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Einstein once said, “Pure mathematics is, in its way, the poetry of logical ideas.” What an interesting concept! Math is poetry.

In the same what that poetry is the masterful rhythm of composition, the intentional putting together of words in a distinct order that is both beautiful and inspiring, math is the use of symbols, forms, and functions to reveal order, quantify measurement, and identify patterns. It helps us logically comprehend God’s amazing created world and validates the idea of objective truth.

Poetry reveals to us the mind and heart of the poet using language; math reveals God’s nature and the order and complexities of the physical world using numbers and symbols. The fact that 1 + 1 will always equal 2 shows us that God has established the universe with a precision and regularity that we can depend on. Math demonstrates His faithfulness!

Since math is necessary for the development and organizing of our children’s minds, let’s consider two primary ways we can go about teaching it in our homeschool.

Spiral Approach

A spiral approach to math presents each concept in part and then goes deeper with each subsequent presentation of the concept, building on what was previously learned and practiced. For instance, a spiral curriculum might first introduce addition and subtraction using only single digits. Then other concepts like skip counting, ordinal numbers, telling time, place value, fractions, graphs, or calendars are taught at an equally basic level. The curriculum then cycles through all the concepts again, expanding on each. There are advantages and disadvantages to learning math this way.

The advantages:

  1. Includes lots of review practice in each lesson to reinforce concepts already taught. This minimizes the chance that a student will forget what he has learned previously. It also decreases the probability of learning gaps. Repetition is an effective teacher.
  2. Concepts are broken down incrementally. If a student keeps getting stuck on a certain kind of problem, a parent can pinpoint exactly what part of the concept is tripping them up.
  3. Allows the student to advance at a typical pace according to their natural development. Concepts are not introduced in too much depth all at once before the student is able to understand and comprehend. Students feel successful as they continue to mature.

The disadvantages:

  1. It can be inefficient and include too much review of a concept the student has already mastered. This can lead to boredom and disinterest in the subject.
  2. The constant changing of topics can confuse students. Some children may prefer to fully focus on a particular concept, building a strong foundation for what comes next.
  3. Students may struggle to find the logical progression in concepts taught. For instance, before a student learns multiplication they must fully understand addition and place value. Presenting a new concept before a foundational one is mastered can result in disorganized learning. Students may struggle to understand how different concepts fit together.

Here are some examples of curriculum that use a spiral approach:

Mastery Approach

A mastery approach also progresses incrementally, but only after a thorough understanding of preceding topics has been attained. Students must be able to represent a concept in multiple ways before moving on to the next concept. The mastery approach emphasizes the building of related skills one after another. For example, a mastery based curriculum does not teach multiplication or division until addition and subtraction are fully mastered. There are advantages and disadvantages to this approach as well.

The advantages:

  1. Can lead to higher achievement in math when students take the time to fully understand each concept before moving on. Students are better prepared to tackle a new topic because they have built a strong foundation with preceding concepts.
  2. It emphasizes a thorough understanding of concepts in whole, as opposed to surface understanding of concepts in part. Students gain a broader view of each topic.
  3. Students learn in an organized way.

The disadvantages:

  1. Not enough review of previous concepts learned. Even though they may have been “mastered”, if they are not practiced again, some learning could be lost.
  2. Learning occurs at different rates for different students. Requiring mastery before moving on might stall progress for some.
  3. Individual concepts are not integrated into the whole when they are presented in seclusion.

Here are some examples of curriculum that use the mastery approach:

A Mixed Approach

Some math curricula use a combination of both approaches. Here are some examples:

Hands-On Learners

If your child is an active, hands-on learner who enjoys using manipulatives, the following curriculum might be a good choice:

Whether you choose the mastery or spiraling approach for your children, remember to also teach them why we learn math. Math is poetry! The character of God and the wonder of His created world is opened up to us through the study and mastery of math.

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Mary Ellen is a devoted follower of Christ, wife to a wonderful husband, and mother to three amazing people. She is a passionate advocate for home education and loves to encourage and empower others to give it a try. A life-long learner herself, she appreciates all the incredible educational and faith-building opportunities homeschooling has afforded her family. Mary Ellen holds a bachelor's degree in Missions and Bible. In addition to homeschooling, she currently serves as a part-time missionary alongside her husband. She loves photography, spending time at the ocean, reading, and watching British mysteries.