The Rebecca Klemm Conjecture: from Numeracy to New Insights


From August 3rd to 6th, 2016, Rebecca Klemm is presenting a provocative proposition to the elite mathematicians of the Math Association of America. The Rebecca Klemm Conjecture proposes that any polygon can be decomposed into an infinite series of polygons with the same number of sides. The conjecture has important ramifications in fields as diverse as IT security and medical imaging.

Even more intriguing than the implications of Rebecca’s conjecture is the story of its basis in developing new learning tools for early STEM education. Rebecca is the founder of NumbersAlive!®, which works to develop foundational numeracy through blended learning that restores math to its origins as a language for describing the world. To develop Number Linx® and help learners link numbers to their physical manifestations as shapes, she began breaking the familiar regular polygons into irregular polygons with the same number of sides. Dividing the polygons again and again, Rebecca realized that the process was infinite!

Rebecca’s story, from her conjecture’s origin in early education tools to its revolutionary implications for science and technology, demonstrates the power of her unique approach to numeracy. For Rebecca, numeracy is not the ability to perform superficial manipulation, but understanding where numbers come from and how they relate to the world. Rebecca’s path to to her conjecture shows what wonderful discoveries await students who learn to use numbers creatively!

Make Math About Learning Not Memorizing

When teaching math, it’s easy to fall into the trap of teaching it the way you were taught, of over-explaining, and of making lessons more about memorization than actual learning. However, when students simply memorize a formula, they don’t comprehend how to get from question to solution in the same way they would if they deduced the relationship themselves – or even at all. “Over-scaffolding” a lesson, i.e. taking the critical thinking out of problem solving, does students a disservice. In an article for A Pass Education Blog, Liz Arcand suggests four ways to improve math lesson planning: de-scaffold, incorporate other content areas, increase the rigor of math questions and tasks, and learn more about PARCC and other standardized exams to understand what will be asked of your students – and how.

Number Linx is a set of cards that fit into our Puzzling Polygons board. They are an example of incorporating content area into math; there are multiple series of cards that fit into each of the ten spaces around the board, including the sign for each number in American Sign Language and different instruments with the correlating number of strings. These cards encourage children to think about how each number relates to a card and therefore to more fully understand the properties of each number and how it is relevant in their lives.

Building NumberOpolis is another activity that encourages children to make connections between numbers and their world. Each number has a personality and now needs its own home; by asking children to create these homes, we are encouraging them to think critically about what belongs in which number’s home. For example, maybe 0 should have round windows and live in a donut-shaped house while 1 lives in a really tall tower and 7’s home is covered in rainbows. The possibilities are endless, and this activity helps children realize how prevalent numbers are in their lives and increase their numerical literacy.

These are just two examples of ways to make math learning more interactive and to encourage more critical thinking in lessons. Let us hear your ideas!


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Common Core Continues to Cause Conflicted Feelings

Teachers had mixed feelings about Common Core State Standards initially, and continue to feel conflicted about them, “saying both that they set unrealistic expectations and will have long-term benefits, according to the results of a survey by the Thomas B. Fordham Institute.” The Fordham Institute conducted a survey of a representative sample of 1000 K-8 public school math teachers and found that, among other things, the new standards have caused parental confusion and decreased their ability to help with math homework, increased math anxiety, and led to teachers spending more time on multiple methods of solving problems which teachers say is frustrating for students. Teacher responses were split nearly evenly over whether provided instructional materials are actually aligned to the standards. Many say that they rely on materials they or colleagues have created. It is clear that Common Core is shaking up math instruction, and it is therefore necessary to also update the instructional materials provided to ensure teachers have an arsenal of high-quality resources on hand with which to teach to these new standards and prepare students to succeed and compete in a global world.


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Integrating Making and Teaching

The Maker Movement has been gaining a lot of attention nationwide. Last week was even the second National Week of Making, kick-started by the Second Annual National Maker Faire in Washington, DC. It has been a primarily casual movement, taking place in “museums, garages, and informal ‘faires.’” Now, however, making is starting to migrate into “the highly regulated world of K-12 education.”

“For fans of hands-on, student-driven learning the shift presents an opportunity to breathe fresh life into old teaching philosophies.” In other words, introducing maker spaces into schools and classrooms will allow educators to make-over their curricula and implement new ways of teaching. This can help reach students who don’t comprehend material well when presented via traditional methods, and it can help students understand topics and concepts more fully.

Another interpretation is turning communal spaces within a school building, such as libraries and computer labs, into maker spaces. This would allow students to independently explore things they are interested in; Monticello High School in Albemarle County, Virginia, for example, has “converted its quiet library into something that now resembles a hipster co-working space,” complete with a student-staffed technology help desk, a writer’s café, and an area where students can work with circuits, programmable microprocessors, and art supplies.”

Some, like Dale Dougherty, founder of MAKE magazine and “godfather of the modern maker phenomenon,” argue that “if schools don’t get the spirit of it,” – i.e. the “do-it-yourself, only-if-you-want-to ethos,” – it won’t “benefit them a whole lot.” While it is true that a learning target-specific project may not fully embody the “spirit” of making, “academics have consistently found that making ‘gives kids agency’ over their learning in ways that traditional classes often don’t.” Making introduces an element of creativity, exploration, and imagination into lessons that may otherwise be, for lack of a better word, boring.

Integrating making into formal education will not be a seamless process; hurdles include agreeing on a definition of making in such a context, deciding whether making should “happen primarily in a dedicated space or inside every classroom,” and whether the purpose is “to help students better learn the established curriculum or to upend traditional notions of what counts as real learning.” However, “the maker movement has also tapped into a deep desire among many educators to return to the type of instruction that drew them to teaching in the first place.” And if educators, administrators, and students alike are all excited by making, doesn’t that mean we’re on to something worth much time and energy to make it work?


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Millennials Love to Learn

Millennials are often criticized as having short attention spans and getting bored quickly. However, Lori Goler, head of HR at Facebook, recently said that millennials move from task to task, and job to job quickly not because they have lost interest, but because they want to learn more. Rafael Solis, co-founder, CMO & SVP of product at Braidio, added that “Millennial employees want to know what they are doing and why they are doing it.”

These observations about millennials’ affinity for learning and understanding what they are doing illustrate just one way workplace culture is changing. In contrast to previous generations, millennials care more about “being open, being transparent internally, being bold, having impact…[and finding a] sense of meaning and fulfillment at work and in your work,” according to Goler.

Solis believes that “To capitalize and instill passion in these life learners, businesses need to create a self-sustaining culture of learning and development.” In other words, modern-day businesses should make changes such as increasing trainings and workshops, being more transparent, and encouraging employees to learn and develop. Embodying millennial values will increase employee job satisfaction and help companies become more successful by showing they understand what today’s consumers find important.


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Congrats to Success Academy Charter Schools for Their Impressive Performance

Congratuations to Success Academy Charter Schools of New York City for their impressive achievements in English, math, and science. Clearly their teaching methods and students’ efforts are adding up to equal magnificent results!

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