Attention kindergarten, first, and second-grade teachers: You likely have a budding and brilliant mathematician among your classroom ranks! That child may sit quietly while the other students “catch up” and learn basic math concepts covered by early primary curriculum, or he might refuse to do the work and goof off during math time. This behavior may suggest that this child is behind, but the following points will help determine if this is a valid conclusion.
There is a wonderful article on gifted young mathematicians, which – in addition to providing important insights about children who have unconventional approaches to math – cites numerous studies that have concluded that differentiation in early primary math is rare.
“By the time these emergent mathematical geniuses arrive for their first formal math lessons in kindergarten, they may have already established their own unique theories of number sense, sequences and patterns, problem-solving, and computational strategies. Too frequently, the teachers following the curriculum merely touch on many math concepts, failing to recognize and nurture young mathematicians” (Pletan, Robinson, Berninger, & Abbott, 1995).
So what do you do with children who have mastered numbers below and above 100 – and maybe into the thousands or millions – well before Mr. Zero swoops down in February? How do you find and nurture these diamonds in the rough before it’s too late?
Primary mathematics is often torturous for mathematically gifted children. It is usually taught from one text, with a broad range of topics that lack depth, and subject matter repeats year after year. A gifted student often absorbs and understands the information the first time around; when she has to learn it again and again and again, year after year, boredom, ill behavior, and deterioration of skills can result. But what strategies should you employ to find and support these students, beginning at age five and extending throughout elementary school?
Here are five ways to discover and support mathematically gifted students:
- Pre-assess, pre-assess, pre-assess!
- Differentiate assignments
- Enrich and use multiple resources – not just the textbook!
- Use ability grouping
- Accelerate: be flexible about pacing
Pre-assessment is one of the easiest steps you can take to understand the extent of your students‘ knowledge, and the results will guide you in your effort to differentiate. You copy a unit review page from the text, hand it out, say, “no pressure if you don’t know the answers – we haven’t covered this yet,” and see how your students do.
In kindergarten, you can do this orally and casually if a print-out isn’t useful with your students. Remember, some will resist the “busy work” if they interpret it as such. You will be amazed and surprised at what your students already know!
Often, the argument against pre-assessment is, “But it will make the kids who don’t understand feel bad.” They won’t feel bad if you consistently approach all of your students with kindness and attention to the individual’s needs. Furthermore, have you considered the potential loss when a natural mathematician tunes out of math altogether because he finds no interest or challenge in it? Or the potential behavioral repercussions in your classroom?!
Use Past State Assessments
Recently I printed a past state assessment test for sixth grade and administered it to a fifth-grader in the middle of her fifth-grade year. The purpose was to demonstrate to her parents and teachers that she would likely fair well if she skipped sixth-grade math altogether. She missed only 12 problems on the entire assessment, and most of them were clustered around a particular concept which she then learned in under 10 minutes. Now, as a sixth-grader, she is thriving in advanced seventh-grade math, one of the very few accelerated programs offered.
Print the year review test or your state assessment, and have the students work on it on their own. This is an important tool to help you know how to differentiate or accelerate, or which practice problems those students can skip.
Preschool & Geometry
On the younger end of the spectrum, I have worked with preschoolers who are fascinated by Andrew Clements’ A Million Dots and love to hear and say the numbers; who were able to identify many of the advanced shapes (decagon, hexagon, nonagon) in Marilyn Burns’ The Greedy Triangle at age two or three, not to mention prisms, cubes, and cylinders; and who have actively watched the digital clock tick through numbers 0 to 59 since they were 13 months old and have related that knowledge to both number sense and analog time-telling.
These students may not be the conventional “high-achievers” when it comes to written work, but you can spot them by the offhand comments they make, their interests, and their desire to connect deeply or follow up on the enriched math concepts to which you expose them. What a delight it is to teach these children, and watch them make connections to the broad, exciting, multidimensional world of math!
Kathryn Haydon, founder of Sparkitivity, is a teacher, nationally-known writer and speaker, and a mentor to students of all ages. A life-long learner herself, she loves to find the most creative, innovative, hands-on ways to present math, writing, history, and science to kids. She has taught second grade, Spanish, creative writing, and journalism at Monica Ros, Topa Topa, and Valley Oak Charter schools in Ojai,CA, and creative writing at the Center for Gifted in Chicago. Katie is a published author on teaching, parenting, and early foreign language instruction, and her work was recently featured in Igniting Creativity in Gifted Learners, K-6, edited by Joan Franklin Smutny. A graduate of Northwestern University, Katie majored in Spanish and Latin American language, literature, and culture, and minored in economics. She serves on the Torrance Legacy Creative Writing Awards committee for the National Association for Gifted Children.
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