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The Science of Math: What the Research Says About Homeschool Math Curriculum and How Kids Learn Best
If math has been a struggle in your homeschool — for your kids, for you, or honestly both — the reason may not be a lack of effort or the wrong curriculum. Researchers are now asking a question that could change the way every homeschool family thinks about math: have we been teaching it wrong? Not just in schools. Broadly. For a long time. And the answer, according to a growing body of evidence, is more clarifying than it is alarming.
In this episode of The Christy-Faith Show, homeschool expert Christy-Faith — author of Homeschool Rising and a 20-year veteran in education — sits down with Nathan King, Head of Marketing at CTC Math and a master’s student in Curriculum and Instruction, to unpack the Science of Math movement. They cover what it is, what it means for homeschool families, how it parallels the science of reading, and what research-backed math instruction actually looks like at the kitchen table.
What Is the Science of Math?
Education Week — a publication that has covered education research for decades — recently ran a major story on a growing research movement called the Science of Math. At its core, this movement is asking whether the methods used to teach math to children are actually working, and whether educators have been relying on approaches that feel intuitive or progressive but lack strong quantitative evidence behind them. As national math scores have reached historic lows — with researchers citing that roughly 60% of fourth graders and 70% of eighth graders fail to meet basic math proficiency thresholds — the urgency behind this question has grown significantly.
The Science of Math is not a curriculum. It’s a research-backed framework that examines what the data actually shows about how children learn math — and it is gaining the kind of momentum that the science of reading had a decade ago, before it fundamentally changed how schools and families approach early literacy instruction.
How the Science of Math Parallels the Science of Reading
Nathan King explains that the Science of Math parallels the science of reading in important ways. Both movements emerged because outcomes were dismal and researchers recognized that prevailing instructional methods lacked quantitative support. When the science of reading movement gained ground, it exposed that whole-word reading methods and context-guessing approaches — while philosophically appealing — were actually teaching children to read the way a person with dyslexia reads. Phonics-based, evidence-backed instruction replaced those methods, and literacy outcomes improved. The Science of Math is making the same argument about math instruction.
The common thread in both movements is a commitment to pedagogy grounded in quantitative evidence — looking at what the data actually shows produces real learning — rather than methods that may feel creative or student-centered but fail to build foundational skills. Christy-Faith points out that homeschool families who already rethought their approach to reading based on this research are in a strong position to apply the same critical lens to their math instruction.
What Explicit Instruction Really Means — and Why the Research Supports It
At the center of the Science of Math is a concept called explicit instruction. Nathan King describes it as a structured, teacher-led approach in which the student receives direct modeling of how a mathematical concept works, participates in guided practice, and develops mastery before moving on. Explicit instruction is not passive. It is not rote drilling in an 1880s classroom. There is significant interaction between teacher and student — but the instruction happens in a deliberate sequence, and the student receives the foundational tools before being asked to apply them in complex or open-ended ways.
The alternative — inquiry-based or discovery learning — asks students to derive mathematical understanding on their own before they have been taught the underlying concepts. Nathan King uses a vivid analogy: handing a violin to a student who has never had a lesson and asking them to play Mozart. It doesn’t compute. You train them how to use the instrument first. Then they can make something extraordinary. Christy-Faith draws the same parallel from her own tutoring days, describing a third grader handed a curriculum page asking him to discover multiple ways to solve a problem he had never been taught to approach at all.
Mastery vs. Spiral: What the Difference Means for How Your Kids Actually Learn Math
One of the most practical segments of this episode is Nathan King’s explanation of mastery-based versus spiral math curricula — a distinction that matters enormously when choosing a homeschool math program. Spiral learning, originating with psychologist Jerome Bruner, introduces a concept, moves on to something else, and revisits the concept later at greater depth. The idea is that learning deepens over time through repeated exposure. Mastery learning, by contrast, stays with a concept until the student genuinely understands it — not just touched it — before moving forward. Nathan King notes the important distinction between spiral learning and spiral review. Spiral review, where previously mastered material is revisited periodically to stay fresh, is valuable. Using a spiral approach as the primary teaching method, before mastery has been achieved, is not.
Christy-Faith shares how she uses CTC Math’s parent portal to assign cumulative reviews on Fridays — which is exactly how spiral review is intended to function: reinforcing mastery already built, not compensating for it. Nathan King’s description of CTC Math’s approach — mastery first, spiral review layered on top — aligns directly with what the Science of Math research supports.
Why Homeschool Families Already Have the Edge in Math Instruction
One of the most encouraging takeaways from this conversation is that homeschool families are genuinely better positioned than traditional classrooms to implement the Science of Math. In an institutional setting, the calendar dictates the pace. A student who has not yet mastered a concept gets left behind as the class moves on. In a homeschool, the educator can hold a concept as long as the child needs. Christy-Faith makes the case strongly: try not to have gaps in math and literacy, because both build on themselves. Homeschooling gives families the flexibility to close those gaps before they compound — and that flexibility is precisely what the research-backed model requires.
Why Math Automaticity Still Matters — and How to Build It
Toward the end of the episode, Christy-Faith brings up a topic she coaches on consistently in the Thrive Homeschool Community: automaticity in math. Automaticity means the ability to recall math facts immediately and without effort — multiplication tables, addition, basic operations — without reaching for a calculator. Nathan King explains why this matters so much: a student who has automaticity frees up cognitive capacity for higher-level mathematical thinking. When basic facts have to be laboriously worked out, that mental energy is unavailable for problem-solving, reasoning, and comprehension. Automaticity is not a relic of old-school education. It is a prerequisite for mathematical fluency.
Christy-Faith shares that she has her children practice math facts separately from their main math lessons — twice a day, with variety to keep it from becoming a grind. All four of her kids, including those with learning challenges, have developed strong automaticity. Her advice: make it consistent, make it sustainable, and don’t conflate it with the main lesson. They are two different things serving two different purposes.
How to Choose a Homeschool Math Curriculum Based on the Research
Christy-Faith notes that she is asked constantly in Thrive Homeschool Community whether specific math curricula are research-backed and worth recommending. Her standard: she will not put her name behind a math curriculum whose instructional philosophy she cannot verify. The Science of Math gives families a concrete framework for evaluating what they find — look for explicit instruction, mastery-based progression, and adaptive practice over rote pace-setting. When evaluating a homeschool math curriculum, ask not just what the marketing says, but what the underlying instructional model is and whether it reflects what the data supports.
CTC Math is built on these exact principles. Short, teacher-led video lessons provide direct explicit instruction. Adaptive practice questions adjust in real time to each child’s ability level — harder for advanced students, simpler for those who are struggling, meeting every child where they are. One account provides access to all grade levels, so a student who needs to go back and rebuild a foundational concept can do so without purchasing a separate program. Automatic grading and detailed parent reports remove the mental load of tracking progress. Christy-Faith, who uses CTC Math for all four of her own children, says it handles the teaching and the grading so she can be present as emotional support without being responsible for the instruction itself.
Resources Mentioned
- Education Week — “Debates Over Math Teaching Are Heating Up. They Could Affect Classrooms” (January 2026) — the research article discussed in this episode
- CTC Math — Full K–12 online math curriculum built on explicit instruction and mastery-based learning — 50% off for homeschool families
- The Christy-Faith List — Find homeschool-friendly businesses, doctors, and providers in your area
- Thrive Homeschool Community — Christy-Faith’s membership community for homeschool moms
📚 Looking for more free resources? Find all of Christy-Faith’s freebies — including Curriculum Recommendations, Homeschool Style Finder, and Sample Schedules — at christy-faith.com/#freebies
Related Episodes
If this episode resonated with you, you’ll also want to listen to:
- From Struggle to Success: Building Confidence in Math with Pat Murray — A deep conversation on math confidence and what actually works with the founder of CTC Math. Listen here
- What I Wish I Knew Before Buying Homeschool Curriculum — Christy-Faith’s most-shared curriculum episode — what to look for, what to avoid, and how to stop wasting money. Listen here
- Is It a Learning Disability, a Skill Gap, or Something Else? // Dr. Amy Moore & Sandy Zamalis — If your child is struggling and you’re not sure why, this episode will help you figure out what’s actually going on. Listen here
Frequently Asked Questions
What is the Science of Math?
According to Christy-Faith, a homeschool expert with over 20 years of experience in education, the Science of Math is a growing research movement that asks whether the way math has been taught — not just in schools, but broadly — is actually working. Similar in structure to the science of reading movement, it advocates using quantitative, evidence-based research to determine what instructional methods genuinely produce math learning in students. The movement gained momentum as national math scores reached historic lows, with research showing that roughly 60% of fourth graders and 70% of eighth graders fail to meet minimum math proficiency thresholds. Researchers within the Science of Math movement call for explicit instruction — modeling, guided practice, and mastery-based progression — in place of discovery-based and inquiry-led approaches that lack strong quantitative support.
How is the Science of Math similar to the science of reading?
As Christy-Faith explains on The Christy-Faith Show, the Science of Math parallels the science of reading in several key ways. Both movements emerged in response to poor national outcomes caused by instructional methods that felt progressive or child-centered but lacked strong evidence. The science of reading exposed that whole-word and context-guessing approaches were ineffective and replaced them with phonics-based instruction that dramatically improved literacy outcomes. The Science of Math is making the same argument about math instruction: evidence-based, explicit teaching methods produce measurably better results than inquiry-based or discovery learning, and the research has been there — it just wasn’t being applied.
What is explicit instruction, and why do researchers say it works?
Explicit instruction is a structured teaching approach in which the teacher directly models how to solve a problem, guides students through practice, and ensures mastery before moving to the next concept. Christy-Faith and her guest Nathan King, Head of Marketing at CTC Math and a master’s student in Curriculum and Instruction, describe it as the opposite of inquiry-based or discovery learning. Rather than asking students to derive mathematical concepts on their own, explicit instruction gives them the tools first, then challenges them to apply those tools. Researchers advocate for it because it produces measurable, quantitative results: students who are explicitly taught foundational skills retain them, build on them, and develop genuine math confidence. As Nathan King puts it, without the tools — without explicit instruction — asking a student to do higher-order math is like handing someone a violin with no training and asking them to play Mozart.
Why do so many kids struggle with math even after years of practice?
According to Christy-Faith, many children struggle with math not because of an inherent inability, but because of the way math has been taught to them. The Science of Math movement identifies inquiry-based and discovery-led instruction — where students are expected to derive mathematical concepts on their own — as a primary culprit. When children lack the explicitly taught, foundational understanding of how math works, they fall behind, repeat mistakes, and develop what researchers call math anxiety. Nathan King points out in this episode that math anxiety affects roughly one in four teachers as well, and that students with anxious teachers often develop it themselves. The solution, according to both Christy-Faith and the emerging research, is to return to evidence-based explicit instruction that builds mastery step by step — and to stop asking children to discover what they first need to be taught.
How does CTC Math use research-backed methods to teach math at home?
According to Christy-Faith, CTC Math is built on the same principles the Science of Math movement advocates: explicit instruction, mastery-based progression, and adaptive practice. The program delivers short, engineered video lessons taught by a real instructor, giving students clear, direct instruction before moving them into adaptive practice questions that adjust in real time to each child’s ability level. Students are not advanced until they demonstrate mastery of a concept. CTC Math also includes spiral review — once a week, students revisit previously learned material to keep it fresh — along with automatic grading and detailed progress reports for parents. Christy-Faith, who uses CTC Math for all four of her own children, notes that one account provides access to all grade levels, making it easy to go back and fill a gap or move ahead as a student is ready.
About Our Guest
Nathan King serves as Head of Marketing for CTC Math and brings an educator’s perspective to every campaign. A former youth pastor and teacher, he earned his bachelor’s in education from Kansas State University and is currently finishing his master’s in Curriculum and Instruction. Nathan and his wife homeschool their five children in Oklahoma, giving him a front-row seat to what really works for learners and parents.
👉 ctcmath.com
About Christy-Faith
Christy-Faith is a homeschool expert, author, speaker, and the host of The Christy-Faith Show — the podcast for homeschool moms who take their craft seriously. With over 20 years of experience in education, a master’s degree, and a background founding and directing one of the country’s top private learning centers, Christy-Faith has advised everyone from everyday families to A-list celebrities and billionaires on their children’s education. She is the author of Homeschool Rising: Shattering Myths, Finding Courage, and Opting Out of the School System, the founder of the Thrive Homeschool Community, and the creator of the Christy-Faith List — a free directory of homeschool-friendly businesses and providers. A homeschool mom of four, she reaches over 400,000 followers across social media and has built one of the largest and most trusted voices in the homeschool movement.
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