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February 2020

(For the Math 54 through Math 87 Textbooks)

I receive several emails each week about the excessive amount of time some home school students spend on their math assignments each day.  In almost every case, the students have spent between thirty minutes and an hour on the “Warm-Up” box and the six to eight “Practice Problems” before they even get started on the thirty problems of the Daily Assignment.

It has been a little more than a decade since I have been in a public classroom, and I am not sure if public school middle school math teachers still lean on what they used to call a math “Warm-Up” at the start of each class.  The purpose of the “Warm-Up” was to settle their students down and get them ready for the math regimen of the day.

Using the “Warm-Up” box at the beginning of each lesson in the Saxon Math 54 through Math 87 textbooks can become quite frustrating to students who do not have the advantage of a seasoned classroom math teacher gently guiding them in the direction of the correct solution for the problem of the day – knowing that problem might come from a concept not yet introduced to the students.

But what about the “Daily Math Facts Practice” and the “Mental Math”; how will students receive training in those areas?  While these two areas are essential to the student becoming well-grounded in the old pen and pencil format of adding, subtracting, multiplying and dividing, graded by the teacher, that format has been improved with a computer model.  Using the computer format allows the students to instantly know whether their answers are right or wrong.  Additionally, while the home educators can easily spot the results tallied on the computer as the student moves along, it saves them the time spent manually grading the documents.  I have placed a link to a wonderful Math Facts site on my website.  Readers can find it by going to my home page, and from the list on the left side of the home page, click on “Useful Links.” When the new window appears, select the second link from the top labeled “On-Line Math Facts Practice.”

That link takes you to a math facts practice site that allows the student to select from seven different levels of difficulty in adding, subtracting, multiplying and dividing.  Five to ten minutes on this site every day at the appropriate level for the student to be challenged without being frustrated is just as good as the mental math or facts practice found in the “Warm-Up” box. While the Math 87 book still reflects the same “Warm-Up” box that the previous three math textbooks do, a student should have mastered the facts practice by this time.  If this is the case, skipping the entire box is acceptable – unless – the student particularly enjoys the challenge of the “Problem Solving” exercise.

Now let’s see if I can explain why I am recommending you stop having the student take time to do the six to eight practice problems at the front of each of the mixed practices (the daily assignments).  The original purpose of these practice problems was for the classroom teacher to use all or some of them in explaining the concept on the board so that the teacher did not have to make up their own or use the homework problems. Sometimes teachers would use some of them to have students come to the board to show their understanding of the new concept. 

My experience in teaching John’s method of mastering math has shown me that there are basically two possibilities that can exist after the student has read and/or had the concept of the daily lesson explained to them.

Possibility 1:  The student understands the concept and after doing the two homework problems dealing with that new concept, completely understands what to do and has no trouble doing them.  Mastery of this concept will occur over the next five to six days as the student does several more each of these for the next few days. If this is a critical concept linked to other steps in the math sequence, they will keep seeing this concept periodically throughout the rest of the book.

Possibility 2: When students encounter the two homework problems that deal with the new concept, they have difficulty doing them.  So, on their own, should they go back to these practice problems and get another six to eight more problems wrong?  If they did the practice problems before they started their daily work, would anything have changed?  If they cannot do the two homework problems because they do not understand the new concept, why give them another six to eight problems dealing with the new concept to also get wrong?  This approach ultimately leads to more frustration on the part of the student.  Students will have spent thirty minutes or more on these additional six to eight practice problems and still not understand the new concept. Not every student completely grasps a new concept on the day it is introduced which is why John’s books do not test a new concept until the student has had five to ten days to practice that concept.

Those practice problems were not placed there to give the student more problems to do in addition to the thirty they are assigned every day.  They were placed there for the classroom teacher to use on the blackboard to teach the new concept so they did not have to develop their own or use the student’s homework problems.  There is nothing wrong with a home school educator asking a student to do one or two of them to show them the student does understand the new concept; however, doing more than that could be a waste of time and effort in either possibility.

Not every child is the same and I realize that because of a particular child’s temperament, there may be some instances where the parent has to go over more than one or two of the practice problems with the child – and this is okay – but for most students this is not necessary.  If the student really enjoys the challenge of the daily “Problem Solving:” that is okay – except parents should make sure that the student does not spend an excessive amount of time on that individual challenge and allow the real goal of completing the thirty problems of the Daily Assignment to become a secondary goal – and later a bother to the student.



January 2020

- or -

Before addressing that question directly, let me first relate a story about a man walking across a bridge spanning a river.  As he looked down at the water, he noticed a boy who had fallen into the swift current.  It was apparent from the boy’s struggle that he could not swim.  The man realized he had only two alternatives.  He could shout instructions to the boy on how to overcome the swift current and perhaps enable him to dog paddle to safety on the shore, or he could dive into the water and rescue him.  Without hesitating, the man dived into the water and immediately swam to the side of the struggling boy.  Now the man had to face another dilemma.  Should he pull the struggling boy to safety or should he immediately try to teach him how to swim?

Everyone would agree that when people are drowning, that is not the time to try to teach them how to swim.  All one can do at that time is try to get them to a place of safety where they can overcome the swift current of the river.  So it is with mathematics.  In any of John Saxon’s math textbooks from Math 54 through Calculus, if student’s begin struggling before reaching lesson thirty or sooner, it is a sign that they will drown in the later lessons of the book unless they are taken to a place of safety where they can better manage and learn the concepts that they are now unfamiliar with. Concepts that are dragging them into deep water!  It should become apparent that they are not prepared for the book they are in, and no amount of supplemental material or expensive tutors will overcome those shortcomings.

Mathematics is like the swift current that challenged the drowning boy.  Like the river, upper level mathematics is challenging and can easily become unforgiving.  Looking for a slower moving or shallower river may create a temporary solution, but eventually that water will again become swifter and deeper and unless one is prepared, all the advice and assistance given at the time of the struggle will come too late.

While it is a noble goal for students to strive towards taking a calculus course in their senior year of high school, it is critical that they first master the algebra.  The calculus is easy! It is the challenge of the algebra and to a lesser degree the trigonometry that causes students to fail calculus.  Any student with a solid algebra background, entering any college or university, will pass that school’s math entrance exam and will be successful in a calculus course should they choose to do so.

When classroom teachers or home school educators take shortcuts with one of John Saxon’s math books, they are not adequately preparing the student for the deeper water ahead.  More than a quarter of a century of experience with Saxon Math textbooks has shown me that classroom teachers and parents who take shortcuts with his curriculum (instead of going slowly and deliberately through as John intended) cause students to “flounder” as they encounter the “deeper” water.  At this point, they find it easier to blame the book – and they look to switch to an easier math course!

The classroom instructions contained within my DVD “video” tutorial series – as well as the online lessons – are not math supplements.  They contain actual classroom instruction on each concept in the book.  Like the book, the classroom instruction is designed for the homeschool student who is in the appropriate level math book. The instruction enhances the written word they have already read from the textbook.  Many of the lessons present a different explanation by an experienced Saxon math teacher that helps the student through the difficult reading of the lesson.

However, regardless of who creates them, neither the CD white-board presentations nor my DVD classroom tutorials – or online lessons – will help students who are taking a course they are ill prepared for.  They will eventually find themselves frustrated and floundering in the “deeper water” of a math course they are not prepared for!

Have a Blessed and Happy New Year


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