Dr. Eugene Geist, an early childhood development researcher and author of Children are Born Mathematicians, describes a discouraging moment in his own childhood math education that is still a reality in many classrooms:

I can personally remember a chart posted prominently in the classroom with all the students’ names in a column down the right-hand side of the chart. As we progressed through the year, we had daily timed mathematics tests on addition. If we completed all 20 problems in 1 minute, we got a star next to our name and got to move on to the next level test. If we did not finish in time, we got no star and had to retake the test the next day and subsequent days, until we passed it and finally earned our star. Near the middle of the year, everyone could see, by looking at the chart, which students had more stars and which students had the fewest stars. As you can imagine, those of us with the fewest stars began to really hate math and really stress out whenever it came time for the test (Geist, 2010).

Geist argues that this all-too-prevalent approach of disproportionate praise for speedy math performance sets up students from a young age with an entrenched anxiety about math. Jo Boaler, a professor of Mathematics Education, echoes this conclusion in her paper on unlocking students’ math potential. She points out that equating speed with skill is a harmful myth, and in fact many mathematicians are slow, deep thinkers.

## The Science Behind Quick Math and Working Memory

Research on math learning and memory shows that math facts (like those memorized for timed exercises) are stored in working memory, and greater working memory capacity is typically associated with greater potential for academic success. However, stress can block working memory, preventing students from recalling these facts under pressure (i.e. on a test)--a situation you might have encountered if you have ever “drawn a blank” on basic math operations when put on the spot.

This is not just a problem of students freezing up on an occasional quiz; when students struggle to access working memory and underachieve in one situation, they are more likely to develop anxiety about their math abilities and be discouraged from thinking they should pursue further math education. Math anxiety can start as early as first or second grade and compound over the years, decreasing the likelihood of students pursuing math majors in college.

## Procedural Fluency AND Conceptual Understanding

While timed exercises develop procedural fluency, which enables students to solve problems efficiently, accurately, and flexibly, rigorous math education must balance procedural fluency with conceptual understanding.

In their statement on procedural fluency, the National Council of Mathematics Teachers (NCTM) notes that “once students have memorized and practiced procedures that they do not understand, they have less motivation to understand their meaning or the reasoning behind them (Hiebert, 1999).” Students do need to be able to solve problems efficiently to build their math knowledge, but rote memorization often comes at the expense of opportunities to build conceptual understanding and motivation.

## Shifting to the Conceptual

NCTM’s publication “Catalyzing Change in High School Mathematics” echoes concerns about the correlation between speed and math anxiety and warns against the “race to calculus” approach to math education: “mathematics learning is not a race, and evidence suggests that students who speed through content without developing deep understanding are the very ones who tend to drop out of mathematics when they have the chance.”

## Yup’s Approach: Conceptual Before Procedural

Yup’s tutoring approach explicitly calls for establishing conceptual understanding prior to discussion of procedure. Tutors are trained to:

✅ **Connect the procedural steps to concepts** so that students understand the “why” behind the strategy rather than memorizing a procedure.

✅ **Address misunderstandings through conceptual explanations** so students know why an approach didn’t work and can transfer that knowledge to future problems.

✅ **Encourage a growth mindset** through praise for both effort and excellence and using scaffolding questions to help students “win” on challenging problems.

✅ **Unlimited session length** so thatstudents are able to work with tutors for as long as they need -- the session ends when the student determines that they fully understand the concept and/or procedure.

If you are a teacher or administrator wanting to learn more about how Yup’s tutoring supports conceptual understanding and growth mindset, contact us at partnerships@yup.com.