The author of the blog Math with Bad Drawings is a current math teacher (and former math student) and discusses the feelings and actions of someone who is floundering at math from both his teaching and his own experiences.
As a math teacher, it’s easy to get frustrated with struggling students. They miss class. They procrastinate. When you take away their calculators, they moan like children who’ve lost their teddy bears. (Admittedly, a trauma.)
Even worse is what they don’t do. Ask questions. Take notes. Correct failing quizzes, even when promised that corrections will raise their scores. Don’t they care that they’re failing? Are they trying not to pass?
I noticed the same things while teaching Algebra I and geometry in Austin. I would offer to help during class or in after-school tutoring sessions, but they would simply decline. They would NEVER remember to bring their books to class. And boy, did they show their despair over no calculators on tests and quizzes! I realized then that many of my Algebra I students did not know 6 x 7 and had no clue about negative numbers. These students were able to pass into 9th grade while having failed the previous middle school math courses. While I did as much pre-algebra review as I could, I offered extra drill practice to the students who hadn’t memorized the basic facts yet. Of course, they declined those as well. Six weeks into the year, one failing student simply remarked, “I’ll retake it in summer school.”
The author of the blog had success with math until his senior year topology course at Yale. Then he started to struggle and wasn’t sure how to handle it.
My failure began as most do: gradually, quietly. I took dutiful notes from my classmates’ lectures, but felt only a hazy half-comprehension. While I could parrot back key phrases, I felt a sense of vagueness, a slight disconnect – I knew I was missing things, but didn’t know quite what, and I clung to the idle hope that one good jolt might shake all the pieces into place.
But I didn’t seek out that jolt. In fact, I never asked for help. (Too scared of looking stupid.) Instead, I just let it all slide by, watching without grasping, feeling those flickers of understanding begin to ebb, until I no longer wondered whether I was lost. Now I knew I was lost.
So I did what most students do. I leaned on a friend who understood things better than I did. I bullied my poor girlfriend (also in the class) into explaining the homework problems to me. I never replicated her work outright, but I didn’t really learn it myself, either. I merely absorbed her explanations enough to write them up in my own words, a misty sort of comprehension that soon evaporated in the sun. (It was the Yale equivalent of my high school students’ worst vice, copying homework. If you’re reading this, guys: Don’t do it!)
I had a similar experience with an upper level college math course, Real Analysis, which I have so blocked from my memory I can’t even tell you what it was about. While I didn’t seek out help either (even though I should have!), I made it through due to the curve as it seemed most people were more clueless than me.
The author, finally desperate, did what he should have done all along. Ask for help from the professor!
I was sweating in the elevator up to his office. The worst thing was that I admired him. Most world-class mathematicians view teaching undergraduates as a burdensome act of charity, like ladling soup for unbathed children. He was different: perceptive, hardworking, sincere. And here I was, knocking on his office door, striding in to tell him that I had come up short. An unbathed child asking for soup.
Teachers have such power. He could have crushed me if he wanted.
He didn’t, of course. Once he recognized my infantile state, he spoon-fed me just enough ideas so that I could survive the lecture.
Teachers want their students to TRULY understand the concepts. Almost all are happy to give extra explanations when asked, but they aren’t mind readers. Encourage your children to not be shy.
Sometimes a student starts a question with, “Sorry, but I need help with…” as if they should be ashamed they haven’t mastered it already. I always remind them, “Don’t apologize. This is my job! You are learning, and this is why I’m here.”
I tell my story to illustrate that failure isn’t about a lack of “natural intelligence,” whatever that is. Instead, failure is born from a messy combination of bad circumstances: high anxiety, low motivation, gaps in background knowledge.
Most of all, we fail because, when the moment comes to confront our shortcomings and open ourselves up to teachers and peers, we panic and deploy our defenses instead. For the same reason that I pushed away Topology, struggling students push me away now.
Not understanding Topology doesn’t make me stupid. It makes me bad at Topology.
And I would argue that like many things had the author had more time and asked for more help with topology (or me with Real Analysis) he would have likely gotten a lot better at it. Writing this blog post has me wishing to be able to retake the class, but I imagine that will wait for another day.
On Joanne Jacob’s blog, she highlighted a recent AP article discussing the correlation between early number sense and math ability several years later. The University of Missouri study found that 7th graders who struggled were the same ones who struggled in 1st grade.
“The gap they started with, they don’t close it,” says Dr. David Geary, a cognitive psychologist who leads the study that is tracking children from kindergarten to high school in the Columbia, Mo., school system. “They’re not catching up” to the kids who started ahead.
If first grade sounds pretty young to be predicting math ability, well, no one expects tots to be scribbling sums. But this number sense, or what Geary more precisely terms “number system knowledge,” turns out to be a fundamental skill that students continually build on, much more than the simple ability to count.
What’s involved? Understanding that numbers represent different quantities – that three dots is the same as the numeral “3” or the word “three.” Grasping magnitude – that 23 is bigger than 17. Getting the concept that numbers can be broken into parts – that 5 is the same as 2 and 3, or 4 and 1. Showing on a number line that the difference between 10 and 12 is the same as the difference between 20 and 22.
Like so many things, practice and repetition can overcome previous shortcomings. When your child does the initial free diagnostic test at Gideon, we are looking for any holes in the foundation such as ability to pick the larger number and whether the addition facts are memorized. Then we start wherever the student is showing a lack of mastery in order to build up on solid ground – no matter if the material is covered several grade levels before or after their current starting point.
Like reading, early and often parent interactions can go a long way. Any time you read or count with a child is good, but they give some even more specific tips if you want to take it that extra step.
… Geary sees a strong parallel with reading. Scientists have long known that preschoolers who know the names of letters and can better distinguish what sounds those letters make go on to read more easily. So parents today are advised to read to their children from birth, and many youngsters’ books use rhyming to focus on sounds.
Likewise for math, “kids need to know number words” early on, he says.
NIH’s Mann Koepke agrees, and offers some tips:
-Don’t teach your toddler to count solely by reciting numbers. Attach numbers to a noun – “Here are five crayons: One crayon, two crayons…” or say “I need to buy two yogurts” as you pick them from the store shelf – so they’ll absorb the quantity concept.
-Talk about distance: How many steps to your ball? The swing is farther away; it takes more steps.
In this blog post at edweek.org, Illina Garon discusses how her many of her 10th grade students don’t believe they will need math or English for their future jobs.
I was incredulous. “You want to be astronauts, and you think you’re not going to need math?” I turned to the actress. “Or English?”
No, they told me. They were certain that most of what they were learning in high school was totally irrelevant to their future career choices. Except for a few kids who muttered “Yo, these naive people are making me tight!” and rolled their eyes, my 10th graders seemed confident in their position.
I was asked many times while teaching Algebra I when this would used in the ‘real world’. While I wished I had researched more about what certain careers require to give them more reasons, I used the argument that I didn’t want to limit them in whatever they wanted to do. Mastering Algebra I would open up many more opportunities. It is difficult to know what you want to do at age 15. How much harder and longer is the road to become an engineer with a weak math background? I believe it can still be done, but many would be discouraged and go down a different, easier path. Engineering is not better than the career not needing math, but I don’t want it blocked off to those would want it due to lack of foresight.
Beyond the inherent frustration, this conversation showed me something I hadn’t realized before. I’ve long advocated for alternatives to the traditional “college for all” academic path, such as trade and career-tech programs (welding, auto mechanics, carpentry, cosmetics, etc.) But I’ve realized the students also need a crash course in career awareness–specifically, letting them know what careers are even out there (many careers such as IT, accounting, engineering, or hospitality management, because of their lack of intrinsic visibility in the kids’ daily lives or in TV, are often off their radar), and what these careers require, both in skills and in day-to-day activities. The fact that my 10th graders do not realize that being an astronaut requires math is, I think, almost as serious a problem as whatever deficits they may have in the subject to begin with.
We know kids love smart phones, ipads, and like. I hear that two year-olds can navigate better than their parents sometimes. While we still believe in limited technology time, here are some learning apps for little ones that will make the time spent on the devices a little more worthwhile.
TheRockfather.com collected some great things from PBS Kids HERE including:
Super Why ABC Adventures: Alphabet app for iPhone/iPod touch, your child can do just that while playing a comprehensive collection of five interactive literacy games that help build strategies and skills to master the alphabet! With each game hosted by a different Super Reader, your child will be introduced to uppercase and lowercase letters and their names, the order of the alphabet, common letter sounds and writing letters in fun and exciting ways!
Also make classic children’s books such as Arthur’s Teacher Trouble come alive with Wanderful’s Story Books App HERE. Each book is bought separately, and there are several to choose from. They also have a free sampler to try it out. Search Wanderful Storybooks on the App Store.
I used to LOVE the Reading Rainbow TV show as a kid and now LaVar Burton has a RR App to keep today’s kids loving books as well. Click HERE to learn more.
Technapex has collected other great apps HERE which includes:
Math Ninja: While there are many math apps available for kids, Math Ninja has been one of the most consistently popular. Users play as a ninja who has to face off against the evil Tomato San and his army of robots, with levels solved through various math problems from mental arithmetic to selecting the correct prime number. This app includes simple comprehension exercises. The app doesn’t require a significant amount of mathematical knowledge, but is a useful way of reinforcing the basics.
Let us know how you like these or recommend your favorites!
In THIS article on edweek.org, author Sarah Sparks discusses the findings of a new study, Why Mental Arithmetic Counts, done on 10th grade students and how they solve simple math problems. The students’ brains were scanned while performing single-digit arithmetic problems such as 8 + 4.
They compared which portion of the brain was activated with their PSAT scores. Students who had high activity in the section of the brain associated with memory of math facts during the activity also scored better on the PSAT than those students who had high activity in the area which is associated with processing number quantities. Conclusion:
The findings suggested that high-achieving students knew these answers by rote memory, while lower-performing students were still mentally calculating even low-level problems.
Both groups solved the problems equally quickly, but Ansari noted that the difference in how students process the problems could add time and effort as students attempt more and more complex equations.
“Perhaps the building of those networks early in development go on to facilitate high-level learning, which in turn allows you to free up working memory. It speaks to this raging debate in math education on procedural versus concept learning,” Ansari said.
We have seen this play out all the time when a student hits fractions, pre-algebra, or Algebra I. If you are still counting up in your head for 8 + 5 or 6 x 7, how can you quickly solve something like 6(3x – 7) + 5x = 50? And if you can’t do that quickly, how can you do 15 of these on test in a timely manner? Not memorizing math facts can quickly lead to a snowball effect where each higher level of math is more difficult, tedious, and burdensome than before. That’s why at Gideon we insist on memorization of math facts as shown though time and accuracy before moving into harder concepts whether the student is in 1st grade or 7th grade. Memorize the easy stuff so you can concentrate later on learning new concepts. It makes that all the difference!
