Teach Your Kid Basic Math
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- Опубліковано 19 тра 2024
- Teaching your kid basic math is a little more complicated than it seems. Here I go over some important learning goals and what I've tried with my own son to try to achieve them.
0:00 So... you want to teach your kid math?
0:15 Four categories of learning goals
1:35 Some important conceptual learning goals
3:14 Some important procedural learning goals
4:36 What does your kid associate math with?
5:09 Becoming a problem solver
5:48 Setting up the time and the environment
6:25 How to use examples and abstractions
7:13 Developing more sophisticated strategies
8:28 Letting them solve the problem
9:07 Developing a skeptical and thorough problem solver
9:42 Flip the asking script
10:32 Modeling how to respond to mistakes
11:41 "Secrets"
12:18 Interesting ways of incorporating number lines
12:55 Scaffolding estimation skills
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REFERENCES:
For readable summaries of the research in these areas, check out these two excellent posts by Gwen Dewar: parentingscience.com/preschoo... (preschool math games) and parentingscience.com/preschoo... (general advice). Parenting Science is just an excellent resource, generally.
On concreteness fading and the power of using both concrete and abstract representations together, see the two references below:
Fyfe, E. R., & Nathan, M. J. (2019). Making “concreteness fading” more concrete as a theory of instruction for promoting transfer. Educational Review, 71(4), 403-422. doi.org/10.1080/00131911.2018...
Moreno, R., Ozogul, G., & Reisslein, M. (2011). Teaching with concrete and abstract visual representations: Effects on students' problem solving, problem representations, and learning perceptions. Journal of educational psychology, 103(1), 32.
On the relationship between conceptual and procedural knowledge and the role that different kinds of examples can play in developing both, see: Rittle-Johnson, B., & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529. dash.harvard.edu/bitstream/ha...
On the use of number lines for learning: Lin, C. H. (2022). Developing mental number line games to improve young children’s number knowledge and basic arithmetic skills. Journal of Experimental Child Psychology, 222, 105479. www.sciencedirect.com/science...
As a new dad I would love to see more videos on early childhood development. This has become one of my favorite videos on youtube. Thank you for this content!
PLEASE NEVER STOP POSTING, I LOVE YOUR VIDEOS!!!
I recently taught multiplication to a 5, almost 6-year-old, and double digit multiplication to a 7-year-old. My strategy was to ground it in something they already knew.
In the case of introducing multiplication, I built upon his understanding of addition. I knew, based on previous lessons, that he could add many numbers together. Since this prerequisite was met, I thought it would interesting to see if he could grasp multiplication despite being quite young. So I took out some playing cards, and put down four '2' cards. I then wrote it as numerals as well. 2 + 2 + 2 + 2. This was easy for him, and I explained the basics of multiplication in that way. I asked him, how many 2 cards are there? He said, there are 4. So I explained we have a 2-card, 4 times. 2 TIMES 4, in other words, '2' appears "4 times". A little more really basic Q&A and then, to see if he understood and reinforce the concept: I put 3 8-cards, and I asked "how many times does an 8 card appear?" 3 times. 8 x 3, then also wrote it out in a form he already knows how to do easily: 8 + 8 + 8. He had never done multiplication before but seemed to grasp the basics within 10 minutes and could do 4 x 9 without any cards by the end of the 10~15 min. It also helps that he likes math, so kudos to whoever taught him addition or any kind of math before.
I find that sometimes teachers want kids to memorize multiplication tables, or, in general, memorize things. This seems highly ineffective and setting the kid up either to dislike math and to find it boring and difficult, or to limit their potential learning speed.
For double digit multiplication, the 7-year-old was pretty good at single digit multiplication, and I felt confident she could try double digits. If it was clearly insurmountable at her current level, I could go more slowly, and stop early on, or if she seemed to be grasping it, I could reinforce with a few more problems at that level and then gradually increase the difficulty. So, I started first with single digits multiplied by double digits, multiplying one digit at a time from the double digit with the single digit. We did problems with single digits multiplied by a number in the 10-19 range. Move to the second line and add a '0' to the right for multiplying the tens-column. And used addition at the end. I wanted her to understand why we did addition at the end, and why we put the 0 when we multiplied the tens column. I explained this by demonstrating that, for example, 4 x 12 is the same as 4 x 10 + 4 x 2. This led her to understand why we multiply one digit at a time to make it more manageable. I also explained that although we are doing 4 x 1 in the tens column, "this isn't really a 1, is it?" What is it? It's actually 10. 1 becomes 10 by putting a 0 to the right. Practice it a little more, explain it a little more, and let her connect the dots in her head, without just spoon-feeding it to her.
I know there are some cool big number multiplication methods that are much faster, but I wanted her to understand the mechanics of it, to understand what was going on, and I felt this was the best way to lead her to a genuine understanding of what we're doing when we multiply bigger numbers. Within 15 minutes or so she could do multiplication like 16 x 17, and the next session she could do 20-something x 30-something. We could easily piggyback off this to introduce triple digits and larger numbers. So, she's within grasp of being able to do any kind of multiplication. I'd like her to solidify and master her application of single and double digit multiplication first.
Division doesn't come very intuitively to me, so I'm going to be giving it a lot of thought before trying to teach it. There's only a very small number of attempts that I can have with a student to have them conceptually grasp and be able to do something before they feel overwhelmed or intimidated by it, so I want to make sure I get it right the first time, or at worst, the second time. There are so many older kids, and adults, who have given up on math because they don't understand relationships between numbers and operations and so on, which I feel is exciting to master and exciting to see a student learn - when that lightbulb just lights right up and I know they actually get what's going on.
I think about their psychology, and I think that the feeling of comprehending something, while also getting the correct answer, has got to feel so rewarding. And it seems so much more important than just getting the right answer because you memorized that 7 x 7 = 49 or something.
By the way, I'm not a math teacher. I'm an English as a foreign language teacher, haha. But math came up by way of doing card games (thus the cards were already out) and 'math in English'. I think that comprehensive instruction, and refraining from compartmentalizing study, is best for young students. So, I am not sure I will do 'math time' with my son, but rather let it spring up naturally in the course of whatever we're doing together, and push his conceptual skills to new boundaries with each opportunity, while making sure that it is really enjoyable. Having taught lots of kids now, and being keenly interested in how the mind works and how learning is best facilitated, I've found that the joy of learning is probably the single greatest thing a teacher can impart upon a student.
This channel is SEVERELY underrated!!
You should definetly make a video on studying subjects like history and biology effectively.
I love your channel!
almost cry with this since i never have experience this kind of patience when i was at school or at my house even with math. I'm trying to re-learn math as 21yr with dyscalculia and been practicing a lot with your videos and other learning youtubers and ya'll giving me hope I could get better over time.
if you could do a video about how us with some learning disabilities could learn math and other study strategies will be so helpful since there isn't much content for us in the media.
thank you so much 🙏
Thanks for the video. I've had reasonable success teaching my 5yo basic math and intuitively used a bunch of advice from this video already. Aside maybe from a number line.
Outside of the things already captured in the video I found the "store" game very engaging and useful for us. The kid is the store owner and he has number of items each priced at a certain amount. This packs all basic operations in one game:
- addition (how much do I owe you if I buy toy A and toy B)?
- multiplication (how much for 3 legos priced at 5 each?)
- division (how many legos priced at 3 can I buy with 30?)
- subtraction (I give you 20, how much would you give me back), this also ties in to any operation above if you want to make things harder.
All of this can naturally be extended to more complex games if you add in price negotiations.
your note about "secrets" activated a deepset memory in me about the origins of my love of heuristics (at a young age, this would come up as gotchas for math problems, like odds and evens, or 0 being a technically-correct answer to many prompts, and in my adulthood it's more things like social scripts and gameplaying processes in Magic or poker for example). My partner and I don't have children yet, but I was also intrigued by your approach to asking "are you sure?" often when your son is incorrect, but still sometimes when he is correct (very game-theoretic!) which reminded me of some strategies I used when teaching math to 9th graders who were (mostly) far behind grade level. This also relates to your technique in which you described saying 14 - 3 = 12. I like the resulting prompt for the learner to pick up on the error and call it out, but I'd have to think more about how I present it (and how to incorporate that presentation into how I speak about math solutions in general to not give away my stance!) because I am committed to not lying, and plainly stating X - Y =
9:00 Ooooohhhhh that's adorable!!!!! Also, all this is so amazing from you.
Nice video. I've realized a lot of my current motivations in learning science are driven by my desire to do a really good job with parenting, so I'll always enjoy videos that explore the distinctions for how you should teach at different levels of development.
Video Idea (sorry this is a lot): Do you think you'd enjoy doing something a little more prescriptive, where you walk people through how to actually apply different learning tools to come up with a training regimine? I've read Peak, Make It Stick, ABCs of Learning, etc., and they all do a good job of discussing different tools, but I'll still sometimes wonder how to properly coordinate them all into an action plan. There are a lot of options.
Example: Someone wants to dedicate their life to being the best 3 point shooter ever. How do they practice? How long? How long should rests be? How do you interleave changes in distance and angle? Should you change positions constantly or only change positions once you get 3 in a row from the current position? I think details like that matter a lot when compounded.
And then: How do the recommendations of learning scientists for something like this compare to the advice of actual professionals/coaches when it comes to improving at 3 pointers?
There seems to be an infinite number of routines one could make for practice, and even though I have a lot of tools, I don't feel comfortable knowing exactly how to apply each one or how much to apply it.
It's a fair video request - you're absolutely right to point out there's a difference between having some understanding of the tool and having the ability to coordinate it all to create an effective learning experience. You can see me making some of these choices on myself with videos like this one: ua-cam.com/video/uCi0_tjOiyQ/v-deo.html (on learning mental math). I have a couple more of this style in the works. Maybe that helps a little bit.
However. I have a few other responses too. : )
Videos from the teaching perspective are by far the worst performing videos I make. For channel growth, they are not high priorities, even if I care about doing them. That said, I still plan on making them from time to time.
Second, although these tools and principles are great for planning, a lot of their real value comes from helping you know what to do next - diagnosing the student's current abilities; understanding how experts do what they do; determining whether one approach or another is working. These are tools to help us navigate the problem space of instruction. Plans must be adaptable.
Third, and to address your question about how a learning scientist would differ from a coach in terms of making the ultimate three-point shooter, it's often best to put the two together. You want a subject-matter expert and a learning scientist to collaborate on a plan of attack. And a lot of the work that a learning scientist would do is to understand the nature of the domain in the first place.
I teach special ed math and I get soooo much guessing. I also get a lot of kids who won't answer until someone else gives them an answer. I really try to work on confidence in math every day.
Also, make sure your kid isn't sneaking a calculator in the closet
This has definitely got me thinking about how I'll use this in the next few years. Great video.
This tickles my brain
Impressive, I plan to incorporate your strategies because that makes total sense. You definitely should do professional development to every teacher who is teaching. I learned so much by the way your broke this down. I feel like I became a better teacher already.
Yes, let's go!
Benny B! 4:42 reminds me of those old Ernest posters. Also, you missed some emotions my daughter often exhibits when I am attempting to teach her: vindictiveness, scorn, pity and, of course, fury.
She's got your genes, eh? We need to share notes, I think.
Hi there! I'm a massive fan of your videos - thank you for the high-quality and informative content! As a law student, I have found your insights extremely helpful.
I have a quick question. Would it be possible for you to share an 'ideal' framework for learning, particularly one geared towards students? Having watched your videos, there are a number of protocols you have shared. I'm currently in the process of watching all your videos to make sure I pick up on all your insights so I can build a learning framework from it all but it would also be super helpful to know if you have a framework you could suggest.
Thank you! All the best.
Appreciate the support!
I'm working on a course geared towards students that would stitch together various threads in the learning literature. But it won't be ready for a while. In the meantime, however, I will be working on some overview videos that might be helpful.
It's important to keep in mind that learning is both path- and goal-dependent. So, really, we're talking about the goal of developing learning skills - the skill of making wise decisions about learning practices and improving skills within those practices.
@@benjaminkeep Thank you for the response!
That sounds wonderful - I look forward to it. All the best with your work on the course.
That most definitely makes sense. I find that a really helpful way of understanding learning. Thank you.
If I may tag on one extra question, I would appreciate if I could ask your thoughts on the following:
I find cued recall more 'comfortable' than freed recall. Especially for the finer details/multitude of details of a subject because it almost 'forces' you to retrieve things. Do you think it is worth persisting through this discomfort in using free recall? Alternatively, would using cued recall (retrieval questions) in my first stage of learning and then free recall in my second stage be effective/the 'best of both worlds'?
Edit: tangentially, I would like to add - I've noted that you argue for greater use of practice tests. Is this not a form of cued recall? If so, am I correct in understanding that a combination of free and cued recall is what you suggest?
Does an encyclopedia of all math strategies and problem-solving techniques discovered over time exist? I had no success with my search. Seems like all research is just scattered in thousands of studies and no one makes an effort to index, categorize and keep track of all known strategies and techniques.
You might check out Paul Zeitz's "The Art and Craft of Problem Solving". He trains students for the math olympiads. Perhaps the Art of Problem Solving has some resources, too. artofproblemsolving.com/
I have a few questions and would be fascinated by either a response explaining the answer or a video delving into the topic.
Why is it that no chess grandmasters or concert pianists start after childhood, and language learners who begin after childhood never sound like natives? I am particularly interested in what changes happen to the brain, and whether the adult chess grandmaster, concert pianist or native-like speaker is even possible. What ages are the cut-off for becoming elite at certain skills?
Hey benjamin, can you share some tips on how to take notes after reading a textbook for better retention. Thank you 🙏
I have a video that I'm working on that might speak to that. But I can tell you what I tend to do.
During reading, I tend to write comments, summaries, or questions on paper or (more often) on a computer as I'm reading an academic article. After reading a chapter or something, sometimes I'll sit down and do free recall. Then I might go back over the notes I took while reading point-by-point. Sometimes I change them, add to them, or realize what I thought was important wasn't really that important. Often, I talk to my wife about what I've been reading and thinking about. The goal is always to have a grasp of the big picture and plenty of examples that illustrate different pieces of that big picture. If I'm reading something difficult, I need to go back and forth between reading and thinking a few times before I feel like I start to understand something well.
I remember seeing a book called something along the lines of 'the science behind how people come up with ideas' in one of your videos but the title of the video it appeared in completely slipped my mind. Do you remember what the book is called if you still own it?
How to deal with confusion when learning sth you're not familiar with? Is confusion good for learning?
Hey any specific books/vids/podcasts you would recommend related to problem solving and efficient learning?
www.benjaminkeep.com/recommended-reading/
Bey benjamin, can you please make a video on watching lectures effectively?
As the internet have become a sea of courses.
Yes - I'm working on it.
💯💯💯💯
Question, what are the different types of knowledge? I can see that something dry and non-conceptual facts are better learned to techniques like the mind palace and method of loci, but more conceptual knowledge is better learned through interleaving recall higher order learning etc.
Are there helpful words to distinguish between things better learned through rote techniques like mind palace/method of loci and things better learned through conceptual targeting techniques like higher-order learning and interleaving recall etc?
You might check out this video and the references in the description for more on different types of knowledge: ua-cam.com/video/7YtC24QnikY/v-deo.html.
This is a bit of a dense article, but it will give you a sense about the complexities of understanding types of knowledge: De Jong, T., & Ferguson-Hessler, M. G. (1996). Types and qualities of knowledge. Educational psychologist, 31(2), 105-113. avys.omu.edu.tr/storage/app/public/otaskin/130066/typesofknowledge.pdf
I've been thinking about a capstone project where I have kindergarten students do active recall (talking to a mirror or stuffy rather than writing it down). Any thoughts on using this with kids that young?
Where do you get that brain model that you have? I want one.
How dont you have a million subs...
So is there a homeschool math curriculum that teaches this way?
Do you have anything to say about New York City's recent decision to force teachers to teach kids how to read using the phonics-based approach because the previous curriculum was a total failure?
Nothing that other people haven't already said. I haven't followed it closely, but know a little bit. Unfortunately, this kind of thing happens relatively frequently.
Perhaps I'm being charitable here, but I think Lucy Calkins was responding to a very dry and rote approach to learning to read. And I think structuring interest and motivation is a good thing. But you know what's really motivating? Being able to actually read. And it's absurd to imagine effective reading instruction without a strong phonics component. There's similar research on writing, where helping people who are reading and writing below grade level to build more and more complex sentences really helps improve their writing (as opposed to having them continually write longer pieces very poorly). It's amazing how long students can be pushed along without someone actually diagnosing their weak skills and helping them to address those skills.
Some of this comes about because teachers, who are with their kids and have a deeper understanding of what they can do, are not actually empowered to push back on ideas coming down from the administration. Some of this comes about because programs are not adaptable - these are holistic solutions provided to teachers to use and not adapting to ongoing research. Part of it is that many programs don't include sufficient diagnostic and decision-making tools (e.g., if your student is doing X, then Y might be a reasonable solution). There's also the conflation of ideas: for instance, that phonics-based instruction must be boring and tedious and kill the desire to read. You can make phonics-based instruction interesting and varied and empowering (b/c the student is actually learning to do something on their own).
There are these pendulum swings in education reforms (e.g., "New Math" in the 60s) that are not really tied to the existing research base, even if they're pitched that way. A fun song to listen to is Tom Lehrer's "New Math" which gives you a sense of it.
I could be completely wrong, but I think you’re missing out on views because the thumbnail text is indirect. Big channels with millions of subscribers can get away with indirect thumbnails, but smaller channels generally do better when the thumbnail directly says what the video is about. For example “How to take the derivative of Log”. “How to read a poem”.