Principles of Mathematics

Over the last thirty years, worldview has become a hot topic within—and without—the Christian community. Understanding that everything one believes is filtered through a set of often unconsciously held beliefs is fundamental to understanding the divide between Christians and non-Christians, or between any philosophical or religious group and another. This discovery (or rediscovery) has led to an explosion of curriculum options that present a given subject from a distinctively biblical and Christian perspective.

Math seems to be one of the few subjects relatively untouched by this movement. Plenty of books explaining the link between math and worldview are available, most notably James D. Nickel's now-classic Mathematics: Is God Silent? which inspired this course, but no math curriculum that dealt with the philosophical and theological foundations of the discipline while actually teaching its principles and operations.

Enter Katharine Loop's Principles of Mathematics, a two-year course for grades 6-8 that introduces algebra, geometry, and statistics and probability while tying each concept back to a biblical understanding of the world. Loop stresses that her approach is not meant to just add a Bible verse to the top of each page, but to show how only a Christian worldview can properly make sense of the study and practice of mathematics. In this sense, Loop's approach resembles an application of presuppositional apologetics to the study of math.

How Do These Work?

There are two parts, one for each year, with a student text and a teacher guide (alternatively, and somewhat confusingly, called a student workbook) for both parts. The student text is instructional—there are no problem sets or sample exercises, just chapters divided into sections that students read on their own. The student workbook/teacher guide contains all the worksheets for daily work, quizzes, and tests, along with a complete answer key and a daily schedule for completing the course in a school year.

Book 1 is for grades 6/7, and Book 2 is for grades 7/8. Each book should take one year to complete at a rate of 4-5 days a week, 30-45 minutes a day. Loop also states that high school students can use either book to fill a gap or to supplement a more traditional course, and offers an accelerated schedule in both teacher guides for completing each book in a single semester rather than an entire school year.

This is a self-directed course. There is no teacher support other than the answer keys and schedules, so if you'd prefer to teach your kids directly rather than simply turn them loose you'll have to read the lessons and do outside prep yourself. One possible way to do this would be to mine Loop's bibliographies at the end of each student text, but many of the books listed there are fairly in-depth and not necessarily the kind you'd want to wade through just to teach two years of math.

The coursework resembles what you'd find in a college contemporary math course. Book 1 starts with a discussion of place value, comparing our modern system to those of past civilizations and other countries, and finding the commonalities in each. Loop then proceeds to review, including mental math, basic arithmetical functions, and fractions, followed by introductory summaries of percentages, ratios, negative numbers, sets, geometry, and more. Book 2 begins by covering similar material to that covered in the beginning of Book 1, then moves on to introduce graphing, algebraic equations, trigonometry, probability and statistics, etc.

Students entering the course will need a good handle on basic arithmetic, as well as basic problem-solving skills. The goal is to prepare them for high school-level algebra and geometry, while giving them a taste of more advanced topics they'll encounter later. An attempt is made throughout to tie math concepts to a biblical worldview, primarily to show how acceptance of the biblical paradigm is necessary to make sense of math's complexity and order.

Our Honest Opinion

Let us say at the outset that we applaud Loop's effort to approach math instruction from a distinctly Christian perspective, rather than treating it as a "neutral" discipline as so many Christian curriculum writers seem to do. God is, as Loop affirms, the creator of math, and its comprehensibility depends on him, his revelation, and the reason he has given human beings. We have no arguments there.

The looming questions are, 1) whether Loop adequately covers the necessary math concepts for middle school, and 2) how effectively she marries her chosen subject to a Christian worldview. As for the first question, the answer would seem to be that all necessary concepts are introduced and covered sufficiently. Middle school is largely transitional as far as math goes, and Principles of Mathematics provides a solid step between elementary and high school math.

The second question is a little harder to answer. First, we have to determine which Christian worldview Loop holds. There is no monolithic "Christian biblical worldview" that all believers hold to, and her use of that phrase itself must be interpreted. Her website includes a typical evangelical statement of beliefs, but there isn't a lot of information about Loop online. Principles of Mathematics is published by Master Books, which perhaps offers better insight—Master Books is closely associated with Ken Ham, and the publisher's website states that it is "the world's largest publisher of creation-based material." With that in mind, we can look at a few of Loop's statements.

Near the beginning of the Book 1 textbook (pp. 40-41), she talks about how raindrops prove that math is the product of God's divine creation rather than the exercise of man's reason. Because human reason states that 1+1=2, it is incapable of explaining the fact that two raindrops, when joined, do not become two but one, says Loop. There's a brief sidebar remark that this "raindrop quandary" was first introduced by a German thinker in 1887, along with a citation for Morris Kline's Mathematics: The Loss of Certainty, but no other explanation. She does, however, insinuate that von Helmholtz was opposed to "those who had enthroned human reason and math."

Is her statement true? It might be helpful to first understand who Hermann von Helmholtz was, and what he was getting at with the so-called raindrop quandary. Von Helmholtz was a 19th century German mathematical physicist and philosopher of science whose work covered everything from electromagnetism to human physiology. In the very book Loop cites, Morris Kline tells us of von Helmholtz that, "His conclusion was that only experience can tell us where the laws of arithmetic do apply. We cannot be sure a priori that they do apply in any given situation" (p. 92). He goes on to explain that von Helmholtz's interest in the nature of raindrops was simply to point out that two objects must be kept distinct in order to be considered equal.

While the ideas Kline deals with are difficult and highly technical, we cannot avoid the fact that Loop uses his material to make a point he was clearly not making, and in so doing she also misrepresents von Helmholtz. The German physicist was not trying to save math from those who saw it as the province only of human reason, but to show that it was in fact a discipline rooted in human experience and observation, not some universally applicable concept.

Loop also frequently uses language that suggests the Bible clearly presents a philosophy of mathematics. On page 63 of the Book 1 textbook, she says that the Bible tells us where math originated, why it is possible, and what to expect when we use it. While the Bible certainly provides all we need to think about everything from a Christian perspective, it's somewhat misleading to say that it speaks directly on the topic of math when it clearly does not per se.

There are references to the fact that Christians sometimes, as Loop says, feel the need to tailor the Bible to fit in with a more humanistic worldview. She even accuses the Medieval church carte blanche of this tendency at one point, then says this same process of Bible twisting is carried out today by those who try to fit Darwinism in with biblical faith. While this isn't the place to open that debate, there are Christians with a solid biblical worldview who believe in evolution (though probably not Darwinism per se), and who explicitly reject the six 24-hour days theory of creation espoused on Loop's website. Even St. Augustine rejected the latter view, but he was Medieval so there you have it.

Throughout the books, Loop makes pronouncements that are by no means accepted by all orthodox Christians. For instance, in the Book 2 textbook on page 302ff., she states that earthquakes are the result of sin entering the world, and had no place in the pre-Fall creation. But this is a theory by no means universally accepted among Christian scientists or theologians (including some big names like C.S. Lewis and Francis Schaeffer!). Many think that earthquakes, volcanoes, etc. were actually given by God so the earth could self-regulate.

Perhaps less problematically, Loop makes statements like "you are no accident" and the like, which while technically true can come off as a bit trite. But phrases like these are much less concerning than the misinterpretation of significant ideas or the a priori dismissal of valid but divergent Christian perspectives to which Loop seems prone. Don't get us wrong—the idea of a course that integrates Christian worldview (and preferably a positive Christian philosophy of mathematics and science) with math instruction is a great one. This just doesn't seem to fill that available niche particularly well, at least as it currently exists. We expectantly await an improvement.

Review by C. Hollis Crossman
C. Hollis Crossman used to be a child. Now he is a husband and father, teaches adult Sunday school in his Presbyterian congregation, and likes weird stuff. He might be a mythical creature, but he's definitely not a centaur. Read more of his reviews here.


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Principles of Mathematics Book 1 - Teacher Guide
by Katherine A. Loop
Teacher from Master Books
for 6th-8th grade
in Principles of Mathematics (Location: MAT-MB2)