Math Pacing - What is too fast?

I am often asked when to teach math concepts. Everyone wants their child to keep “moving along” with math concepts, but is that always the best solution? I have taught six kids of varying mathematical abilities, and I have tested a few thousand kids over the last 19 years (dozens I see year in and year out over many years). I have developed a strong notion of what works best for kids – Go slow, teach thoroughly, and practice rigorously.

Here is my philosophy of math. All kids, regardless of their aptitude in math, should move at the speed of their mastery. What do I mean by that? When children first start learning calculation skills, they should learn the addition, and subtraction facts (teach at about the same time) from 0 – 10 completely, meaning all problems which the answer is 10 or less. (2+2, 4+3, 8+1, 5+5…and the matching subtraction problems.) They should know them inside and out, front and back with no hesitation. This may take a while, but don’t move on to harder problems until this is mastered. Next teach the problems between10 - 20. This should not take too long, as it is almost the same as 0 - 10. Then teach 0 - 20. Notice I skipped all the problems that jump across the 10 like 8+7 and 9+6 until after the teen facts are learned. These are harder and on a higher cognitive step than 0 – 10 and 10 – 20. Once a child has mastered ALL of these facts then they are ready for larger numbers in addition, and shortly after, long addition.

This is the pace you take at each level. Obviously, there is more to learn in math than just addition and subtraction facts while in first and second grade. While the child is mastering these facts, teach shapes, patterns, clocks, coins, skip counting, one half… Most good curricula will cover all of these concepts in an orderly fashion, some faster than others, some with more repetition, and some with more work. The exception will be math curricula which are considered conceptual or developmental (I will talk about these later). While your math curriculum is slowly teaching these different math concepts, make sure that you are helping your child MASTER their facts. If a child is handed a worksheet to complete and they do not know their facts, they can still easily complete the sheet with the help of fingers, counting, or tic marks. Do not consider correct answers mastery. You will need to quiz them on their facts regularly to ensure that they are actually mastering them.

All homeschool parents worry that they may be allowing their child to fall behind, but there are many years ahead to learn all there is to learn in arithmetic. The best way to be ahead is to learn the basics thoroughly. A child who must count or “figure out” the answer to 7 + 9 is going to find a problem like 59 + 127 extremely difficult. A child with all their facts memorized will find it fun and will want the challenge of learning how to carry.

Conceptual math is math such as Miquon, Singapore, Right Start and many others which teach the concepts more than the facts. These programs work great for many kids for many reasons, IF you add a lot of facts practice to them, and IF you go at your kid’s speed. Often these curricula move too fast for the cognition of the child. Math cognition is like stair steps. As your child grows in age, knowledge, and understanding they progress up the steps, but until they are on a step they cannot understand the concept. However, a child who is not yet on the multiplication step can still memorize their multiplication facts. Knowing the facts is not the same as understanding why that is the answer. So no matter what step your child is on there is always math which can be worked on. Parents can tell when a new concept is too hard. The child will be frustrated, they will “throw a fit” which will look different on every kid, but basically, they will want nothing to do with this “new” math. When this happens, just put that curriculum away for a month or two while you review, practice facts, or simply take a math break. It is impossible to teach a child math that is above their cognitive “step.”

Developmental math curricula is the most closely in line with my notion of mastery. Math U See, Developmental Math and others use the idea of mastering one concept at a time. However, there are flaws in assuming these curricula are moving with your child. Math U See works primarily in addition during first grade and subtraction in second grade, but it has first graders working hard addition problems, which many will not be ready for. Developmental Math is gentler, and each workbook covers a micro concept. It is easier to test mastery at the end of each of these. But again, many children may need time and more practice before moving on to the next concept.

So to sum it up. Every child is their own unique person, learning at their own speed. Jumping ahead will only make it harder for them. Think of math like reading. Would you jump to reading words before teaching the alphabet and basic phonics? Of course not, that would not make sense. In order to build the sounds of a word a child needs to know the sounds each letter or letter combinations make. Same with math. Children must KNOW how to add and subtract (not be able to figure it out, but KNOW it), before they can move on to harder concepts.

PS – Do not give your kids an Algebra book until they have thoroughly mastered fractions – they will be unable to understand what they are doing.