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Mathematical notes

The purpose of this page is link to documents to inform educators and others on information to facilitate mathematical literacy. Information is organized in four broad areas:


Knowledge base & pedagogical tools for mathematical literacy

Knowledge base

The mathematical knowledge base includes concepts necessary for learners to conceptualize to become mathemtically literate and misconceptions that must be over come. Includes concepts, outcomes, & vocabulary by content, processes, and attitudinal (values & dispositions) dimensions by levels.
Math knowledge base diagram

Information to facilitate mathematical literacy & tools to achieve it

Different fields of mathematics map & explanation video (11:05)


Map of mathematics


Resources for professional development

Math teacher's planning tool box

General planning

Planning information

Examples to prep intended learnings

Suggestions for selecting problems and investigations

Sample parts and pieces of sequence plans

Activity plans

  • Estimating chocolate chip | Has potential, but needs a lot more information for integration of mathematical dimensions and extended activities.

Assorted tools


Sample assessments


Workshops, courses, tutorials


Technology, computer programming, software, 3D printing

--- Coding software ---

Mozilla free

Google free


  • History of the cell phone Read... Cell phone mathematics. The story of how Brad Parkinson used creativity and mathematics to enable the use of cell phones.

Math software

Coding resources

Pedagogical resources

3 D printing




Page Overview



girl with beach ball


There are 10 kinds of people in the world. Those who understand binary and those who don't.


Jeffery Weld asks:

Why is it whenever students don't do well on a national test the news agencies report one or a few particular items that were on the test by stating the test questions, then they believe it is necessary to provide the answers.


If their listeners need the answers, why should we expect students to be able to answer it correctly?


The Jibaro Indians of the Amazon rain forest express the number five by the phrase:
"wehe amukei,"
"I have finished one hand,"

and the number ten by
"mai wehe amukei,"
"I have finished both hands."

Frank J. Swetz


"These landmarks must not be treated as objectives to be marked off. The goal is to mathematize not pass landmarks. Enjoy the journey create systems to do mathematics with the knowledge that students have. One should recognize the fallacy of thinking there can be one activity or sequence of activities for all students."

Catherine Twomey Fosnot & Maarten Dolk in Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction


One of the universal customs that man has successfully established on earth is the
Hindu - Arabic numerals
to record numbers.


Math is meditation for thinking about the world.


Geometry is the science of correct reasoning on incorrect figures.

George Polya


Galileo was put under house arrest and allowed visitors, but no mathematicians.





Mathmaticians think about more than math.

Earth will run out of the basic resources, and we cannot predict what will happen after that. We will run out of water, air, soil, rare metals, not to mention oil. Everything will essentially come to an end within fifty years. What will happen after that? I am scared. It may be okay if we find solutions, but if we don’t then everything may come to an end very quickly. Mathematics may help to solve the problem, but if we are not successful, there will not be any mathematics left, I am afraid!

Mikhail L. Gromov, 2010


U.S. Students

Score in the top tier on
the PISA 2012 Math Creative Problem SolvingAssessment


Layne and Ben