Why Math Might Be the Secret to School Success

i heared age four as the beginning to mathematical understanding. sure socialization is important, but why would that precludes the abillity to calculation, maybe without the formal approach.

I would second this. I just thought my 5 year old cousin grids and locations on a grid simply because I wanted him to play battleship.

Next up: difference in distance between one battleship to another; difference in distance across two axis; difference in x and y being called slope.

Then the possibilities are endless.

You are correct, but it's still astounding. (I edited the parent comment, thanks!)

Is it because many people find it more intellectually gratifying to watch children develop literacy than numeracy? (i.e. Learning to talk makes a child into someone you can interact with and share experience, while learning to count has little immediate impact on how a child can interact with a parent or teacher)

Well, yes and no. I can only speak from my experience of doing grades 1 through 7 in a Ukrainian school and then 8-12 in Canada. The year I went into school I was placed into the "Sapling" (Rostok) programme, which was a very accelerated "experimental" programme. I remember that in Grade 2 we were learning Venn Diagrams and basic set notation. And so on. By Grade 4 we were allegedly 2-3 years ahead of the "regular" system. Now when I got to Canada in Grade 8 I honestly did not know what to do with myself, the level of math I was exposed simply eclipsed what was being taught (Integer beads, the fuck?) and this has been my general experience of the school system up until Grade 12 where we started doing Calculus (which in "Sapling" was supposed to be done in Gr. 9-10).

The problem, I think, is not that kids can't learn (in fact the amount neuroplasticity in young children is simply off the charts, to the point where 6-7 year olds who can play really good violin are not something special), but is that the educational system simply does want to go there, to increase the levels of math taught in schools.

Coming from Delaware, most every school, public and private, that I know of partitions students into math courses based on achievement level. They typically don't let students go "out of grade" by more than a year, but that's a sizable amount in high school (e.g., some juniors learning the same material as some freshman). I didn't know there were places that didn't do it that way-- do your local schools not have advanced math & regular math tracks for their students?

I haven't heard of this being attempted, though I would surprised to find that it hasn't.

However, one reason it might be avoided is due to the potential negative effects tracking [1] strategies may have on some students. In my public school district, any form of tracking at the elementary level was difficult to implement due to pushback from parents, even in situations where the educators felt it was beneficial.

1 - http://en.wikipedia.org/wiki/Tracking_%28education%29

The elementary school that my kids attended had a couple of approaches. In higher grades, teachers paired up, and swapped classrooms so the stronger math teacher taught math to both classes. They also had "math specialists" who could float from one classroom to another, along with other kinds of special teachers and aides of various stripes.

A decent fraction of the kids learned math at home, making it hard to assess how well the school was actually doing.

I imagine that anywhere it is suggested it would be shot down by logistical concerns as well as sociological concerns of mixing age groups. You need a relatively common level of maturity, etc.

In general, free play and basic obedience training.

I teach high school right now. I ask students in each class what their math experiences have been; I give them space to vent, and make it okay to say, "I hate math." In every class I've had, there's also been someone who says, "I love math." We then talk about what has worked for people and what hasn't. I explain much of what I wrote in the comment above; many students have been blaming themselves for years of failure, and have never realized that weren't offered a way back into math. On the other hand, some students have blamed everyone but themselves and they need to start taking responsibility for themselves, and we have that honest conversation.

Everyone needs motivation to learn anything meaningful. Motivation for students can come from a desire to earn credit and graduate, a desire to be able to do a certain job, or a desire to catch up on things they haven't understood for a long time.

I connect each student's math learning plan with their job and career goals. Most of my students are at an age where that can work, if they can see the connection. This isn't just a utilitarian approach; we also talk on a regular basis about the wonders of math, and how there are efficient strategies but there are no math "tricks". I break their work into the smallest possible chunks they can earn credit for, so they get to see academic success as soon as possible.

I'm happy to share more specific thoughts here or through email, if you have a particular situation you're trying to sort out.

Why require the "sit down" part? As the article states, you can do math without sitting down, too.

Let them estimate how many steps a walk from A to B takes, or what distance is larger and check it by walking, ask them to count how many tiles cover a square (multiplication as a fast way of counting every tile), to estimate the number of beans in a jar and from it the weight of a single bean (combine that with Archimedes' law and let them predict whether it floats), the height of buildings (3 to 3.5 meters per floor, but also a trigonometry exercise when combined with measuring the length of its shade) etc.

You don't need to. I remember when I was a child, our family have this tradition of walking around the park after dinner. My parents would talk about work and ask about my day. And sometimes my father would throw questions like "why do you think there are 60 minutes in an hour instead of say 57" "why is 1/3 = 0.33333... is there a possibility there's a digit of 4 down the road?". I'm not sure if he come up with these question randomly or he has a system, but I still remembers a lot of them today.

> You compare how kids are self motivated to learn complex tasks like walking, talking, etc. but lose a lot of motivation when required to memorize dull facts about the interior angles of triangle.

Funny you mention this. I remember being taught the sum of the internal angles, the pythagorean theorem and other facts by folding paper triangles.

Seymour Papert is a big name in Constructivist learning circles and "Mindstorms" is, indeed, a great text. Constructivist learning can work wonderfully for motivated learners, but it can run into problems with low-motivation/maturity and/or a results-oriented school system (which we have in the US).

In the US, students are expected to know/be able to perform a variety of standards-based tasks when they finish each grade. Constructivist learning is typically too exploratory and inefficient for these standards to be reliably fulfilled for every student within a definite period of time (and, as we know, teachers are expected to get every child over the line regardless of interest/ability/stability). Whether or not the learning is authentic, meaningful, long-lasting is besides the point - teachers are incentivized by standards-based testing to focus specifically and efficiently on those limited topics/skills.

Accordingly, you are more likely to see this style of learning in the earlier grades (simply because the expectations/rigor are different for primary vs secondary ed. with the former having a stronger focus on social-emotional learning than the latter) - but most often it springs out of informal learning environments (like home, after school clubs, camps, etc.). Constructivism is great if you're trying to foster creativity, self-management, and teamwork.

My 5 and 7 year old LOVE DragonBox. (I would be bragging more, but they get into pretty big fights over whose turn it is.) The way it eased them into algebra is so simple that it is genius.

All math should be that approachable.

Here is a fun game then... BTW you happen to be doing math.

Speaking of Minecraft, you might want to check out something like:

http://www.stuffaboutcode.com/2014/05/minecraft-graphics-tur...

...my goal is to eventually get something like that working with FMS Logo.

Take a look at DragonBox (http://www.dragonboxapp.com/). It does a great job of presenting algebra as more than just arithmetic and wrote memorization.