I often encounter this teacher’s dilemma when it comes to their highly capable math students. It doesn’t matter if the classes are “levelled” or if the curriculum includes “honors” and “regular” sections of math; this is the core tension that will emerge regardless of the school’s classroom structure:
Should we give our (truly) highly capable students an accelerated math curriculum which will take them to the next grade level of math in a much more compressed period of time, like a few months, or should we find enrichment experiences for these students to pursue that will provide them more sophisticated versions of the concepts that the entire class is learning together?
This is the faster versus deeper dilemma—typically, parents would be the constituency pushing for acceleration (“My 5th grader should be in the Algebra I class right now!”), whereas teachers tend to consider enrichment as the preferred approach (“Let’s see if Johnny can apply our probability concept to these contemporary economic issues.”) Thus creates the stresses that nearly all math teachers experience, especially through the middle school years. My 7th/8th grade teacher faces this tension on a daily basis. She wonders whether to pull the next textbook off her shelf and relocate her one or two talented math students into a new corner pod in the classroom to crack open next year’s textbook and see how far they can go… or, should she deepen their understanding of concepts by searching for more complex word problems to solve or by assigning a longer term project designed to keep them stimulated while she devotes her attention to the struggling students?
The answer to this dilemma must embrace a few core teaching and learning questions: What factors contribute to an outstanding math learning experience? And, what elements are crucial to providing excellence in teaching?
Let me outline the main concepts in the companion bibles on these topics, The Elements of Teaching and The Elements of Learning, by Banner and Cannon.
Their concepts are largely humanistic in context, like for teachers: imagination, compassion, ethics, real thinking, vitality, authority, patience, and much more. For students: adventure, curiosity, pleasure, aspiration, self-discipline, initiative, and the like.
While it can be very important, for practical reasons, to offer accelerated opportunities for these students, teachers should always be mindful of enriching and deepening a child’s understanding of mathematical concepts; nurturing the spirit of problem-solving through open-ended problems and projects; enlivening and stimulating that student’s pursuit of math learning by guiding them down surprising and invigorating pathways; stoking that student’s curiosities and motivations by turning to a variety of sources.
That last point, the one about turning to a variety of source, I would emphasize the most, as the teacher who clings to that available textbook on the shelf is headed toward a very dry and stale approach. I always encourage my math teachers to take a “multiple source approach to math curricula.” The good math teachers need to be life-long searchers for new sources, mostly nowadays that means searchers among the vast ocean of fantastic online math approaches and problems and games and competitions.
Without providing an assessment or review of each of these online sources mentioned here, the purpose of sharing them is to give you a taste of the range of strategies that are out there. Anyone can take a few minutes and concoct a list that is entirely different than this one, and it will still be a terrific list to plumb for teachers. The idea here is that acceleration and enrichment are pathways that can be followed simultaneously, but I submit that enrichment and depth are, in the end, more valuable to our young learners.
Ten Online Math Sources Worth Your Consideration:
www.insidemathematics.org — a great source to inspire teachers to upgrade/transform their teaching practices; their cornerstone project is their Math Problem of the Month. Check out http://www.insidemathematics.org/problems-of-the-month.
http://www.dreambox.com/ — lots of explanations and rationale via videos and testimonials; their math approach is geared toward differentiation to address a full range of math levels and needs.
Www.mathschallenge.co.uk — this UK site has a global audience of schools and students participating in their fun competitions, many with a STEM focus.
Www.ixl.com/math — this site provides real time scoring for its timed and mostly computational math problems.
http://worldmathday.com/ — here’s a popular annual math competition website offering students and schools a chance to view their progress alongside schools around the world.
www.tenmarks.com/overview-how-it-works — here’s a full service online math curriculum that provides dynamic methods of accommodating individual pacing and levels, with excellent student-to-teacher informational flow.
www.wolframalpha.com – the elite tool for solving any math problem… showing step-by-step and multiple solutions.
http://www.noetic-learning.com – designed for the gifted kids to enhance reasoning and problem-solving.
http://mathpickle.com – math video problems that should challenge any class, often presenting games and puzzles for groups of students to collaborate on.
http://www.mathletics.com – another popular global competition site for the math athletes out there.