Number Stories are real-world questions based on real-world contexts supported by factual sources. Both contexts and questions are written for, and by, a wide variety of individual users such as school students at any level, teachers, teacher-educators, home-schoolers, district supervisors, curriculum developers, and others who are simply interested in how mathematics can be used to solve problems or model situations in their lives.
Any of these users can write, edit, or use other people’s stories in the online Number Stories environment to make personalized curriculum. A premise of the project is that an individual’s true curriculum is basically the set of problems he or she attempts to solve. Traditional, print-based curricula understandably have to present material to an idealized “typical” student and, these days in particular, are based on an imposed scope and sequence of objectives. Personalized Number Stories problem sets can be built by sequencing problems from the collection and/or new problems written by the user to meet individual interests and needs.
A digital collection of mathematics resources is not a unique idea. The online Khan Academy, for example, is a collection of demonstrations of mathematical skills and properties supported by problems for students to practice those skills (Kahn 2014). The website also helps students navigate between related skills. We at the Number Stories Project applaud this work, along with some of the better apps and individual sites that help students learn and practice skills. But we believe that an individual’s mathematical understanding is greatly improved by also applying those skills to solve relevant problems that they or others face in their real-world experience. Thus we are focusing on collecting and writing high-quality real-world problems and their solutions. When particular skills are used in a Number Story solution, we plan to link the user to places such as Kahn Academy to learn more about those skills. However, the main purpose of the Number Stories Project is to promote understanding about how mathematics is used in daily life, not abstract skill development.
Focusing on applications of mathematics is not a unique idea either. The University of Chicago School Mathematics Project Grades 6-12 (UCSMP 2014), Everyday Mathematics (EM 2014), and the many fine resources from the Consortium for Mathematics and Its Applications (COMAP 2001) have based mathematics curricula on applications for decades. And although they have had a variety of digital resources connected to their curricula during much of that time, the mathematical and pedagogical content of the curricula have been limited by the need to deliver the content via traditional print materials. Thus the digital resources have tended to remain ancillary to the content and relegated to enrichment or “if we have time” use.
The Number Stories problems are web based. There is no expectation that they be downloaded, printed, and solved with pencil-and-paper techniques. In fact, problems that can be solved with only pencil-and-paper approaches are not good candidates for the Number Stories collection. This does not mean that problems have to include elaborate animations, for example, but it does mean that our project is committed to making each problem take advantage of something that Internet-based software has to offer. These include, but are by no means limited to, links to the source material of contexts and questions, feedback to questions that have well-defined answers, and the ability of any user to comment on other people’s contexts, questions or solutions.
Yet even these goals are not unique. The Building Better Math Project is in the process of developing a collection of applications of mathematics for tenth-graders in Canada (BBMP 2014). Unlike the Number Stories Project, the BBMP is aimed at supplementing existing curricula and standards and supporting classroom implementation of their lessons. However, the projects are similar in that BBMP problems are also solved online. They are based on the Maple engine, a venerable computer algebra system with a growing number of visual enhancements.
Although the Number Stories Project differs from the BBMP approach to curriculum development, we applaud their efforts to improve the digital problem-solving experience via the Maple engine. We are partnering with Cabrilog S.A.S., authors of the Cabri dynamic-mathematics authoring environment to make a rich problem-solving environment that exceeds many of the capabilities of Maple, especially for younger users. Cabri allows problem authors to manipulate objects in 2- and 3-dimensional environments and act on those manipulations within a comprehensive Boolean logic framework. For example, in the screen shot below a user is moving copies of the animals in the group picture to the lower part of the screen. He or she can click the green check button at any time to check whether the animals are in the proper sequence. Other buttons reset the problem so the user can start over or move to a page of sources for the question and images.
We hope this brief introduction to the goals of the Number Stories Project interests you and prompts you to learn more. If so, please contact:
Jim Flanders, Senior Author and Curriculum Developer
Kathryn Rich, Curriculum Developer
Nicole Carlson, Project Manager
UChicago STEM Education
University of Chicago
COMAP (2001) Mathematics: Modeling Our World. MMOWoverview.pdf retrieved from http://www.comap.com/mmow/PDF/MMOWoverview.pdf, 28 September 2014.
EM (2014) Everyday Mathematics Overview. Retrieved from http://ucsmp.uchicago.edu/elementary/overview/, 28 September 2014.
Kahn (2014) Kahn Academy. Retrieved from http://www.khanacademy.org/exercisedashboard, 28 September 2014.
MSEB/NRC (1990) Reshaping School Mathematics: A Philosophy and Framework for Curriculum. National Academy Press: Washington, D.C.
UCSMP (2014) UCSMP Grades 6-12 Curriculum Features. Retrieved from http://ucsmp.uchicago.edu/secondary/curriculum-features/, 28 September 2014.