The Other Half
A podcast begun earlier this month promises to explore "the
other half of math — the fun half you might be missing when
you learn math in school, the half that helps you makes sense
of your own life."
Anna Haensch and Annie Rorem first met while pursuing advanced
degrees in mathematics. As they shared an office on their
university campus, they discovered a mutual affinity for that
subject as well as for the social issues of the day ... and
Beyond responding to the perennial student protest that begins
"When am I ever going to use this ...," the two women aim to
bring "much needed lady voices" to discuss everyday scenarios
that can be better understood by thinking like a mathematician.
PoW taking place: math problem-solving moment of the week
"But also because there was an extra side length of the
triangle added to the bottom, we have to subtract 12.85 from
16.18. After subtracting the side lengths, I am left with 3.33
inches. What the 3.33 inches stands for is the side length of
the right side of the smaller triangle. From this information,
I can continue to find the bottom length by using cosine...."
- Pauline, highlighted in the Geometry PoW's Latest Solution
STEM Behind Health
A recent collaboration between Texas Instruments (TI) and The
Sanford Project seeks to dispel disease myths as it advances
science, technology, engineering, and mathematics (STEM).
Freely download the activity files for STEM Behind Health — as
well as trials of TI-Nspire™ for Macintosh and PC
platforms — by scrolling down TI's education technology page:
The collaboration's inaugural activity, "Type 1 Diabetes:
Managing a Critical Ratio," provides interactive simulations
that promote concepts and practices such as
engaging in ratios and proportional thinking
analyzing biological control mechanisms
planning and carrying out investigations
using computational thinking
TI and The Sanford Project have already planned subsequent
topics for similar treatment, including Type 2 diabetes, rare
genetic diseases, and — in time for Breast Cancer Awareness
Month in October — breast cancer.
Now taking place: math education conversation of the day
"I am going to weigh in on the other side of the debate.... I
have watched our Algebra and Geometry teacher struggle the
past two years as she tried to teach two curriculums during
the same year, and she was constantly worried that she was not
doing a good enough job with either. Now that I know that my
students will be tested on the Common Core next year, I can
devote myself to completely understanding the new curriculum
without trying to save some parts of my old curriculum."
- Frank, posted to the secondary (grades 9-12) discussion group
of the Association of Math Teachers of New York State
Building Thinking Classrooms
A math education professor has identified nine elements that
foster student persistence, discussion, participation, and
other indicators of what he calls a "thinking classroom."
"Building Thinking Classrooms: Conditions For Problem Solving"
opens with a story of the failure that came from Peter
Liljedahl's attempt to plug "a-ha!" problems into a seventh
grade classroom. It goes on to present the research behind two
of the elements that emerged after the Simon Fraser University
(British Columbia) professor persevered in observing the class
that got stuck on those "a-ha!" problems and repeatedly
Liljedahl's decade-long study of over 150 high school students
and 300 in-service teachers across all levels revealed that
task adoption and productivity differed significantly
depending on the common writing surface that students shared.
Even the orientation of that work space mattered. The method
teachers used to assign students to group (for educational
goals rather than social ones) also made a significant
difference in cultivating what Liljedahl defines as a place
where students and teachers alike "think collectively, learn
together, and construct knowledge and understanding through
activity and discussion."
Forthcoming as a chapter of a book currently in press,
"Building Thinking Classrooms" lists seven more elements
conducive to thinking classrooms, further rating them
chronologically for impact and ease of implemention.
An early version of Liljedahl's original research into "a-ha!"
moments — what they share in common and what sets them apart
from other mathematical experiences — appears in the article
"The AHA! Experience: Mathematical Contexts, Pedagogical
Implications." It begins on page 141 of the Proceedings of the
2004 Annual Meeting of the Canadian Mathematics Education
Study Group, freely available from the Educational Resources
Information Center (ERIC):
Hat tip to Henri Picciotto for bringing Liljedahl's work to
our attention. Picciotto, regularly featured in these pages,
has blogged about and linked to "Building Thinking Classrooms"
as well as another essay by Liljedahl:
Explore Liljedahl's site for more of his publications,
presentations, and teacher resources such as numeracy tasks,
videos of card tricks to explain, and problems of the week: