Oxton House Publishers, LLC


Workshop: Math thru Its History

Where? When?

How much?

“How can I help my students make sense of fractions and negative numbers?”

“Some of my students don’t really get place value.  Is there a different approach that might help them?”

Each participant receives a free copy of Pathways from the Past, Set I, a 64-page handbook and set of 19 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 Whole Numbers: Place Value

Learn about our base-ten, place-value system by comparing it with ancient systems — Egyptian, Babylonian, Mayan, Roman — that did not have one or more of its essential properties.

III.  Zero Is Not Nothing: Special Properties of Zero

See the different roles of zero in elementary math: as a place holder, as a number, and as a valuable tool in solving equations.

IV.  Broken Numbers: Fraction Arithmetic

Trace unit fractions back to ancient Egypt.
See how the Babylonians’ of place-value fractions foreshadowed decimals.
Translate the Latin numerator and denominator as “counting parts.”
Connect place value with decimals and percent.

V.  Less than Nothing?: Negative Numbers

How long did it take for negatives to be recognized as numbers?
Why do the rules for signed numbers work the way they do?
What makes ordering negatives puzzling and difficult?
How can patterns guide our thinking about negative numbers?

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

10:30-11:00  Part II, cont’d

11:00-12:00   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 I: Using History to Teach Numbers, Numerals,
and Arithmetic

Writing Numbers in Base Ten

Zero in Arithmetic and Algebra

Fractions, Decimals, & Percent

Negative Numbers

Teach Math thru History

Dr. William Berlinghoff has been teaching and writing math text materials for more than 40 years.  He is author or co-author of 5 college textbooks, including The Mathematics of the Elementary Grades and the award-winning Math through the Ages, and he was Senior Writer for MATH Connections, an NSF-sponsored secondary core curriculum.

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 number sense and understanding of whole numbers, negatives, and fractions.

This workshop’s topics are in the Numbers and Operations parts of the NCTM Focal Points for grades 5 - 8, and are basic to the curriculum and assessment guidelines of most states.  Moreover, fractions and negatives give many students trouble well into high school, limiting their success in algebra and all future work in math, science, business, and the technical trades — in fact, in any field that uses numbers.

Dr. Berlinghoff’s approach implements the spirit of the NCTM’s 2009 document, Reasoning and Sense Making, as well as the Standards for Mathematical Practice if the Common Core.

Teach Math thru Its History

Topics in Arithmetic & Pre-Algebra


by William Berlinghoff, Ph.D.

Some participants’ comments:

“I am very excited to use these [materials] in the classroom.  The info correlates with the standards I teach and are the areas my students struggle with.” (8th grade teacher)

“I love the materials. The activities are well constructed and ready to use with kids.”
(7th grade teacher)

“The presenter was really good at explaining things.” (6th grade teacher)

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