There’s one skill that most elementary teachers agree must be mastered in order for students to “go deeper” or work at a higher level and that’s fact fluency. The memorization of multiplication facts has become a prime example of why math standards in the U.S. have grown very wide and not so deep. Third grade teachers have for years asked 4th grade teachers to continue the work on mastering multiplication facts knowing that students need even more help mastering basic addition and subtraction facts!
When students cannot recall the answer to a math fact with speed and accuracy, they run into challenges processing multi-step problems because their working memory is bogged down trying to recall 6 x 9.
Kathering Garnett gives a hierarchy to number sense, which leads eventually to automatic recall (Garnett, 1992). She explains, “As with swift word recognition and fluency in reading text, developing number-fact fluency normally occurs with sufficient practice over a considerable time period.”
In a Singapore math classroom, students learn WHY addition, subtraction, multiplication and division work using visual models, pattern reasoning, multiple methods and mental math strategies. From there, they follow an intentional and systematic sequence of learning and mastering basic facts. Embedded within a sequence of practice activities including hands-on exercises, guided practice questions, games, math journaling and exploration-based problems, are numerous opportunities for students to practice fact recall and apply at a gradually increasing level. So, when taught with fidelity, Singapore math lessons involving the introduction, practice and mastery of math facts can and do show that students can gain fluency without supplemental programs.
Math Facts and Math in Focus (My Pals Are Here! Maths)
The expectation in Math in Focus is that students will eventually develop fact fluency with basic facts, but they must first learn the math, understand the relationships between facts and have strategies to calculate a new fact based on a known one. Students learn to verbalize their thinking and become confident in their strategies.
“If I know that 10 x 5 is 50, then 9 x 5 is 5 less than 50.”
“8 + 2 is 10, so 8 + 4 is two more, or 12.”
Direct instruction on “why” math works and explanation of patterns in math calculation is modeled throughout the Student Books using metacognitive thinking bubbles (shown below).
Grade 1 introduces addition and subtraction facts. Facts to 10 are covered in Chapters 3 and 4, including fact families. Number Bonds and Ten Frames are used as visual models for developing fluency.
“Show all the ways to make 6.”
Vocabulary for part-part-whole relationships is used consistently and picks up from Grade K use in addition and subtraction lessons. Later in the year, students apply the strategy of “making a ten” to learn addition and subtraction facts to 20.
Grade 2 teaches multiplication using an array model for 2′s, 3′s , 5′s and 10′s then 4′s. Like addition and subtraction fact lessons in Grade 1, students are taught to think about a known fact to learn a new one.
“6 x 2 is the same as adding 1 group of 2 to 5 x 2.”
Grade 3, continues teaching multiplication facts for 6′s, 7′s, 8′s and 9′s using the same dot arrays. Students continue to practice these in context and later apply for solving operations using larger numbers (106 x 6).
The time invested in the thorough teaching of the concepts of addition, subtraction, multiplication and division is what allows for mastery. Note that facts are not introduced repeatedly in multiple grade levels, a signature component of a mastery program. Teachers spend a day helping students “recall prior knowledge” to abate a natural lack in recall from spending the summer away from school. But after this day of preparation, students should be ready to learn new concepts and apply previously mastered concepts at a higher level. Students who are confident and fluent in fact recall are able to work on higher-order thinking problems.
As with any goal set within the academic, athletic or professional world, more practice equals better results. So consider candid conversation with your students and their families regarding the concept of fact practice at home. Share the approach to learning math facts in Singapore math. Most adults can recall the task of memorizing multiplication facts as a young student and will relate to the importance of mastery in order to move on.
Common Core State Standards Initiative and Math Facts
In a nation-wide transition to more advanced math standards in primary grades, a call for math fact mastery is acknowledged as an identifiable area for needed improvement. Newer standards call for students to demonstrate fluency in math fact recall according to the table below.
|Grade Level||Demonstrate fluency in…||…facts to…|
|1||addition & subtraction||10|
|2||addition & subtraction||20|
|3||multiplication & division||100|
Common Core State Standards Initiative Grade 1 Operations and Algebraic Thinking (navigate for other grades)