28 March 2011

Educating at Home, Part Two: Teaching Mathematics

Dear Lissy,
The days are growing longer and finally a bit warmer.  Our first flowers, snowdrops, made their appearance over the weekend, and I hope to see crocuses soon.  You've shot up nearly 6 inches and put on 10 pounds over the winter, so I'm working to put together a spring and summer wardrobe for you.

I'd like to take a few minutes today to cover how I taught math at home.  Even if your children are in school, much of the training in mathematics will occur in your home.  Because Math/Science Education was my college major, it's one of the subjects in which I have the most confidence teaching.

All upper level mathematics is based on sets of memorized facts.  Drill is, therefore, an essential part of elementary work.

Drill:  The daily repetition of "fact families" in addition, subtraction, multiplication, and division.  A family is defined as any set of facts that produce the same answer (sum, difference) in addition or subtraction or have the same product or divisor in a multiplication or division problem.

A good teacher makes drill fun!

  1. Say the tables in varying voices (robot, alien, princess, etc.).  
  2. Plan to drill the current table the child is learning and one review table each day until the facts are mastered. Don't try to drill more than 2-3 tables a day.
  3. Make up fun songs, rhymes and rhythms (1,3,5, 7 and 9, odd numbers coming down the line.  0,2,4,6, and 8, even numbers are great, GREAT, GREAT!)  Kids usually enjoy yelling.
  4. Have your child write their tables in a funky colored pen, or race to see who can write it first.
  5. Print off a fact family worksheet from one of dozens of free websites
Once fact families have been mastered, add the flashcards for those families to the stack the child reviews regularly.
Flashcards are a BAD way to learn facts, but a GREAT way to review them.  Ditto for computer games that require the child to solve "mixed" facts to work their way through a level.  If your child is in school, don't make the mistake of running through a stack of cards every night to try to improve their math facts.  Only chanting/reciting families will dramatically improve retention of math facts.  

In twenty years of teaching and tutoring kids from private and public schools, 90% of them I've helped remediate are struggling with basic math facts, not concepts.

Mathematics is a skill subject...teach it that way!

Whether you're helping your second grader with carrying addition or your 10th grader with Algebra 2, the process is the same.

  1. Completely solve a sample problem for the student start to finish, carefully explaining each step.  This may be done by video, but be SURE that the video program you order is a teacher working out individual problems for the students, and not a video teaching the parent how to teach the concept.
  2. Have your student direct you as you solve the the next sample problem.   Repeat this step until they can accurately tell you how to do it every time.  Use a process "cheat sheet" for them to refer to if you're teaching a multi-step technique like long division.  If the student is using a video, have them pause the video before each step and direct the video teacher.
  3. Have your student solve the next problem, carefully explaining and showing each step to you as if you were the student.  Repeat this step until they demonstrate that they have a good understanding of the process.  On video, pause before each step, complete it, and then use the video to "check" their own work.
  4. Have the student complete all additional problems, checking after each one to be sure they are accurate.  Practice makes permanent, not perfect!
Mathematics is one of two core subjects that must be taught.  
Part of educating at home is training children to work independently.  Math and writing are the two exceptions. Whether it's you, your husband, a video, or an older sibling, Math has to be taught one-on-one.  This is not the place to hand a child a workbook and hope for the best.  

Video teachers can be an excellent option, but be sure you are purchasing a video instructor, and not simply a video that teaches the parent how to teach that subject (Math U See, for example).   A good Math video will have solutions worked out for every single problem, even on the tests.  Videos that teach you how to teach are a valuable tool (I use the IEW system, and love their program), but are not designed for or capable of teaching a child a new skill.

In Mathematics, doing precedes understanding
Once a child has done several problems, they'll start seeing patterns.  Don't try to overwhelm them with theory and definitions before they've learned how to do the problems.  Look at textbooks before you buy.  There are publishers that are notorious for requiring students to understand theory before they have had a chance to see the patterns emerge by doing problems.  That's all backwards, and only works with gifted students.

We wanted each of you to have rockin' Math skills, so I chose A Beka for K - 5th grade Math, and then transitioned to Saxon Math in 6th grade.
Kindergarten through third grade should focus on mastery of math facts.  This is also the time to learn weights and measures, reading a clock, and other "real world" Math.  No one does this better than A Beka, but you have to buy the curriculum and the workbook for each grade.  The workbooks alone will not comprehensively teach and reinforce the skills.
Fourth and Fifth grade focus on learning fractions, decimals, more complicated problems in the basic functions, and introduce Geometry.  Again, A Beka does a fantastic job when the curriculum guide and workbook are used in conjunction.

Sixth through Eighth grade are different in American curricula than in every other industrialized country.
Because American teachers chose to drop mastery of basic facts in grades 1 - 3, they are forced to spend an addtional 2-3 years reviewing  fourth and fifth grade material.  In every other industrialized country, children begin pre-algebra in 6th grade, and are taking algebra in Junior High.

In order to compensate for this difference, I switch curriculum between 5th and 6th grade.  Saxon has a free placement test you administer at home.  Nate jumped directly to Algebra 1/2 in 6th grade, Matt went into Math 8/7 because he was still struggling a bit with decimals.   Don't accelerate your child beyond their abilities and frustrate them, but also don't give them 3 years of review when they could go directly into more challenging material.

In ninth through twelfth grade, Saxon does an excellent job preparing students for the SAT/ACT as well as college.  Videos are available for every course.  I highly recommend tailoring Mathematics courses to the child's area of interest.  Business, Bookkeeping, or Prob and Stats courses may be a much wiser choice than Calculus, even if the child has the mental capability for higher math.

Your attitude about Math is infectious.
If you have an excited, can-do attitude, so will your kids.  If they (or you) are frustrated, skip the problem and come back to it later, solutions manual in hand.  "Wow, that's a doozy!  Let's finish up this page and then come back to this one" is much better than hammering away on a problem until you're both in tears.

Your child may be using different algorithms to solve long multiplication or division than you did.  Most teachers are happy to teach you the "new" methods so you can help your student at home.  Don't attempt to teach a child a different way to solve the problem than what his teacher and class are using or you'll only confuse them.

Math was by far my favorite subject to teach.  Yup, I'm more than a little weird!  I hope you and your kids have the same love for Math that we enjoyed in our home.  If all else fails, send 'em over to Grammy's house.



  1. I almost didn't homeschool because I was scared to teach math. I hated it so much when I was going to school, I didn't think I could do it.

    I find myself getting excited about it now as I remember how to do some of these problems. I am relearning math with my kids!

    Great ideas! Thank you for sharing.

  2. Stacie,
    I feel your pain! I was nervous about grammar and writing. My grammar has improved dramatically as I've taught it to my children. The writing program I chose (IEW) encourages parents to write along with their children, so hopefully writing will improve as well.