There are many wonderful books and curriculum on this subject which we won't belabor here as each family is so unique. (For reviews of writing curriculum, see Cathy Duffy's Reviews ).

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, and ample opportunity to develop their skills.

Do not be afraid to sit beside your child with his first writing efforts at each level and write the work with him. It's not cheating when you are teaching! Then have him begin to do more and more of the work by his own efforts until he is writing confidently on his own.

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:

Style and the writer's unique voice will develop in time as your child grows in his writing abilities.

Children should be allowed ample time to enjoy writing a story for fun without undue criticism on their technique.

**Good Reading and Oral Narration Helps with Good Writing**

Reading well written literature does much to help a developing writer begin to visualize good writing.

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, and then, 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**

For focused instruction of composition skills, generally it is best to teach the basics first, then add embellishments and variety to the basic styles.

This means that for many children their assignment writing may be a bit short and dry especially if they are naturally logical and scientific-minded. For this kind of child, creativity and variety generally come in time as the child grows more accustomed to writing.

Often it is the naturally creative child who easily writes with vivid description that struggles with expository composition as it is difficult for them to stay on point and organize their thoughts logically since it's much funner to go off onto all their whimsical directions.

Again be patient and encouraging as your child develops. Also, help your child be patient with himself and the writing process. Much of writer's block comes with the mistaken belief that every word on the page must be perfect and the piece brilliant from the first writing.

**Learn to Rewrite!**

Frustration also arises out of the false belief 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).

**From the Sentence to the Paragraph to the Essay**

When starting the basic concepts of expository composition, it is usually good to begin with sentence construction (understanding how the parts of a sentence work, first simple and then complex sentences, and also where to place modifiers--those words that describe a subject or describe the action).

RHL School has free grammar and writing instruction worksheets. Write Guide has free skill sheets for more advanced but common errors in sentence construction and how to fix them. HyperGrammar is a free, online grammar course produced by the University of Ottowa that provides a pretty full set of grammar lessons with interactive review.

Even better, English 101 provides pre-tests and a complete interactive grammar course aimed at middle through high school students for free (click on "home users" to access the lessons).

Next have your child work on doing a good paragraph (topic sentence, supporting sentences, conclusion).

After he/she can write solid paragraphs (in the various types), then broaden their skills into tackling the multi-paragraph or 5-paragraph essay (intro/thesis paragraph, three supporting paragraphs, conclusion).

The TRIAC method is another useful essay pattern, especially for literary analysis essays. TRIAC stands for: T- thesis (general opening paragraph); R - restatement of thesis (from general to specific point); I - illustrations (examples given to support point); A - analysis (analyze how your examples support your main point); C - Conclusion. The whole TRIAC method can be used within one paragraph or as a pattern for a multi-paragraph essay. Often the illustration and analysis happens in the same paragraph.

Finally, they will be ready to tackle the major work (which amusingly follows the same pattern with just more)--opening intro section with thesis, supporting sections--which usually have developed subthemes, then conclusion.

Creative writing, while not developed exactly along expository lines,will still utilize good sentence structure, then good descriptive paragraphs, then small story to larger work learning to develop theme, point of view, characters, setting, plot, developing action, climax, and anti-climax.

**Use a Physical Method to Manipulate Essay or Story Parts **

Many children benefit from a physically-manipulative method of putting a story together.

A story board uses a white erase board with bubbles (drawn circles) where the main idea is in the main bubble and each supporting idea is in an attached bubble--like an octopus with legs holding bubbles.

Some children prefer using notecards with the main idea on the first card, supporting ideas on subsequent cards, conclusion on the final card.

*CHOC Board Tip:* We do like to recommend "Format Writing" by Frode Jensen for expository writing and "Learn to Write the Novel Way" for creative writing, even if glanced through only as a teacher's reference, as these two programs especially seem to walk the reader through the whole writing process itself while giving a good overview of their types.

Ruth Beechick's "You Can Teach Your Child Successfully, Grades 4-8" has excellent sections on developing writing skills.

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 (as the last time most of us were graded, we were in college or high school!).

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 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 librarires have a copy of it).

"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.

Remeber, though, not to get hung up on grades. Highlight what the child did right, then encouragingly work for mastery over time rather than a letter grade. *(When appropriate, we told our children it doesn't matter if you got a 99%, the bridge still fell down. Let's do it all right. The goal was always mastery rather than a letter grade or percentage of acceptability.)*

We waited to write this section until we had completed our math journey in our homeschool and felt we had a bigger picture in focus rather than just a few curriculum ideas and math approaches. (We've graduated 3 students to college...one to veterinary technology and medical math, one to a liberal arts journalism degree and "real world" math, and one to electronics engineering to enter calculus level 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. And anything but understandable. The fear of teaching upper math is one of the major reasons we've heard from homeschoolers for giving up on attempting to homeschool 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. And 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 with the material presented in a way that didn't match our learning style, add to that little teacher support and a lot of heckling from our classmates. (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. However, avoid comparative computing when it means trying to keep up with your homeschooling neighbor's math savant. Just as you have to crawl before you can walk, you have to be able to do basic math before you can do advanced. And every student develops at their own unique pace. You can't force honest brain cell growth or synapsis connections.

Math is very foundational. What you learn before will be applied to what you will learn later. 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 to tedium, but do drill the basics until the student knows them thoroughly and can answer without hesitation. Always, however, 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 length or space 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 a sense of mathematical relationships in the basic skills. There are many programs on the market that utilize different senses and approaches for basic math skills (see Exodus Books and Cathy Duffy's online reviews for a great list of those).

As students age, most math curricula turn 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 homeschoolers we have choices that can be made that institutional schools don't have.

There are numerous programs that utilize manipulatives and visual aids right through the high school math for those who need that approach in upper 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). These are usually solutions worked out on a chalkboard or a teacher talking over the solution at a chalkboard rather than truly manipulative, visually based programs.

Do be aware the programs that use a predominately visually based, literature-oriented, or a 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, in at least the uncovered areas, to best prepare the student for college level math.

**Incremental Spiral Approach v. Sequential Approach**

Another distinguishing feature in math programs is the methodology used to teach the different math 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 can retain what was previously taught and not be 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 that are similar which can prevent abstract connections and applications being made. 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 and thus forgotten. 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 teach application "tricks" and make applications achievable and understandable even to the average math learner. Much of the application of story problems is learning to apply visual symbols and language understanding to the task at hand and then attack it with computational skills...defining what needs to be solved, drawing a picture, and then finding the math to solve it. If your curriculum does not offer a lot of story problems and application, there are supplemental books available to teach critical thinking skills and offer additional math application problems. (See the Critical Thinking series as an example.)

**Consider Teaching More Rather Than Less Math Than is Needed.**

Do consider your child's gifts and bents and the likely direction they will take after homeschool, and do be realistic with their ultimate abilities. However, don't esteem math too lightly and aim too low in math simply because you don't like to teach it or you don't feel upper math will be important to your child's later life or vocation. Life has funny ways of changing paths on us when we least expect it. Don't shut educational doors that could be left open, not this early in the game.

Math is a portal to many skills and professions. A major time waster for adult students is trying to get under-used and unlearned math skills up to standard when they figure out later in life that they do want to go into a math based profession afterall or find that certain math skills would be 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 (Johannes Kepler, a mathematician and early astronomer proclaimed he was "thinking God's thoughts after Him" in studying planetary motion; Sir Isaac Newton developed Newtonian calculus to build upon Kepler's work to derive the universal laws that explained planetary motion in the universe.)

You will also build a confidence into the next generation of homeschoolers who then won't be so easily tempted to jump out of homeschooling highschool over the fear of math. And you might be surprised that even you have taken on a new appreciation to a previously despised subject 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 student was able to achieve that much math with the right curriculum type...this was the same student that as a child we finally "bribed" into understanding the concept of "carrying" in subtraction with opening up bundles of Laffy Taffy candies). There are excellent resources available to homeschoolers for all these levels.

Homeschool materials at the pre-calculus/calculus level are currently very limited. Pre-calculus materials available often include a "baby calculus" course, which can be helpful but often is not particularly well done. (We hated the curriculum by an "old standard" we had chosen, to our dismay.) However, don't panic if you don't make it through calculus in homeschool if your student is headed into an engineering field or math/technology. While ideally the student should go through calculus at home, we've observed that the most successful students in college calculus may or may not have had calculus before but definitely had a very solid foundation in basic math and algebra/trig first...and there are lots of materials for those levels available to homeschoolers. Homeschoolers we know who did calculus at home generally used Saxon calculus, but felt the incremental/spiral approach was a hinderance at this level of math because it made the topic disjointed.

Pre-Calculus and Calculus is an area that could be better developed for homeschoolers to make this a topic area that could be better student directed and parent supported, especially if the parent is rusty at that level of math. However, more and more curriculum is coming to market for homeschoolers every year, and we will keep this section updated as we learn more.

**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 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. Yes, well-crafted objects for specific concepts can be very helpful, but sometimes they were simply a different way to teach the same concept. 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.

However, 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 because of the need for a student's brain to mature to that 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! Go to our math links page to get help.

__If you've not 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 and find another curriculum can cost valuable time. Sometimes at a time cost that can't be recovered.

Make the point to really go over the curriclum in the summer, or if you school year round, 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.

To see helps we've discovered over the years, please go to our "Math" section in our Handy Links page. We update this section as new helps become known.

**The CHOC Board **

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