At some point, your child will reach a challenging math concept that will be hard to overcome.
In many math classrooms, students are expected to demonstrate basic math solving skills.
But once that bar is reached, the teacher moves on to harder concepts. Ensuring their students can find the right answer on a state-administered test is often the goal.
Students aren’t always learning the reasons how and why the math solution works, they’re just learning steps to find the right answer.
This is why many students lack the fundamentals of true math concept mastery.
Homeschooled students face a similar set of challenges. It can be hard for parents to gauge whether their child truly understands a math concept, or whether they’ve simply memorized the steps.
For Dustin, memorization was the only tool he was using to assess his daughter, 13-year-old Hannah, at home.
Once Hannah hit a roadblock in her math understanding, he didn’t have any tools to help her. It became clear that memorizing answers wasn’t the same as understanding how to solve math problems.
He was “struggling to find other ways to get through to her besides traditional flashcards, memorization, etc.”
Though Hannah was in 7th grade, she was struggling with math at a 5th-grade level. He wasn’t sure how to help her because the lessons “didn’t make sense to her.” She didn’t even know where to begin when homework time came around.
Like many parents, Dustin was worried that Hannah would remain perpetually behind in math.
He didn’t want her “to get further behind… and suffer into the future.”
Most parents know that they aren’t doing their kids any favors trying to find the easy way out. The only way to help Hannah was to find something to help her truly understand math.
Related: Conceptual Learning vs. Memorization
Memorization is an important skill in math, but not for the reasons you might think.
First, a student needs a conceptual understanding — the how and why — that differentiates addition, subtraction, multiplication, and division. Once they understand how numbers relate to each other in these different scenarios, it’s good for students to finally memorize that 2 times 10 equals 20, for example.
They need the conceptual foundation in order to understand when and how to apply that knowledge down the line in other situations.
For example, memorizing 6 times 8 equals 48 won’t automatically help students figure out the perimeter of a hexagon. But seeing a shape with six sides of equivalent lengths will help students recognize a multiplication process they can use to find the perimeter.
Memorization is helpful when it comes to working memory. When a student has some basic facts memorized, it frees up space in their brain to process more complex ideas. Like the previous example, instead of trying to remember what 8 times 6 is, they can focus on the more complicated concept of finding an equilateral shape’s perimeter.
Memorization lends a helping hand to your working memory, which is used to solve math problems.
Our working memory is extremely limited and can only cope with processing a few items at a time.
Mahesh Sharma, the president of the Center for Teaching/Learning of Mathematics in Framingham, Massachusetts, provides a helpful description of a child’s working memory in solving math problems.
“Whenever a child faces a new concept, particularly a secondary concept (a concept involving several primary concepts), s/he faces an overload on the working memory.
The more a child is free from constructing basic facts when needed, the more the child is able to devote the limited working memory resources on learning the new language, concept, or procedure and their relationships.
Automatizing basic arithmetic facts, therefore, is important for two reasons: (i) the student is able to discern patterns in number relationships and therefore make more connections, and (ii) the working memory is freed from constructing these facts every time there is a need for them.”
But remember: Memorization is not always the result of successful comprehension, which is why a student’s struggle to memorize is not necessarily a lack of comprehension.
Sharma notes, “The child’s ability is dependent on whether effective strategies have been used in teaching them. Poor strategies do not leave residue from a learning experience.
Most of the time, therefore, it is not poor long-term memory, but poor strategies of learning a concept or skill and lack of proper and efficient practice that are responsible for children not remembering their facts.”
In Hannah’s case, the limited role of flashcards was showing Dustin that she lacked a strong conceptual understanding — not a poor long-term memory, per se.
But if her long-term memory was also proving a barrier, “distributed practice” was the way to improve it. That means spreading out math practice sessions over a long period of time.
Luckily for Hannah, Elephant Learning teaches math concepts in a distributed practice model.
Dustin wasn’t sure what was holding Hannah back. She might have lacked a strong math concept foundation, which in turn was impacting her working memory.
Dustin wasn’t sure “how to help her best” because her math lessons didn’t “make sense to her.”
Sharma would likely point out that “learning is not just acquiring knowledge or facts; it is linking them and freely connecting old and new knowledge. An isolated fact can be tough to remember or recollect unless it is overlearned, connected, or accompanied with a strategy.”
By playing the math games on Elephant Learning, Hannah was applying math concepts to a variety of game scenarios. This is called math gamification.
Elephant Learning is a math games app designed to keep kids aged 2 through 16 engaged with fun activities.
These activities are not rote memorization drills. Rather, a student might be asked to fill in a shape to reflect a fraction. Or, they might have to group animated objects in a variety of ways before they can advance to the next level.
These are not tests with scores, which can make kids easily frustrated.
But the Elephant Learning app is still assessing your child’s abilities. It presents a variety of games to ensure your child has mastered a concept — and the many forms it can take in the real world — before providing more challenging games.
In Hannah’s case, it became clear that she was only comfortable performing math at an 8-year-old’s level.
So Elephant Learning built her confidence by first enabling her to play games she could excel in. All the while, Elephant Learning was identifying the specific math concepts that were challenging to her.
Those concepts got reinforced routinely during her game sessions. Elephant Learning provides enough variety and challenge to keep kids interested in playing.
Holding their interest is important to make sure they’ll play for several weeks or months. That long-term reinforcement of math concepts helps the brain retain the information. Once that information is solidly retained, the brain’s working memory is free to process more complex math.
That means Hannah could get over some critical concept hurdles at her own pace without feeling bad. And once those concepts became more second nature to her, she could start tackling harder concepts.
One of the most important impacts of having more working memory available is that it allows the brain to see more patterns and make more connections. And those patterns and connections are critical for understanding and retaining more complex math.
If all of this sounds like it’s one big cycle, you’re right.
In math, strong conceptual knowledge means you understand mathematical relationships.
Once you understand relationships, you can rely on memorized facts as a fast track when tackling harder problems.
Memorized facts will give your brain more processing power to tackle harder problems, rather than wasting energy trying to recall information.
With all that extra processing power available, your brain can more easily identify new patterns and connections. New mathematical relationships emerge, get reinforced, and are eventually stored away for the next round of more complex math.
Sharma describes it best:
“The feeling of automaticity is a result of brain circuitry that’s been strengthened through repetition. When we have automatized basic facts, the brain doesn’t have to work as hard on simple math. It has more working memory free to process the teacher’s new lesson on more complex math, and more patterns can be seen and more connections are made.”
By playing Elephant Learning repeatedly — for about 30 minutes spread out over the week — Hannah was reinforcing her math concepts without getting bored. That eventually led her to more automatic math recall, which helped her advance to harder math.
Within six months, she learned over two years’ worth of math. And she’s still learning.
Elephant Learning has been so successful for Hannah, her sister Faith has also played to improve her skills.
Though Hannah’s sister Faith was “doing fine in math” Dustin was hoping to “deepen her understanding.”
Elephant Learning found that 11-year-old Faith was actually doing math at a 9-year-old’s level. So while Faith was likely getting by with this learning gap, Elephant Learning caught it and made sure to fill in those missing gaps.
Finding those gaps is critical, and it's hard for parents to find them on their own. Parents like Dustin know that “falling further behind” is possible unless those gaps are overcome.
Like her sister, Faith has also learned two years of math in six months, and now Dustin can rest easy knowing both daughters are on a path to lasting math confidence.
The beauty of Elephant Learning is that it inspires kids of all ages and abilities. No matter how confident your child is in their abilities, there’s always room for improvement. And Elephant Learning makes that learning journey fun.
Take advantage of our free trial to see how Elephant Learning can get your child over their personal math hurdles.
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Many parents find common core frustrating and confusing. Our system is straightforward, and our reports allow parents to understand how we intend to teach each subject. We also provide activities that parents can do with their students to take learning outside of the system.
We cover from counting through Algebra. We have seen students as young as 2 years of age achieve success. If you have an older student who is struggling with upper level mathematics, it tends to be due to a misconception that occurs in Algebra or earlier. Our system will detect gaps in understanding and fill them with activities that were proven by third-party research to teach the concepts effectively.