Math Education Needs To Slow Down, Stop and Smell Its Roses
That is how a great article which refers to the problem of timed tests and always rushing through math starts. As a society, we are fans of efficiency, but with a culture of rush, hurry, skim, it seems many students are missing out on the deeper, important, higher order thinking skills suggested by Bloom's Taxonomy such as critical thinking, explanation, synthesis, and problem solving (application). All of these take time to implement.
In his article, Sunil Singh references Carl Honore, a popular TED speaker, author and founder of the slow movement. When children are taught and experience these aspects of thinking at a young age, advanced coursework in all area but especially in math, comes easier and more naturally.
Paul Lockhart wrote, “Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity — to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs — you deny them mathematics itself.” In order for kids to engage in higher order thinking, they must be allowed time. Something that is missing in most modern classrooms.
Children who are given time to think deeply about mathematics and numerals, develop a critical key to success in math, number sense. A recent Huffington Post article confirms that number sense is where it's at!
Number sense is an ease and fluidity with numbers. It is similar to common sense in that points to the practical, often most efficient method to achieve an answer. For example, when interviewing new prospective instructors, I will often ask, "How would you solve 999+999+999?" Frequently, the candidate will say something like, "Well, I know that 9 times 3 is 27, so I would put the 7 in the ones place and carry the two. Then 9 times 3 is 27 again but I have to add the 2 I carried, so it is 29. The 9 goes next to the 7 and then I carry the 2. 9 times 3 once more is 27, add the 2 and I get 29. I would put that in front of the 97 for an answer of 2,997." Basically, all they did was take their paper method and use it in their head. Some people can keep track of numbers and columns that way but many cannot. Number sense would look at the problem and say, "999 is very close to 1,000 so if I have 1,000 3 times that is 3,000. I need to take away 3 because I added 1 to 999 to make 1,000 and I did that 3 times. So, 3,000 take away 3 is 2,997." Much quicker and less chance of mistakes.
Another example we use often has to do with percents. When we ask a student what 25% of 240 is, they will often start multiplying 240 times .25. We let them get started and then ask them to stop and step back from the problem a bit. "What fraction is 25%," I'll ask. Usually, they can answer, "1/4." If they can't, we need to work on some more basic concepts. "Right," I'll say. "So what is 1/4 of 240?" "Oh!" the student will exclaim and say "60." Yep! No muss. No fuss!
Jo Boaler is doing great work with promoting awareness of the need to develop number sense among our students. It allows for and promotes the inherent beauty and creativity of math and allows for learners with different ways of seeing numbers to be equally successful. Here is a great, short video that Jo created explaining number sense.
At Mathnasium of Parker, we definitely spend time helping children with the structures of numeric fluency and helping them develop number sense. We also get them to talk about their math. "How did you do this problem? Why did that work with #4 but not #5? How are #2 and #6 similar or different?" "Can you find another way of solving this problem?" All of these questions, support children in developing their higher order thinking skills. Drawing conclusions, making mistakes, and sharing their thinking through their Mathnasium instructor's socratic questioning helps our students grow!
Come check us out and see if we might be a good fit for your child's math education!
