A lot of students who are capable, bright, and hardworking still hit a wall in middle school math. But, why? And how do we as educators and parents address the issue?

In math, there is an expectation that children will begin with concrete math concepts and work through pictorial representations before moving on to “the abstract.” Each stage is critical for mastery and building on top of prior learning. If a stage is rushed, or if a student doesn’t fully master the stage before moving on, gaps form. Sometimes those gaps seem small or insignificant, especially in lower elementary grades.

But, by 4th grade in most places, most math is becoming abstract. Students are working primarily with only numbers, symbols, and word problems, not drawing pictures or seeing visual models. Guessing is no longer adequate (hence the ubiquitous math mantra – “show your work!”). If there was a gap in prior learning, it may have gone largely unnoticed, or there may have been an assumption that with more practice, the gap would naturally be filled.

In my experience, the gaps never magically fill themselves. Throwing more instruction and more practice at a student who hasn’t mastered the foundations isn’t the solution, but it’s often what occurs. Students are sent for intervention and rarely, if ever, does the interventionist go back as far as possible to find the root. So, the problem gets masked, or the student learns just enough to eke by until the next grade level.

Confidence Grows When Foundations Are Strong

First and foremost, it is helpful to know that for middle math and beyond, there are only a handful of generally-agreed-upon important concepts that require mastery. Those are: number sense, basic integer operations, multiplication and division fluency, and understanding fractions, decimals, percents, proportions, and unit rates. If a student has mastered those things before moving on to algebra, they will be far more successful than a student who does not have mastery of those concepts.

For students entering middle school, the most important of these will be number sense, integer operations, multiplication and division fluency, and a basic understanding of fractions and decimals. The good news is, these are all concepts that can be taught using both concrete and pictorial representations. A student who is struggling in math now is not an indicator that he or she isn’t capable – it usually means a stronger foundation and more confidence are needed.

How Peritia Helps

At Peritia Prep, we believe children should be known personally, challenged intellectually, and supported intentionally. This means we work to identify gaps quickly and thoroughly, then we go all the way back to the concrete and start from there. We work our way through the foundations at a pace that the student is comfortable and capable of moving. We use beautiful wooden manipulatives and paper materials that are high quality, so our tweens and teens don’t feel like they are being treated like small children.

We strongly believe in developing a love of learning, so our goal is not to get students through a particular grade level, but rather to get them to a point where they are confident enough to ask, “What’s next?” Our small-group instruction model allows for a low-pressure environment, individualized pacing with peer support, and is accessible to families who are looking for an alternative to one-on-one tutoring.