I’m going to present you with a question today, one that is based on a conversation that was happening over at the SQE site that I referenced yesterday. We were having a conversation about what is necessary to support the development of “21st century skills” in our learners/students.
From that conversation, one of the contributors commented that drill/practice is the most important component of teaching. She argued that without a firm foundation in the basics, then there is nothing to build on.
I agree that foundations are important, and I also agree that there is a perception on the part of some that public education may have strayed from their commitment to the basics, but something disturbed me a little about the idea that the key component to what I do is drill and practice.
So, I’ll throw the question out to you. As a teacher, what do you perceive the key component of your work to be? Can you identify the “essence” of what you do?
As a parent, what is your perception? What do you think is at the heart of the work that your child’s teacher does? What should be at the heart of what they do?
Looking forward to your responses!
First off, thanks for pointing out the discussions on SQE. My reaction to your comments is naturally two sided. I am always supportive of your thoughts and what you write but I have – maybe considered old school – supportive thoughts to SQE about drill and practice. I think there are somethings that need to be automatic, 2 x 2 =4 for example. I believe we should be able to do mental math and we should challenge our brain to exercise by recall of the basics. We should be able to do 3 digit multiplication in our head. We can’t rely on computers and we need to have the ability to provide checks and balances to technology. Having said that – is drill and practice the most important part of learning? No, not in my opinion. Being a self-directed learner who can solve problems and visualize solutions is more important. The drill and practice just makes that process easier.
Always good to hear from you Lorna. No argument from me on this. In fact, I think that we have more tools at our fingertips these days to help us better integrate the practice of essential skills. And you know something? The deeper work that you talk about becomes much more enjoyable if students have the basic skills at hand. Math is the subject most often cited for lack of basic skill acquisition.
One question that seems to be a bone of contention for some is the progression of skills and the deeper work that we want to do with those skills. Should the first years of school be devoted solely to skill drill and practice, or is it important to continually embed problems and activities that make use of those skills along the way?
I also agree that those basic skills are important. I am suggesting however that they are not the foundation of the “house”, that the core concept of what multiplication IS should come prior. I can memorize that 3 x 3 = 9 but if I don’t have an understanding of WHY, then the problem solving “roof” is sure to cave in! To stick to the multiplication example, I think that early number sense must begin with visual and manipulative representations to help students begin to build a deeper understanding of what multiplication is and then they can move on to the automaticity of fact recall. IMHO, collaborative problem solving (that allows for self selected strategies) is embedded throughout the process, and extending far beyond fact recall.
As a parent I agree with Lorna’s comment , that in subjects like math or physics, chemistry certain basics have to be there. How these are taught is the question. As with every kind of learning, individuals do so in different ways. .. some individuals need to see the material in front of them, with others it sticks by hearing the information. And there are many more ways. I believe the education system has to integrate technology. But I do recommend for every teacher to have a close look at the students. Find out what would be the best way for the group of students , and not forgetting the ones that do not fit the groups’ needs.Respect the different styles, and adapt accordingly.
Hi Birgit,
Yes, the how question is so important. Sometimes we are left with the impression that, in order for drill and practice to be valuable and, indeed, valid, it needs to be gruelling, boring and unattractive. In another post, the idea of the Etude came to mind…musical pieces designed to zero in on a particular technical skill. Many of these are beautiful, enjoyable to play, and compelling to hear. Many “studies” have actually made it into our standard concert repertoire.
Your comment about looking closely at the students is so important. I think that this is where the move towards “differentiated instruction” is right on. Beginning with the curriculum on one hand and your students on the other allows the work of the teacher, challenging as it may be, to be the attempt to bring the two together. Do you think that our systems of schooling are adequately equipped/designed to take this type of differentiation seriously?
From another teacher’s blog – “But I think that’s the best description of what we do. Teachers build the builders. I can’t tell you how happy I was when I heard that Lisa’s class decided to call themselves the “Builders of Tomorrow” – ’cause that’s what they are. But with all the different types of builders needed, we need different teachers with different skills. What makes a good teacher depends on what builder that teacher is trying to build.”
http://theclassroom.ca/2007/04/what-exactly-does-a-teacher-do/
In the About tab – “To do this I have to try to reach every student as an individual, emphasize each child’s strength, point out their weaknesses, and help them to turn those into strengths as well. I have to create an atmosphere that will encourage questioning, and intellectual risk, where all my students are not afraid to fail, and do in fact thrive on those failures. For it is those ” lost attempts” from which we learn the most. I will use my own enthusiasm for learning to show my students how wonderful it is. The language I use (both physical and verbal), the lessons I teach, even the assignments I give, everything I do will be to motivate my students into opening up the wings of their minds and rise upon a thermal of information and ideas. And when my students go home, and are asked “What did you do in school today?” I want them to be able to honestly reply, “Today, I soared.”
“This child has grown, he’s been taught the rules. He’s learned the new way, changed his tools. But the strength remains to betray the lie. This child has chosen not to die.” – Don Ross, 1992″
http://theclassroom.ca/about-mr-g/a-child-must-grow-the-educational-philosophy-of-shane-grundy/
As a parent, without the foundation a teacher has nothing to work with. In the same way a carpenter without his hammer cannot work, or a chemist without his Bunsen burner. As Shane Grundy explains teachers are the builders of students, and builders must know the strengths and weaknesses of their students, in the same way a builder must know the strengths and weaknesses of the various materials needed to build a home. A teacher needs to look at the foundation of a student, to were most academic weaknesses forms at the foundation level, to determined the strengths and build a more sturdy foundation, to unmasked the strengths.
Stephen, I know you are very well aware of the struggles my 16 year old has in school. Most of the learning struggles came from the shaky foundation that she was made to stand on, and her academic strengths became the supports to hold the foundation in place, rather than having the academic strengths to rest on the foundation, It is the foundation that supports the frame of a house, in the same way the foundation of a student will support the strengths to stand on. But if the foundational knowledge is shaky, the strengths will no longer be able to rest on the foundation knowledge, but now must support the foundation.
Teachers must mind the gaps of students, and more often than not, drills and practice according to the research in the cognitive, learning and neuroscience fields, is best use to build a sturdy foundation for students, so the 21st century skills can shine by allowing the strengths of the students to rest on the foundation.
A post on Educhatter, from a teacher – “The difficulty which faces me every single day is that I am prevented from teaching the basic skills to my students. ….I face challenges from the mathematical department in our school division as well as from the administrators from within our school. It is discouraged to teach students the foundations of math. Math worksheets and drills are frowned upon. Written tests are a definite no-no. … Marks on report cards are not to be less than 50%; in fact low grades in any subject area are not encouraged/permitted and frequently are forced to be changed before the reports are sent home to the parents. Accountability in teaching is becoming highly questionable.
Without a doubt, I can state that the academic skills in Mathematics and Language Arts are deteriorating.”
http://educhatter.wordpress.com/2012/02/12/the-muffled-voices-of-teachers-why-are-teachers-so-reluctant-to-speak-out-of-school/
Is it not the essence of a teacher’s job, is to build a sturdy foundation, so the students can soar?
Nancy, thank you for taking the time to write such an elaborate response. I agree that foundations are important, and I also agree that without a strong base of knowledge and understanding, quality work in any area of the curriculum is difficult. As Lorna has commented here, there are some things that need to be automatic. Not that we want to create robotic individuals, but there are some skills, facts, a pieces of information that just make deeper and more complex work possible. The building metaphor is one of the powerful ways of looking at this. I often told students, you don’t want to have to figure out how to hammer a nail each time you set to work on a construction project. I agree that “soaring” is possible when you are gradually become more confident in your ability to fly.
At the same time, I wouldn’t want us to get to the point where all we are doing is learning how to hammer nails, and never get to try building structures. Similarly, birds learn to fly by being pushed out of the nest. At what stage do teachers push students out of the nest, and into real flying?
That’s a question that just came to mind as I was re-reading your post.
Thanks again for the links, and the conversation!
Great question! As reflect on my own best experiences as a student and a teacher -times when I was most excited about learning and teaching, I note that those occasions have all happened within, and because of, powerful and engaging relationships. At those times learning was effortless and exciting, and was happening for student and teacher both – shared curiousity spurred efforts that in a less compelling context would never have been put forth. For me, without relationship, teaching and learning are pale.
Thanks for jumping in on this Paul! I have had similar experiences and I completely understand. The connectedness that occurs when relationships are valued and nurtured is incredibly powerful. I think that we’re also learning more and more about how the emotional well-being of students and teachers is important on a neurological level. Recent work on emotional intelligence can’t be overlooked when we’re looking closely at the dynamic of schools.
Do you have a couple of specific examples that you can relate?
I recall my grade 7 teacher choosing to read a novel that i had just finished reading, so that we could chat about it together. i I thought that was pretty cool, and we did have great conversations aboutbthat book and others. It led to me getting really engaged in the writing process and see what she thought about my own writing. Later, a group of students with special learning needs got really excited about hovercrafts because of a show they had seen. They asked (not thinking the answer might be “yes”) whether we could build a hovercraft. We ended up researching how to build one, building a hovercraft that could carry an adult, documenting the building process photographically and with process writing, sharing through a website and videotaping our various tests. I don’t think those boys had ever written so much in their lives! They wanted to know what project was next which meant the rest of that year was a blast – full of rich, engaging exploration that became the conduit for lots of work on ‘the basics’
Woah! What a great story. What, would you say, were the “basics” that you got to through this work. How did you do embed the basics in this type of work, especially for those students who may have been struggling? Were there “mini-lessons”, sidebars, discrete skill work alongside the project work? Inquiring minds will want to know!
I agree with Paul completely. I’m convinced I went into the sciences because my high school science teachers were engaging, supportive and motivating.
I also agree with many of the comments above. We do need to be able to do mental math, we do need to have a “foundation” of knowledge. What I question, however, is drill and practice the only way to build that foundation? Just because we were taught that way? Do strategies on how to come up with those math facts not go further than simple memorization? Does working on rich problems and gaining an understanding of what 2×2 really means in the world also build a foundation that allows me to recall the facts I need on demand? I’ve recently read or heard that most math anxiety was determined to be caused by people not understanding what numbers actually mean. Rote memorization of math facts tells us nothing of the value of a number. Working on rich problems involving those numbers may. I fully agree with the desired goal of drill and kill, but question if it’s the only way to that goal?
Hi Jaclyn,
I’m reminded of Bill Cosby’s “Kindergarten” sketch where he talks about learning math facts in Grade One. “One and one is two…yeah, one and one is two…right on…What’s a two?”
I know that there are some that knowledge of the basic facts means the ability to easily recall bits of knowledge; full understanding is secondary. The ability to quickly bring to mind the facts, without thinking too much about them, is important when solving more complex problems. I understand that; if you have to think too long and hard about hammering a nail, the house will never get built.
At the same time, spouting multiplication facts without a sense of what you are actually doing with the numbers is of questionable value. I think that this is why this type of conversation is so important. It becomes unclear as to what we’re talking about when we speak of “baby and bathwater”.
The math teacher in me couldn’t resist adding a reply.
There’s a difference between drill and effective practice. These are often confused with each other in casual conversation. Drill, in my mind, in more like sending a kid home with 20 math problems to do. Effective practice has a feedback component that gives a student feedback as they work through a set of problems. Due to this feedback loop it’s often the case fewer practise problems are necessary to help a student consolidate what they’ve learned.
One of the problems with drill is: if a student consistently makes the same error in a worksheet of 20 or more problems they are still learning through repetition. Unfortunately, they’re learning the wrong thing.
I had quite a lively discussion about this on my blog in a post titled: The Difference Between Curriculum and Pedagogy.
I agree with Jaclyn and Paul that good teaching begins by building a solid learning relationship with our students. It continues by structuring student learning around experiences that help them build an understanding of what they’re learning. Drill has very little to do with helping a child develop an understanding of the sense behind what they’re learning. Especially in math. It creates a culture of fear masked as hate of the subject. When I’m introduced to people as a math teacher they probably have the same reaction you do:
“Really? That’s awesome! I LOVE math! Come, let’s work together on this wonderful optimization problem I’ve been thinking about!”
The sad truth is they more often say: “Sorry to hear that. I hate math myself. I suck at math. I think it’s genetic; my parents were no good at it and neither were my grandparents.”
Imagine if kids understood the interconnectedness of math and the world around us. How the number of bees in a hive is connected to the way leaves sprout on the stems of branches and the number of petals in a flower and the way a tree grows its branches and rabbit populations grow … all this starts with a set of numbers like this:
1, 1, 2, 3, 5, 8, 13, 21, 34, …
Can you see the pattern? Maybe we can talk about patterns and addition now too. Then we’ll take a walk outside and find that pattern in the world around us. It’s even in a pinecone we may find left on the ground. In sunflowers too. And cauliflower. And … enough already, right?
Once you find the pattern find the next three numbers. Talk to a friend about it and compare your results. If you’re doing your addition right the pattern will persist. If the pattern doesn’t persist you did something wrong. Find it together. You might not need me to give you the feedback you need as you learn this. You two, just talk with each other a bit. Compare notes. Tomorrow I’ll bring in a sunflower.
Hi Darren,
What a compelling vision of a math class. Sexy in fact! Just reading your enthusiasm for the subject is contagious, and I’m not even in your class.
I think you’ve hit on an important question: Why do we teach math in school? Is it so students will be able to progress to the next grade, or the next course? Or is it so that students can walk out of your classroom and see the world a little bit differently? Or is it a combination of both?
To paraphrase a conversation I once had with an educator south of the border, “Is it for Monday, or for someday?”
I tend to think that we teach math for somewhere down the road in a students’ life. You have reminded us about the immediate pleasure of learning the language of math.
I will be interested in the responses that you receive on this!
As a parent, it is good to see discussions on the differences between drills and effective practice. I had to learned it the hard way, in order to help my dyslexic child at home, and prove the folks at the school board all wrong, about the academic potential of my child. Oh yes, I forgot, since all extra support were denied to my child.
The cognitive science is behind effective practice, the need for repetition, and yes drills have their place to asphalt the new cognitive pathways, instead of gravel or sand.
You write, ” One of the problems with drill is: if a student consistently makes the same error in a worksheet of 20 or more problems they are still learning through repetition. Unfortunately, they’re learning the wrong thing.”
As a parent, I can tell you how frustrated I was when teachers insisted on certain math methods or for that matter in other subject areas, using drills. When a primary or junior student makes the same error in a worksheet consistently, stopped at number 4, before the brain begins incorporating the new knowledge and build new pathways. Undoing the old pathways is difficult remediation work, and as a parent, I simply said to my child, forget everything you have learned in math at school, we are starting over. So prepared your brain, we are burying the old pathways, and making new pathways.
What my child and myself had discovered, and was key to my child becoming highly proficient and achievement in math, was patterns. My child only needed to spend 4 months in the SE math class, but she spent 2 years. She only needed 4 months to catch up, because her breakthrough came at perceiving the patterns in numbers, formulas, and why 2 + 4 = 3+ 3. As a parent, at the end of the 4 months, I kept pushing for my child to have one to one instruction and/or a few students like my child, following along the regular grade 4 curriculum. To no avail, including using the reasons of patterns. As a parent I did not have the knowledge background back in 2004, but today, having students to perceived patterns in numbers is a skill that should be taught as a priority.
1, 1, 2, 3, 5, 8, 13, 21, 34, ….. Ah the Fibonacci Numbers – My child who was 15 at the time, had her science project on the Fibonacci Numbers. She made the math proofs of the Fibonacci Numbers look so easy, a ten year old to 99 years old would not have a problem understanding the Fibonacci Numbers. Perceiving the patterns in numbers is how my child understands and learns her math in grade 11. When she discovers a new pattern to her, she runs to me telling me and showing the teacher the next day. But she is really proud when the grade 11 teacher sometimes uses her method to calculate, which 9 times out of 10, is completely different from what was taught, but is actually easier to learned because it based on the patterns. Now, that is coming from a student, who started out in grade 4, with barely a grade 1 level in math.
My child has not discovered anything new, that the mathematicians have not discovered. Math to her is easy thinking, and it should be easy thinking for all students. What a math professor said to me, when I went searching for advice to help my child succeed in math. All about the practice, and effective instruction and key is perceiving the patterns for deep understanding to occur.
You touched on the heart of mathematics here Nancy. Something I said to my students almost as a mantra: Mathematics is the science of patterns. It’s so much easier to encode a host of isolated facts into a pattern.
Would you believe finger counter was heavily discouraged in the primary grades. In grade 4 SE math class, the SE teacher taught her how to count and subtract numbers from 1 to 100 on her fingers. She learned other methods of counting on fingers on her own, but she made her own creations. But I am sure she doesn’t know this one, but I will show it to her. Might not be impressed, since she is quite proud of her version of the the number line, and rather a novel way, simplistic to add, subtract, multiply and divide, and the only numbers one needs to know is 0 to 9.
She got into a boat load of trouble when she she was the grade 1 monitor for the grade 1 class. She felt real sorry over a few grade one kids, who was really having difficulties learning to add and subtract. She took them under her wing, and by the end of first session, the kids were adding, and by the second week, not only adding and subtracting, by now all the grade one kids were learning division and multiplication. Until she was caught, and she promptly dismissed as the grade one monitor, until the grade one kids went on a strike demanding her back. She came back and she had to promise that she would not teach the kids any math tricks. Pity, the number line is not a trick, but the counting of buttons and blocks is a trick and a poor one to understand number operations.
As for the kids who she helped first, they have not forgotten her, nor their parents. She showed them they were just as smart as the rest of the kids, they just needed to be taught differently and do things differently to get the right answer.
What is the most important component of teaching? What should be at the heart of what they (teachers) do?
Learning itself. Be a student. We are all learners and there is much we can learn from one another. To instill a love of learning in others, be it yourself, show it, let the inner student help guide. Break down the teacher vs. student, us vs. them barriers and share in the learning together. I can just imagine how high the kids in Darren’s class (above) soar, kudos!
Hi Tracy,
The idea of modeling can be scary for some, right? Do you have an example of when you were able to do it effectively (I know that you do!) Would love to hear about it. I’m a sucker for a good story.
Nice to see you here!
Thanks Tracy. Yes, some of them knocked my socks off on a regular basis. Eventually I had to announce in class one day: “I no longer own anymore socks.”
What’s the most important thing in teaching? Knowing your craft. Everything else will come from tha –the good relationships with students, parents, and colleagues; respect from same; love of your vocation; concern and care for the students; pride in accomplishment.
Loving kids or is not enough, it’s nice if it’s there, but it’s not crucial. I read somewhere something to this effect: A good surgeon isn’t a great surgeon because they like to cut things. They have to know a lot about being a surgeon.
Thanks for the comments Doretta. Interesting that you make reference to “craft knowledge”; it is often the term used to refer to the everyday knowledge that a teacher brings with them to the classroom everyday. Difficult to get a handle on, somewhat esoteric and, as a result, difficult to objectify.
Now you have me wanting to go back and look at the concept more carefully!
I agree that knowledge of teaching, and what that means, is important to unpack. Often we do it in private, but perhaps it might be good to unpack in public.
I wonder what others think of just what it means to “know your craft”.