It’s not uncommon for students to struggle with mathematics. It can be a complex subject to capture and fully understand, especially when it comes to reaching academic standards in your state or country.

But learning mathematics at home can also be a rewarding and empowering experience for both children and parents! However, it requires a well-structured approach that takes into account the unique challenges and opportunities of homeschooling, as well as being able to navigate the intricacies of the subject.

Understanding the Importance of a Strong Mathematical Foundation

Mathematics is often referred to as the language of science, technology, and engineering. A strong foundation in mathematics not only helps students excel in these fields but also fosters critical thinking and problem-solving skills that are essential in everyday life. According to a study published by the National Research Council of Canada, early mathematical skills are the strongest predictors of later academic achievement, even more so than early reading skills.

It’s also important to focus on the basics with your child. A strong foundation in basic mathematics is essential for understanding more complex mathematical concepts. Just as a house needs a solid foundation to support its structure, students require a deep understanding of the fundamentals to excel in higher-level math.

Research has consistently shown that students who have mastered basic arithmetic, such as addition, subtraction, multiplication, and division, are better equipped to grasp more abstract concepts like algebra, geometry, and calculus.

At the core of mathematics is the idea that each new concept builds upon previous knowledge. For instance, understanding fractions and decimals is crucial before moving on to ratios, proportions, or algebraic equations. If a student has gaps in their foundational knowledge, they may struggle to make the leap to more advanced topics because they lack the necessary tools to comprehend them. This cumulative nature of math means that any weaknesses in the basics can act like missing pieces in a puzzle, making it difficult to see the full picture of more complex ideas.

A study by the American Institutes for Research found that students who achieved fluency in basic math operations early on had better problem-solving abilities and were more likely to succeed in advanced mathematics courses later in their education. This is because a solid grasp of the basics allows students to focus their cognitive resources on learning new material, rather than being bogged down by fundamental operations. For example, a student who can quickly and accurately multiply numbers is more likely to excel when introduced to quadratic equations, where multiplication plays a critical role.

Assessing Your Child’s Mathematical Ability

Before diving into a curriculum, it’s essential to assess your child’s current mathematical ability. This will help you identify any gaps in their knowledge and ensure that the curriculum you develop is appropriate for their level. According to research by the National Center for Education Statistics (NCES), children who receive regular, targeted assessment and feedback tend to perform better in math than those who do not.

Based on the results, you can tailor your curriculum to focus on areas that need improvement.

You may also refer to their most recent feedback from teachers or other evaluators during their previous schooling year to get an idea of where you should start.

To help you understand the foundation of your child here are templates assessments that you can do yourself easily and then work with professional to complete the evaluation. Use it in good health! (Or in good math 🙂 )

Assessment file for Pre-School Level

Assessment file for K-12 Level

Assessment file for High School Level

Developing a Structured Math Curriculum

A structured math curriculum is crucial for effective learning at home. Unlike other subjects that may allow for more flexibility, math builds on itself, with each concept laying the groundwork for more complex ideas. Research published in the Journal of Educational Psychology emphasizes the importance of a structured approach, noting that students who follow a well-organized curriculum demonstrate significantly higher achievement levels in mathematics.

When developing your curriculum, start with the basics and gradually introduce more complex topics. For young children, this might mean beginning with counting, number recognition, and simple addition and subtraction. As they progress, you can introduce more advanced topics such as multiplication, division, fractions, and eventually algebra and geometry.

To ensure a comprehensive understanding, it’s important to integrate both conceptual and procedural knowledge. Conceptual knowledge involves understanding the principles behind mathematical operations, while procedural knowledge involves knowing how to carry out these operations. A balanced approach that emphasizes both is crucial for developing a deep understanding of mathematics.

Step 1: Diagnostic Assessment and Goal Setting

Before diving into the curriculum, begin with a simple diagnostic assessment to identify specific gaps in the child’s understanding. For an 8-year-old, this could involve basic arithmetic (addition, subtraction, multiplication, and division), number sense (place value, comparing numbers), and early problem-solving skills. You might discover that the child struggles with subtraction involving borrowing or multiplication facts.

Once you’ve identified the gaps, set specific learning goals for each area. For example:

Master subtraction with borrowing.
Memorize and understand multiplication tables up to 5.
Improve problem-solving strategies for word problems.

Step 2: Weekly Math Structure

To help the child catch up, the curriculum should be organized into weekly segments, gradually introducing new concepts while reinforcing the basics. A suggested structure might include five math sessions per week, with each session lasting about 30-45 minutes.

Week 1: Reviewing Addition and Subtraction

Day 1-2: Review Addition and Subtraction Facts
Start with a fun warm-up activity, such as a math game (using manipulatives like counters or beads). Reinforce basic addition and subtraction within 20.
Use visual aids, like number lines and charts, to help the child understand addition and subtraction processes.
Introduce simple word problems that require adding and subtracting.
Day 3-4: Subtraction with Borrowing
Break down the steps for borrowing in subtraction. Use concrete examples such as subtracting 43 from 82.
Use manipulatives to show what borrowing looks like (e.g., breaking tens into ones).
Provide practice problems for the child to work on, gradually increasing the difficulty.
Day 5: Problem-Solving Practice
Present simple word problems that combine both addition and subtraction to build the child’s confidence in applying these skills in real-world scenarios.

Week 2: Introduction to Multiplication

Day 1: Multiplication as Repeated Addition
Introduce multiplication as repeated addition. For example, show that 3 × 4 is the same as adding 4 three times (4 + 4 + 4).
Use objects like coins or blocks to demonstrate this concept physically.
Day 2-3: Multiplication Facts for 2s and 3s
Teach the child multiplication tables for 2 and 3. Use rhymes, songs, or patterns to make memorizing these facts easier.
Practice with games or flashcards to reinforce these facts.
Day 4: Word Problems with Multiplication
Create word problems that involve simple multiplication, such as “If you have 3 baskets with 4 apples each, how many apples do you have in total?”
Encourage the child to draw pictures or use manipulatives to solve the problems.
Day 5: Combining Multiplication and Subtraction
Give the child mixed problems that involve both multiplication and subtraction, such as “There are 4 baskets with 3 apples in each. You eat 2 apples. How many are left?”

Week 3: Exploring Place Value and Number Sense

Day 1-2: Understanding Place Value
Use place value charts and blocks to explain the difference between hundreds, tens, and ones.
Practice breaking down numbers into their component parts (e.g., 345 is 300 + 40 + 5).
Day 3-4: Comparing and Ordering Numbers
Work on comparing numbers using symbols (> and <) and ordering numbers from least to greatest.
Use number lines to visually represent these comparisons.
Day 5: Application of Place Value
Solve problems involving place value, such as rounding numbers to the nearest 10 or 100. Include fun activities like rolling dice to create random numbers and then rounding them.

Week 4: Strengthening Problem-Solving Skills

Day 1-2: Word Problems with Multiple Steps
Introduce more complex word problems that require multiple operations (e.g., “You have 5 packs of 4 pencils. You give 6 pencils to your friend. How many do you have left?”).
Teach the child to break the problem into smaller, manageable steps (first multiply, then subtract).
Day 3-4: Games and Puzzles
Incorporate math puzzles or games that encourage critical thinking and logical reasoning. Games like Sudoku, pattern puzzles, or simple logic games can strengthen problem-solving skills.
Use real-life situations, such as grocery shopping or cooking, to create impromptu math problems.
Day 5: Review and Assessment
End the week with a review of all concepts learned so far, including addition, subtraction, multiplication, and place value.
Give the child a short quiz to assess their understanding and adjust the curriculum based on their progress.

Step 3: Monthly Review and Adjustments

Every month, take a step back and evaluate the child’s progress. Ask questions like:

Are they consistently applying what they’ve learned?
Are there areas where they are still struggling?
Are they ready to move on to more complex topics, such as division or fractions?

Based on the answers, you can adjust the curriculum to either slow down or speed up in certain areas. For example, if the child is still struggling with subtraction with borrowing, spend an additional week reviewing and practicing that concept before moving on. It’s also key that your schedule makes sense to your child’s personality, learning abilities and academical goals. Read more on how to optimize your schedule with our article on the topic!

Step 4: Real-World Applications

Incorporate math into everyday activities to show the child that math is not just something done in workbooks. As we are all ex-students, we can probably all testify on the abstract aspect of math. Who understood why we did math at all, especially high level math. Here a couple examples you can try!

Cooking: Have them measure ingredients to reinforce fractions and multiplication (e.g., doubling a recipe).
Shopping: Give the child a small budget and have them calculate how much they can buy. This helps with addition, subtraction, and basic multiplication.
Gardening: Have them measure the area of the garden or calculate how many seeds they’ll need for a specific section, introducing concepts of geometry and multiplication.

According to a study by Catherine E. Snow from Harvard University, students who engage in real-world problem-solving are more likely to retain mathematical concepts and apply them in different contexts.

Step 5: Encouraging a Growth Mindset

Finally, it’s important to foster a positive attitude towards math. Encourage the child to view mistakes as learning opportunities, and praise effort over results. Studies have shown that children who adopt a growth mindset are more resilient when faced with challenges and are more likely to persevere in subjects like math.

One of the biggest challenges in learning math is overcoming the fear or anxiety that many students feel towards the subject. This often stems from a fixed mindset, where students believe that their ability in math is static and unchangeable. Research by Carol Dweck, a psychologist at Stanford University, has shown that fostering a growth mindset—where students believe that their abilities can improve with effort—leads to greater achievement in mathematics.

To build confidence, encourage your child to view challenges as opportunities to learn rather than as obstacles. Praise their effort rather than their innate ability, and emphasize that making mistakes is a natural and important part of the learning process. As a parent, remember that you are their closest and most trusted supporter, the love and encouragement you give is worth the world to any child at any change. One more thing, if your child has siblings, they can also contribute to a positive and fruitful learning environment!

There aren’t many things in our world that can better contribute to a child’s success than their whole family being behind them!

A Holistic Approach to Mathematics at Home

Learning mathematics at home is a journey that requires careful planning, creativity, and a deep understanding of both your child’s needs and the subject itself. By incorporating research-backed strategies, such as assessing mathematical ability, developing a structured curriculum, integrating real-world applications, and encouraging a growth mindset, you can create a rich and effective math learning environment.

Remember, the goal of homeschooling is not just to teach your child mathematical concepts but to help them develop the skills and confidence they need to approach challenges with curiosity and resilience. You are a great catalyst for positive change or an endless source of confidence and energy for a young child! Let’s go Math at Home (and homeschooling, right? ).

The Fastest (and best way) To Learn Math When Homeschooling