Pathways from the Pastis a pair of teacher’s manuals and two sets of activity sheets
for helping students master various topics in arithmetic, pre-algebra, and algebra.
Building on ideas from their award-winning book, Math through the Ages, Drs. Berlinghoff
and Gouvêa have crafted teacher-friendly tools for helping students understand basic
topics that often cause trouble. Their approach implements the spirit of the NCTM
document, Reasoning and Sense Making, as well as the “Standards for Mathematical
Practice” of the Common Core State Standards for Mathematics (CCSSM). The first
Pathways from the Past
I: Using History to Teach Numbers, Numerals, and Arithmetic
This is a 64-page manual and a set of reproducible masters for 19 two-page activity
sheets. Its topics are basic to the curriculum and assessment guidelines of most
states and are in the Numbers and Operations parts of the NCTM Focal Points for grades
5 - 8.
Each of the four major chapters is organized like this:
Its mathematical focus is stated first.
“Historical Connections” lists the relevant regions and time frames.
A summary of the historical ideas comes next.
A section for each Activity Sheet starts with its main mathematical ideas and its
pedagogical purpose, followed by a detailed solution for each question.
Chapter 1 links up well with the “ancient civilizations” part of any social studies
curriculum. Chapters 2, 3, and 4 explore how the mathematics of earlier non-Western
cultures can provide alternative ways to understand some often troublesome ideas
about fractions and negative numbers. The activity sheets for all four chapters
encourage students to practice essential skills by presenting them in novel contexts.