The school where I serve as Academic Dean is currently in the midst of our review of math curriculum. (We are on a five-year cycle reviewing curriculum in our five core subjects.) One of the first things we do in that study is to outline our philosophy of mathematics instruction. Here is the statement we have developed. I hope it might be useful for others to consider.
Our philosophy of mathematics is structured around the school’s mission statement:
Glorify God by assisting parents, providing a Christ-centered academically excellent education edifying the whole child, resulting in Godly leadership through service.
Glorify God by Assisting Parents
The focus here is on the desire to “glorify God.” As we study mathematics, we can see God’s greatness and glory. Students come to know that mathematical results are certain because of God's laws and faithfulness to his creation. Doing mathematics Christianly focuses on God's role and adopts an attitude of humility.
Christ-Centered Education
When we look at specific teachings of Scripture, we see that God is concerned about mathematics. When God issued Adam the dominion mandate [1], and then reaffirmed it with Noah [2], he expected man to exercise stewardship over creation. Mathematics is one language in which we describe creation and in its application we exercise dominion. As such, it is a necessary component of stewardship. “By faith we understand that the universe was formed at God's command, so that what is seen was not made out of what was visible.” [3] Mathematics not only describes what is seen but provides insight into things not visible. It is through mathematics that new expressions of dominion surface each generation, reflecting God’s perfect order and His great glory.
All areas of study in the mathematics department, as with all other subjects, are governed by one’s worldview. There is no neutrality in any area of study, as if one can think about the subject matter totally uninfluenced by one’s religious presuppositions. One’s ultimate assumptions about the nature of reality, the nature of truth, the nature of knowledge, and the nature of good and evil all influence the results of study. In the area of math, for example, one’s presuppositions will determine which topics are selected as important for study, and which are ignored (since it is impossible to study every mathematical fact or theory).
In contrast to this position, it is often assumed that mathematics is an area of life that is truly neutral. For example, a Hindu, a Buddhist, an atheist, and a Christian would all agree that 2+2=4 (in the base 10 system). [4] However, we recognize that man does not have total or complete knowledge, of mathematics or of anything else. Only the God of Scripture has such omniscience, and He is the one who must reveal absolute truth about any area of life, including mathematics. Since the work of Gödel, mathematics cannot be seen as a self-sufficient, all-encompassing consistent set of theorems. [5] Mathematical truth depends upon presuppositions and concepts outside of itself. These foundations can only be found in the revelation of the God of Scripture.
Since our school is a Christian school, we teach all things based on the assumption of the truth of the Bible as the Word of God. This underlying assumption will influence and govern all of our studies in the department of math.
The very possibility of mathematics is based on the fact that the Christian worldview is true.[6] There are several key elements of this worldview that provide a foundation for mathematics. First, a Christian view of metaphysics (the nature of reality) provides an answer to the age-old philosophical problem of the one and the many. Which is more ultimate – unity, oneness, sameness (as posited by the Greek philosopher Parmenides), or plurality and diversity (as taught by the Greek philosopher Democritus)? With either choice, there is no foundation for mathematics at all. If all is unity, then there is no real plurality in the universe, and there cannot even be real counting. If all is diversity, on the other hand, then there is no ability to make abstract principles of mathematics. From the Christian perspective, however, because God is both One and Three (the Trinity), and since He created the world to reflect His nature and character[7], creation itself evidences both unity and plurality, thus providing a foundation for mathematics.
Second, a Christian worldview deals with the area of epistemology (the nature of knowledge). In mathematics, this answers the question of how men can know mathematical truths. While non-Christian philosophy vacillates between a priori (universal truths apart from experience) and a posteriori (deductions based upon experience) approaches to knowledge (neither of which provide a consistent foundation for mathematical knowledge), the Christian world view teaches that universal, abstract truths of mathematics (a priori thought) corresponds to the “real world” particulars (a posteriori thought) because the God of Scripture has created both the mind of man and the world of particulars. Mathematical thought corresponds to reality because God has created them to so correspond. Since man is finite and fallible, there will always be errors and inadequacies in our mathematical knowledge. But the truth of the Christian worldview provides a sure foundation for a true knowledge of mathematics.
Academic Excellence
God has given man the ability to understand mathematics, and thus man is able to demonstrate excellence in this field of study. This is based, first of all on the fact that the number concept began with God, who initiated mathematics in the act of creation.[8] Man’s ability to understand and work with numbers, as well as with other subject matter, is a gift from the God who created it.[9] We must keep in mind, however, that man’s ability to use numbers completely, effectively, and for the glory of God has been marred by sin.[10] Therefore, success and excellence in mathematics, as in every other area of life, requires hard work.[11]
Edifying the Whole Child
Scripture teaches the value of mathematics as a subject, and thus mathematics is one means for building up (edifying) the child. The consistency of mathematical truths demonstrates the orderliness and precision of God. These truths exist, and are always the same, because God made them so.[12] As a result, the study of mathematics should result in greater appreciation of the works of God in His creation.[13] Man’s God-given creativity, like God’s, often requires some mathematical understanding.[14] Finally, the understanding of mathematical concepts adds to our understanding of expressions in other areas of life.[15]
Godly Leadership through Service
The Christian worldview establishes the area of ethics (the nature of good and evil). While mathematics is not generally considered in terms of “right” and “wrong,” yet we must give consideration to the ethical, proper use of mathematics. One could use certain mathematical formulas to determine the most effective dispersion of poison gas in the atmosphere to commit mass murder, or he can use the same formulas to calculate the dispersion of insecticides in the atmosphere to control harmful mosquitoes. To what ends will our mathematical knowledge be used? In the Biblical worldview, man is to use mathematics, as he is to use all knowledge, for the glory of God[16] and to advance dominion over the earth.[17] Only the Christian worldview can provide justification for this ethical perspective on mathematics. The Bible also gives students an ethical justification for doing mathematics; God gives happiness and joy to a Christian’s labor under the sun, and all is not vanity.[18]
Summary
From this, we can state four overall objectives of a distinctively Christian mathematics curriculum[19]:
[1] Gen. 1:28
[2] Gen. 9
[3] Heb. 11:3
[4] James Nickel, Mathematics: Is God Silent?. Vallecito, CA: Ross House Books, 2001. 4.
[5] Nickel, 190-192.
[6] Nickel, 229-233.
[7] Romans 1:20
[8] Gen. 1:5, 8, 13, 19, 23, 31; 2:2, 3; 4:19, 24; 5:3-32
[9] Job 32:8,9; 1 Cor. 2:14-16
[10] Prov. 1:7; Rom. 1:18-32
[11] Gen. 3:17-19
[12] Gen. 6:14-16; Ex. 25:8,9,40; 26:30; 27:8; 30:7-9, 34-38; Num. 1-10
[13] Gen. 15:5,6; Job 38:22; Ps. 8:3-9; 139:14; Jer. 31:37; 33:22; Rom. 11:33,34; Col. 1:16-17
[14] Gen. 1:26-28; 2:18-23; Ex. 31:1-6
[15] Gen. 1:22,28; 3:16; 8:17; 9:1,7; Ex. 7:3; 11:9; Lev. 5:16; 6:5; 27:13-31; Deut. 4:2; 8:13; 11:21; 12:32; Deut. 17:16,17; 1 Sam. 12:19; 1 Kings 12:11-14; Job 9:17; 34:37; 35:6,16; Ps. 16:4; 38:19; Prov. 3:1,2; 9:11; 16:23; 29:16; 30:5-6; Isa. 59:12; Jer. 45:3; Ezek. 16:29,51; 23:19; 35:13; Dan. 4:1; 6:25; Hos. 2:8; 8:14; Amos 4:4; Matt. 6:27,33; Luke 12:25,31; Acts 2:41,47; 5:14; 6:1,7; 11:24; 12:24; 1 Peter 1:2; 2 Peter 1:2,5-7; Jude 2; Rev. 22:18-19
[16] Romans 11:36
[17] Genesis 1:28
[18] Ecclesiastes 3:12-13
[19] Nickel, 235
[20] Romans 1:20
Our philosophy of mathematics is structured around the school’s mission statement:
Glorify God by assisting parents, providing a Christ-centered academically excellent education edifying the whole child, resulting in Godly leadership through service.
Glorify God by Assisting Parents
The focus here is on the desire to “glorify God.” As we study mathematics, we can see God’s greatness and glory. Students come to know that mathematical results are certain because of God's laws and faithfulness to his creation. Doing mathematics Christianly focuses on God's role and adopts an attitude of humility.
Christ-Centered Education
When we look at specific teachings of Scripture, we see that God is concerned about mathematics. When God issued Adam the dominion mandate [1], and then reaffirmed it with Noah [2], he expected man to exercise stewardship over creation. Mathematics is one language in which we describe creation and in its application we exercise dominion. As such, it is a necessary component of stewardship. “By faith we understand that the universe was formed at God's command, so that what is seen was not made out of what was visible.” [3] Mathematics not only describes what is seen but provides insight into things not visible. It is through mathematics that new expressions of dominion surface each generation, reflecting God’s perfect order and His great glory.
All areas of study in the mathematics department, as with all other subjects, are governed by one’s worldview. There is no neutrality in any area of study, as if one can think about the subject matter totally uninfluenced by one’s religious presuppositions. One’s ultimate assumptions about the nature of reality, the nature of truth, the nature of knowledge, and the nature of good and evil all influence the results of study. In the area of math, for example, one’s presuppositions will determine which topics are selected as important for study, and which are ignored (since it is impossible to study every mathematical fact or theory).
In contrast to this position, it is often assumed that mathematics is an area of life that is truly neutral. For example, a Hindu, a Buddhist, an atheist, and a Christian would all agree that 2+2=4 (in the base 10 system). [4] However, we recognize that man does not have total or complete knowledge, of mathematics or of anything else. Only the God of Scripture has such omniscience, and He is the one who must reveal absolute truth about any area of life, including mathematics. Since the work of Gödel, mathematics cannot be seen as a self-sufficient, all-encompassing consistent set of theorems. [5] Mathematical truth depends upon presuppositions and concepts outside of itself. These foundations can only be found in the revelation of the God of Scripture.
Since our school is a Christian school, we teach all things based on the assumption of the truth of the Bible as the Word of God. This underlying assumption will influence and govern all of our studies in the department of math.
The very possibility of mathematics is based on the fact that the Christian worldview is true.[6] There are several key elements of this worldview that provide a foundation for mathematics. First, a Christian view of metaphysics (the nature of reality) provides an answer to the age-old philosophical problem of the one and the many. Which is more ultimate – unity, oneness, sameness (as posited by the Greek philosopher Parmenides), or plurality and diversity (as taught by the Greek philosopher Democritus)? With either choice, there is no foundation for mathematics at all. If all is unity, then there is no real plurality in the universe, and there cannot even be real counting. If all is diversity, on the other hand, then there is no ability to make abstract principles of mathematics. From the Christian perspective, however, because God is both One and Three (the Trinity), and since He created the world to reflect His nature and character[7], creation itself evidences both unity and plurality, thus providing a foundation for mathematics.
Second, a Christian worldview deals with the area of epistemology (the nature of knowledge). In mathematics, this answers the question of how men can know mathematical truths. While non-Christian philosophy vacillates between a priori (universal truths apart from experience) and a posteriori (deductions based upon experience) approaches to knowledge (neither of which provide a consistent foundation for mathematical knowledge), the Christian world view teaches that universal, abstract truths of mathematics (a priori thought) corresponds to the “real world” particulars (a posteriori thought) because the God of Scripture has created both the mind of man and the world of particulars. Mathematical thought corresponds to reality because God has created them to so correspond. Since man is finite and fallible, there will always be errors and inadequacies in our mathematical knowledge. But the truth of the Christian worldview provides a sure foundation for a true knowledge of mathematics.
Academic Excellence
God has given man the ability to understand mathematics, and thus man is able to demonstrate excellence in this field of study. This is based, first of all on the fact that the number concept began with God, who initiated mathematics in the act of creation.[8] Man’s ability to understand and work with numbers, as well as with other subject matter, is a gift from the God who created it.[9] We must keep in mind, however, that man’s ability to use numbers completely, effectively, and for the glory of God has been marred by sin.[10] Therefore, success and excellence in mathematics, as in every other area of life, requires hard work.[11]
Edifying the Whole Child
Scripture teaches the value of mathematics as a subject, and thus mathematics is one means for building up (edifying) the child. The consistency of mathematical truths demonstrates the orderliness and precision of God. These truths exist, and are always the same, because God made them so.[12] As a result, the study of mathematics should result in greater appreciation of the works of God in His creation.[13] Man’s God-given creativity, like God’s, often requires some mathematical understanding.[14] Finally, the understanding of mathematical concepts adds to our understanding of expressions in other areas of life.[15]
Godly Leadership through Service
The Christian worldview establishes the area of ethics (the nature of good and evil). While mathematics is not generally considered in terms of “right” and “wrong,” yet we must give consideration to the ethical, proper use of mathematics. One could use certain mathematical formulas to determine the most effective dispersion of poison gas in the atmosphere to commit mass murder, or he can use the same formulas to calculate the dispersion of insecticides in the atmosphere to control harmful mosquitoes. To what ends will our mathematical knowledge be used? In the Biblical worldview, man is to use mathematics, as he is to use all knowledge, for the glory of God[16] and to advance dominion over the earth.[17] Only the Christian worldview can provide justification for this ethical perspective on mathematics. The Bible also gives students an ethical justification for doing mathematics; God gives happiness and joy to a Christian’s labor under the sun, and all is not vanity.[18]
Summary
From this, we can state four overall objectives of a distinctively Christian mathematics curriculum[19]:
- Biblical Christian mathematics describes the wonders of God’s creation. Since God has created the mind of man to correspond to the realities of His creation, man’s mathematical study will open up many wonders in God’s creation. Some examples are the relationship between music, trigonometry, and wave motion; the Fibonacci sequence; and conic sections.
- Biblical Christian mathematics reveals the invisible attributes of God. Since all creation reveals the attributes of God,[20] a mathematical study of creation will likewise help us to understand more about God. Some examples are the concept of infinity, His unchangeableness, and His orderliness.
- Biblical Christian mathematics serves to aid man in fulfilling God’s mandate of dominion. As an aspect of scientific study, mathematics helps man to understand creation better, thus enabling him to exercise dominion over it more effectively. Some examples are the study of logic, mathematical modeling, and statistics.
- Biblical Christian mathematics serves to assist God’s people in fulfilling God’s mandate of worldwide evangelism. Those whose particular calling is in the area of evangelism can make use of mathematical insights and calculations. Some examples are tools for navigation, statistical research, and mathematical logic (which can aid in the translation of previously unknown languages).
[1] Gen. 1:28
[2] Gen. 9
[3] Heb. 11:3
[4] James Nickel, Mathematics: Is God Silent?. Vallecito, CA: Ross House Books, 2001. 4.
[5] Nickel, 190-192.
[6] Nickel, 229-233.
[7] Romans 1:20
[8] Gen. 1:5, 8, 13, 19, 23, 31; 2:2, 3; 4:19, 24; 5:3-32
[9] Job 32:8,9; 1 Cor. 2:14-16
[10] Prov. 1:7; Rom. 1:18-32
[11] Gen. 3:17-19
[12] Gen. 6:14-16; Ex. 25:8,9,40; 26:30; 27:8; 30:7-9, 34-38; Num. 1-10
[13] Gen. 15:5,6; Job 38:22; Ps. 8:3-9; 139:14; Jer. 31:37; 33:22; Rom. 11:33,34; Col. 1:16-17
[14] Gen. 1:26-28; 2:18-23; Ex. 31:1-6
[15] Gen. 1:22,28; 3:16; 8:17; 9:1,7; Ex. 7:3; 11:9; Lev. 5:16; 6:5; 27:13-31; Deut. 4:2; 8:13; 11:21; 12:32; Deut. 17:16,17; 1 Sam. 12:19; 1 Kings 12:11-14; Job 9:17; 34:37; 35:6,16; Ps. 16:4; 38:19; Prov. 3:1,2; 9:11; 16:23; 29:16; 30:5-6; Isa. 59:12; Jer. 45:3; Ezek. 16:29,51; 23:19; 35:13; Dan. 4:1; 6:25; Hos. 2:8; 8:14; Amos 4:4; Matt. 6:27,33; Luke 12:25,31; Acts 2:41,47; 5:14; 6:1,7; 11:24; 12:24; 1 Peter 1:2; 2 Peter 1:2,5-7; Jude 2; Rev. 22:18-19
[16] Romans 11:36
[17] Genesis 1:28
[18] Ecclesiastes 3:12-13
[19] Nickel, 235
[20] Romans 1:20