MORRISTOWN, NJ - Recently Unity’s mathematics lead teacher, Kristopher, and their gifted and talented mathematics teacher, Jeanette, were asked by a parent how to properly “challenge” a child excelling in mathematics. Here is what they had to say.   

“Our goal is to engage all students in a challenging curriculum of high quality mathematics. Nobody wants students to feel bored in class and not reach their maximum learning potential. The question becomes, what should be done with our math high achievers? When students are successful with all of the math presented to them and not feeling challenged in class, one conclusion people come to is to have them do multiple years of math in a single year or skip ahead a grade level. But skipping content isn't always the answer. Consider another possibility: what if students could be challenged with grade level content that would keep them engaged and learning with alike-level peers?

Higher level math classes promote a mindset of inquiry, risk taking, flexible thinking, and problem solving - not necessarily just skipping ahead a math level. Adding additional levels of math classes will allow each child to experience success, challenge, and growth while building a strong foundation of mathematical understanding and skill. Rather than just passing quickly through skills students seem to have mastered, students should be provided extension and enrichment of content, striving for greater rigor and deeper understanding of all grade-level math skills.  At Unity, we have an opportunity to provide this in a multi-age setting allowing for a unique opportunity for students to build this deeper understanding together - the mixed level of experience will push both the younger and older students as they work together on enrichment content. At the same time, students will have a personalized math learning plan to guide them through math content specific to the grade level they are working on (and beyond). 

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Mathematics is a two-pronged process: a process of both learning math content and a process of gaining math maturity. Math expertise can be divided into two major components: math content and math maturity. Most math classes focus on math content—for example, learning many different arithmetic, algebraic, and geometric procedures and how to use these procedures to solve a wide range of problems. Math maturity focuses on areas such as understanding, solving math problems you have not previously encountered, theorem proving, precise mathematical communication, mathematical logic and reasoning, knowing how to learn math, problem posing, transfer of learning (being able to use one’s math knowledge and make math connections over a wide range of disciplines and in novel settings), and interest—including intrinsic motivation. The idea that a math problem may have no solutions, one solution, or more than one solution is part of math maturity. The idea that a solution or a solution process may be more or less clever, beautiful, or elegant is also part of math maturity. Math maturity is an idea that is not specific to any particular content area in math. To a large extent, math maturity does not depend on knowing some specific part of the content of math. A person may have a high level of math content knowledge and a low level of math maturity, or vice versa. A deeper understanding can reap huge benefits for students as they move forward.

Placement of students in their math class needs to be based on multiple measures, both of student achievement in mathematics and their personal motivation to put in the necessary effort to be successful. With these placement options already existing here at Unity, we have given students the opportunity to proceed in high school level Algebra I and Geometry classes while in middle school, and multi-age mathematics fusion classes in our elementary school. Our curriculum, rooted in Singapore Math, has proven itself to be the optimal launching point for our constructive and innovative approach to mathematics.”

Unity Charter School is a K-8 public charter school in Morristown/Morris Township; Unity opened in 1998 and is currently in its 20th year of operation.

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