Teaching the Three R's
Of all the things you teach your child, arguably the three key skills are still "reading, 'riting, and 'rithmetic.
How Do I Teach My Child to Read?
Many homeschoolers struggle with what to use to teach reading. There are SO MANY programs out there! Which one is the right one for your family? Your child? How do you as a teacher teach phonics if you learned by sight? (Uhem, like me, I didn't know what phonics was until homeschooling.)
Ruth Beechick's books "The Language Wars" and "The 3 R's" were indispensable for my family. I like how Mrs. Beechick's books take away the mystery to encourage parents that they can indeed teach their own children.
Overall, the right program is the one that works with your child. Do what works not what is popular. You also will need to assess every child individually because unfortunately one program that worked swimmingly for one child may not for the next. (Kids are like that...think used curriculum.)
I can also say that children learn to read by seeing the importance of reading to their lives. Read to them. Let them see you reading. Have fun with your books. Act out the characters as you read along. Create the treats or crafts mentioned. Have your children make little paper puppet characters on craft sticks to re-tell the story. (This is actually early preparation for writing too.)
But don't think you have to over-work each book. There's nothing like curling up together for a quiet story time.
After 20 years of homeschooling, and teaching ESL reading for almost 10 years, I can honestly say a phonics based approach has overall proven to be the best reinforcement for long term reading. Choose a program that truly teaches the sounds of the letter symbols. I personally prefer the "ladder" approach (used in Abeka, Writing Road to Reading, Phonics Pathways, etc.).
I personally avoid those programs that practice by sight patterns unless you have a very strong visual learner. Even then, I have seen phonics reinforcement improve strong visual readers.
I also highly recommend coordinating the early reading material with phonics development to avoid forcing the child to sight memorize. Reading phonetically reduces the memorization to key sound patterns (the phonemes) which can be used to unlock the thousands of words in the English language.
However, again, use the program that works best for your child.
To help sort out the confusion of all the methods available, please go to our in depth CHOC Board article entitled:
Cathy Duffy's Reviews. give individual reviews of the most popular reading programs on the market today.
How Do I Teach Writing Skills?
We at the CHOC Board think one of the most important things to remember is that a young writer, no matter what age, will need time, lots of patient encouragement with ample opportunity to develop their skills.
Do not be afraid to sit beside your children in their first writing efforts at each level and write with them. It's not cheating when you are teaching! Then have them begin to do more and more of the work on their own effort until they are confidently writing at that level.
In a simplified overview, writing composition can be boiled down to several types and some simple steps.
The Elements of Written Work
Writing encompasses two main types: creative writing (fiction/story/narrative writing) and expository writing (the non-fictional instructive, analytical, informative, or persuasive writing).
Good expository writing uses enough descriptive language to make it interesting. Good creative writing follows enough logical organization to make it understandable.
No matter which major type of work, these elements are usually included:
There should be a clear overall point (creative theme or expository thesis);
The body sentences or paragraphs should support the theme or thesis;
It should use proper grammar and spelling (unless colloquial language is used purposefully for a character)
It should have a logical beginning, middle, and end with connecting transitions in between for flow.
Style and the writer's unique voice will develop in time as your child grows in his writing abilities. Also, children should be allowed ample time to enjoy writing a story for fun without undue criticism of their technique.
Good Reading and Oral Narration Helps with Good Writing
Reading well written literature helps children visualize good writing. Then oral narration is an excellent way to begin the writing process (as Laura Ingall Wilder instructed--write it as if you were telling it to me). Have the child retell the story to you in their own words. As they grow older, have them write it down. Retelling familiar, well-written stories will help develop your chlid's inner writing sense and help them develop their own voice and style.
Begin Simple Then Add More Structure and Flourish
Usually story writing comes naturally first to most children as the beginning level books are narrative. Through their stories, gently work on sentence structure, grammar, and spelling. As they mature, begin expository writing with a focused topic. Develop paragraph structure from the topic sentence adding support and detail in the body ending with a concluding sentence. Finally begin the essay. The five paragraph essay is an excellent start: Intro ending in topic statement, body paragraphs that develop elements of the topic, then concluding paragraph that wraps up the essay.
Generally it is best to teach the basics first, then add embellishments and variety to the basic styles, ie transitions, literary tools. This means that for many children their assignment writing may be a bit short and dry especially if they are naturally fact-minded. For this kind of child, creativity and variety generally come in time as the child grows more accustomed, and less fearful, to writing.
Often it is the naturally creative child who easily writes with vivid description that struggles with expository composition. It is often difficult for them to stay on point and organize their thoughts since it's a lot more fun to go off in whimsical directions. Outlines can help creative writers pre-think their direction. Encourage them to stick to their given details rather than add too many embellishments.
Learn to Rewrite!
Frustration also arises out of the false belief that the first thing written must be perfect or that good writers use little effort. Writers write and REWRITE! "Natural" writers just don't seem to mind the effort as much as others.
Teach your child how to get down their initial ideas either in note form, outline form, on white board, or however it works best. Next have them flesh it out into a fuller picture; then rewrite for flow and errors, then do a final check and polish.
This takes time and effort, but diligence will pay off in the end product (and yes, someday he or she will thank you for those valuable writing skills).
Ruth Beechick's "You Can Teach Your Child Successfully, Grades 4-8" has excellent sections on developing writing skills.
How Do I Grade My Child's Writing Composition?
This would be another most frequently asked question to us as support group leaders. As homeschoolers we are somewhat isolated from seeing the work of others, and as mothers we worry that our children's writing somehow is just not up to the level of other children at our child's age/level/grade.
We are often tempted to see our child's work through adult eyes with expectations of adult writing.
Even if we could compare our children's work to another's, this might be foolish as we need to let our child develop at his or her natural ability and pace. Focus on mastery of the skills, a step at a time, rather than fretting over your child's time table of development.
There are some helpful aids in learning how to grade a child's compositions.
Ruth Beechick's "You Can Teach Your Child Successfully, Grades 4-8" has an excellent chapter on how to evalutate your child's writing skills at the various levels (and most libraries have a copy of that book).
"Format Writing" by Frode Jensen has good grading sheets at the back of his book which walk you through the assessment process. Do a google search on "writing evaluation sheets," and you generally get several examples (which are constantly changing as links go on and off, so we won't link any here).
Also, go to a CHOC Board article entitled "Written Work Evaluation" to see our example of an evaluation sheet rubrics if you have trouble finding one.
Remember, try not to get hung up on grades. Highlight what the child did right, then encouragingly work for mastery over time.
For reviews of individual writing curriculum, see Cathy Duffy's Reviews.
What About Teaching Math?
Somehow, the thought of teaching math can send fear into the heart of many homeschoolers. Math is often seen as mystical, abstract, complex and confusing. Anything but understandable. The fear of teaching upper math is one of the major reasons we've heard that homeschoolers give up on attempting to home school high school. But it doesn't need to be that way.
Math is well, just math. It is the language of numbers. It is an abstract expression of our concrete world, just like talking. Of all the subjects, it is the least subjective. 2 plus 2 always equals 4. Much of our math phobias came from being shuffled along, at a pace we weren't ready for, in an institutional school setting. We often received instruction that didn't match our learning style. Add to that little teacher support and a lot of heckling from our classmates, and math phobia is born. (Can you still feel the fear rise up in your throat as you were called to the chalkboard?)
We won't solve everyone's math woes here in this article, but we can offer some concrete suggestions from a thing (or two) that we've learned over the years.
Get the Basics Down First...Really.
Sometimes we as homeschoolers are in a hurry to get to the "real stuff" in math, often because we've heard about those bright homeschool kids that are in Algebra at 9 years of age. Avoid comparative computing when it means trying to keep up with your homeschooling neighbor's math savant. Just as you had to crawl before you could walk, you have to be able to do basic math before you can do advanced. Every student develops at their own unique pace. You can't force honest brain cell growth.
Math is very foundational. What you learn at this level will be applied to the next. Do not underestimate the importance of learning addition, subtraction, multiplication, division and ratios (fractions, decimals, and percentages). A lot of advanced math still makes use of simple basic math skills. Overlearning (the term for mastery) is important in the basic skills. This can be carried out excessively ad naseum, but do drill the basics until the student can answer without hesitation. Always teach with understanding as to what is happening rather than by just rote memory. (Get it explained to you if you need to do so first!) Story problems often trip people up because they cannot apply the math with understanding. Application is as important as computation.
We've seen homeschoolers stop fearing math when they found a good program and re-learned math skills along with their kids. Math is about the real world after all.
Observe the Student's (And Teacher's) Learning Mode for Math Skills.
There are many math programs available on the market. There is a reason for that. Math can be learned in different ways. Some people are bean counters; they think "in the quantity of." Others are spatially oriented; they think "in the spatial size of." And yet others are visual learners or language oriented; they think along the lines of "this visually represents that" or "this means that." Math is all this, and more.
Math manipulatives address different learning styles. Cuisinaire Rods appeal to the spatial learner. (A two inch length, plus a two inch length, equals a four inch length.) Base Ten Blocks, Equivalency Cubes, and Colored Tiles appeal to the quantity counter and help them make spatial and relational connections (two blocks plus two blocks equals 4 blocks that also take up this much space). Learning Wrap Ups and math board games can appeal to the language oriented learner.
Observe how your child interacts and measures his or her world. This can give you indication of how they think mathematically. Using whole body movement can help the kinesthetic (hands-on) learner relate to his world mathematically. Colorful visual aids and flashcards will help the visually oriented learner. Songs and rhymes will help the auditory learner. Make use of the different senses to teach mathematical relationships in the basic skills.
As students age, most math curriculum turns to a textbook or workbook approach. Eventually, by high school, almost all math curriculum will center on a textbook approach. By college, no other choice is generally offered. Fortunately as home schoolers we have choices that institutional schools don't have.
There are numerous programs that utilize manipulatives and visual aids right through the high school math. (Miquon Math, Math U See are some examples).
Several programs take a language-oriented or symbolic approach. (Video Text Algebra, Harold Jacobs Math, Thinkwell, Life With Fred series).
Some textbook programs also offer visual aids as a supplement to learning which can be very helpful, especially if the parent needs additional support (Teaching Textbooks, DIVE videos for Saxon, Chalkdust Math, Kahn Academy Math). These are usually solutions worked out on a chalkboard or a teacher talking over the solution at a chalkboard rather than truly manipulative based programs.
Do be aware the programs that use a predominately visually based, literature-oriented, or manipulative approach in upper math generally do not cover all topic areas at the depth that a rigorous textbook program covers. If your student is bound for a technology or engineering field, it may be best to leave time to do a more rigorous textbook program after the alternative program.
Incremental Spiral Approach v. Sequential Approach
Another distinguishing feature in math programs is the methodology used to teach the different concepts. Neither method is right or wrong, and both offer advantages and disadvantages. Unfortunately math programs tend to favor one or the other at the expense of the other.
Some programs use what is called an incremental (little by little) spiral (repetitive) approach. New concepts are introduced very slowly and split apart over many different areas in the book so they are not overwhelming. Most of the daily exercise is over previously taught material so that constant review, and success, is achieved. The curriculum focus is on review drilling and rote memorization so that a student is not overwhelmed with new material. Saxon math uses this approach, and many homeschoolers have found it very successful. The negative about this approach is that it disjoints concepts which are similar preventing helpful connections and applications being formed. A student may never connect that a decimal is a ratio because the concepts are taught in different sections of the book. This method also makes it difficult to use the book as a reference later because so many sections must be read to cover a single concept.
The sequential approach places like concepts together sequentially. Ie., a ratio is a comparison, a fraction is a comparison to a whole, a decimal is a comparison to 10, a percentage is a comparison to 100. These concepts would be taught in sequence to build one to the next. The focus of the daily exercise is on the new concept being taught, so the lesson material and most exercises will be on the new concept. Some review is done, but often it is at the end of the chapter or only a few problems assigned at the end of the day's lesson. The advantage of this method is that students often anticipate the sequential connection which can make the understanding of the math deeper (ie, they will figure out that if a decimal is a comparison to 10, then a percentage is a comparison to 100, that's just another ratio!) The disadvantage will be if the curriculum does little spiral review so that older concepts are not reinforced well. Bob Jones Math and Modern Curriculum Press are two curriculums that use the sequential approach.
Some students do best in the Incremental Spiral Approach. Some do best in the Sequential Approach. Use the math curriculum that best fits your student and family, and politely smile when your homeschool neighbor yet again raves about how their curriculum approach is superior.
All good math programs will include practical application, ie "story problems."
Don't skimp or skim over these sections as that is where math is put to real use. Good math programs will make applications achievable and understandable even to the average math learner. Story problems are about decoding what facts are given, figuring out what math to use, then using the math to solve it. If your curriculum does not offer a lot of story problems for application, there are supplemental books available.(See the Critical Thinking series as an example.)
Consider Teaching More Rather Than Less Math Than is Needed.
Math is a portal to many skills and professions. A major time waster for adult students is getting math skills up to standard when they figure out later in life that certain math skills would have been useful for a desired pursuit.
Also consider that math skills build stronger thinking skills, even if your student isn't going to go into a profession that uses upper math. At the very least, you will pass on an appreciation for the orderliness of God's world and the majesty of His creation. Evolution is not a precision mechanism. We see mathematical precision in our world that testifies directly to the Hand of God. (Many foundational mathematicians and scientists saw this.)
You will also build a confidence into the next generation of homeschoolers who won't be so easily tempted to jump out of homeschooling highschool over math phobia. And you might be surprised that even you have taken on a new appreciation for mathematics as good materials make math real to you.
We recommend teaching a minimum of Geometry, Algebra I and Algebra II/Trigonometry to all students unless there is a realistic reason why that is not possible (even our liberal arts, non-math daughter was able to achieve that much math with the right curriculum type)
Pre-Calculus and Calculus is an area that could be better developed for homeschoolers. Fortunately, the homeschool curriculum market seems to be responding. Many colleges have a methodolgy they teach in pre-calculus for their calculus classes. You may need to look at the ultimate goals for calculus to help choose your materials.
Our Tips for Teaching Math.
We've learned the following in our journey through math, which we offer for your consideration:
You Don't Need Every Expensive Math Manipulative and Game to Teach Math.
Wow. There is so much of that fun stuff on the market. And they all seem so important. We bought the Cuisinaire Rods, the Base Ten Blocks, the Geo Squares. Numerous math games. And while a number of them became treasures, we also discovered many of the products only covered a tiny portion of math skills or were redundant with something else we had. Decide what's the best fit for your child and family and stretch those math dollars before the vendors stretch them from you.
We got a lot of mileage out of a bucket of beans, figuring out what day it was on a calendar and computing when an eagerly anticipated event would occur, and turning cardboard strips into an oversized math number line to race our son's hotwheels up and down. By the way, he learned a lot of math that way too...cheaply.
Avoid Switching Between Math Programs Frequently.
Math publishers develop their curriculum slightly different in sequence. Avoid jumping a lot from one program to the next as you can miss key concepts taught in a prior book or level. Most publishers offer a placement test that will help you decide where your child fits in their curriculum, but you can still leave gaps if you switch curriculum between publishers a lot. Natural breaks occur after the primary grades and after sixth grade before algebra.
Especially avoid switching a lot in upper math as publishers not only scope differently, especially in the progression from Algebra I, Algebra II and Trigonometry/Pre-Calculus, but publishers also use different methodologies for explanation and will assume the student has had that in earlier books in the series.
Consider Amending the Traditional Sequence of Upper Math.
Usually, upper math is taught in the sequence of Algebra I, Geometry, Algebra II/Trigonometry, Pre-Calculus/Trigonometry, Calculus. (Though more public schools are integrating math subjects.)
We've found it better to go from Algebra I right into Algebra II. We inserted Geometry after Algebra II, before Pre-Calculus, but if we had it to do again, we'd seriously think about doing Geometry first. Geometry is in its own separate world, and most elementary math series cover basic geometry, which is forgotten by the time we got to Geometry in high school. While Geometry is important, for the logic skills learned especially, we'd get it out of the way and then start the Algebra to Trig series to keep those concepts growing right into Pre-Calculus and Calculus especially for the technology/engineering bound student.
If your homeschool is not comfortable with Calculus (and some educators believe that calculus is really best taught at the college level), focus on algebra and trigonometry skills. Having those skills down to mastery level really helps prepare a student for college level calculus. If you didn't catch this fact in an earlier paragraph, we've personally noted that those students taking college calculus for the first time who are doing exceptionally well, are those students who really mastered algebra and trig.
Use the Answer Key As Part of the Lesson.
Stop thinking about grades and how much you got right, or didn't, on the homework (that was institutional school thinking). Hand your student the solutions manual as they work their homework (but not while taking the tests). The solutions manual is a valuable tool as they learn how to do the exercises on the new concept. And the tests? Have them take the tests, then after noting their score, hand them the test solution manual and make them correct everything that was missed. The point is to learn how to do the math. And assign plenty (but not all) of the homework exercises so that the student really gets the concepts down into long term memory.
Also, many college professors allow one "cheat sheet" of equations for tests. Basic formulas should be memorized, but not everything has to be memorized. Professional engineers don't trust their memory for complicated formulas.
Allow lots of time for math.
Upper math is more complex and one math problem can take up a whole page, or more, for solution. Don't load your student down with so much other activity, especially extracurricular activities, that you can't allow several hours for math if needed.
Don't overuse calculators, but do get a good graphing calculator for upper math.
We first taught the manual method for graphing algebra problems (with grid paper and pencil). Then, over the summer we bought a graphing calculator and taught that. Calculators are necessary, but the student should understand the concepts of what is actually happening rather than simply what keys to push to get the answer.
And there is help in learning how to use those complicated graphing calculators. (A quick Google search will bring up plenty or see Kahn Academy).
If you've not previously used the math curriculum, go over it carefully before relying on it for the year.
Math, espeically upper math, can become unbearable if the curriculum is poor. And unfortunately, there is so much math and so little school year that having to abort mid-year to find another curriculum can cost valuable time. Sometimes at a time cost that can't be recovered.
Allow enough time to sufficiently review the whole curriculum before you have to teach it. We unfortunately lost valuable time as an old series favorite had a really, really lousy book in the upper math series. We floundered for several months before we realized it was a loss and had to look for something else mid-year. Just because you like the series doesn't mean every book is good. Often the math books are written by different authors in the math series.
And check those return policies if you purchase online! We lost a lot of money on a much advertised curriculum that turned out to be totally wrong for our family when we found out we did not have a good return policy because we did not discover our error until after school had started.
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(Permission is given to print for personal use or link to this article as long as credit is given to Tammy R. Arp at the CHOC Board and our website address is shown.)