Jun 27

Using Rich Problems for Differentiated Instruction

This is a good paper describing the use and characteristics of rich problems.

(The teaching method here is Teaching With Tasks.)

Has 3 examples of rich problems

  • First is rich and fairly basic and doable.
  • Second is excellent. #differenceofsquares (I like this one the best. 😀) 
  • Third is quite open-ended.

The article does a nice job of showing how instruction and (formative) assessment go hand-in-hand.

Finally, and perhaps most importantly, it has good mathematics.

Apr 17

Hidden Figures Curriculum for Schools

Check out http://mentalfloss.com/article/94297/hidden-figures-coming-classrooms

Free download of a curriculum based on the movie Hidden Figures.

Mar 29

Technical website note

I have disabled the comment feature of this website.  I do welcome feedback and comments on this website. Please use the phone, twitter, or email to comment on this website.

Mar 02

Educational technology that helps kids learn — and doesn’t

Good Article:

Silicon Valley teacher: Don’t confuse educational technology that helps kids learn — and doesn’t


Mar 02

Spring Math 304 Websites

Here are the websites of students in Math 304 at WIU in Spring 2017

These contain many ideas for how to make learning math meaningful our students. More will be added as the semester progresses.

Here’s one more — from Julie. She’s doing some things similar to the Math 304 students.

Feb 18

Weebly and other Internet/Web notes

My top 3 sites for creating free websites are WordPress, Blogger, and Weebly.

I have a fairly big section on my Teacher Resources page titled:

Web Page Development, Internet Stuff, Computer Hints, Graphics, Music, & Software ‘n Fonts

Check it out for more info.

Feb 14

Website Evaluation Form Here

Here is the Website Evaluation Form (.docx):  WEB SITE EVALUATION Form

Jan 27

Apply for the ICTM Scholarship

The Illinois Council of Teachers of Mathematics gives scholarships each year. We have had WIU math majors will the scholarship.



Jan 16

Welcome Spring 2017 Math 304 Students


I welcome the spring 2017 Math 304 students. I look forward to working with you.

Three Websites for This Course

We use three websites for this course

My Other Key Webpages

Nov 19

The CCSSM, and now the new SAT, have Moved the Needle


Two days ago I was at an excellent presentation on the new SAT test. It was at the WIU Mini Conference on Secondary Mathematics Teaching. For the second time in 3 years, I experienced, in one 40-minute presentation, a paradigm shift.

I was very impressed by what I saw with the new SAT. I feel that the new SAT very much reflects the philosophy of the Common Core authors, while at the same time creating a realistic assessment instrument. (I would welcome those that would argue against either claim.)

Here I’ll make some observations about the new SAT and comment on how I want to adjust my teaching.

I think the new SAT expects students to: (show the following important characteristics of successful mathematics students):

  • Make sense of problems and persevere in solving them,
  • Reason abstractly and quantitatively (in particular, the decontextualize and recontextualize process for word problems),
  • Apply, and model with, mathematics.

Quick aside on assessment: The College Board (who produces the SAT) has the advantage of the ‘second golfer to putt on the green.’ (If you putt second, you can watch, and learn from, how the ball broke for the first putter.) The PARCC test also reflected the philosophy of the CCSS, but they tried to ‘create the perfect storm,’ from an assessment point of view. Assessment is very difficult! The PARCC test (which I support, from a philosophical point of view), to a large extent has crashed and burned. Mathematically, it’s OK, but their expectations, from an assessment point of view, were unreasonably too lofty.

SAT Design

The SAT is designed to measure the essential ingredients for college and career readiness and success.


Much of what is emphasized on the new SAT is applications* of important fundamental concepts from middle school and elementary algebra (as we see in what follows). *There is an emphasis on multi-step word problems from real-world contexts.  It is useful to look at sample items.

The Page 84 ‘Note’ from the CCSSM (the ‘needle has moved’)

In the appendices of the Common Core State Standards for Mathematics it states:

“…Indeed, some of the highest priority content for college and career readiness comes from Grades 6-8. This body of material includes powerfully useful proficiencies such as applying ratio reasoning in real-world and mathematical problems, computing fluently with positive and negative fractions and decimals, and solving real-world and mathematical problems…”

This is born out in the new SAT. More and more of the mathematics education community (everyone involved with the teaching of mathematics) is understanding this shift of emphasis. I concur.

The (138-word) Description of the SAT Math

Math that Matters Most

The Math Test focuses in-depth on three essential areas of math: Problem Solving and Data Analysis, Heart of Algebra, and Passport to Advanced Math.

Problem Solving and Data Analysis is about being quantitatively literate. It includes using ratios, percentages, and proportional reasoning to solve problems in science, social science, and career contexts.

Heart of Algebra focuses on the mastery of linear equations and systems, which helps students develop key powers of abstraction.

Passport to Advanced Math focuses on more-complex equations and the manipulation they require.

Current research shows that these areas are used in a wide range of majors and careers. The redesigned SAT also includes questions on other topics in math, including the kinds of geometric and trigonometric skills that are most relevant to college and careers. (Learn more about the Math Test.)

I am especially happy to see ratios, percentages, and proportional reasoning.

36 of the 58 questions on the Math Test are are in the Problem Solving and Data Analysis and Heart of Algebra (and 22 questions from other areas and higher math).

Heart of Algebra

  1. Linear equations
  2. Fluency

Problem Solving and Data Analysis

  1. Ratios, rates, proportions
  2. Interpreting and synthesizing data

Kahn Academy Practice

It was emphasized (in the mini conference presentation) that for the new SAT, the college board is in favor of making preparation materials (including practice items) available for free. They have partnered with Kahn Academy to provide preparation materials.

What I plan to change in my teacher education content courses

I like to start the course with a problem-solving unit. I will continue to so, but the unit will change. The problem-solving strategies I’ll emphasize/teach will be:

  1. Look for a pattern.
  2. Look at a similar-easier problem.
  3. Dimensional analysis (use the units)
  4. Use multiple steps (use sub-goals)

The problem-solving unit will dovetail directly into the Problems-of-the-Week (POWs).

There needs to be more emphasis on multi-step problems (from real-world contexts).

Extra Info

Multi-step Contextual Problems and PARCC

From the PARCC evidence tables for the Math III test:

“HS.C.CCR Solve multi-step…7-RP.A.3, …8-EE…”

“HS.D.CCR Solve problems using modeling…7-RP, 8-EE, 8-F…”

“F-Int.3 Solve multi-step contextual word problems with degree of difficulty appropriate to the course, requiring application of course-level knowledge and skills articulated in F-TF.5, F-IF.B, F-IF.7, limited to trigonometric functions.” Comments on this at another point.



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