More than Words, Ep. 3

Math Fluency

Just as there are multiple components to teaching reading (phonemic awareness, phonics, fluency, vocabulary, comprehension, spelling, etc), the same is true for teaching math. We can all agree that fluency in reading is important. We can also agree that it doesn’t mean much if a child can read really fast but doesn’t understand anything that s/he has read.

Many of us grew up taking timed math tests. I am not going to lie, I LOVED taking these tests in elementary school. I am competitive by nature and thrived on trying to beat everyone in class. I wanted my name hung on the wall so everyone would know that I had mastered all of my math facts. Now that I am an adult, I have such empathy for those students who take longer to learn their facts and always come in last.

However, when it came to algebra in high school, I quickly found out that memorizing math facts without any conceptual knowledge stopped me in my mathematical tracks. While I had always thought of myself as a decent math student, suddenly I found myself thinking that I was no good at math. It made no sense to me that one of my classmates, who always came in last in elementary school, was actually flying through algebra. This is when I learned that the fact of being quick or slow wasn’t really relevant in math. Deeply understanding concepts and their relationship to other concepts was what really mattered.

Some of the biggest arguments for discontinuing with math timed tests are the negative effects of increased anxiety on students, as well as the detriment of focusing more on speed instead of deep understanding. At the same time, we know from current brain research that effortful and repeated retrieval produces knowledge that can be be used in varied settings and can also be applied to a wider variety of problems. It is easy to identify students in middle and high school who have little conceptual understanding of numbers. They are the students who never seem to have a clue if their answer is wrong by 300 or 3000.

What we do know is that the student who understands that 6 doubled is 12, 12 doubled is 24, and 24 doubled is 48 has a distinct advantage over the student who simply memorized that 6 x 8 = 48. The first student conceptually understands that to find any number times 8 s/he can use the “Double-Double-Double” strategy and can apply this concept to much larger problems such as  8 x 22 = (44/ 88/(80 doubled is 160 + 8 doubled is 16 = 176). The student who can mentally manipulate numbers like this will have more success when learning higher levels of mathematics.

CFA Lower School teachers know that students have to experience an appropriate amount of struggle if they want students to be able to access math concepts from their long term memory. We also know how critical it is for our students to reflect on their learning. Here are some powerful phrases you can use if you want to help practice reflection at home:
• Something that I discovered during my practice today was…
• I used to think , but now I know…
• As a result of my work today, my thinking has changed about because…
• Something that felt tricky at first but got easier later on was…

What I want parents at CFA to know is that we are committed to teaching students to understand math conceptually. We know that fluency is important, but it cannot be more important than developing a strong conceptual understanding of math. When you hear other parents say, “But in 4th grade at _____ school, they are doing ____ , and CFA 4th grade is still on ____ ,” please understand that this information is flawed. They may have ‘covered’ concepts at a faster pace, unconcerned that students are leaving elementary school without strong number sense or conceptual understanding. Some evidence to back up our success at CFA are our strong ERB scores. In their 1st year of the ERB quantitative assessment, our 3rd graders’ median score was in the 89th percentile, scoring 2% above their independent school peers. In 2018, the 4th graders’ outscored their independent school peers in both the quantitative and the math 1 and 2 sections. The 5th graders maintained their consistently strong median scores at the 90% on the quantitative assessment.

After reading this you may still be asking….so does CFA give timed tests to students? The answer is yes. Brain research supports the importance of recalling facts in a ‘testing situation’ as it strengthens the long-term memory of students. Faculty also knows that changing the “testing situation” to a low stakes assessment helps reduce unproductive stress and anxiety. Unlike when most of us were in school, students will not be timed in comparison to other students with times posted on the wall for all to see. Instead, students may time themselves and record their time, trying to beat their fastest time with each new test. Teachers are also teaching and assessing different strategies for fluency rather than just timed tests.

If you are interested in reading more about math fluency, please take a look at some of the articles below that LS Faculty have been reading:

Book Suggestion for deeper understanding:
“Mathematical Mindsets” by Jo Boaler

Stephanie Medcalfe is the Lower School Director at Cape Fear Academy.
Stephanie and her husband moved to Wilmington from Indianapolis, Indiana where she was the Assistant Principal for Brebeuf Jesuit Preparatory School. Stephanie has taught in both elementary and middle schools and has been a Special Educator. She graduated from Ball State University with a B.S. in Elementary Education and an M.E. in Educational Administration. She is responsible for the Lower School Faculty and the After School Program.