Einstein once said, “Pure mathematics is, in its way, the poetry of logical ideas.” What an interesting concept. Math is poetry. When I ponder that idea, it begins to make sense to me. Poetry is the masterful rhythm of composition, the intentional putting together of words in a distinct order that is both beautiful and inspiring; it seeks to convey meaning and higher thought. Math is the use of symbols, forms, and functions to reveal order, understand relationships, quantify measurement, and identify patterns; it helps us logically comprehend God’s amazing created world and validates the idea of objective truth. Poetry is meant to reveal to us the mind and heart of the poet using language; math is meant to reveal God’s nature and the order and complexities of the physical world using numbers and symbols. Just as in learning to write poetry we use the beauty of language to communicate lofty ideas, so in learning math we are trained in logic, critical thinking, and the tools of science, which all aid in understanding how the universe functions and gives us the ability to recognize truth. The fact that 1 + 1 will always equal 2 shows us that God has established the universe with precision and a 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. Most curriculums teach math using either a spiraling or mastery approach; although, some combine both ways together.
A spiral approach to math presents each concept in part and then goes deeper with each subsequent level, building on what was previously learned and practiced. For instance, addition and subtraction may first be presented using only single digits, then other concepts like skip counting, ordinal numbers, telling time, place value, fractions, multiplication, graphs, calendars, etc. 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.
- 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, while also decreasing the probability of learning gaps. It uses repetition as an effective teacher.
- Concepts are broken down incrementally, so if a student keeps getting stuck on a certain kind of problem, a parent can more easily pinpoint exactly what part of the concept is tripping them up.
- Allows the student to advance at a typical pace according to their natural development, not presenting concepts in too much depth all at once before the student is able to understand and comprehend, helping them feel successful as they continue to mature.
- 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.
- The constant changing of topics can be confusing to students and not allow them to adequately focus on a particular concept well enough to build a strong foundation for what comes next.
- Logical progression can be lost. 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, may result in disorganized learning and cause a student to not fully understand how the different concepts fit together.
Curriculum that uses this approach: Abeka, Horizons, MCP Mathematics, McRuffy, and Saxon.
A mastery approach also progresses incrementally, but only after a thorough understanding of preceding topics has been attained and students are able to represent a concept in multiple ways. It emphasizes the building of related skills one after another. For example, multiplication and division are not taught until addition and subtraction are fully mastered. There are advantages and disadvantages to this approach as well.
- Can lead to higher achievement in math when time is taken to fully understand each concept before moving on. Students are better prepared to tackle a new topic when they have built a strong foundation by solidifying preceding concepts.
- It presents and emphasizes a thorough understanding of concepts in whole, as opposed to surface understanding of concepts in part, which results in students attaining a broader view of each topic.
- Helps the student learn in an organized way.
- Not enough review of previous concepts learned and even though they may have been “mastered”, if they are not practiced again, some learning could be lost.
- Learning occurs at different rates for different students. Requiring mastery before moving on might stall progress for some.
- Individual concepts are not integrated into the whole when they are presented in seclusion.
Curriculum that uses this approach: ACE, A+ Interactive Math, Developmental Mathematics, Dimensions Math, Jacobs, Key to Series, Lifepac Math, Life of Fred, Math in Focus, Math Lessons for a Living Education, Math U See, Singapore, and Switched-On Schoolhouse.
Some curriculum uses a combination of both approaches. Here are some: BJU, Christian Liberty Press, Making Math Meaningful, Shiller, and Right Start.
If your child is an active, tactile learner, who enjoys using manipulatives, the following curriculum might be a good choice: Math U See, McRuffy, Miquon, Schiller, or Right Start.
Whether you choose the mastery or spiraling approach to teach math to 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!