People say “Math is boring”; that’s obviously not true in your classroom.

Thanks!
Aviva

I’m not familiar with the “slide”. Or I’ve forgotten what it is.

I already knew of Daniel’s and Matt’s blogs and their great work. I show the Powers of Ten video when we do exponents and scientific notation.

Thank you for bringing me to Larry’s and Tom’s sites. The highlighted posts are wonderful and I just spent a combined hour at their sites! I left a comment for Larry’s post on Learning Styles also.
Fawn Nguyen recently posted..A Famous Bridge Problem

Yes, that’s very clear, Peter. Kids are smart and they will ask questions. And as teachers we need to be grounded enough in the math and be prepared to hear those questions and reply in ways that still allow the student to explore and hopefully seek his/her own solution. I find it challenging sometimes to give just enough hint without robbing the student of valuable critical thinking.

Sometimes I will offer a trick or shortcut AFTER I hope the kids have understood the concept; one in particular is showing them how to use the “slide” to find GCF and LCM.

My intention up to now has been to write for teachers and parents (who might also be homeschoolers), rather than students. I have some ideas for doing videos for students, which a couple of people have mentioned, so thanks for mentioning it. There are weekly videos on the Free Math Worksheets “sub-site” which students could view, perhaps.

Your comment about students taking the easy road is spot on, I think. We have to find ways to encourage and persuade students to work hard to think mathematically.

Nevertheless, it would seem to me that creativity, while it can be generated through some sorts of repetitive activity, does not depend on it. In fact, I would expect that other activity types would be more likely to lead to creativity; do you agree? Perhaps children could develop some creativity while using KA materials; but perhaps this happens in spite of KA’s limitations, rather than because of its particular features.

Have you researched brain function and development in classrooms using other teaching styles, strategies and resources? I would be interested to hear how they compare.

I think that mathematics has to come first in the teacher’s mind, in the planning, when thinking about the foundations of the lesson. No watering down, get serious about the actual, real, honest to God mathematics that are at the heart of the topic at hand.

Then, when teaching, give the students experiences to explore and talk about the mathematics in their own words, on their terms. In other words, they need to own the math themselves, and make sense of it for themselves. But what they should be making sense of is the math, not some “exercise” or “trick” or game.

I need to write another post about introducing the language; this one (in my head, at least) is about the intellectual core of the lesson, which the teacher has to own before setting out to plan and to teach the next generation of mathematical thinkers.

Is that clearer? I’m in new territory here, trying to capture what I feel is so important about teaching math properly, and putting into plain language to hopefully capture the attention and the hearts of primary / elementary teachers.

To make math “fun” already implies that math in itself is boring, unworthy of students’ precious time and attention. I cringe when I see teachers doing sing-and-dance or dog-and-pony shows in math and think they should get a prize medal.

I have a question about your #1 above. Yes, I agree that the math is at the heart of the lesson (of course). I wonder if you have to START a lesson with the vocabulary as you say, “… is needed right at the beginning, at the planning stage.” I’d be curious to learn what kids call “symmetry” if they see symmetry as defined. I’m afraid if I inject MY vocabulary on to their natural observations, I might lose that connection to their world. What do you think?

Thanks, Peter!

Wow – your description reminded me of times in the old days when teachers used a stick to motivate us to learn. I thought those methods had finished before my readers’ childhood obviously not.

I’d forgotten about casting out 9s, and none of my teachers mentioned it at school. It’s a pretty cool trick, discovered by the Romans, according to Wikipedia: http://en.wikipedia.org/wiki/Casting_out_nines .

There’s just so much cool mathematics to teach our students, it’s a wonder that so many think math is boring!

I think we must be on the same page about how children learn – I find what I read on your posts resonates straight away.

Thanks for the reference at NCTM, if you do use it. I’m hoping to get there in 2013; I had a great time when I spoke at the 1999 conference.

Thanks for your kind words and for including my post on your list. Looks like you’re doing great work too–I love what you wrote about moving the decimal point, and may refer to it (giving credit where it’s due, of course) in a presentation on math fluency that I’m giving at the NCTM Conference next week.

David

Most children (indeed, most adults) don’t appear to really understand the powers of 10 basis for our numeration system. As a result, the question of moving digits or moving the decimal point is rather unimportant.

The idea of having students hold up numerals and a decimal point, and model the multiplication or division process is a great one.

Thanks for your contribution!

What i find is that students do not understand that our place value system is based on the power of 10. No matter how much work is done with MAB blocks etc they just don’t seem to understand that. Until that is firmly understood they will always have problems with multiplication and division by powers of 10.

I had known and read 3 of the other 4 blogs you’d mentioned, David Ginsburg’s new to me, so thank you. Ms. Cookie was one of the first people I’d invited to read my blog, she graciously did and placed me on her blogroll.

Some sort of “round-up” like this is always helpful and appreciated, Peter. We all can’t read everything and be everywhere, and Twitter is so fleeting. Kristen Fouss at http://myweb20journey.blogspot.com/ does a weekly list of her tags which I look forward to catching anything that I’d missed during the week.

Thank you, thank you, thank you.

Modeling decimals is really tricky, mostly because the pieces are so darned small (especially thousandths), and seeing the pieces in relation to the “one” is difficult.

The only models I’ve come up with are a square region model, which can be divided into ten even strips and than 100 little squares. Thousandths can be shown this way, via little tiny strips inside the 100 squares.

The other model is a “cut up base ten block”. Take a wooden “one” block and carefully cut it with a razor blade into 10 slices (tenths), then 100 chips (hundredths), then up to 1000 little 1 mm cubes (thousandths).

See the next post in this series for software I designed to illustrate this model on a computer. We have had great success using this for students to learn the sizes of decimal fractions, all the way down to thousandths.

The problem, as I see it, with KA is the idea that the class teacher needs *replacing* with some sort of “expert teacher” video, so the teacher’s role is relegated to that of tutor or follow-up coach. Excellent teachers do that anyway, but they don’t give up on teaching in the first place.

I’m not sure, but was your comment aimed at Dan Meyer?

I haven’t tried using KA with my own students, so have no first-hand experience of students’ reactions. The way Khan tells it, his videos are extremely popular; perhaps that’s among students with teachers who don’t have what it takes to truly engage learners.

Thanks for your thoughts, Fawn.

Those of us who work hard every day to make mathematics relevant and engaging to young students would never prescribe to KA. But the kids themselves speak volumes about KA, they find the videos boring. Parents tell me that after a short while on KA, their kids can’t stand watching any more.

KA is for those who don’t have anything better, so it’s better than nothing.
Thanks, Peter!

Note that just having a snazzy video will not necessarily translate into the highest quantity of the students taking a professor’s class. It will be more dependent on how entertaining and absorbing the class is to the student. Ultimately, that is what matters.

I like this website, your podcasts and your philosophy of mathematics education. I will be recommending your site to my students and I hope you manage to keep going.

Best wishes,

Richard

I love the fact that you and I are in agreement on so much about teaching math – it is encouraging to know that other teachers and I believe the same stuff.

I will have to look at TinkerPlots and Geometer’s Sketchpad; I’ve heard of the latter, but not seen it in action.

Give your husband my best regards! You made me laugh that you love math that much… I have always loved math, I think, but as a teacher the challenge is to reach those who have been “burned” and just hate it.

So, do I get the job? I know August can’t come soon enough for you. Congratulations!!

Thank you for your wonderful and informative blog, Peter, and I’ll add yours to my blogroll. Keep up the great work!

I am hearing from a lot of teachers that in their view, number facts are vital. They really are a foundation for virtually all later math topics.

In my own year six class throughout term one I noticed a deficiency in the quality of my students’ number facts skills. After two terms of almost daily practice not only are their speed and accuracy much improved but our lessons are smoother and cover more. Children need that foundation because it gives them the confidence to explore and develop other strategies.

You can try the software risk-free for 30 days, so if it doesn’t suit your needs in any way, you can request a full refund.

Let me know what you think!

Thanks for watching!

It appears you and I are on the same page about teaching math. All the best for Maths Insider!

I run the Maths Insider website which offers tips and advice for parents to support their children’s maths learning.

It’s interesting that the results of the survey show that teachers and parents are searching for similar resources.

Thanks for watching and leaving comments!

Just as children learn language informally through natural, everyday interactions with significant adults in their lives, number facts should be seen as a natural part of learning about numbers from early years.

Short and sweet, but still very effective.

I think maths lessons need special preparation if they are to grab and retain students’ attention – partly because of the bad press maths has for many, and partly because of its abstract nature.

Love the sound of the book you’ve been reading – sounds like they and I are on the same page. I should definitely check it out for my classes.

Are you able to watch the first two videos? I have tried this on three separate computers, an iPhone and an iPad, and they all work, both from this site or iTunes.

Please let me know how you go; I may have another option for you to try if you still can’t get it.

Thanks for the great resource
Nick