How to Teach Math

Many homeschool parents are intimidated by math. If this is you, it’s probably because you never really learned math properly the first time. But never fear, you can learn it right alongside your child.  We will teach you how to teach math.

how to teach math

Be positive

The biggest problem most kids face with mathematics is their inner voice.  They believe they are bad at math and so they give up, inside if not outwardly.  Of course, this is true in all subjects, but for some reason math seems to be the biggie.  Kids are told they are smart or that they made a mistake as though these are mutually exclusive possibilities.  If they get an answer right we say “you are so smart” and while this seems positive, what is happening inside the child is they are equating the correct answer with the ability of their brain.  They have developed a fixed mindset.  They are smart, until they get an answer wrong and then they are dumb.  We want to create a growth mindset in our children, where they believe they can work hard and get better at things and persist and overcome difficulties.  So adjust your language during math class to say things like, “wow, your brain just grew about ten sizes while you wrested with that problem” or “you worked super hard on that and I’m proud of you”.  Notice the struggles, praise the mistakes and the learning, much more than you praise the correct answers.

Be Consistent

A problem with most math educations is a lack of consistency.  Different teachers teach math differently, using different text books, different emphasis, and even different methods for arriving at answers.  This creates confusion.

Your goal is to find a curriculum that you can stick with all the way through.  Of all the school subjects this is absolutely the most important to research carefully.  We both, Karen and Michelle, have used Saxon math all the way through with our kids. We think it’s the best written math curriculum on the planet.  It is very clear, step by tiny step, and uses the spiral approach, where math skills are practiced all the way through, not learned and then dropped and forgotten.

However, we realize that different people think and learn differently so Saxon may not be for you.

On our Math Helps page you can read more about some different math programs and start there as you chose one for your family.

Don’t Hurry

The second problem with math instruction is that often children are moved on to the next concept before they have ever learned the current one.

Math skills build, one upon the other.  This is a mistake I made when teaching my two oldest sons. They were a bit shaky on fractions in the upper elementary years.  Not being well math-educated myself I did not understand how crucial an understanding of fractions is to understanding algebra. If you can’t do fractions, if you don’t have a mental picture of what is happening when fractions are added, subtracted, multiplied, and divided you will never be able to grasp algebra.  This is true of all parts of mathematics.

The exact same principles are used to solve the problem on the left as are used to solve the problem on the right.

So slow down.  Let your child gain a firm understanding. Repeat lessons.  If they get stuck on a concept, look for manipulatives, subject specific workbooks, video lectures, or activities to aid in understanding.  Khan Academy and Math Antics are two of our favorite video sites for math instruction.

I actually like Math Antics better because the teacher goes so slowly, very step by step, which is what struggling mathematicians need.  But I do disagree with Math Antic’s calculator usage in the early grades.  Kids must not make calculators into a crutch.  Calculators, if used before basic operations are automatic and easy, make kids mentally lazy and actually hinder math reasoning skills.  For most kids, automatic recall of math facts doesn’t happen until at least the early teen years and certainly not in 5th or 6th grade when Math Antics begins to recommend calculator usage.  Doing difficult multi-step multiplication reasoning is not unreasonable to expect from kids who later you will ask to understand factoring or complicated algebraic division problems.

It is far more important for your child to understand the math than it is for them to finish the text book by June. so slow down and repeat lessons until your child is comfortable with the concepts.

Memorization is Essential

Memorization in math is an essential component of a math curriculum.  Kids really do need to know the times tables by heart.  Again, this may seem unimportant until you hit algebra and suddenly your child is struggling with basic operations and pulling out the calculator instead of being able to focus on the algebra.  Also, the SAT does have a portion on which calculators are not allowed.  How embarrassing to be seventeen years old (or an adult) and counting out multiplication on your fingers.

Things to make sure they memorize. (Though ideally they discover these on their own and the concepts and patterns become part of the world that just make sense.)

  • Times tables.
  • Geometry definitions like rhombus, cylinder, acute angle, parallel, isosceles triangle, oblique, horizontal, pi, and so on.
  • Formulas like finding the circumference of a circle, area, volume, and so on.
  • How to count money, including counting back change.
  • Square numbers up to 100.
  • Prime numbers up to 100.
  • How to spell number words.

Memorization has fallen out of fashion in a lot of schools.  This is a huge mistake. Memorization isn’t drudgery, it’s freeing.  Your mind is always faster and more reliable than a calculator.

Creative Thinking Is Even More Essential

We tend to not think of math as a creative subject, but it really is.  There are dozens of ways of arriving at answers.  There are incalculable answers not yet discovered.  There are mathematical questions not yet thought of.  Math is every bit as creative as art or writing class.

When this spider created its web, it first made a logarithmically spaced spiral that grew larger as the spiral moved away from the center.  Then to give the web further strength and close the gaps, the spider made another spiral, this time arithmetically spaced from the center. The spider was doing algebra. Math is a real subject in the real world with real applications and real patterns we can actually see. It’s not merely abstract, the way we teach it. Photo by Brocken Inaglory, CC by SA 3.0, Wikimedia.

One of the best things you can do for the creative math muscles in your child’s brain is to give them math challenges without giving them a step-by-step demonstration on how to solve the problem.  The next step is to have them come up with their own math questions.

In science we know that we’re not really doing experiments if we’re just following a recipe.  The same is true in math.  You’re not really doing math like a mathematician if you’re just following a series of steps to get a right answer.  Real math involves searching out patterns and using logic to discover rules and then applying those rule to new situations.

The newi-sh trend in elementary classrooms of doing “number talks” allows students to discover the rules of mathematics on their own in logical, creative ways.  We’re fans.

Use the Tests, If You Must

When I was in school we had math tests, almost all of which I bombed.  The teacher never went over the tests, we never discussed common problems or sought to rectify misunderstandings. We just moved on.  This approach makes the tests pointless. Math tests should be a learning tool.

Actually it’s worse than pointless, because, testing in general promotes a fixed mindset and remember we want our kids to feel they can learn not develop attitudes about what they are.  If you don’t have to use testing, skip the tests, especially up through 8th grade. But some of you live in jurisdictions that require some sort of math testing.

Tests do give practice with taking tests and help kids deal with anxiety, working efficiently, and showing their work.  The test also forces children to make mental efforts because they can’t just look back in the book for instructions or to follow the steps in the example problem.  They have to understand and memorize.  So testing can have value, but it’s main value is in learning how to take tests.

If you do use the tests go over all the missed problems.  Emphasize to your student that the mistakes made their brain grow a lot more than their correct answers and that’s why you’re ignoring the correct answers.  Then talk though the child’s reasoning. A friend of mine schedules every Friday math period in her homeschool just for going over the math tests.  If your child has really struggled on certain concepts, slow down, repeat the lessons, then give the test again in a week or whenever you think they are ready.

Start With the End in Mind

To do well on the SAT and get into college kids need to understand (not just have moved through the text books) up through algebra 2.  But there’s more to math than this.  A lot of people think math isn’t that important.  “I never use anything but basic math in everyday life” they say.  That’s probably because you don’t understand anything but everyday math.  If you don’t know it, you can’t use it.  People who can’t read don’t ever use books either.

Mathematical thinking is a different type of thinking, a different language and  the foundations, the grammar for that language, is laid in the first six years of schooling.  Elementary school math may seem easy, but it’s so, so important.

The point is that to understand algebra and beyond you have to really have good number sense. You have to understand what the numbers are doing, not just plug them into a formula. You have to be able to do mental math.  You have to be able to find patterns. You have to be able to calculate without calculators.  So approach your elementary math with the idea that you are teaching your kids a new way to look at the world, a whole new language, and strive for real understanding.

If your kids aren’t having “ah-ha!” moments then they’re not understanding math and they will suffer for it later.

Learn With Your Child

You can learn the math concepts with your child.  This is easiest if you are starting at the beginning. But you can do it starting in the middle as well.  Again, we recommend Saxon because it has such clear instructions. If/when you reach concepts you don’t understand, ask your child to explain them to you. If neither of you understands, this is where you need to slow down, look for online videos like Khan Academy, or back up a bit.

If adding algebraic fractions is confusing you, go back and review how to add normal fractions, then take a shot at the algebra again.  The same goes for functions, the distributive property, and so on.  Take out the variables (the letters in the math problem), learn the concept, then put back in the variables.  Math is extremely orderly and consistent.  If a principle is true in fourth grade math then it is still true in differential calculus.

I have a math notebook and I do math with all of my kids each day.  I may not do every single problem of all of their assignments (because I have lots of kids), but I do a great many math problems every single day.  Do the work with your kids.  Be a team.  No matter what your math skill level is, you will both benefit from doing to the work side-by-side and really learning together.  There will be less resistance and resentment, and better attitudes and understanding.

Library List

If you want to be a better math teacher here are some resources to check out.

More About Math

 

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