I was shocked listening this morning that only 58 seconds of every 5 hour preschool day are spent on math.
In my experience, elementary school teachers tend to be soft-skills people who primarily just love working with young children. Many didn't enjoy math, felt they were bad at it, and would prefer to teach children reading and writing. And because elementary schools have one teacher guide the same group of children through all four core subjects instead of specializing in one subject (like middle or high school teachers) the teacher's less-preferenced subjects get less time.
Source: former (public) high school science teacher
> elementary school teachers tend to be soft-skills people who primarily just love working with young children.
Your description summarizes my experience meeting elementary education majors in college quite well. They weren't the hardcore intellectual types, but they really like working with kids. So they optimized for a route that made sense for them. Unfortunately for the children, they won't get exposed to the intellectual areas because the teachers really weren't into that.
I guess at that age (preschool, first grade), math doesn't have to be math to be math. It can be jumping up and down and counting as article says. I can be counting stairs going up and down, building a tower out of sliced cucumbers during lunch. I feel an intuition about quantities and being familiar with numbers is a good foundation. At least that is what I am trying with my 3 year old.
I agree with you that the way we teach school is completely ridiculous, but 58 seconds for _preschool_ on math is probably fine. Ages 3-5 are really about learning how to socialize, play and interact with the world, and it isn't until about age 6-7 when many kids even develop an aptitude for mathematics. Scandinavian countries use a concept called "Readiness to Learn" and don't teach reading or mathematics until age 7. Your children will likely be much better off playing and being kids in pre-school and learning things like how to sit still as well as fine motor control.
That said, yes, public schooling is insane. We pile children into classrooms and then expect them to all learn the same subjects at the same rate. We grade them based on arbitrary deadlines and we force them to learn more complex topics without making sure that they have mastered basic concepts. How someone can get an 'A' and not know 10% of subject matter is beyond me. Oh, and in the US we force all children into the schizophrenic "No Child Left Behind" program which encourages teachers to only teach to tests administered at arbitrary times.
In any kind of reasonable system, children would be able to learn at their own pace, and wouldn't advance to more difficult subject matter until they had achieved 100% mastery. Montessori teaching has elements of this, but I think it will really take new tools like Khan Academy and "flipping the classroom" to make it practicable.
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.
Nothing precludes you teaching your children about mathematics. That's something you can easily do at home for 5-10 minutes every day or two. With my four year old I do this, and also practice things like the alphabet, but it's not something I expect her preschool to do.
Preschool should be about group play, socialization and getting ready for kindergarden. It shouldn't be about academics.
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)
There's lots of math you can teach that isn't basic numbers though!
Symmetries, commutativity, associativity, transitivity, basic algebra/equation solving, some geometry, etc.
Teaching these ideas gives children a language to describe the world they're in and make sense of the ideas and concepts that bombard them - they're perhaps even more useful than numbers in this regard. The problem is that most elementary teachers aren't up to explaining these more advanced math concepts (lots of them have trouble with advanced middle school level math), and instead focus on just basic arithmetic.
This does a huge disservice to our children, because kids soak these topics up when well explained, and seem to really enjoy the learning (which is often hands on). I spent a fair bit of time in university (where I studied math) volunteering along with a professor to teach lectures to young children (1st-4th grade in the US) about math.
I honestly wish we could just accept that mathematics is as much of a specialized language/topic as foreign languages, and get specialist teachers starting early on.
Our son was in a cooperative preschool for a while, so I got to see it in action a number of times. They weren't teaching literacy either. The main focus of the classes were developing the skills you need to be able to function in kindergarten -- things like doing what the teacher tells you, raising your hand, being quiet, playing nicely with the other kids, etc. There was basic learning of the alphabet and numbers. Generalized world knowledge. And lots of play time.
That said, my impression would certainly be that the numbers and/or patterns work (which I would consider low-level fundamental math stuff) amounted to more than one minute a day.
I am interested to hear if high-school/college style teaching has been tried at the elementary level. And what were the outcomes?
Specifically, have schools tried to partition students into courses based on achievement level, regardless of age? There would be the Math 1 course that might have 1st, 2nd, and 3rd graders in it, and Math 2 might have brighter 1st graders, etc.
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?
Most schools do it at the high school and maybe jr. high level but I have never heard of this happening at the elementary level. We had separate math "groups" in elementary school but this was still within the same classroom and the more advanced group simply learned more about the concepts we were covering.
you're totally right -- I was talking about the jr. high and high school levels. Occasionally you'll see exceptions and some kids will be allowed up a grade or two in elementary, but it's not embedded in the process the way it is in jr. high and high school.
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.
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.
Another Hacker News participant recently kindly shared in a comment a 2007 report by Educational Testing Service (ETS) titled "Teacher Quality in a Changing Policy Landscape: Improvements in the Teaching Pool".[1] The report showed that even though changes in teacher license requirements are boosting selection of higher-SAT-score rather than lower-SAT-score aspiring teachers, elementary teachers are drawn from college students who scored significantly lower than most college graduates on the SAT math section (Figure 21 in the report). The mean score of a recent prospective elementary school teacher in the United States when that teacher took the SAT for college entrance was barely above 500 on the math section.
Alas, in general, American schools are underperforming in teaching the most advantaged members of American society,[2] especially in mathematics,[3]
while not doing well by the least advantaged young people in American society either.[4] The current efforts in preschools reported in the interesting article submitted here should be followed up by further reform of elementary school mathematics instruction. The book Knowing and Teaching Elementary Mathematics by Liping Ma[5] is especially informative about what to do to help all learners in the United States learn mathematics better in early schooling.
We should probably start to separate the teaching away from the supervising. Have some high quality instructional videos to demo to students along with some learning software. Use the instructors mainly to monitor and supervise students.
I've spent much of the last twenty years teaching math to middle and high school students who had previously been burned out on math. I teach in an environment where I get to let students progress at their own pace. Everyone gets a clear set of math milestones laid out, and they earn their credit when they reach those milestones. Students see me mostly as someone who helps them reach objective milestones, not as someone who tells them they can't do math again.
One of the most significant issues I see is there's often no way back into math if a student gets off track early on. My students typically got confused in 2nd-5th grade, and then math never made sense again. When given the space to work independently, with support, at their own pace, they get to clear up old confusions and realize how much they're capable of when they're not under pressure to keep up with everyone else.
One of the things I enjoy most is taking students who haven't understood math since 3rd grade, and bringing them to a place where they can start to use algebra to solve problems they care about. From then on, they are set up to make good use of math the rest of their lives.
I have a 3 1/2 year old son now, and it's fascinating to watch his development after having been a teacher for so long. He's in that wonderful stage now where "22" is just as big as "a million", and when he wants to describe a large number of things he just strings random numbers together: "Dad, there's 23 45 8 17 100 stars in the sky tonight!" Just the other night he asked, "What do you get when you add 3 and 3?" It's fascinating to watch that understanding develop, and to just keep answering his questions honestly, with the mindset of giving him a strong foundation for more advanced concepts later on.
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.
That's great and major props for helping those who fell behind. I remember taking classes at the maritime college and watching all these people (who were probably way better at ships or engines than I was) struggle mightily with speed-distance-time calculations, batteries in series/parallel or Ohm's law. It was really depressing - how can our education systems fail so many people?
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.
As someone who hated math in k-12 and excelled in reading, this is interesting to me. I have gotten more into math as a soon to be college graduate, (Econ/Acct) where I have learned I am not bad at math, and the math I have done for my degree, econometrics, calculus, were all interesting (though not on a high level). I think if I had been taught math as a child better than what I was, I would have moved more toward a CS/CE/data engineering degree instead of business. The math scared me off.
For my kids I look forward to trying to supplement their K-12 education (math especially) with other forms of education that I hope foster an interest in math. K-12 never really gave me a chance to find math interesting.
Does anyone have any great tools/resources to help supplement public math education?
Mindstorms: Children, Computers, and Powerful Ideas
...which I found my self saying "yes" to out loud while reading it. It's premise is that people can learn better when there is an aspect they can interact with, and computers can provide simulated environments in which to explore concepts. Some of the examples given are younger kids exploring ideas in differential geometry through the use of turtle graphics. It is hard to get across in a small snippet of text, but I kept thinking that was how I wanted to be taught back in school. 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.
There's not a lot of concrete actionable items here, other than getting that book, and maybe downloading a Logo interpreter to play with.
I've just started to work with teaching my own kids programming, so I don't have a lot of advice at this point, but I hope the book is as inspirational to you, as it was to me.
> 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.
DragonBox is one of my favorites to teach basic algebra to my eight year old nephew: http://www.dragonboxapp.com/. It came out of a research project at U of Washington.
I also love doing Maker projects because I believe the best way to teach math is to build real-world, functional things that show the end purpose of math. For example, I have done this workshop with my nephew too which really engaged his interest in math and STEM more broadly: http://www.einsteinsworkshop.com/now-enrolling.
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.
My 8 year old son hates math. I've tried introducing him to some of the apps like Scratch and its ilk, but he's not interested. The closest I've successfully come is using the blocks in Minecraft to illustrate why/how multiplication is not simply repeated addition.
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.
Is this actually a secret? Having recently gone through the 'math gauntlet' that is a formal CS education, it is astounding the number of people frightened to death of mathematics.
Gayle Conigliaro's preschool students are jumping as they count,
to get the feeling of the numbers into their bodies — a concept
called "embodied cognition."
My 4 year-old learned all about circles by spinning round and round. Math makes her just giddy with excitement! She can't calculate circumference yet, but that doesn't matter, because I feel confident that she has embodied the cognition. I'm taking her to the playground tomorrow so she can do line integrals on the monkey bars.
My father played math games with me when I was little. Made it exciting, not fearful. Grade school math was kind of slow and boring. Didnt get more interesting until algebra.
In my experience, elementary school teachers tend to be soft-skills people who primarily just love working with young children. Many didn't enjoy math, felt they were bad at it, and would prefer to teach children reading and writing. And because elementary schools have one teacher guide the same group of children through all four core subjects instead of specializing in one subject (like middle or high school teachers) the teacher's less-preferenced subjects get less time.
Source: former (public) high school science teacher