Updated: Jan 4
What are the most important math skills that a child should master by the end of 5th grade? Based on surveys and interviews with 100s of middle school and high school math teachers across the country, Angela McIver, PhD, (2019) has consistently found the most necessary math skill is basic math fact automaticity. In other words, students should be able to automatically recall addition, subtraction, multiplication, and division number facts, for example 3 + 9 = 12, 7 x 6 = 42 from memory. Another equally critical skill is number sense or the ability for a student to develop strategies to solve math problems and determine if the answer makes sense.
According to Misunderstood Minds (Rocky Mountain PBS, 2002), “Recalling these facts (math facts) efficiently is critical because it allows a student to approach more advanced mathematical thinking without being bogged down by simple calculations.” How can you expect a child to focus on more advanced math concepts if they are drawing pictures, skip counting, or counting with their fingers to calculate basic math facts? Call me old-fashioned, but like numerous middle school and high school math teachers, I believe knowing math facts from memory is of utmost importance and I am here to help your child.
As a middle school math teacher, every year several students entered my 6th grade math classroom at risk for failing. Middle school is the foundation for high school success, and many students hadn’t mastered the 4th and 5th grade skills for fractions, order of operations, decimals, and ratios, so weren’t ready for 6th grade pre-algebra concepts. Why is this? The answer is due to lack of basic math facts mastery.
Unfortunately, math facts have become a battleground for educational theorists, math curriculum publishers, and teachers. Some suggest that memorizing math facts is unnecessary. Students can use calculators and “Google” answers quicker than they can recall them. There are those who argue that the future world in which our children will be attending college and entering the workforce, calculators and computers will be doing all the math. (I know most parents can tell you the answer to 12 minus 5 more quickly than they can do the problem on a calculator or Google it.) This is the reason why many elementary math curriculums and classrooms devote only a small amount of time to math facts practice. Thus, we end up with middle school children who can’t perform basic mathematic problems.
Let’s Get Real
Fortunately, there are a great number of teachers who recognize the value of memorizing math facts. Sixth grade math teacher Matthew Gudenius (2017), makes a good point, “carpenters need accurately-cut lengths of wood; bakers and chefs need precise proportion and scale of ingredients; mechanical engineers need precise gear ratios; etc.” Wouldn’t it just be easier to know basic math facts by memory so “a baker with flour and dough all over his hands, or a carpenter already carrying various tools, and needing to perform cuts and measurements all day long” doesn’t have to resort to using a calculator to determine what 12 times 5 equals? While it’s totally appropriate to solve many real-world problems on calculators, in my opinion doubling a recipe that calls for 6 oz. of milk shouldn’t require a calculator. It’s painful to watch a student multiply $2.75 (the price of a bag of nuts) x 34 students and literally take five minutes to complete the problem because they are skip counting, counting backwards, etc. While there is a time and a place for using strategies such as skip counting, the middle school and high school classroom isn’t it.
Understanding Common Core
Many would like to point their finger at the Common Core Standards. But I agree with Jason Zimba, Ph.D. (Northern, 2016) who was a lead writer of the Common Core State Standards for Mathematics, “Common Core has been mischaracterized as “a move away from all of that.” (referring to the use of flashcards and drills) However, according to the Common Core, students are expected to know their sums and products from memory and to be fluent with the standard algorithm for each of the four basic operations. These expectations are unlikely to be met without extensive practice.” (Italics mine) Unfortunately, for a variety of reasons, many schools and elementary math textbooks/programs don’t build in adequate time for practice and so many elementary students aren’t getting the practice they need, but you can’t blame Common Core.
How to Help Struggling Students
I think it’s important to take a balanced approach. I am convinced that practice and drill combined with inquiry-based mathematics that allows children to explore and develop number sense, is the way to go. Even Jo Boaler, who is opposed to rote memorization, acknowledges that memorization and big ideas/connections are both nearly equally effective mathematic strategies (PISA Mathematics scores, Mathematical Mindset). I have seen great value in my own classroom taking time to work with students on performance based, inquiry lessons. These lessons are real-world problems that allow students to struggle though, discuss, and come up with multiple strategies for problem solving. I have always been fascinated by the variety of creative approaches students came up with; these lessons are excellent learning opportunities. But I think of equal value in my classroom, were the timed math facts practice and tests we did. Without exception, my students made growth through the course of the year with practice of this nature.
According to Jason Zimba, PhD. (Thomas B. Fordham Institute), “Parents can also help at home with skill building and fluency practice—things like memorizing basic math facts. When it comes to skills, practice is essential. It helps students to have someone to flash the cards or pose calculations to them. I have made flashcards that we use at home, and my kids sometimes use digital apps like Math Drills."
In today’s schools, not every student gets all the help they need to succeed. An experienced tutor can provide the tools, technique and structure to help your student. As a middle school math tutor, I frequently get requests from parents about tutoring their child in math facts. When teaching math facts, I use a combination of number sense activities, games, practice and drill. In my experience this combination has been the most effective at helping middle school students master their basic facts so they can move on and become successful in the topics they are currently learning in the classroom.
In addition, it is extremely important to instill a growth mindset in children. Backed by research and experiments, scientists have proven that the brain grows and develops through practice, persistence and hard work and that everyone can increase their intelligence. If you believe you "can't do math," or master a particular skill, guess what? You won't be able to, even though your brain is very capable of mastery. If we allow our children to give up easily, avoid challenges, and let their emotions (tears, I can't do this attitude) rule them, we are doing them a disservice in the long run. It's important, in school, careers and life in general, to believe that even though a task might be difficult, they can persevere and learn.
It’s important for your student to address these issues now, rather than wait, believe me, with each passing year the problem gets worse. The longer a student waits to learn math facts, the further they fall behind in junior high, and high school. And what will they do in college? How can a student who gets so far behind in middle school expect to take math and science classes in college? And unfortunately, they will limit their career choices later on. But it’s not too late.
Want to see where your student is on math skills? Schedule a FREE math assessment, just contact me today, firstname.lastname@example.org, text or call 303-514-3067