Math is the perfect time to reinvent the wheel. Children in elementary school should be given every opportunity to explore mathematical concepts with manipulatives, pictures, and other visuals so that they have a firm grasp of a concept before leaping into the memorization of an algorithm.
Many times, students figure out what they need to do to solve an equation before an adult needs to step in and tell them. Especially when students have difficulty with math, they need to be able to see what is happening. Once they do, they are less likely to make an error in the process because they can reason through the problem if they get stuck.
Just telling your children that they are “moving over 10” when regrouping in subtraction is probably not enough information; they need to actually see the base 10 blocks being traded in. It is all the better if your learners have the chance to break the blocks apart themselves. Keeping them active during the lesson not only keeps them focused, but deepens their understanding.
Here is one of my favorite ways to engage children in math with multiplication facts:
Two, five, and 10 multiplication facts are usually the first facts memorized. I want the children to see that by memorizing three sets of facts, they can quickly learn the rest. My students arrange single-colored manipulatives (base-ten cubes, poker chips, etc.) and create arrays of a given multiplication fact (let’s say 3x2).
Next, my students place another 3x2 array right next to the first, but in a different color. Now they have 3x4. After a couple of examples, the children begin to see that when the array is doubled, the product is also doubled. They now have doubled the number of facts they know, and will know the four-facts and eight-facts.
We practice a similar method while learning the three-facts. When the children are learning 3x6, I have them build an array of 3x5, a fact they should know. Then they just add on one more group of three. Rather than memorizing an entire list of multiples, they can quickly figure the five-fact and add one more group to get the six-fact. Of course, eventually quick recall of facts is necessary, but early on, helping your students see these patterns is crucial to developing a strong math foundation.
Math is fun to teach and should be fun to learn. Math instruction should not be a time for memorization of processes without first giving ample opportunity to try out the concepts on their own. Eventually, yes, children need to buckle down and rehearse algorithms, but not on day one! Give your students a chance to see the interrelation of numbers and they will learn to love math.-Patricia Guest, M.Ed
Second and Third Grade Magnet
Grosse Pointe Public Schools
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