Learning vs Teaching

Do you ever write a blog post and leave it in “drafts” for so long… you forget your wrote it? That happened with this post. This post was initiated last spring and completed today with some additions.

For too long now, we have equated “learning” with the “result of being taught.” I’m not refuting the fact that we can learn from great teachers… in fact, that’s not my point at all. Teachers make a significant impact in whether students have an opportunity to learn or not in a school environment.

Rather, the point I want to make is that, for too long, we have equated learning with consuming what has been delivered TO learners. Traditional schooling has tried to make learning a passive activity, and I feel the damage we’re doing to children is resulting in generations of people who cannot think for themselves. Additionally, they have a difficult time learning anything that is new or unfamiliar – if a problem is put in front of them that doesn’t resemble a problem they’ve already seen, most students will struggle.

Recently, I’ve noticed a lot of educators talking about how we need to help students learn “how to learn.” I vehemently disagree. Children come to us as innate learners. If anything, most schooling conditions children to turn off their learning brains and substitute with their compliance/consumer brains. If you think you have students who need to be taught how to learn… you’re wrong. They just need help reprogramming themselves to actually learn, and that requires removing almost everything they have been conditioned to do in a traditional school environment.

Learning isn’t memorizing something and then performing on a test. If you disagree with me, pull out a test from one or two months ago and give it to your students. Most of them will not be able to pass this test, even if they aced it before. Now, if those same students created something through building, baking, composing, painting, etc. – something where the learning was meaningful, my guess is that they would be able to replicate (and most likely improve) their creations over and over again.  

When I speak to other educators about learning, they usually agree… except when it comes to facts and skills they strongly believe must be TAUGHT.

EXAMPLE: I am constantly asked how I TEACH my students to read, considering I do not focus on teaching and drilling sight words, phonemic awareness, etc.
I usually answer, “I don’t TEACH my students to read.”
I get the same questions when it comes to math… “How do they learn math if you don’t practice math facts?” *
And the question, especially from other educators, “How will your students learn to read, learn their math facts (etc.) if you don’t TEACH them?”
Yet… my students DO learn to read. They do learn their math facts, and so, SO much more!
How is it at all possible that the students in my classroom are reading, are applying math facts to actual math problems that they find (not necessarily problems I give them to solve)?
The answer is simple, and it’s one we’ve forgotten over years – nearly a century really- of delivering information to kids to “learn.” Consuming information that is delivered from a teacher is not LEARNING. 
When I memorize a bunch of stuff that someone else decides is important for me to know, that process takes one of the most important facets of learning out of the learners hands– the agency of the learner.

Human beings learn about the world around them when they’re curious… when they see a need to know and understand something… and then want to USE that newly found knowledge/skill. Good teachers know this and help provide an environment where kids are able to learn and pursue those things that make them curious. Master teachers know how to expose children to new experiences – those they may not discover on their own – to create new opportunities for learning to occur. 

Inventing, planning, and building a new form of mass transportation for water.

Inventing, planning, and building a new form of mass transportation for water.

When WE (educators) decide what students should learn, it becomes a chore. Curiosity lessens. And the opportunity to actually use that new knowledge is rarely provided outside an artificial environment.
Case in point… I have observed years and years of children sitting in science class “learning” from a textbook. THAT is not science! That’s reading comprehension. When you have never practiced actual science and only read about it… that is not learning science.
In discussions with other educators, I often hear things along the lines of “Well, if I don’t explain it to them first, how will they learn it?” This line of thinking misses the beauty of true learning. Ask any adult what they remember the most from high school. I guarantee it won’t be anything they were “taught” and memorized for a test. Delivered information resides in our short-term memory if we don’t do anything beyond memorizing it. We KNOW this… it’s not new to teachers. We learn that memorization is the lowest order of thinking. So why do we still concentrate more in this area in education than the others? Short answer: it’s the quickest and easiest to test. Efficiency for the win (or not). The longer answer is much more complicated.
I’ve written several posts like this before with explanations about what learning IS and what it IS NOT.  So have a lot of other people. I’ll add some to comments and welcome your additions as well! 
So to get back to my original example (and reason for writing this post)…
The answer to the questions I get from educators who see what we do at Anastasis Academy  – and wonder how on earth my K/1s learn how to read, write, understand math, etc.  -without teaching via traditional methods educators are used to seeing –  is THIS:
I don’t teach kids to read.
I don’t teach kids to write.
I don’t teach kids to memorize math facts… or vocabulary… or any of those other delivered items/standards to which we have clung so tightly in traditional education.
I facilitate a learning environment where they are curious.
I facilitate a learning environment where they want to learn to read.
I facilitate a learning environment where they want to make sense of numbers.
(I could go on, but I think you get the picture.)
We do not drill phonics or math facts. We read all the time. We talk about letters, sounds, word endings, rhyming words, patterns, etc. IN THE CONTEXT OF WHAT WE ARE LEARNING. Always.
Let me emphasize that…
Yes, sometimes we’ll stop and talk about how verbs in the past tense sound like they end in a “t,” but the patterns we see in our books are “-ed.” We remark about this pattern every time we see it, and then we also start noticing it in our writing.
Pretty soon, the students start to think and edit themselves in their writing of past tense verbs. It makes sense to them, because it comes up in the context of what they’re already doing. These types of little mini or “pop out” lessons happen all the time, but the most important part is this: it’s always in the context of what we’re learning. I cannot stress this enough.
So if you ask me how I teach my kids to read if I don’t focus on all the traditional 20th/21st century methods of teaching reading, I will tell you…
I don’t teach them to read. They LEARN to read.
You can substitute any other concept/skill in the above sentences, because the emphasis is always on LEARNING, not teaching.
 (My class and I blog at architectsofwonder.edublogs.org… we share a lot of what we do and how we learn there. We also tweet from @TeamBaldwin and would love to hear from you!)

*Two of my “learning and math” posts that are relevant:

It’s All About Context

Apologies to Meghan Trainor and her 2014 earworm… but it really is all about context

Have you ever heard a parent or teacher say something to the effect, “My child/student has regressed in the last 6 months. She knew this stuff last year! She passed tests and everything.”

Learning is fluid. Period. Brains are remarkable and in constant states of learning, unlearning, and relearning.  (Research in neuroplasticity is fascinating, and if you have any contact with kids, I hope you are reading about it.)

But here’s the deal: if your child has truly LEARNED something, she most likely won’t forget it or regress. While there are exceptions, most kids do not forget things they have truly learned.

What is more likely the case is that something was introduced without context. Kids- and adults- forget things they have committed to short-term memory that do not connect to something meaningful and relevant in their lives.

(OR… the context was only briefly visited because there wasn’t enough time to develop a real connection. Mile-wide curriculum that’s about an inch deep doesn’t leave a lot of room or time for context. But I digress…)

I’m on a math kick, so let’s use this as an example.

Young children who learn to count to ten do not actually understand counting. They’re simply mimicking a verbal pattern they memorized. Put 4 objects in front of a child who has just learned to count to 10, and he’ll point to each object, multiple times, and count to 10, not 4. This is a developmental issue, because the child does not connect the numbers he learned to say versus the number of objects in front of him.

If you put 3+2=5 in front of a child, she might memorize it easily, but if you give her the same number of objects to count, can she separate it into a group of 3 and a group of 2?

Children do not have context for numbers in print UNLESS they have something concrete in front of them. Even still, they need more exposure and experience with the concrete long before they begin to comprehend the abstract (number sentences in print).

I feel the same way about teaching music. Children should be singing songs and playing instruments long before they ever learn musical notation. You can memorize where the notes go on a staff and which note’s duration is a “ta” or a “ti-ti,” but if you have not had extensive experience with playing and singing those notes, you have no context for the notation. Some really brilliant man named Karl Orff believed this, too. (My fellow music teachers are laughing at me right now, because Orff is a really big deal).

Think about this: small children learn the alphabet song long before they’re able to make sense of the letters in the alphabet. You can recite the alphabet but not know which letters make which sounds. And you most definitely cannot read simply by reciting the alphabet.

I can sing hundreds of songs in various languages –  Italian, Portuguese, German, etc. – but I did not LEARN these languages. I memorized them and how to pronounce words in these languages. There’s no context there, other than what’s in the songs.

Those in real estate have their mantra, “Location, location, location.”

Educators should add to their repertoire, “Context, context, context.” Context helps kids make connections and move to deeper understanding, even if that deeper understanding happens down the road.

A recent example…

My 5 and 6 year old students have been using base ten blocks to help them think about adding and subtracting larger numbers. They know that, to subtract 35 from 50, they will have to swap out a ten for 10 ones. If I gave them 50-35 and taught them to “borrow,” some of them would remember HOW to do this, but they would not understand WHY. Most of them would not understand how to borrow and would become easily frustrated. Developmentally, they’re not in this place yet, but when working with the base ten blocks… every single one of them knows he has to swap a ten for 10 ones. There’s context there.

When I asked them to help me cover a wall with some paper, we learned that we had to measure the wall first. Our tape measure wasn’t long enough to measure the entire wall, so we measured in two steps. The tape measure ends at 120 inches. The second measurement was 58 inches.

I asked them to add 120 and 58. Blank stares. (Of course)

When I asked them what 120 would look like in base ten blocks (without actually using the blocks), they were able to tell me it was one blue (100) and 2 greens (10). I asked them to pretend the blue one was put off to the side for now. “You have two greens and 58. What does that mean?” They counted 58… 68… 78.

The said, “The answer is 78!” When I reminded them we still had a blue one off to the side, they were able to quickly say, “it’s 178!”

They did all of this in their heads without actually handling the base ten blocks. Because of our previous work with the blocks, they now have context about place value and adding larger numbers. Are they consistently able to do this? No. Not yet, and I want to really emphasize yet. They are 5 / 6 year old kids! But if they are able to get context in everything we’re doing – math and all the other things we learn every day – think about where they can go!

I could share so many more examples, but this post would never end. I will share a “part two” soon, because I have another wonderful example of poetry and context with my students.

A Math Tale – How I Know They Are Learning

Backstory to this post:

Teaching in an inquiry-based school, we don’t isolate “subjects” as most traditional schools do.  The beauty of this model is that kids really get to make connections. Science doesn’t just happen at a certain time of day, and it usually involves many other content areas as well. I love when my students are able to connect on their own that music is science is math is history is communication… and so on.

Although we don’t teach subjects in isolation all day, we do spend some time looking at content areas on their own for supporting understanding.

Math is a great example of one “subject” in our school that receives some supplemental time. It still looks different, though, because we meet each child where he/she is and help to move more deeply into understanding.

(I started to type “move forward,” but that’s not necessarily what happens, nor should it.)


The FOCUS of this post:

The problem with math in so many traditional schools is that there is a push to move kids along, rather than guide them into understanding. If you memorize facts easily, you’re going to do well in math early on. The problem with how math is often taught – and how most people think it should be taught – is that we focus so much on the “abstract” — the written facts. My friend Rafranz Davis says, “experiencing math starts with the ‘why,’ not the ‘how.'” I love this! Multiplication tables and formulas, for example, are the how, not the why.

Because so many of us, educators and non-educators alike, were taught with a focus on the math facts, we tend to forget that the conceptual understanding — the “concrete” and “representational” aspects of numbers — is entirely more important than what we memorize. A lot of students who do well in elementary or primary math classes find themselves struggling in pre-algebra or other math classes that require an understanding of what those facts mean, how numbers are related, the underlying patterns in those facts, and how it all connects. <— The WHY

Flash cards, worksheets, and apps that only focus on drilling facts are not what our kids need. They do not show us what our children have learned and understand about math.

BUT… this is where so much time, effort, and concerns lie. If students do not have their multiplication tables memorized by 3rd or 4th grade, they’re labeled as behind their peers. As a teacher, this frustrates me immeasurably. Yes, we want kids to be fluent in their facts, but the problem is when we assign a date and time to when they must have these facts memorized.

You might have a child who memorizes easily, but doesn’t truly understand what the fact means. I once had a student who knew that 5×3=15, but did not know that 5 groups of 3 items was the meaning behind it. Another one of my students understood that multiplication was grouping, but she could not recall fluently each fact if put on the spot.

Teaching a K/1 class for the first time has reinforced my philosophy of how I teach math- they WHY comes before the HOW. An example from today sealed the deal:

I have four students, all boys, in my class. (I know. Yes, I typed “four.”)

Every one of these boys, ages 5 and 6, is in a different place in his understanding of addition and subtraction facts. Some can skip count by 7s. Some are still struggling with addition and subtraction facts up to 10.

Today, we did some problem-solving with an activity I found on MathPickle.com: Addition Boomerang. (Watch the video – it explains how the boomerangs work. Definitely worth the 5 minutes.)

I started with all 4 of the kids together and demonstrated how the boomerangs work. We started with one boomerang with a +1 to reach the target of 10. Then we changed it to +2 to the target of 10. The boys were seeing this as an easy activity, and liked the idea of going around the boomerang circle.

Next, I changed it to two boomerangs: +3 and +4 with the same target of 10. I asked them to find every combination, both successful and “fails.”

This is what we produced together:



After we discussed other combinations, they determined that they had found all the successful combinations. Anything else we we might try would result in similar fails. This discussion was incredible, because some of them still don’t always remember the commutative property of addition. We often have to review that if 3+4=7, then 4+3 also equals 7. Epiphany moment!

After our discussion, I paired them up and gave them their own boomerangs to solve. One group had to get to the target of 20 with +4 and +5. The other group needed to get to 12 with +2 and +3.



Here’s the beauty of what I witnessed today. One of my boys who is very fluent in addition facts well past 10 struggled with this activity at first. He didn’t understand what we were trying to do. After working with his partner, he exclaimed, “Oh! I get it!” Exuberant smiles followed. Those facts he memorized are beginning to come to life for him.

Another one of my boys who is not fluent in addition facts to 10 whizzed through this activity. He was counting so quickly, his partner had to ask him to slow down so he could figure it out as well. I can still ask him, “what is 4+5?” and it will take him as long as it takes to put up 4 fingers followed by 5 fingers. But when I asked him which combinations would work in his boomerang, he amazed me at how quickly he could come up with different combinations, AS WELL AS explain WHY. This is a kid who would fail a standardized fill-in-the-blank or multiple choice math test on addition facts to 10. Give him a method in which to find a pattern or solve a puzzle, and he is able to show exactly what he understands.

When parents have come to me over the years with concerns- or outright nervousness- about where their kids are in math, I have tried to reassure them that a) kids don’t learn at the same pace, b) knowing facts is NOT understanding mathematics, and c) kids need a variety of activities that help them explore the relationship of numbers in meaningful and relevant ways.

Drilling facts, and even emphasizing facts over understanding of the concrete and representational aspects of what numbers and operators mean does a lot of damage to how kids view “math.”

So here’s my advice:

  1. Take a deep breath. Your child’s math progress does not reflect poorly on you as a parent. I promise.
  2. If you have taken your child to a math tutoring business*, remember that it is a business. They will find something (anything!) wrong with your child’s progress to sell you their services.
  3. If you really want to help your child understand the relationship of numbers, find activities that involve, but do not focus on math. Baking, building, measuring, counting, budgeting for groceries– all of these are great ways to involve your child in something that requires some skills and concepts without it being the only focus. Math facts, by themselves, can be tedious and tiresome for a lot of kids (especially for those who have been told they are “behind”).
  4. One of my students can count by 7s because he is a huge football fan. Ask him how many points have been scored with 6 touchdowns… he knows the answer. And he is SIX. Football matters to him, so groups of 7s and 3s are meaningful to him, too. What matters to your child? Build on that.
  5. Puzzles and patterns are fabulous ways to help kids make sense of numbers. If your child loves patterns, but hates “math,” there is a disconnect here. Find puzzles that your child might enjoy and do them together. Be patient, and don’t feed answers.
  6. Do a little research on Concrete-Representational-Abstract instruction (CRA). This has been my underlying philosophy of how I help kids learn concepts in math (and music, for that matter), and I’ve seen kids’ understanding improve significantly. This method connects the HOW with the WHY.
  7. If you’re teaching math, where is your emphasis? I know many of you have pacing guides, material/textbooks to cover, and even scripts you are required to follow… but are you helping your students understand? If yes, please add some of your resources or suggestions in the comments. (Thanks!)


I’m fortunate to teach at a school** where we MAKE time for kids to explore and have those epiphany moments, whether it’s in their mathematic abilities, reading, asking questions, creating, building, or discovering their passions. (It’s a pretty awesome place to be a kid AND an adult who gets to witness it all.)

Above all else, I want to do what’s right for each of the children in my care every day. There’s a reason “Drill and Kill” became a thing in describing math practice activities. I don’t have any place for that when I want to help children understand.

(+10,000 points to you if you read all the way to the end. TL:DR is not in my vocabulary.)


*”math tutoring business” in this sense refers to corporate and for-profit businesses, not individuals.

**Shameless plug: if you want to witness in person what we do in our school, please join us at 5sigmaeducon.com next month!

Content-Specific Marketing

cc licensed Flickr photo by neptunecanada

I read this article today on CNN’s Schools of Thought Blog: “Want more kids to take calculus? Convince mom first,” by Jamie Gumbrecht. In the post, there is research stating that involving parents in talking points about math and science electives will be more likely to influence kids to choose those classes:

“These are the critical years in which mathematics and science courses are elective, and our results indicate that parents can become more influential in their children’s academic choices if given the proper support,” the study says.

How simple was that support? Just a couple of brochures, a web site and a little guidance about how to use the information.

My initial reaction after reading was one of wanting to push back.

First, as some of you know, I tire of the constant push for more STEM, more STEM, more STEM. Please don’t misunderstand. I love math and science! When I had the options in school to select electives, I chose calculus and advanced science classes. As a teacher, I get all geeked out with my students when we stumble upon interesting activities that involve math and/or science (read “geeked out” as getting extremely excited about all the amazing learning possibilities). [photo credit: Science Lab by neptunecanada]

BUT… shouldn’t we be concerned about pushing certain content areas at the expense of others? What about the kids who really don’t have an interest in pursuing careers in math, science, engineering, etc? I believe in exposing kids to many areas so they can discover what they don’t know they don’t know, as well as to start to put the pieces together to understand the world around them.

And how about the misguided information from those who form education policy stating that we don’t have enough scientists or engineers? Read:

Do We Really Have A Scientist Shortage?

US Pushes for more scientists, but the jobs aren’t there

(There are many more… I’d be glad to link them here if you add them to the comments section.)


We know that what is valued eventually becomes policy. And in current US education, that also means what is assessed. Again, placing too much emphasis upon certain content areas does so at the expense of other areas… and at the expense of kids.

My oldest daughter graduated high school in 2007. She liked science, and declared biology as her major at university. After almost two years of that, she called me and was rather upset. She felt she needed to change her major to English. After a long discussion reassuring her 1) that changing her major was not a horrible thing and 2) that she should do what she loves, she promptly changed her major. She adores writing and editing and is now an assistant editor for a local publication company. After the fact, I asked her why she was so upset about changing her major. She said she felt pressured to go into something “more academic,” and she was worried about availability of jobs for a BA in English. Science and math classes were heavily encouraged in her high school.

Now to argue with myself – sometimes “marketing” helps kids to see themselves in a future they didn’t realize was possible. This could be due to stereotypes based in race, gender, status. My favorite way to ‘combat’ the stereotypes is to share examples with my students of strong role models who cross those lines. Is that enough, though?

Marketing can go horribly wrong, though, as evidenced here: How not to market science to girls

(That’s fodder for another blog post.) Moving right along…

Another question I  am still wondering and have blogged about before: why do we continue to teach content areas only in isolation? I agree that there are concepts that probably should be taught separately to avoid confusion and to allow deeper exploration. However, if we want kids to be able to think about what they want to learn and how they will apply that to a career or lifestyle, they must see how those concepts apply in their world. Content areas must overlap, because that’s what they do in everyday life.

In other words, in order to specialize later, they must see how everything fits together at an early age. We are  not doing this in most schools.

So again… having mom and dad sit you down with a glossy brochure (as noted in the calculus/science article I mentioned at the beginning of the post) essentially marketing math and science classes… is that really where we want to take our kids? Aren’t they already get enough marketing thrown at them every single day?

I’m not sure exactly how to feel about this. I do know I sat with my own kids when they were filling out their choices or class schedules. We talked a lot about options and how those choices could possibly shape where they wanted to go in their learning adventures.

Help me, please… share your thoughts.