Friday, October 24, 2014

Benjamin Banneker Week

By Brea Ratliff, RME Secondary Mathematics Coordinator

For many students, mathematics is viewed as a faceless, and sometimes meaningless, course of study, but learning more about the fascinating and prodigious minds who have shaped the subject can be inspiring. In the face of doubt, criticism, failure, and even seemingly impossible circumstances, many great men and women have been intellectual trailblazers whose extraordinary contributions to society are a testament to the power and importance of teaching mathematical processes and critical thinking. One such individual was African-American mathematician, author, scientist, agriculturalist, astronomer, publisher, and urban planner, Benjamin Banneker.

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Benjamin Banneker was born outside of Baltimore, Maryland on November 9, 1731. He was born a free black, and was generally self-taught through most of his young adult life. Banneker began to display his brilliance as an engineer while he was a young man; first through his often noted affinity toward solving puzzles, and later through his mathematically-perfect creation of the first clock made entirely of hand carved wooden parts and pinions (Washington Interdependence Council, 2014). This clock, which Banneker built after carefully studying a borrowed pocket watch, accurately kept time for decades.

Benjamin Banneker’s love for learning encouraged him to begin studying astronomy and advanced mathematics from sets of books loaned to him by a neighbor. As a result of these studies, he was able to accurately predict solar and lunar eclipses, and became the author of an internationally published almanac, which contained his many scientific and mathematical calculations. The international recognition of his almanac also served as a springboard for Banneker to become a recognized proponent for the abolishment of slavery. He famously composed a letter addressed to Thomas Jefferson, in which he insisted black Americans possess the same intellectual ability and should be afforded the same opportunities as white Americans (Chamberlain, 2012). This letter led to an ongoing correspondence between the two men, and led to Banneker receiving a considerable amount of support by abolitionist groups in Maryland and Pennsylvania (Biography, 2014).

Banneker was also selected to assist Major Pierre L’Enfant to survey and develop the city plans for our nation’s capital, which was later named the District of Columbia. After L’Enfant abruptly quit the project, Benjamin Banneker was able to reproduce the plans – from memory - for the entire city in just 2 days. These plans provided the layout for the streets, buildings, and monuments that still exist in Washington D.C. (Chamberlain, 2012).

During the week of November 9th through the 15th, individuals and groups across the nation will honor the many contributions of this great mathematician by celebrating “Benjamin Banneker Week”. The Benjamin Banneker Association, an organization dedicated to mathematics education advocacy by providing support and leadership for educators and students in order to ensure equity exists for all students, is sponsoring a mathematical task competition to continue his legacy.

Schools, libraries, community and professional organizations, or interested citizens are urged to make mathematics a significant part of children’s lives by coordinating a Benjamin Banneker Celebration event in their communities. Visit the Benjamin Banneker Day website ( to learn more about Benjamin Banneker, and how you and your community can participate in this year’s celebration.

Benjamin Banneker: A Memorial to America’s First Black Man of Science (2014). Retrieved Oct 13, 2014 from

Benjamin Banneker. (2014). The website. Retrieved Oct 13, 2014, from

Chamberlain, G. (2012) Benjamin Banneker – The Black Inventor Online Museum. Retrieved Oct 13, 2014 from

Tuesday, October 14, 2014

Bringing the Associative Property of Multiplication to Life

By Cassandra Hatfield, RME Assessment Coordinator, and Megan Hancock, Graduate Research Assistant

The Institute of Education Science (IES) Practice Guide for Improving Mathematical Problem Solving in Grades 4 through 8 Recommendation five states that it is important to “help students recognize and articulate mathematical concepts and notation” (Woodward et al., 2012). One way to carry out this recommendation is to “ask students to explain each step used to solve a problem in a worked example” and “help students make sense of algebraic notation” (Woodward et al., 2012).

The Associative Property of Multiplication will illustrate this recommendation by going beyond a procedural skill and making connections conceptually that support the symbolic notation. Our goal is to give evidence that the Associative Property of Multiplication can be taught through multiple representations. Through our research we found that some representations are mathematically accurate, but may not provide students with a compelling reason to use this property.
When developing the concept of volume of rectangular prisms, decomposing the rectangular prism into layers allows students to make the connection with content they are already familiar with, arrays and area. This decomposition also exemplifies the Associative Property of Multiplication. Here are some examples of how the rectangular prism shown above can be decomposed in different ways.

  • A: 2 × (6 × 4)
  • B: (2 × 6) × 4
  • C: Supports commutative property of multiplication too
    • 2 × 6 × 4; 2 × 4 × 6; (2 × 4) × 6
By designing activities and lessons that support the decomposition of rectangular prisms into different layers, teachers can support students in making sense of the notation of Associative Property of Multiplication, A x (B x C) = (A x B) x C, and finding the volume of rectangular prisms. Explorations like this also support teachers in holding students accountable for understanding the notation because students can use the different models to support their explanation of their understanding.

Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide (NCEE 2012-4055). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://