She can do her homework. She sits at the kitchen table every night with her book open to her homework for that night. She goes through each problem step by step and most of the time she gets them right. Therefore, she believes that she is okay with math. But then the test results come back and she gets a 62% and her face falls. It’s not disappointment or anger or even confusion. It’s more like a door has closed.
I have seen this movie play out many times and it is truly agonizing. My student knows her math. She has worked very hard to understand it. She even completes her nightly homework to a reasonable degree of accuracy. But when it counts, she fails. Horrifyingly. And what looks on the surface to be despair, turns out to be disappointment and disappointment looks to me to be anger and that anger looks to me to be sadness.
The speed trap nobody warns students about
First, speed is often equated with intelligence in math classes. A big problem with the way that we teach math in most of our classrooms is that timed drills and competitions to solve problem sets quickly and other ways to compare students to see who is smartest are all counterproductive to the development of confident math students. The way that we typically teach math in classrooms means that the fastest student is perceived to be the smartest. However, for most people, math does not work that way and so gives the wrong impression to students about themselves.
However, there are times where a student has mastered a mathematical concept and yet takes longer to work out a problem. As a teacher, I have found that these students can begin to think that they are “just not good at math” when in reality their lack of speed is their only limitation.
One important study on how math is taught to students found that the pressure to complete problems in a timely manner causes the same part of the brain to be activated as stress or anxiety. Thus, when a student is performing math problems and is worried about not getting them right because of pressure to complete them on time, then their brain cannot hold as much information in working memory as it could have under normal circumstances. Then when the student makes mistakes, the student’s anxiety about not being able to do math well is further solidified. This is an example of a self-fulfilling prophecy.
Careless mistakes don’t feel careless to a kid
Adults look at the same careless mistakes on a student’s work and say, “Oh that was careless.” However, all the student sees is evidence that they are not careful enough. That they are not focused enough. That they are not good enough.
Students believe their mistakes are proof of their carelessness or inattention. A student writes a negative number where a positive number or zero should be. Another student multiplies numbers incorrectly even though otherwise he or she is completing the problems correctly. Students believe their errors are proof of their fallibility. They believe that they are not as careful or as focused as they need to be. They believe that they are not as good as they need to be at math.
Yes, careless errors occur with great frequency when students are under pressure to perform math. But the student perceives these errors as proof of error on their part. The student believes that mistakes are entirely under their control. This is why the student making the error feels so terrible. Every math error is perceived as evidence of incompetence on the part of the student making the error.
What classroom gaps actually look like
In terms of where these classroom gaps can have an impact on future learning it is better to understand the implications of a specific concept that a student is having trouble with than it is to attempt to understand the “gap” itself. As an example, a student who has a very shaky understanding of fractions will be having trouble solving problems that involve fractions but will also have trouble understanding pre-algebra, algebra, and functions in later years. Thus, a week or two of poor math instruction in 5th grade could have a huge affect on an 8th grade student’s ability to learn mathematical concepts and understand how to apply them in a variety of situations.
Note also that children can struggle for long periods of time with math concepts without realizing that they are struggling. Because of their incomplete or inaccurate understandings of math concepts, children may perform adequately on assessments and complete math homework assignments without errors. However, because of their anxiety, children who are struggling to make sense of math concepts may realize that they are in over their heads at some point.
- Missing a foundational concept (like place value or integer rules) that teachers assumed everyone absorbed
- Falling behind during a life disruption, illness, or rough semester and never quite catching up
- Learning a procedure without understanding why it works, so any variation shatters the whole thing
- Feeling too embarrassed to ask questions after a certain point, so the gaps just compound in the dark
Pinpointing the one specific area where a child is struggling can be the heart of fixing that child’s perceived shortcomings with math. It can be the entirety of the solution, or it could be more than that.
The thing about one-on-one support
As mentioned earlier, in typical classroom settings students fill in holes in their knowledge in order to continue to learn using partial knowledge and fear. The spaces left by missing knowledge can be difficult to fill in regular classroom settings. In addition to trying to reach all students for support in learning within a timeframe, the typical classroom setting has 30-35 students and one teacher. The one tutor in a one-on-one tutoring setting can provide individualized attention and rebuild a student’s trust and achieve competence in math while the typical classroom setting cannot. The setting of a regular classroom can actually reinforce a student’s fear that he or she is not good at math when the student is struggling.
One-on-one tutoring with a student is a very different experience from a classroom of thirty or thirty-five students. While the tutor may not be perfect for your child, the fact that you are meeting one-on-one for study sessions allows for a much deeper and more thorough review of the material. The tutor can also create a learning environment where your child feels safe to make mistakes and to ask questions. While it can be difficult to find a tutor, it is worth searching for a local, in-person tutor for your child. Consistent, relationship-based support can make all the difference for your child who is struggling in math. And while you may be tempted to look for a cheap online program to use with your child, remember that finding the right tutor for your child is a process and is worth taking the time to get it right for your child’s specific needs.
| What erodes confidence | What rebuilds it |
| Timed tests with public results | Low-stakes practice with immediate feedback |
| Moving ahead before foundations are solid | Identifying and filling the actual gap |
| Mistakes treated as failure | Mistakes treated as data |
| One-size-fits-all pacing | Progress measured against the student’s own baseline |
Step 6: Recovery of confidence in math is possible and is a skill.
Beliefs about math can be positive or negative and can affect math performance. However, these beliefs can also be changed by math experiences. In order to foster mathematical confidence it is very important to recognize and to allow students to have moments of success. These “wins” are incredibly powerful for children. Sometimes the student may even discover a new way of thinking about something that they had previously struggled with. Other times they may simply complete a problem correctly. Either way, these experiences can go a long way in building up a child’s confidence in mathematics, where a math tutor Newark can provide the necessary guidance.
(And, interestingly, how kids perceive whether or not they are “math people” can solidify as early as 3rd grade. So the intervention window is very early and very brief).
Kids who recover from math phobia have generally accumulated enough small successes so that they have begun to perceive themselves as being able to do math. Recovery from math phobia is a slow process of coming to terms with past mistakes, learning from those mistakes, and moving on from them. It is so slow that it is often hard to even see that it is happening. But it does change. That is the important thing.
It does change. That shift is real. It just almost never happens on its own.
