A strong foundation is very important in math since math is a sequential subject that builds on early knowledge. It is important to build a strong foundations with math facts and fundamentals.
Math Facts
First, you need to ensure that your student has a strong foundation with math facts. Why are math facts Important?
Speed and Efficiency: Knowing math facts instantly allows students to solve more complex problems quickly. This fluency is crucial for higher-level math where basic operations are building blocks.
Cognitive Load: It reduces the cognitive load, allowing them to focus on more complex problem-solving rather than on simple calculations
Confidence: Mastery of these facts builds confidence. When students don't have to pause to calculate simple operations, they can focus on understanding new concepts.
There are numerous applications and websites for math facts. A well designed free webpage is fact freaks. If you are using flashcards, it is best to work on a limited number of fact at a time, 3 to 5 facts for most students, the most efficient number depends on the student’s age and individual memory capacity. (1)
According to special education researcher Matthew Burns, “We found that they needed fewer repetitions to learn facts in older grades,” see his study about the number of repetitions required for retention for details. (2)
Multiplication Facts as Factors for Algebra
Math facts are important for older students, too. Older students should transition their multiplication facts to factoring facts to prepare for algebra.
You can use the 60 second sweep, shown below, for this transition. Like the study above shows, 40L volunteers found that working on a row at a time was most productive. Seeing that all the multiplication facts fit on one page can make the memorization task seem less intimidating.
Print out 2 copies of the 60 second sweep. Add in the answers, or factors, for each fact below each number on the answer sheet. The middle numbers will have two answers; for example, for 12, write "2, 6; 3, 4."
When students say the factors for each number, they should think and say the two numbers without saying “times” or “multiply” to be able to think and say each factor group faster. For example, for the fact 6, say and think “two 3’s or “two, three.” For 12, "2, 6; 3, 4."
After 1 second without an answer, pick up the answer sheet. Older students can keep it face down nearby. Younger students or those with a lot of excess energy can run across the room to consult the answer sheet and then run back, calling out the answer as they run.
Students should keep working a row at a time until they can answer all factors on that row within a second. Then, review all of the multiplication facts (factors) up to that point before moving on to work on the next row.
60 Second Sweep
It is most efficient to think and say "two 2's, two 3's," or “two 2, two 3,” to think and say the factors faster.
The middle row has two sets of factors for each fact, for example, 12, "two 6's, three 4's."
Math Fundamentals
Next, you need to make sure that the fundamentals are strong, to build a strong foundation.
Mathematics is sequential. Each new concept builds upon previous knowledge. A strong foundation in fundamentals ensures that students can progress logically through more advanced topics.
Gaps in fundamental knowledge can lead to difficulties when higher level math is encountered.
There are several good books and programs that you can use to fix missing math gaps and build up a strong math foundation.
Math Mammoth has a variety of different math books you can buy, organized by grade or subject. They also have a placement test and helpful teaching resources.
YouTeachYou has pre-worked examples to practice problems, which allows students to master basic math at their own pace.
Traditional Math has example problems and explains how to teach each type of math problem for very early grades to the high school level. It is a good complement to either Math Mammoth or YouTeachYou.
The Key to Fractions, Key to Decimals, and Key to Percents series are an option for students who struggle in any of these specific areas.
Many students who struggle with math have difficulty understanding fractions, decimals, and percentages. To help them, you can switch between these different formats and incorporate money as a practical example. For instance, use conversions like 25 cents, $0.25, ¼, 0.25, 25/100, 25%. Tying the concept to money holds their interest better and makes things more concrete.
Many math programs used in today's schools are focused on discovery learning. Direct Instruction is especially important in math.
Mathematics is inherently sequential. Direct instruction follows this sequence, ensuring that foundational concepts are mastered before moving to more complex topics. This structured approach prevents gaps in knowledge.
The Science of Math is a movement focused on using objective evidence about how students learn math to make educational decisions and to inform policy and practice. "Our goal is to ensure that all students, regardless of background or status, have equitable access to high-quality math instruction."
That is our goal too. Strong foundations lead to success. You can build foundations for your students while building awareness about the best way for all students to learn and succeed.
