By Larry Zimmerman
Employing "word" problems as puzzles just for fun may be acceptable, but using them to motivate student interest in mathematics is counter-productive.
The Christian mathematics teacher does not need these phony, far-fetched devices to motivate interest in the subject. Since mathematics is an entity which always exists in the mind of God, and is for us the universal expression of His creative and sustaining word of power, the Christian studies it for two valid reasons:
As I pointed out in Part I, the more powerful methods in number two must wait for the calculus.
I believe that students who are well grounded in the topics of a traditional program based on good mathematics (as opposed to memorizing lists of gimmicks to fit special cases) will be prepared to "function in this modern world."
Business and industry are pleading for educated people with some cultural awareness who can communicate and follow directions. The companies want to do the training in applications for their own special requirements.
I think Wendell Berry had a point in his book, Think Little, when he said, "If life were as predictable as the small talkers of politics would have it, then relevance would be a consideration. But life is large and surprising and mysterious and we don't know what we need to know." He adds, "When I was a student, I refused certain subjects because I thought they were irrelevant to the duties of a writer, and I've had to take them, clumsily and late, to understand my duties as a man. What we need in education is. . . abundance, variety, adventure, thoroughness. A student should suppose that he will need to know much more than he can learn."
It is the Christian teacher's heaviest responsibility before God to ensure that Christian kids understand the nature and purpose of mathematics. Its nature is revelatory of God and its purpose is to glorify God.
Otherwise, the children may aim to use mathematics only to obtain a high-paying job, and thus end up as impractical, dichotomistic materialists, worshipping and serving the creation rather than the Creator.
I'm reminded of a cartoon I saw recently. A group of corporate moguls with puzzled expressions were gathered around one of their number who was on an intercom to a secretary saying, "Miss Bascom, will you please send someone in here who can tell right from wrong?" Let's give our Christian kids the theistic perspective on all of life, including mathematics, so they can reinforce the depleted ranks of those who can (and will) tell right from wrong outside as well as inside their church building.
During the N.C.T.M. Conference, I was surprised to hear a general session speaker make a comment which I'll use to summarize these remarks on Recommendation 1: "It appears to me that this is a return of the pendulum to the old process-over-content emphasis which we have tried in the past, found wanting, and discarded." I think his assessment is accurate.
I agree in general with N.C.T.M. Recommendation 3, though I have some reservations. Most of the teachers at the seminar did also. We want to avoid the possibility of kids becoming so dependent on calculators that if the batteries fail the youngster is helpless.
The opposite extreme is more likely to occur. Most elementary schools, especially the Christian ones, not only are teaching but emphasizing computational skills which have become obsolete outside school walls. No one on the outside computes with numbers of more than three digits, using pencil and paper. When calculators can be purchased for as little as $9.00, it seems silly to practice page after page of arithmetic manipulations using large numbers. We can spend the time more profitably practicing ratio and proportion.
After children have learned their tables and fractions, and have practiced computing with numbers up to 3 digits, give them a calculator and teach them how to use it. Of the many high-schoolers who own calculators, only a few know how to get all that their calculators can give them.
Calculators can free us from learning how to use the trigonometric and logarithmic tables, including interpolating, and learning how to compute with logs. The time is much better spent studying log and trig functions.
High schools are at least as far behind in utilizing computers as the grade schools are with calculators. One of the N.C.T.M. speakers quoted R. W. Hamming, who pointed out that "computers have improved in speed by at least six orders of magnitude over hand calculations—a millionfold. It is a common observation that a change in order of magnitude in technology produce fundamentally new effects. . . There has been a corresponding decrease in the cost—more than one thousand times cheaper."
It is obvious that computers have become necessary to us Christians who are carrying out our God-given mandate to be caretakers in/of the creation.
Finally, if any Christian mathematics teachers remain unconvinced about the importance of reading, thinking, talking and writing about these recommendations, they should consider the remarks made at the N.C.T.M. Conference by past president nominee Shirley Frye: "No longer will results or cognitive measures only be valued," she said, "but importance will be placed on the process in the context of the humanistic approach where helping students realize their potential and develop a positive self-concept are primary goals. In the past, man focused on solving problems in the world as it existed. Now and in the future, society will focus on problems in the world as humans have shaped it." Then, quoting Dennis Avery, she said, "There will be a need to redefine knowledge, schooling, and education. The emphasis will be on learning how to learn, rather than on learning facts."
When leaders in mathematics education promote projects like "redefining knowledge," we Christian teachers need to take notice or soon, as John Gardner claimed, "neither our theories nor our plumbing will hold water."
We need to devise alternatives to even the Christian college. Apprenticeships were the practice of our godly forefathers, and biblically have much to commend them. Commitment to the faith may even entail a change of vocational plans. Government or union demands may render some jobs off limits for the Christian, at least temporarily.
I have prepared a more lengthy discussion of the university and the apprenticeship plan, which you may have for the asking. If you feel you have a student who absolutely must attend a secular university, this writer would like to hear from you. Write the editorial office.
BOOK REVIEW
By J. S. Larson
Accompanying the growth of Christian schools is the increasing number of books related to this subject. One such book is Educating for Eternity: The Case for Christian Schools, by Claude E. Schindler, Jr., (Tyndale House, $2.95). The author not only covers the reasons for a Christian school but also shows how a school can work using biblical principles as its basis.
Claude Schindler helped form the Dayton (Ohio) Christian Schools (DCS) from its beginning and is presently serving as its superintendent. He uses many of his own experiences to show how the schools have successfully developed to its present 1400 student capacity.
At the onset he confronts the usual questions raised by parents as to why their children should attend a Christian school (i.e., why remove the Christian witness from the secular school; why not prepare their children for the "real world," etc.). Schindler answers these questions through the examples of several well know Christians and points out the problems involved in the public schools.
The factors that truly determine what a Christian school is to be are explained:
A Christian school is far more than an educational program with a religious coating. A school that is truly Christian is first of all centered in the authority of the Scriptures and the Person of Jesus Christ . . . The Christian school seeks to train its students to view the whole of life from God's perspective, not just from man's point of view ... All philosophies narrow down to be either man-centered (humanist) or God-centered (p. 29-30).
Although the parents have given to the Christian school the responsibility of their child's formal education, this is in no way a complete delegation of responsibility for the child. For, in fact, the Christian school cannot be a substitute for the home or the church. In order for a Christian education to be truly effective, the parents must practice their Christian faith in the home, actively participating in their child's education.
Besides giving an encouraging report on how the Dayton Christian schools evolved, Schindler provides a list of Christian school associations and addresses that offer help to the parent where there are no Christian schools available:
One particular chapter entitled "How Different Should I Be?" reflects much of Schindler's own denominational background. The desire to balance the intellectual and the spiritual education is sought but the spiritual aspect is more apparent.
A practical example of how positive characteristics are sought after was given:
In the high school drama department, our speech teacher has made up a list of twenty-one positive character qualities that young people can develop by being involved in dramatic productions. The list of qualities includes diligence, endurance, discernment, flexibility, orderliness, self-control, resourcefulness. These make up her guideline in working with her students in preparing productions (p. 57).
The subject of textbooks is briefly discussed by Schindler. At the outset of DCS, textbooks were chosen on the basis of intellectual value; however, they have increasingly implemented Christian textbooks feeling that "it is easier for a teacher to add academic excellence to a text-book, if necessary, than to add God's eternal perspective" (p. 57).
Schindler's application of Jay Adams' approach to the principles of interpersonal relationships between administrators, teachers, parents, and students is quite effective. If a parent is giving the superintendent a bad report about a teacher, he is kindly asked if he has confronted the teacher (m accordance to Matt. 18:15-17) and if he has not, he is advised to do so rust. This has met with remarkable success in settling difficult matters.
Another interesting application of this is used in the hiring of teachers:
When we sent out letters asking for references on our teacher candidates, we ask the person not to give us any negative report about the candidate unless he has first pointed out the problem to the candidate (p. 86).
Although the book tends to emphasize the spiritual goals of the Christian school it did not neglect the practical, active applications of God's Word. It is very useful reading.
The Education of Our Children—Whose Task? by T. M. Moore (Christian Studies Center, 1979)
This is an excellent booklet which might be passed on to parents who need to be convinced of the necessity of a Christian education. Obviously influenced by R. J. Rushdoony, Moore sets forth Biblical directives, historical precedents, and philosophical foundations for Christian education. It can easily be read in one sitting. For information on how to obtain this booklet from other than your local bookstore, write:
Christian Studies Center
P. O. Box 11110
Memphis, TN 38111
VOCATION AND THE UNIVERSITY
By Kevin Craig
One of the most difficult decisions in the life of many Christians is the decision of what to do upon graduation from high school. Parents who have been careful to keep their children out of public, humanistic schools for twelve (eighteen!) years have grave doubts about the propriety of sending their children off to a more radically humanistic school: The University. The students are equally concerned about whether or not the Christian college has the academic credentials to help them in their vocation plans. Many of the questions that are asked at this time reflect presuppositions that need to be closely examined in terms of the Word of God.
The history and present function of the University reveals that its purpose and content are rooted in radical humanism. Its purpose is the construction and promulgation of a humanistic plan of salvation. Every area of life is thought out in terms of man's autonomy, and applications in the sciences, arts, and public policy fields are made with a view towards the saving of man by the laws of man. Many have seen that the secular college or university is not a viable option for the Christian. Consider just three reasons: Fast, our purpose as Christians is to apply the Word of God to every area of our lives; not just the "religious" areas, but our families and our callings as well. How can one exercise dominion (Genesis 1:26-28) according to the plan of God if he has spent his years learning instead the plans of men? Second, the same arguments against a humanistic curriculum for elementary and secondary education apply equally well to the university (Col. 2:3-8; I Cor. 3:18-21; Deut. 20:16-18; I Tim. 4:7; Prov. 19:27). The university is designed to "liberate" students from the shackles of Jesus Christ. Third, we are commanded in Scripture to avoid false prophets. It would be wrong to join a Unitarian church. Their "preachers" are humanists: ACLU officials, group therapists, homosexual leaders, evolutionists, and others. In many cases, however, enrollment at the university puts one in the classes of these very same people. The speakers at the Unitarian church are often professors (full- or part-time) at the university. If it is wrong to join a Unitarian Sunday school (and it is), it is wrong as well to join a Unitarian Monday school (Romans 16:17; I Tim. 6:20-21; II Tim. 3:9-11; Prov. 14:7; Psalm 1:1-2; Prov. 13:20).
The content of the university is structured around the so-called "Liberal Arts curriculum." What is a "Liberal Arts" education? From the Latin word for "free," "Liberal Arts" means the classes required to make a man "free." Christians know from John 8 what is required to make a man free: knowledge of Jesus Christ (cf. also Col. 2:3). Humanists, of course, disagree. This shows that the question of what education makes a man free is essentially a religious question.
Christianity is concerned with action and service in the cause of Jesus Christ, and in terms of His Word. Hard, diligent work in one's calling is the highlight of the "Protestant Work Ethic." Note II Tim. 2:15 below: "a workman." The Puritans, recognizing this, placed a great emphasis on a system of training that would emphasize work, dominion, and calling, all set in the context of biblical truth: This system was the apprenticeship system. In the environment of a godly home, a young man would both do and learn, getting on-the-job training from a man expert in his calling. It is not strictly book-work, because man, according to God's Word, is not just "intellectual"; godly work is basic to his purpose under God.
Humanists are opposed to this concept of man. The university was designed by humanists to produce the great humanist intellectual, a man who does not work, but merely thinks lofty, abstract, man-exalting thoughts. It is anti-Christian to the core.
Education is impossible without the truth of God's Word. That is why universities would have long ago collapsed without the help of Christians. But Christians who were involved in the university were, to that extent, inconsistent. Thus R. J. Rushdoony notes,
"The question, What constitutes a free man, is also an historical and cultural question. Thus the American college before 1860 was ostensibly geared to a Christian concept of life, while following a medieval and celibate pattern and a classical Greco-Roman curriculum, aiming to produce young gentlemen in terms of the Enlightenment concept of man.”
Christians who developed the university rather than an apprenticeship system followed the traditions of humanists, rather than scripture. For humanists, true learning is "the pursuit of truth for its own sake." On-the-job training for godly dominion in an honest calling is in the eyes of humanist educator R. M. Hutchins, - "anti-intellectual." And as Rushdoony notes, "The Christian presupposition that truth and calling are inseparable was nowhere in consideration in (his) thinking" (The Messianic Character of American Education, pp. 1, 292). In short, universities were designed to create an elite of humanistic intellectuals who would control and rule over the working masses. This is why only the "qualified" are allowed to go to the university. The rest of the men must work! Even those in the technical fields of the physical sciences are coercively exposed to the humanistic "Liberal Arts."
How unfortunate, then, that the overwhelming majority of Christian colleges are merely imitation universities! They have not thought through the presuppositions behind the humanistic "Liberal Arts," nor are they familiar with the apprenticeship system of the Puritans.
A question arises: "Don't we need the academic accreditation of the large university? Greg Bahnsen says:
"Attempting to be neutral in one's intellectual endeavors (whether research, argumentation, reasoning, or teaching) is tantamount to striving to erase the antithesis between the Christian and the unbeliever. Christ declared that the Christian was set apart from the unbeliever by the truth of God's Word (John 17:17). Those who wish to gain dignity in the eyes of the world's intellectuals by wearing the badge of "neutrality" only do so at the expense of refusing to be set apart by God's Truth.One has to make this basic choice in his thinking: to be set apart by God's truth OR to be alienated from the life of God. It cannot be two ways. One shall be set apart, set against, or alienated from either the world or the Word of God. He will stand in contrast to that intellectual method which he refused to follow (Eph. 4:17). "Whosoever therefore would be a friend of the world maketh himself an enemy of God." (James 4:4)
Paul writes in II Tim. 2:15-16, "Be diligent to show thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth. But shun secular and vain babblings, for they will increase unto more ungodliness."
To question the idea of attending an accredited university is to bring up some serious and practical issues. Suppose a student wishes to become a lawyer. He cannot take the bar exam to gain a license to practice unless he has an accredited education. What does he do, if he rightly believes that seven years of secular babblings are forbidden? Fortunately, there are options; very good options. In California, for example, the bar examiners have made a provision whereby one may study law in an apprenticeship program! On the job, and under the personal supervision of a Christian attorney, one can learn the trade and qualify for the licensing examination (should his conscience permit).
We cannot examine every field here, but almost invariably there are alternatives for the Christian. Joseph did not seek the accreditation of Potiphar's wife. He had short-term trouble. But because he was diligent and faithful, he received long-term success and blessing. Often, university training is utterly irrelevant to the vocation. Job skills are always more efficiently learned on the job. It is not at all accidental that the university education is required for precisely the most objectionable areas: the "Liberal Arts education."
And again, how unfortunate that most Christian colleges are merely imitation universities. Hearing the humanistic demands for accreditation, they have succumbed to the temptation to be a friend of the world.
A great deal of thinking about the purpose of the Christian in his calling, the purpose of education, and the most biblical method of training for one's vocation needs to be done. The creative Christian, the Christian who wants to be a leader, will infiltrate Egypt without compromise.
HIGH SCHOOL CLASSROOM DISCIPLINE
By Jim West
Joe Christian was a brilliant student in both high school and college. His communication skills were refined and clear and no one questioned his diligence and zeal for this work. But there was one crucial deficiency in Joe's pedagogical armor: his (inveterate?) inability to control the students.
Sound familiar? Parents with children in Christian schools as well as fellow faculty who may engage in more intra-faculty scuttlebutt than desirable, understand by experience (sometimes personal observation) that although a teacher may know his subject thoroughly, he may still be a hopeless misfit as far as actual discipline is concerned. Almost paradoxical is the truism that apart from personal godliness, the number one qualification for teaching is not academic prowess, but the ability to keep classroom law and order.
In this light it is more than just interesting that one of the cardinal prerequisites for one who aspires to the ministry is the ability to rule his own home: "for if a man know not how to rule his own house, how shall he take care of the church of God?" (1 Timothy 3:5). The main thought in this passage is not that this aspirant is qualified for the ministry "except" for this, etc., but rather that he is not qualified. High school teachers of course are not ministers, but they must operate in a climate where the communication of knowledge is impossible apart from proper control. Therefore, it is difficult to conceive that a teacher is qualified unless he exercises such leadership. I would guess from my teaching experience that at least 50 percent of rookie high school teachers (in Christian schools!) do not know how to control the students.
Two questions must now be asked: why does such an abysmal state exist and what can be done about it? The answer to the former, of course, is the answer to the latter. Let me offer the following suggestions:
1. Excessive chumminess.
Just as the Bible speaks of the creature-Creator distinction, it also speaks of the teacher-pupil distinction. Many teachers try to pull a Bing Crosby who befriended the Dead End Kids without any loss of clerical prestige. That is good Hollywood folklore; it is poor Christian practice. (Besides, he got them to go his way in "Going My Way!") To become all things to all men does not mean you become a pupil in order to teach pupils. Just as the child is to reverence his father and mother (Leviticus 19:13) so the students are to reverence the teacher (loco parentis). In other words, there should be a healthy arm's distance between teacher and student. This does not mean that the teacher cannot be a friend of the student; it means that it is a friendship founded upon the authoritarian structure of the "superior-inferior principle."
I taught a Communism course once when a student after class greeted me with the words "Comrade West." I immediately corrected him: "No. That is not my name; my name is MR. West." I did not want my relationship to that student to be a relationship of equality. On the other hand, two high school girls referred to me as Comrade West and went unadmonished for the simple reason that I trusted them enough to know that their humor was sanctified and that our relationship would not deteriorate into a friendship of equals. The "familiarity breeds contempt" adage may very well have sprung from the practice of excessive teacher-student comradery. When this occurs it will be like the days of the French Revolution when it was both the best of times and the worst of times!
2. The Facilitator Syndrome.
This is one of the most common causes of classroom disarray. The idea is this: the teacher is really a kind of facilitator. His job is to act like an Academic midwife by getting the students to express themselves. If he can just get the students to come out of their shells, —then the teacher imagines that both he and they have arrived at scholastic Nirvana. Not surprisingly, such teachers emphasize oral reports, group discussions, etc. They may even ask the students to teach the class! (This ploy was performed many times in seminary. It was not until after graduation that I finally caught on.) The important thing is not really the truth; the important thing is the student's opinion. (And the expression of the student's opinion). In a democracy where everyone's opinion is supposedly valid, this emphasis should not surprise us. It is what prospective Christian teachers have been learning from the secular priests in the State (humanist) Church. The presupposition of this approach is that the students are able to make accurate subjective judgments on the basis of objective ignorance! Such an approach is Rogerian to the core and seriously compromises the authoritative calling of the teacher. Students will quickly perceive that if their opinion is just as good as the teacher's, then they have just as much right to teach the "teacher" as the "teacher" them!
3. Popularity-Seeking.
This stems from an ordinate self-love. Every teacher wants to be well-liked and end his teaching career a la Mr. Chips. Every teacher should be well-liked. But true popularity does not come from popularity seeking; it comes from seeking popularity with God. It should never be said of the teacher that when the students assert that the sun is not shining that he always tries to hide his shadow. Christ said: "If you love me, keep my commandments." This means that the schoolteacher should be God-fearing, not man-fearing.
4. Benumbed Law Enforcement.
A teacher who threatens without 'putting teeth' into his commands will be despised and ridiculed by everyone (including God). This is the old Eli syndrome (syndrome) who reproved his sons Hophni and Phinehas, but flagged when confronted with the responsibility to follow through. His son's lecherous behavior was the result. When a teacher gives a test and says there is to be no talking, let him follow through with the necessary discipline should such instructions be disregarded. It will take great courage to do this. Teachers with grasshopper complexes are no more worthy to teach than the Israelites were to take the Promised Land.
5. Women Teachers.
I believe it is unwise for young women to teach high school students. Students will learn more from, and respect more, the rule of a male teacher.
6. Lack of support from the administration,
as well as parents, is another cause of classroom anarchy. The teacher's commands will fall on the proverbial deaf ear if his discipline is constantly countermanded. If the principal is unwilling to back up the teacher or if the parents demean the teacher in the presence of their own children, the result will be devastating. What happens when the teacher is better equipped to administer discipline than either the principal or parents? This is a hard question.
7. Incorrigibles.
Occasionally, a teacher will find a student who simply will not respond properly to godly discipline. The solution to this dilemma is not to suspend him so that he can watch TV for the rest of the week, but to expel him permanently from the school. Such a move will prove financially difficult but is necessary for the school's godliness. (As Ananias and Sapphira's judgment was for the church—Acts 5:1-11.)
My experience has been that if the teacher is exercising a loving boldness, then classroom order will result. Of course, some allowance must be made for the sinfulness of the teacher, too. This is especially true if he is a 'diamond in the rough' first-year teacher. Yet, progress in achieving classroom control should be discernible to all. Such progress will be made when the teacher realizes that he is the teacher and that he must intrepidly exercise control.
One final note: do not be afraid to express some controlled anger. Not all anger is wrong (as the emotional life of our Lord shows). Anger does not consist in uncontrolled belching and harsh statements for the students to "shut-up!" It should be clear to the students that you are angry with their sinful behavior; not because your personal applecart has been overturned.
Biblical Educator, Vol. 3, No, 4 (April 1981)
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