Math is a subject that builds upon itself over time. Children are taught the fundamentals of counting and number identification in pre-school and kindergarten and from there they begin playing with numbers to achieve more and more complex problems. Each level has several pre-requisite skills and knowledge that must be solidly in place in order for the mathematician to be successful at that level. Everything from kindergarten through pre-algebra cumulates in preparing a child for Algebra, and Algebra is the stepping off point for all higher math.
Without the pre-requisite knowledge in place, math is like a Jenga Tower™ with gaps or holes in the base levels. The tower may even appear stable as it builds higher, despite there being missing pieces - the tower’s apparent stability depends on where the gaps are situated and how deep in the base they are located. The tower eventually falls down and it is fun as everyone shouts “Jenga!” Unfortunately, when a child’s math tower collapses it is not fun. For some children, their tower collapses early (4th or 5th grade). For others, it is in middle school when they start to feel like a math failure and begin to hate math. For many children, their math tower appears stable until they hit algebra - usually in high school, sometimes in 8th grade. Then it all falls down and they decide math is not for them. They shun math, turn to liberal arts pursuits and have a lifelong dislike of math. This is a shame because even adults who pursued the arts or a non-math career benefit from studying algebra and higher mathematics.
There are many factors that contribute to math gaps, and math gaps can go unnoticed for years. Parents wonder how this can happen?
First, let’s look at some of the causes of math gaps.
- Missing time from school. When a child misses school for any reason - travel, illness, appointments, sports, etc. they miss the instruction for the day or days they are absent. If it is just a single day, typically that won’t result in a significant gap, however, multiple days can. Certain grades at the elementary level such as 1st, 3rd, 4th and 6th are pivotal years where many new math concepts are introduced. Missing multiple days during these years can set a child back significantly.
- Stress at home or school. If a child is having trouble at home (parent’s divorcing, death in the family, sibling bullying, moving, etc.) or feeling stressed at school (bullying, feeling inadequate in an academic topic(s), being compared to an older sibling, not getting along with the teacher, etc.), this can result in an inability to focus which can result in missing key topics or concepts. Once a pre-requisite topic is missed in math, it starts a downward spiral of stress and frustration. The child feels lost and as concepts build upon those missing skills, the child starts to lose confidence in their ability to succeed in math. When the child begins to feel like they are “just no good at math,” they give up trying and get a “why bother?” attitude. More concepts are missed and they start feeling badly about themselves in general and it affects other academic areas.
- Lack of focus. Children can have a lack of focus for many reasons. They may have a bit of ADHD or ADD. Perhaps they have had a concussion in sports that leads to an inability to focus. They may have a math learning disability such as dyscalculia or some foundational gaps went unnoticed and they are spiraling downward as in point 2.
- Skipping a grade. Many very bright young mathematicians have gaps because the school and/or parents felt they needed to be moved ahead and they ended up skipping a grade. Or possibly when they changed schools they were tested into a higher math class and missed key concepts. Additionally, accelerated math classes often move at a much quicker pace than do the "regular" math courses, causing children to feel stressed and then miss out on concepts.
- Colorado's adoption of the Common Core State Standards in Math in 2014. When Colorado adopted these new standards in math and reading, the curriculum load (topics taught) at each grade level increased by about 30%. This means that there are now about 21/2 - 3 months worth of additional concepts and topics that need to be covered at each grade level. This is not a problem for children who started school in 2014 or later, because they have gotten all the material and are accustomed to the new pace, but for kids who were already in school at the time of the new standards, they have automatic gaps just by the nature of the change. Unfortunately, with more topics and concepts to teach in the same number of school days, teachers do not have the time or resources to fill in those gaps. Furthermore, most elementary teachers are not taught how to identify gaps nor do they have the time and the tools to fill in those gaps, and most parents do not understand the methods being used by schools to implement the new standards.
It’s easy to see how math gaps can develop, why can they go unnoticed for years?
This is a tricky question that has many, many variables. Below are just some of those:
- Many kids can fake it, hoping they’ll make it. This can work until they reach algebra. Some children are very good at acting like they know what’s going on. They want to please their parents and their teachers and they quickly adapt to the new “methods.” For example, many students I assess these days know that teachers will be asking them to explain how they arrived at their answer and they have become very good at coming up with either reasonable sounding answers or very convoluted answers that can impress someone who is not a mathematician. One student whom I recently assessed was asked, “What is 7 + 8 + 9?” They answered 25 which immediately made me think they were counting by ones in their head. I asked how they arrived at that answer and got, “Well, I know that 7 + 3 is 10 and so 9 is 3 3‘s,therefore it must be 19 and then 19 plus 8 is 27 but I used a 3 so I had to take 2 away.” That sounds pretty fancy for someone who is not a mathematician or who is only vaguely paying attention. They assume the child has a strategy and just made a careless error. The child then gets a nod and smile. These kids can often bluff their way through elementary math with lucky guesses and charm. Without homework (or with teachers who don’t grade the homework but only give a completion score) the child doesn’t get correct practice to improve on the skill and gaps build.
- Elementary and many middle school teachers do not have the tools, and often lack the skills, to identify math gaps. Many elementary teachers are not mathematicians. Mathematicians can easily get higher paying, less demanding jobs and so do not enter the field of education. If they do teach, mathematicians often go for high school or college level courses which are frequently more interesting and engaging. Elementary teachers are typically generalists, knowing a little about a lot of topics, rather than specialists. The elementary homeroom teacher often teaches reading, writing, science, math, social studies, spelling, cursive (if the school still teaches cursive) and more in the course of a 7-hour school day. Plus the children have specials and other pullout classes and lunch and recess. A majority of the subjects taught require good language arts skills and that is often the area of strength and focus for many elementary teachers. Those are the lessons into which they pour their passion and creativity and they frequently put the least amount of effort into their math lessons. How do I know this? Because I was one of these elementary teachers until I started running Mathnasium and spent 3500 hours getting master certified!The irony is I was good at math throughout my schooling and I like math a lot. I just identified more with language arts and social studies and in my teacher training I had been better taught how to teach those subjects. Teachers who are not mathematicians often struggle to know if a student’s manner of solving a problem is accurate or not, and will be happy with the results if the answer is correct or if the child solved the problem the way they know how to solve it. They are less concerned with the child actually understanding what is going on with the numbers and how concepts and skills relate.
- There is a significant lack of time and resources for classroom teachers. In today’s competitive market, teachers must cover more concepts in the course of the year than ever before. Add to that the larger classroom size in many schools and there just is not enough time in a day or a week to address the needs of the children at the two ends of the spectrum (high ability and low ability). When push comes to shove, teachers will typically address the needs of the higher end kids over the challenged students because with less effort they can achieve more noticeable results. Struggling children often need more time to grasp the concepts being taught and time is at a premium in the classroom.
- Teachers are under pressure to show progress in many schools. At my school there was an unspoken “rule” that the majority of the kids in your classroom had to show some progress over the course of the year. This meant we graded more strictly in September than we did in May. That kept parents appeased and kids happy but it also allowed some math gaps to go unnoticed and unresolved.
What should you as a parent do about this?
Listen to your gut! I have many parents tell me that their child’s teacher said everything was OK but they just felt something was off with their child regarding math.
Get your child assessed. Mathnasium of Littleton offers a free, no obligation math assessment. It is one of the best tools I have ever worked with to determine if a child is at grade level or if they have some gaps.
Familiarize yourself with the standards and what children are expected to know in math at each grade level. Take Mathnasium’s quick, online check up to get a rough idea of where your child is in math.
Start as early as you can! Math gaps are typically easier and significantly less costly to address the earlier your child starts. They don’t have as many concepts to cover and they haven’t usually built up as much of a resistance to math early on in their school years.
Never give up! Math is a skill like dribbling a basketball. Everyone can learn how to do it. Some will catch on quicker and need less practice and coaching. Others will take a lot of focused practice and effort but everyone can do math!
Remember, no matter how much effort a child puts into math and how much homework help or traditional tutoring they receive, they will always struggle until the gaps in their math education are identified and filled.
Read some of our related articles and call us today! We’re math experts and we’re here to help! 303-979-9077
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