensions with height on one axis and weight on another you will get a 'scattering' of points. At this point you tend to ask questions about regression and/or correlation.

Anyway, when I use Google for lessons for scatter plot or lessons for scatterplot, I get a number of lesson plans. Here is one from the NCTM, for example http://illuminations.nctm.org/index_o.aspx?id=125

On the other hand this may not be what you want sice I have no idea what a scatter diagram is.

Ed Wall


Date: Fri, 30 Sep 2005 14:21:08 -0400
From: Ann Williams <amwilliams@forsythtech.edu>
To: numeracy@europe.std.com
Subject: Re: Seeking lessons on scatter diagrams

Scatter plots, or scatter diagrams, would be discussed in most current textbooks for college algebra or elementary statistics with exercises for looking at data graphically. The ideas are simpler that those courses suggest.

One useful activity at any level of instruction is to have the students measure height and length of armspan. I would suggest using metric measure for one and inches for the other. This collection of data is naturally paired by a height and an armspan of an individual student. One scale can be drawn horizontally and used to represent one of the measurements and another scale drawn perpendicular to the first, or vertically, and used to represent the other measurement. A single point will locate on the resulting grid the height and armspan for each student. With proper labeling, the scatter plot is constructed. All kinds of comparisons can then be made visually as well as looking for a relationship between the two variables, height and length of armspan, for the group as a whole. Students usually are very cooperative with this activity. Many skills are reviewed in the process in addition to the new idea of a scatter plot for representing data visually.

Enjoy.
Ann

Ann M. Williams Mathematics Department Chair Forsyth Technical Community College 2100 Forsyth Technical Community College Winston-Salem, NC 27103 336.734.7398 amwilliams@forsythtech.edu



Date: Fri, 30 Sep 2005 20:47:53 +0300
From: iddo@research.haifa.ac.il
To: numeracy@world.std.com
Subject: Re: Seeking lessons on scatter diagrams

For Jackie's teacher -

I doubt there is a specific lesson plan on scatterplots because it is not a topic that normally gets a lesson all by itself - scatterplots are a visual display which is part of larger topics.

If the intention is to help students see linear (or nonlinear) relationships between variables, especially when learning about correlation (and regression), you'd emphasize ability to detect and udnerstand positive and negative relationships, or strong and weak relationships, among various other things.

But if you want to discuss how relationships between two variables can be examined or displayed, scatterplots can be viewed as a variant on histograms or line and bar graphs which also can display relationships between two variables, albeit in different ways, so again do not stand on their own.

The upshot: what and how you teach about scatterplots depends on what you want students to derive from learning about them. Your lesson plan will be different depending on your larger agenda. It thus pays to analyse the knowledge demands of the GED materials and from it derive learning needs and a teaching plan.

I'd suggest two resources.

(1) several internet-based resources have basic info about scatterplots in the context of correlations. One of them is "Statistics: Power from Data!" a book published online by Statistics Canada:
http://www.statcan.ca/english/edu/power/toc/contents.htm

This is a modified version of the Australian book, "Statistics: A Powerful Edge!", (published online by the Australian Bureau of Statistics, ABS. The Canadian book is more detailed, and aimed primarily at secondary students but is written in an accessible language making it of interest to students in other context and to adult educators and the general population. It has been created using comments from teachers about topics they would like to see covered, and includes exercises and lesson plans as well.

(2) More broadly, it is worth browsing some of the links offered by the International Statistical Literacy Project (ISLP): http://course1.winona.edu/cblumberg/islphome.htm

The ISLP is your best single point of contact resource to online statistics education materials worldwide, created by the Int'l. Association for Statistical Education (IASE),and presently hosted by Winona University (hence the somewhat obscure address).

When you enter the ISLP website, click on "List of ISLP Resource Webpages"m and you'll see a list of different target populations. One of them is "Adult educators", from which I took the above link to the Stat Canada web site. But info on scatterplots is likely to pop up in the resource listings for high-school and even elementary school students, because scatterplots are a basic display. So it makes sense to browse some more.

If you do find something of interest, let us know.

Iddo Gal


Date: Fri, 30 Sep 2005 13:30:28 -0400
From: Orla Hegarty <ohegarty@gmail.com>
To: numeracy@world.std.com
Subject: Re: Seeking lessons on scatter diagrams


I teach this in my intro stats class. The activity at this site: http://www.pbs.org/safarchive/4_class/45_pguides/pguide_702/4572_firstpeople.html is a good backgrounder.

A scatter plot can be developed with the data (bone length vs height - choose only one bone to measure). The scatterplot that is developed should confirm/negate the proposed ratios from this site - remember to develop one scatter plot each for men and women since the ratios are different :).

Don't forget to emphasize what a scatterplot with no apparent relationship looks like. I would suggest developing a scatterplot with both the female and the male data on it to demonstrate this.

Cheers,

-- Orla Hegarty Continuing Education Instructor Ryerson University (orla@ryerson.ca) Toronto, ON Canada


Date: Sat, 1 Oct 2005 05:49:08 -0700
From: Steve Sparling <sparling@loudpipe.com>
To: numeracy@world.std.com
Subject: RE: Seeking lessons on scatter diagrams

Hi Jackie

A few years ago I taught scatter diagrams to a group of fifteen year old rather reluctant learners. I got my hands on some scales and some metre sticks. We, as a class, decided to weigh each student and measure height as well. We also decided to use pounds and inches (rather than kg and cm). Participation was optional to avoid those embarassed by their weight. I asked if we should put all of us together or separate the data by gender. this led to an interesting discussion and we decided to do both. Once the data was in we plotted the whole group (height vs weight) as well as the gender plots. We discussed trends and outliers and all of those good things.

The above experience gave the students a feel for where data comes from etc. I followed up with some data I got out of books and we plotted that data too. A good introductory statistics book will have lots. If you have access to spreadsheet programs you can illustrate how technology can be used to generate scatter plots. I used the TI-83 with an overhead projector to show how it can be done (it is important for students to do a number by hand).

In the discussion I introduced the idea of correlation coeficient. Even though this was well beyond the curriculum it does give a number to what they see. I referred them to a correlation coefficient game that I installed on my web site (long since deleted) but I see a copy of the game at the following site: http://www.stat.uiuc.edu/courses/stat100/java/GCApplet/GCAppletFrame.html

This game proved to be very popular and the students became quite competative. by the end they could look at a scatter plot and pass pretty good judgement on it.

I hope the above helps.

Steve Sparling Campbell River


Date: Mon, 3 Oct 2005 14:24:25 -0400
From: Peter Timusk <ptimusk@sympatico.ca>
To: numeracy@europe.std.com
Subject: Re: Seeking lessons on scatter diagrams

I am a teaching assistant in basic university statistics courses. I help teach engineers, science students and business students. Teaching them sensible graphing using a ruler(choosing the right intervals etc and axis) and graphing using a software such as Minitab or SAS is what we do. We generally teach this with linear regression. This seems to make a good solid end to scatter plots. Regressions are powerful and for general use can be affective. They are also too powerful for some uses as these models can be misused. We try to teach this too about the validity of a regression model. There are more advanced course in just regressions.


Again I would suggest a basic statistics textbook from university for this work.

Peter Timusk, B.Math, just trying to stay linear. Read by hundreds of lurkers every week.



Date: Tue, 4 Oct 2005 12:28:22 -0400
From: Esther D Leonelli <edl@world.std.com>
To: ANN Numeracy List <numeracy@world.std.com>
Subject: Re: Scatter plots

This suggestion was sent to me off-list by a list member:

There is a book by Contemporary, "Top 50 Math Skills for GED Success." The lesson pn page 76 is called, "Understand Line of Best Fit." I see there have been some good lesson ideas on the list, too. Have fun.


Esther, Moderator, Numeracy list


Date: October 8, 2005
From: Jackie Taylor <jataylor@utk.edu>
To: Numeracy wikiteers
Subject: Thank You!

Hello Everyone,
Thank you so very much for all of the resources and ideas for teaching with scatter plots! I really appreciate the assistance and taking the time out of your busy schedules to share. I am glad to see this in the Numeracy area of the ALE wiki, so that others may benefit.

Below are two suggestions emailed to me off-list:

  • "One of the NCTM Navigations series is on Data Analysis beginning with pre K

through grade 2, 3-5, 6-8 and 9-12. The 6-8 book includes a section that gives a description of all the different type graphs, the data used for each one, and the advantages and disadvantages of each. Activities for Exploring Bivariate Data (Scatterplots) are in the 6-8 book. I use many of the activities in this series including several from the pre K - 2. All the activities are excellent and are great for adults."

Practitioners shared a few ideas on the Tennessee discussion list:

  • I've just been searching through the science and numeracy special collection at http://literacynet.org/sciencelincs/ , but I didn't find anything specific to scatter plots. I think I may have come up with an idea of an easy way to illustrate it though. You could have students chart the price of gasoline at several different stations for several days in a row. Put the price on the vertical axle and the days on the horizontal. Make the vertical axle expansive enough on either side of the data that the data will tend to bunch. If you do a couple weeks worth of data, there should be a trend that would show up on this scatter plot. Wouldn't that do it? (PS: I wasn't a math major, but this sounded like a fun exercise. Hope I'm not way off base!)
  • Smart Solutions: Measurement and Data Analysis from New Readers Press (1996) also has lessons on scatter diagrams
  • I could not find anything on this either so, I made up a data set of dance club heights and weights and let the students plot the points. Then I explained and let the plot another set.


Thanks again, and best wishes,

Jackie Taylor
Program Coordinator
Center for Literacy Studies at the University of Tennessee
600 Henley Street, Suite 312
Knoxville, TN 37996
http://cls.coe.utk.edu/
jataylor at utk.edu

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