Five Representations

Jim Olsen's Home Page
HenryFord Quote
James R. Olsen, Ph.D.
Western Illinois University
Teaching Resources
For Students
Info on Dr. O.

Annual Western Illinois University Mathematics Teachers Conference - April 13, 2018, on the WIU Macomb campus. Join us for this great conference.

Investigations in School Geometry - Fall 2018 Online Course Offering ~ WIU ~ Math 402(G). Click here for details.

Slides [WIU Math Ts Conference] for Look For and Make Use of Structure, Symmetry, and Similarity, presentation at the Annual Western Illinois University Mathematics Teachers Conference, April 13, 2018.

Slides [Math Club] for Some Rich Geometric Diagrams and Connecting the Mathematics Beneath, presentation at the W.I.U. Math Club, April 11, 2018.

Slides [Valpo] for Some Rich Geometric Diagrams and Connecting the Mathematics Beneath, presentation at the TRISECTION MEETING of the Indiana, Illinois, and Michigan Sections of the MAA, March 23, 2018. - this is a new (therefore under construction) web site. This website provides geometry problems which are mathematically beautiful in their own right, and which also help our students reason mathematically, see connections in mathematics, and improve problem-solving abilities.

Mini-Conference on Secondary Mathematics Teaching - Thursday, November 16, 2017 from 5-8 p.m. at the W.I.U.-Quad Cities campus.  This mini-conference is intended for grade 7-12 mathematics teachers. Register for this enjoyable evening of sharing and connecting today. More info here.

Desmos Tools - Workshop at Rock Island ROE, Feb., 6, 2018. Slides - Handout.

Desmos Updates - presentation at the NCTM Regional Conference in Chicago, IL, November 30, 2017. Click here for the Google Slides, which have links.

Percent: From 7RP.3 through College and Career Readiness (.PPT) - presented at the Mini-Conference on Secondary Mathematics Teaching - Thursday, November 16, 2017.

Mental Math Strategies PowerPoint - created and presented for WIU Math Club, 10/4/2017. This is an overview of mental math strategies with seven strategies highlighted.

added 3/2017New SAT Test

added 3/2017SAT / ACT / TAP Preparation Page

STEM through A Wind Turbine

Desmos and GeoGebra Updates - Handouts: page 1; page 2 Illinois Math and Science (ICTM/ISTA) Conference presentation, Oct. 7, 2016 at 4:00 p.m., in Peoria, IL.

Standards Based Grading - presentations at the ICTM Annual Conference, Oct. 24, 2015, at Tinley Park, IL; the W.I.U. Mini-Conference on Secondary Mathematics Teaching, Nov. 19, 2015, in Moline, IL; NCTM Annual Meeting, San Antonio, TX, April 6, 2017 at 11:00 a.m.

TI-73 Graphics Calculator Information

Beauty of Three Dimensional Polyhedra Workshop (in Celebration of the MAA's Centennial) at MAA MathFest, August 7, 2015 (Washington, DC) and at the ISMAA Annual Meeting April 8, 2016 (Illinois College, Jacksonville, IL). Links to the presentation and resources.

Brain-Based Learning and Learning Theories - much has been discovered and written lately -- and this helps us help our students learn.

Math Education Research and a Plethora of Committee and Government Reports - Originally compiled on the occasion of the Common Core State Standards (the reports were the precursors for the CCSS). Updated periodically.

The 24 Percent Tweets project is 24 quick lessons on percent.  Click>>24 Percent Tweets for the information webpage with links. I hope you can use this to teach or learn about percent and its applications.

Mental Math Curriculum Course Specific Mental Math Curriculum - For Eighth Grade and for Algebra I. 30 worksheets each, teaching 30 strategies.  Free download.

CCSSMCommon Core Math Standards: Information, Links, and Resources


24 Percent Tweets

Math Contests at Western Illinois University For Middle School and High School Students - This is as ongoing initiative at W.I.U. Get your students involved!

Mathematics Teacher Education Summit, Saturday, March 1, 2014, 9am – 4pm at Lincoln Land Community College. This teacher education summit is designed to provide updates, networking, and sharing opportunities for all involved in the teacher education process in Illinois. The focus is on the new math standards for elementary ('Part 20') and middle school teachers ('Part 21'). For more information, and to register, see

My Spring 2018 Courses: (Click here for office hours.)

Quizlet Page - Quizlet is a great program (and app for iPad or other tablet) for making flash cards and review materials.

Volume and Surface Area Webpage - Prisms, Pyramids, Cylinders, and Cones

Online Math Games, Demonstration/Exploration Tools, & Puzzles IndexOnline Math Games, Demonstration/Exploration Tools, & Puzzles IndexOnline Math Games, Demonstration/Exploration Tools, & Puzzles Index
       Online Math Games, Demonstration/Exploration Tools, & Puzzles
, organized by grade, K through 12.
       Spreadsheet of All Games ~ ~ Spreadsheet of All Demonstration/Exploration Tools

Navigating the Landscape of Fraction, Decimal, and Percent Problems - Documents, problems, and handouts from our presentations at the Illinois Council of Teachers of Mathematics Annual Meeting, October 22, 2011, the International Conference on College Teaching and Learning, April 8, 2011, and the Western Illinois University Mathematics Teachers' Conference, March 23, 2012.

PFD Boot Camp (Percents, Fractions, and Decimals) and Basic Training.

RATES Project - Real-world Applications Teaching Everyday Solutions curriculum development project

Math Fundamentals - How ~ Why ~ Games ~ Practice

My PowerPoint on the Berlin Wall.

I am a professor in the Mathematics and Philosophy Department at Western Illinois University. I teach mathematics courses and teaching methods courses for prospective and practicing teachers. My research interests are student understanding of the function concept, educational uses of technology, and problem solving. For more detailed information, click Info on Dr. O.

Some things which have caught my interest lately are:

  • The Five Star Representations - These are five good categories of representations of mathematical ideas (physical, verbal, analytic/algebraic, numerical, graphical). Dr. Mann and I often emphasize the benefits of these five representations for enhancing student understanding of concepts. They are also found in a wonderful lesson titled, Using Linear Equations to Define Geometric Solids, found here.
  • Henry Ford Quote - Dr. Thomas quoted Henry Ford in his state of the university address on 8/17/17. This principle certainly applies to teams. In addition, and perhaps more importantly, we need individuals from our society's diverse groups, and even political parties, to learn how to come together to work together, to better our society.
  • The WIU Women's Basketball team is having a great year. Update: They are outright Regular Season Summit League Champions and also Conference Tournament Champions. Follow them online or twitter (@WIUWBB). The NCAA National Tournament (aka Big Dance) is next. Go Leathernecks!
  • The WIU Women's Basketball team members were asked what it meant to be a Leatherneck and this is what they came up with. Tweet. These are good words for all of us,WIU Team words living our daily lives. (click at right)
  • Jason Allemann is a LEGO Artist. He makes lots of really neat things, including models with moving (and motorized) parts with gears and pullies. LEGO is a great, fun, learning tool/toy. Many STEM concepts can be learned via LEGO. Jason's website is He's on twitter at @jasonallemann. For us mortals, we won't be able to create things on Jason's level right away, but we can learn much from his videos. Then we can get out the LEGO and start playing and creating.
  • There is much good information in the Sketchnote by Tanmay Vora @tnvora. I was particularly interested in interleaved learning. See this page ( for more information and links.
  • Top Graphics: (a) Western Illinois University has 12 Signature Programs. WIU is a great place for students to further their education and prepare for life and a career. (b) The National College and Career Readiness Indicators website was created by the AASA. Their Redefining Ready! campaign is a national campaign to introduce new research-based metrics to more appropriately assess that students are college ready, career ready and life ready. The campaign is a response to dismal college and career readiness scores reported by standardized test makers that fail to portray a comprehensive picture of student potential.
  • We are in a very difficult situation here at W.I.U., but we are staying positive. The State of the Student Address video shows that our students are remaining positive andproud about Western's future and the student learning that continues. I recommend watching the video. Speakers included (1) SGA Speaker of the Senate Jacob Tomlinson, (2) WIU Student Trustee Michael Quigley, and (3) SGA President Wil Gradle. The address was given March 9, 2016.
  • The Amazon company is launching a national movement to eradicate the fear math imparts in many U.S. students and get them to adopt the growth mindset ( I have two webpages ("Everyone Can Learn") also touting the Growth Mindset. It's time to put an end to the phrase, "I am not a math person," and get everyone to adopt the growth mindset (the truth of which has been proved by learning and brain researchers) and get rid of the fixed mindset. Check out my pages for videos and information on the growth mindset.
  • Geodesic Domes are real cool. You (and a group of people) can make one in less than 2 hours out of newspaper and masking tape. The AlWood Science Club built one. I've built them with teachers and with students. To learn how click here. To learn more about Geodesics Domes and Spheres Page click here.
  • Wir sind ein Volk (We are one people) - In 2015, a 2 Euro commemorative coin was released commemorating the 25th anniversary of the reunification of Germany. The Berlin Wall going up, and coming down, in my lifetime is a big deal. The coins show people celebrating in front of the Brandenburg Gate, in Berlin. Also on the coin: on the edge of the coin: EINIGKEIT UND RECHT UND FREIHEIT (Unity and Justice and Freedom), 25 Jahre Deutsche Einheit 2015 (25 years of German Unity25 years of German Unity). A number of years ago I made a PowerPoint on the Berlin Wall, chronicling the history of the Wall (my perspective). Berlin is one of my favorite cities. The Wall came down in 1989 and Germany was reunified in 1990. I have the 2 Euro coin and a LEGO model of the Brandenburg Gate in my office. Stop by and see it.
  • MAA Centennial - The MAA MathFest (which has been an annual event for years) will be extra big this year because it will be the Centennial Celebration of the MAA. It will be held August 5-8, 2015 (twitter). MathFest will be held in Washington, DC. I'm doing a workshop at MathFest. Workshop Info here. Workshop Webpage here.

WIU Home Page ~ Department of Mathematics and Philosophy ~ MRO

James R. Olsen, Ph.D.
Mathematics and Philosophy Department
Western Illinois University
1 University Circle
Macomb, IL 61455
phone: 309/298-2317
Page URL:  or
Old (past) announcements archive.
updated: April 12, 2018
QR Code

The ultimate goals of mathematics education are to find meaning and to solve problems.

Love ~ Learn ~ Engage ~ Empower

Counter since 9/17/05

Frank and Ernest (comic), by Tom Thaves, is often subtly profound with a light-hearted approach. "You just need an outlet" - which provides power - has meaning on multiple levels.

You Just Need an Outlet