Math Curriculum

Cate Quirk Bishop England High School Charleston

Melanie Cummings Bishop England High School Charleston

Mary Ann Tucker Bishop England High School Charleston

Kathy Romer Blessed Sacrament Charleston

Kelsey Davis Christ Our King Stella Maris Mount Pleasant

Tracy Sklarin John Paul II Ridgeland

Sara Lynn Williams John Paul II Ridgeland

Melissa Lewis St. Andrews Myrtle Beach

Donna Nance-Deese St. Anne Rock Hill

Jennifer French St. Anne Rock Hill

Julie Peter St. Anne Rock Hill

Jennifer Vawter St. Anne Rock Hill

Alexandria Toborg St. Anthony Florence

Kristine Galemmo St. Anthony Florence

Beverly Wade-Battle St. Anthony Greenville

Susan Hudgins St. Gregory the Great Blufton

Bridget Abel St. John Charleston

Diana Von Plinksy St. Joseph Columbia

Donavan Yarnell St. Joseph Columbia

Judith Barrineau St. Joseph Columbia

Marie Phillips St. Peter’s Columbia

Rahel Grant St. Peter’s Columbia

Shaileen Riginos Assistant Superintendent, Diocese of Charleston

At first, the ideas of faith and mathematics might seem to be as divergent as ideas can be. Mathematics represents the height of objective reason, where personal opinions and preferences cease to carry weight. Yet, when we really think about it, faith and reason are not incompatible. Rather, they are complementary and intimately connected. Any sense of divergence between the two comes from a misunderstanding either of what faith is or of what reason is, or both.

With that said, integrating faith into mathematics (or any other curricular area for that matter) cannot be done in a mere facile, superficial manner. Rather, it must be intimately bound up with one’s own spirituality and mindset as a teacher. This begins with a fundamental question: what exactly is it that we are learning about when we embark on the journey of learning mathematics? While in answer to this, we could give a number of specific elements of the mathematical curriculum, the deeper answer is much more simple and direct. Simply put, when we discover the wonders of mathematics, we are uncovering the orderliness and wonder of God’s creation. In the process, we come to know our Creator better.

Christ tells us, “I am the way and the truth and the life. No one comes to the Father except through me” (Jn 14:6). In that particular passage, while he is concerned with directing us to the divine life that is salvation, he also points to himself as the truth. With this in mind, we know that all truth, wherever we find, points us ultimately to him. The compatibility between faith and reason, including all of the natural sciences (among which we can enumerate mathematics), has consistently been a part of the Church’s understanding. Towards this end, the Catechism of the Catholic Church cites both the First and Second Vatican Councils:

Faith and science: “Though faith is above reason, there can never be any real discrepancy between faith and reason. Since the same God who reveals mysteries and infuses faith has bestowed the light of reason on the human mind, God cannot deny himself, nor can truth ever contradict truth.” “Consequently, methodical research in all branches of knowledge, provided it is carried out in a truly scientific manner and does not override moral laws, can never conflict with the faith, because the things of the world and the things of faith derive from the same God. the humble and persevering investigator of the secrets of nature is being led, as it were, by the hand of God in spite of himself, for it is God, the conserver of all things, who made them what they are” (CCC 159; cf. Dei Filius 4; Gaudium et Spes 36 #1).

We see this compatibility of faith and reason exhibited throughout the history of the Church. St. Anselm of Canterbury described the relationship between faith and reason as fides quaerens intellectum, or ‘faith seeking understanding’ (see Anselm, Proslogion, Preface). This shows us that faith helps us reach beyond what reason alone can provide, yet it never does violence to our reason. St. Thomas Aquinas taught us that rather than being something irrational, faith perfects the intellect by directing it to our ultimate end or goal of union with God (ST II-II 1, 1). So, rather than the two being opposed to each other, the Church sees reason as always pointing us to deeper faith and faith spurring us on to deeper understanding.

Mathematics also explicitly makes its way into the articulation of the faith through the centuries. St. Augustine of Hippo, for instance, marveled at numbers. By their very existence, they demonstrate that something can be real without being a physical thing. In today’s world which is often characterized by attitudes of materialism, it is helpful to realize that the world we observe around us only ‘works’ because numbers ‘work’ and really exist. St. Augustine notes that for this reason, Ecclesiastes connects wisdom with the idea of numbering (Eccl 7:26), directing us to the use of numbers throughout scripture (See Augustine, On Free Choice of the Will II, 8, 20-24).

This can lead us to some very fruitful reflection. For example, when we look at scripture, we see the importance of measurements throughout both the Old and New Testaments. For instance, the plan of the ark and the temple are given to exact specifications. This shows the orderliness of God’s plan and indicates that we are called to imitate and participate in God’s plan. It also mirrors the orderliness of God’s act of creation. There is also a frequent concern in the Law for establishing fair and just measurements, which is also a human imitation of divine justice (see, for instance, Lev 19:36).

Numbers are constantly used to make a variety of points. The book of numbers contains a census (from which it derives its name), which shows the fulfillment of God’s promise to Abraham (numerous descendants) (see Gen 15:5), and to Moses (liberation from slavery). Counting the people of Israel is a way of illustrating the wonders God has worked for his people. We also see in apocalyptic literature and elsewhere the use numbers symbolically to point to the divine plan of salvation. Numbers, then, can be important ways of communicating other concepts (See ‘The Symbolism of Numbers in the Bible’ compiled by Felix Just, S.J., Ph.D., http://catholic-resources.org/Bible/Numbers.htm).

The idea of multiplication is constantly seen in how God deals with his people and how he calls us to deal with each other. It communicates to us the abundance of God’s love and mercy. God multiplies blessings. Christ also multiplies the loaves and fish, showing both his divine identity as one who has power over creation and also his merciful love, which seeks to give us what we need, even when it appears that what we can provide ourselves is inadequate (see, for instance, Mk 6:34-44). He also asks us to use multiplication in our imitation of his merciful love, such as when he tells us to forgive seven times seventy times (Mt 18:22).

Most importantly, without a firm grasp of numbers, we would have no way to conceive of the infinite. It is only by knowing that the divine transcends our human concepts (not by falsifying them, but by constantly being ‘more’ than they can communicate) that we can begin to understand just a little about God. This includes our Trinitarian understanding of God. Although it is not a mathematical formula, Trinity would be hard to understand without some idea of numbers, particularly that of the number one, which points us to divine unity. This divine unity, in turn, points us ethically to the unity we seek within our human family and with all of creation (a notion we call ‘solidarity’).

Mathematics, then, points us to the beauty and order of God’s creation. Far from being foreign to Faith, it is an integral part of our humanity and our understanding, which allows us to know and grow closer to God. Mathematics then is a piece of our relationship with an Infinite God whose love for us goes beyond measure. In receiving Mathematics as a gift from God, we should respond by maintaining both within ourselves and within our classrooms a ‘mathematical spirituality’ and by applying the faith mathematically.

Maintain a ‘Mathematical Spirituality’

• Frame the class period in prayer, articulating the wonder at the order of God’s creation

• Use ‘numerical’ scripture passages in prayer

• Give thanks to God for the gift of Mathematics and the gift of our ability to understand it

• Bring the subject of Mathematics into your own personal prayer

• Constantly give voice to the same wonder and awe outside of prayer

Apply the Faith Mathematically

• Go beyond simply using religious examples (although that can be a start)

• Highlight anywhere where the concept being taught appears in scripture (e.g. construction dimensions, multiplication, just weights and measures, statistics and census taking, currency, infinity, etc.)

• Apply Mathematics to the ethical demands of the faith, particularly Catholic Social

Thought, for instance:

• Use plentiful examples of how mathematics has been used to develop technology and solve problems. While doing so, try to include examples that help solve social problems, such as hunger, etc.

• When formulating word problems and other narrative questions, try to use real world statistics that draw attention to issues of justice (e.g. hunger, poverty, inequity, etc.).

• Use current events to raise consciousness of issues of justice/injustice making news in the world and allow them to inform class discussions (while remaining focused on class material).

• Conduct an occasional internet search for reliable justice-related statistics (e.g. poverty, life issues, etc.) to utilize in the classroom.

• Use mathematics in some type of a service project that serves those in need either locally or globally. Be creative.

Archdiocese of Superior (n.d.) Integrating Faith and Math. Diocese of Superior. Retrieved from:

https://catholicdos.org/math-curriculum-integrating-faith

Algebra House (2021). Volume of a rectangular prism using algebraic expressions.

Retrieved from: https://www.algebrahouse.com

The Cardinal Newman Society (n.d.). Catholic Curriculum Standards. Cardinal Newman Society. Retrieved from: https://newmansociety.org/educator-resources/resources/academics/catholic-curriculum-standards/downloading-the-standards/

Catholic Identity Curriculum Integration (n.d.) Introduction to Math Lessons. Retrieved from:

https://cici-online.org/shared-units/math-lessons

CK-12 Foundation (2022). Mathematics. Retrieved from:

https://www.ck12.org/book/ck-12-basic-geometry-concepts

Crawfordsville Community School Corporation (n.d). Crawfordsville Curriculum Map. CCSC. Retrieved from: https://www.cville.k12.in.us/Page/549

Fish Tank Learning (2022). Curriculum Mathematics. Retrieved from:

https://www.matchfishtank.org/curriculum/mathematics/geometry

Illustrative Mathematics (2021). Math Curriculum Retrieved from:

https://illustrativemathematics.org/

Indiana Department of Education (2020). K-12 Indiana Academic Mathematics Standards. Department of Education. Retrieved from: https://www.in.gov/doe/students/indiana-academic-standards/mathematics/

National Council of Teachers of Mathematics (n.d). Principals to Action: Ensuring Mathematical Success for All. NCTM. Retrieved from: https://www.nctm.org/PtA/

New York State Department of Education (n/d). Mathematics Curriculum Modules.

Retrieved from: https://www.engageny.org/resource

Open Middle (2016-2019). Trig Ratios. Retrieved from: https://www.openmiddle.com/trig-ratios/

Office of Education, Evangelization, and Catechesis (2017). Archdiocese of Hartford Mathematics Standards-based Curriculum. Archdiocese of Hartford. Retrieved from: https://www.norwichdiocese.org/Portals/dioceseofnorwich/CMAdmin/ADH%20MATH%20STANDARDS%20BASED%20CURRICULUM%202017.pdf

Rowe, John (2011). How I Teach Maths.

Retrieved from: https://mrrowe.com/reversingthequestion/

Shmoop University Inc. (2022). Surface Area and Volume - Congruent and Similar Solids.

Retrieved from:

https://www.shmoop.com/study-guides/math/surface-area-volume/congruent-similar-solids

Virginia Department of Education (2016). Just in Time Mathematics Quick Checks. Retrieved from: https://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2016/jit/index.shtml

Virginia Department of Education (2016). Math Instructional Plans. Retrieved from:

https://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2016/mip/index.shtml

Wiggins, G., & McTighe, J. (1998). Understanding by Design. Alexandria. VA: Association for Supervision and Curriculum Development.