Middle School Math and the Web

A session for Math in Action 2000


The goal of mathematics instruction in the middle grades is to lay a solid mathematical foundation for secondary school and beyond. During this time period, many students will form conceptions about themselves as learners of mathematics—about their interest, their competence, their attitude, and their motivation. These conceptions will influence how they approach the study of mathematics in high school, which will in turn influence their life opportunities.
-- NCTM Standards 2000 draft, Chapter 6 introduction

Oh, is that all? That can be an intimidating mission. Similarly trying to incorporate the Web into your classroom can be intimidating -- it's just too huge to know where to start. This page/session is an attempt to provide an introduction and starting point for investigating middle school mathematics on the web. Associated is a web page with Michigan's Curriculum Framework for Mathematics in Middle School .

This session is in two parts: Part 1 -- resources for the teachers of middle school math and Part 2 -- good mathematics that can be done with access to the web. In general this is either a lesson where the web is the resource for the idea or a lesson where web access is needed for the students to be able to do the lesson.



The National Council of Teachers of Mathematics (NCTM) is certainly one of the best friends a math teacher of any level can have. Their publications include Mathematics Teaching in the Middle School , which is free to members of the NCTM. Samples of their materials are available online. Also online are the current Principles and Standards and the draft for Principles and Standards 2000 . There is a local affiliate, the Michigan Council of Teachers of Mathematics which sponsors many opportunities for collaboration with other teachers and for professional development.

The Math Forum is an amazingly broad collection of links, lesson plans and problems. It offers a student area for exploration and explanation, a teacher area with lesson plans, links, and problems, discussion forums and more. Really the best internet math resource I've seen, with good search facilities also.

The Show-Me Center is a National Science Foundation (NSF) funded project to iprove access to and publicize Standards based curricula. There is a lot of information here for teachers and schools evaluating their own curricula, and for those already using Standards based texts. The particular curricula covered are Connected Math, Math in Context, MathScape, MathThematics, and MMAP. They also provide inservice help and professional development.

The Michigan Department of Education has lots of information, including an education poll , MEAP results and the state Curriculum Framework . The Curriculum Framework for mathematics is closely modeled after the 1989 NCTM Standards. It is broken down by topic ( mathematics ) and then by strand, with distinctions for school level (example: measurement ). I have also set just the middle school strands for math here .

There are many websites which serve as collection points for lesson plans. You have to be a discriminating consumer with these, often sifting through some serious chaff to find the gold. (I know it's a mixed metaphor, but...)
Possibly the best: Middle School Teachers' Place: Collections of Lesson Plans .
The biggest: AskERIC Math .
Broken down by standard: SCORE Mathematics Lessons -- California lesson plans, aligned with their state curriculum framework, which is similar to Michigan's for mathematics.
Somewhat random, but has some good things: SMILE PROGRAM a collection of almost 200 single concept lessons.


The Math

The following are just some sites with neat mathematics. Except where noted, you can get the information from these sites and present it to your class without them needing internet access.

Mega-Math is a collection of really neat, powerful mathematics in a form accessible to many -- certainly to most middle school students with your guidance. Nancy Casey, the Mega-Math webmaster, has some other neat Projects and Investigations in Math . Another site with awesome activities and puzzles is the Centre for Innovation in Mathematics Teaching . At a higher level is Cut the Knot . My college geometry students loved the site, and it has some puzzlers accessible to middle school students.

Weekly challenges to your class can be found at several sites. Most allow for submission of solutions and recognition of those who submit them. Some challenges for your students can be found at Brain Teasers by Houghton Mifflin, although they don't compare to the Math Forum's Middle School Problem of the Week. Another challenge site is Aunty Math . Aunty's problems are very accessible, but she has hints for parents and teachers to present them and connections to the NCTM standards.

Math with the hook of a magic trick is at Mathemagic Activities . These can be performed for students to have them figure the trick out, or the students can present them to each other. There is a similar appeal to having your students can generate their own puzzles at Puzzlemaker's Number blocks and Math Squares . The math squares are an excellent source for order of operations practice.

The Math Forum's web units : these generally do require student access, but has a great variety of topic and level.

I have to put in a plug for my geometry students' websites . This also includes a link to their reviews of more than 50 geometry sites on the web.

If you have public TV in class, PBS has a site with connections and extensions to the math they show at PBS Teachersource -- math .


Concrete ideas

Let's examine a few of the Michigan Curriculum Framework strands and see concrete ways to address them.

Patterns: Describe, analyze and generalize patterns arising in a variety of contexts and express them in general terms.
This can be addressed best by having real life data in which to find and explore patterns. Two good sites for doin this are: The Data and Story Library and Dr. B's Wide World of Web Data . Both provide statistical data for classroom use, sorted by subject and statistics topic. (My education students always seem to find teacher pay by state .) By having students find and analyze their own data set, you also address all the topics in Description and Interpretation . Other examples of these standards can be found in Exponential Functions on the Web from a presentation by myself and Esther Billings.

Patterns: Explore and describe visual and numeric patterns, including linear expressions, near-linear patterns and symmetric and spatial patterns.
An excellent application -- which requires web access for students -- is the project Linear Equations and Housing Prices . Students find prices and square footage of houses in a single market and compare them. Also makes for interesting comparisons between housing markets.

Inference and Prediction: Design experiments to model and solve problems using sampling, simulations and controlled investigations.
Traffic light timing is modeled at this website. There is some work for the teacher to do in explaing the variables used in the model, but the computer simulation enables the students to completely control the simulation.

Shape and Shape Relationships: Use shape, shape properties and shape relationships to describe the physical world and to solve problems.
Tangram paradoxes presents different situations you make with two sets of Tangrams in which they appear to be congruent but can not be. This also addresses
Measurement: Interpret measurements and recognize that two objects may have the same measurement on one attribute (e.g., area) but not necessarily on another (e.g., perimeter).
Area with tangrams (and without formulas) is yet another tangram activity which addresses these.

Collection, Organization and Presentation of Data: Collect and explore data through observation, measurement, surveys, sampling techniques and simulations and Organize data using tables, charts, graphs, spreadsheets and data bases.
The Great Chocolate Experience III (see TEACHER MATERIALS) offers a different opportunity -- to use the web to link your students to others investigating similar ideas. Be sure to follow up with the official M&M scoop . To work off the previous activity, consider the World Records for the Mile (Men) activity. It addresses
Description and Interpretation: Draw, explain and justify conclusions based on data.


Pat's Problem

Students pick historical and natural history locations in Michigan that they would like to visit. They then plan their trip using graph theory to minimize distance, time, and expense. Through this activity, the students will discover graph theory techniques and algorithms and be introduced to related terminology.

Sites that enable this: Michigan Live , a state guide to cities and events, Mapquest , a very flexible mapping site which can give door to door directions and distances as well, Mackinac State Historic Parks with Michigan history and guides to the four historical parks, and Michigan's Historical Center with guides to nearly all of Michigan's historical sites.

Pat's problem strongly addresses
Algebraic and Analytic Thinking: explore problems that reflect the contemporary uses of mathematics in significant contexts and use the power of technology and algebraic and analytic reasoning to experience the ways mathematics is used in society.


What's Next?

The following definitely requires student access to the internet.

Java is a programming language that allows programs to be run over the web regardless of computer type. This is a rapidly growing area which provides many neat hands-on manipulation and visualization. As an example, Java Geometry is a collection of more than 200 java applets at the middle school level. Interactive Physics and Math with Java allows on-line experimenting. (But gives too much away in my opinon! In terms of telling the students the formulas, etc.) A site that allows students to make conjectures is Basic Geometry applets . The father of all java geometry sites (almost literally), though, is Euclid's Elements with Java . If these interest you, try Java Mathematical Activities as a starting point for exploring lots of these. dot

Who's Next?


Seriously! One of the best things about the web is the accessibility. You can write and publish and share your ideas with the world. As Grand Valley's Department of Mathematics and Statistics website evolves, I would like to see it connect to regional leaders in mathematics education. And that's you. One thing to notice as you explore what's there for middle school is the lack of student generated content. When you have them working on projects and writing up results, they can publish it! Most word processing software now comes with a "save to HTML" feature and Netscape's free browser comes with a Web Page Editor (the "Composer" option on the Communicator menu). It's easy! And if I can be of help, just ask. I'm at goldenj@gvsu.edu and www2.gvsu.edu/~goldenj . Or if you find something cool , let me know.