Oxton House Publishers, LLC


Teach Algebra thru Its History


by William Berlinghoff, Ph.D.

Workshop: Algebra thru Its History

Where? When?

How much?

“Some of my students don’t understand what algebraic symbols mean . Is there a different approach that might help them?”

“How can I help my students see that algebra is more than just a bunch of rules for pushing symbols around?”

Each participant receives a free copy of Pathways from the Past, Set II, a 72-page handbook and set of 18 reproducible student activity sheets.

I.  History in Math Class: First Thoughts

Why should I use history?  How will it help my students learn the math they need?  What do I need to know before I start?

II.  Writing Algebra: Using Algebraic Symbols

This part focuses on interpreting and using algebraic notation.  Working through the evolution of some of our most basic symbols gives students a clearer picture of what they mean and how they help to clarify ideas.

III.  Linear Thinking: Ratio, Proportion, and Slope

Linearity, the preservation of ratio, is one of the truly foundational ideas in all of mathematics.  Its value in commerce and many trades spawned methods for utilizing its power without algebra.  Examining some of them from an algebraic perspective deepens students’ understanding of linear functions and equations.

IV.  A Square and Things: Quadratic Equations

Solving quadratic problems was an important part of mathematical lore many centuries before polynomial manipulation was even considered.  This part examines some ways in which people dealt with quadratic problems before the development of symbolic algebra, and it connects those ways with our current algebraic methods.

V.  Cubics and Imaginaries: Third-Degree Equations

This part traces the pursuit of a very difficult problem — finding a general solution for third-degree equations — from its roots in Greek mathematics to its final resolution in 16th-century Italy.  The quest for that solution was the motivation for constructing the complex numbers, which provide a powerful link between algebra and the geometry of the plane.

The Day

8:00-8:30  Continental Breakfast

8:30-9:15  Introduction & Part I

9:15 - 10:15 Part II

10:15 - 10:30 Break

10:30-12:00   Part III

12:00-12:45  Lunch

12:45-2:00  Part IV

2:00-2:15  Break

2:15-3:15  Part V

3:15-3:30  Closing Comments

6-hour professional development
Certificates of Attendance
 will be provided.

Set II: Using History to
Teach Algebra

Symbols Then and Now
Quadratic Equations
Cubics and Imaginaries

Teach Algebra thru History

Some participants’ comments:

“I would recommend this workshop to any high school math teacher.”

 “This was a great workshop.”

“This material is something that I can see fitting into various grade levels .”

The value of algebra in a high school education is directly proportional to its effectiveness in enhancing the student’s ability to think clearly and reason effectively.  For most students, knowing how to manipulate symbols is far less important than understanding the underlying ideas. The Common Core State Standards assert the importance of this conceptual understanding, both in the algebra standards and in the broader Standards for Mathematical Practice.

Dr. William Berlinghoff has been teaching and writing math text materials for more than 40 years.  He was the Senior Writer for MATH Connections, an NSF-sponsored secondary core curriculum, and is co-author of the award-winning book, Math through the Ages.  In this full-day workshop, Dr. Berlinghoff guides you through a series of history-based activities that you can use with your students to strengthen their ability to think clearly and reason effectively as they learn algebra.  His approach reflects the standards of the Common Core and the spirit of the NCTM’s 2009 document, Reasoning and Sense Making.

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